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Some factors influencing the reflection of ultra-violet light by paints

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GQISlu FACTGKS LHTLUZTCCILO 2‘
IL, LUWLEQ'flQU
OF ULTltA-VIOLET L1GBT
rry’ •)*.ri'rn*-'.
A dissertation
submitted to the faculty
of tho
la s T iT u r a oy s c iin r r ii- ic hhghahch
of tho
UiaV'sBSm OF ClKCXi\'i:Afl
in partial fulfillment
of tho requirements
for the de&L’oe of
BOCXGH OF 2IiGini2S3Xi;G GCJ1FIICE
by
Honald FredericI:J7ilcock
Bf S» in C. £* Harvard ihiginearinG school 1934
lU E* S. University of Cincinnati 1938
Baaio Science rteaearch Laboratory
August 1, 1939
University of Cincinnati UDrary
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UMI Number: DP16787
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1
TABUS OiP COIJTI25TS.
Foreword
1
2 * Apparatus
S
1« Description
2
S« Testing
IX
3. Reliabilityof Measurements
14
II. Development of Ultra VioletPaints
21
1, Reflection and Transmission of Paint
j&itorialo
21
2. Properties of Simple Paints: Two Component
Systems
22
5. Properties of simple Puints: Three Compo­
nent Systems
4. Unpifiaented Films
51
U. Milled Paints
65
6. Exposure Tests
74
7. Other Requirements
S3
8. Other Factors Affecting Reflection Factor
03
III. Influence of Pigaent Properties
JAN 2 9 1964
51
06
1. Particle Cine
GO
2* X5crticle structure o r Aggregation
91
IV. Film Thickness end Hiding Power
101
1. Theoretical Relations
101
2. Experimental Results
110
V. summary
121
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ii
Keferences
124
Appendices
131
An theory of Integrating Spliere
132
B» Analysis of Transmission Cell
139
C* Calculation of X’i^ent Absorption
143
D» Derivation on Bhodes and Fonda’s
Assumptions
2* Film Thickness and Hiding Power
147
150
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Foreword*
It is well known that irradiation by ultra-violet rayc
of vmve lengths shorter than approximately 3200 Angstroms
will prevent end cure rickets end possibly other dioceses by
production of vitamin D-3 in tho skin* Eliot suoli irradiation
may produce* beneficial effects other then those attributed to
tho formation of this vitamin is perhaps less certain* Irra­
diation with wave lengths shorter than 2800-2900 Angstroms is
known to be harmful to tho skin*
Luckiesh and ilolladay* state i "Little is known definite­
ly about the benefits of erythemal (2GOO-32QQ A*} radiation to
so-called healthy persons, but an impressive case can be con­
structed”, and argue that an ultra-violet component in every­
day lighting will provide "whutever beneficence there is in
mimcr sunlight"* Tho efficient use of such lighting v/ill re­
quire interior paints with high ultra-violet reflectances,
and Luckieoh has propared casein paints with reflectances oo
high as 04i per cent*
This dissertation is an attempt to apply tho methods of
science to tho study of ultra-violet reflecting paints, and
describes puinto of superior film properties which attain re­
flectances over 70 per cent*
In this study, the importance
of aggregates in producing high reflectivity from inert pig­
ments beocne evident*
Stucty of the reflection from paints of
different thicknesses led to a functional relation between
reflection and thickness which permits accurate evaluation of
hiding power for visible as v^ell as ultra-violet light*
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£•>*
«*ii
X.
1* Description#
An apparatus eras designed to measure the transmission
coefficients of liquids and the integrated reflection
factors of pigments rad solid surfa c o g in tho near ultraviolet band, 8000 to 3200 Angstroms*
It is shewn diagram.**
musically in Figure 1, and consists of an ultra-violet
source with current end temperature regulation, a sphere
reflectoneter, phototubes with balancing circuit, and an
amplifier*
The source is a General Electric i>l sunlamp# A
clear Cores gloss envelope encloses o tungsten filament
and a mercury arc between tungsten electrodes#
flinco Corex
glass does not transmit moro than anall amounts of radiation
of wave length leas than 2800 Angstroms, the envelope acts
as a filter to provide tho lower limit of tho bond of
measurement#
through
g
?2io current input to tho Sunlamp is passed
bank of HCA UVG76 constant current tubes# A
variable speed fan provides temperature control of the
mercury arc in the Sunlamp, since ito output is temperature
sensitive#
Two quartz lenses are used to focus u beam of light
from the Sunlamp on the window of the sphere) refloctomoter#
The sphere integrates^ oil the light reflected from a
sample, a property which is important in testing sanplos
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3-
oh
Apparatus
□
99
66
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Schem atic
66
Diagram
C3-
which reflect diffusely*
The inside surface of the sphere
is coated with magnesium oxide, o substance with a very
high reflection factor in the ultra-violet*
a
phototube,
{?!), placed at a v.'indov: at tho hottest of tho sphere,
acaaurec tho light intensity within the sphere*
a
reflec­
tion factor is determined by talcing the ratio of tho
phototube currents when the light been is directed on the
cample, and when it is directed on the sphere wall#
She sphere refhectometer, so used in this apparatus,
gives an absolute measurement of reflection factor; that is,
the measurement does not depend on the reflection factor
of the sphcro coating or any other substance cs a standard#
The accuracy, therefor, is affected only by slight sources
o f error due to the construction of the cohere itsolf •
The accuracy of transmission measurementa, although depend­
ent on the reflection factor of the sphere conting, is not
affected by it since tho reflection factor is constant for
magnesium oxide at 08 per cent from 2030 to DdGl Angstroms^*#
The theory involved in measurements with the sphere is
5
that of the Taylor reflectoneter*
6
which measures diffuse
reflection factors feu* light, cud which has been applied by
Taylor to ultra-violet measurements5# Tho theory applied
to this equipment, together with an analysis of the ei*roro
to be expected, is x’resontod in Appendix A*
The phototubes arc General Electric FJ-135 cadmium
alloy cells#
They do not respond to light of v/ave length
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n
greater than 3200 Angstroms, and thus provide the upper
limit oi* the bc.nd of measurement*
Despite tho constant current input to the sunlanp,
there are relatively rapid, irregular variations of several
per cent in the output, and, since two conaccutivo readings
are required for each measurement, it is important that tho
effect of those variations be eliminated#
This is accom­
plished by using a second phototube, (P*), so ialaced no to
receive light directly from the source.
By employing the
ratio of the ourrcnts from both phototubes instead of the
current from tho single cell (P^) beneath tho sphere, it is
possible to correct automatically for fluctuations in light
intensity.
The phototubes, of course, should have identical
characteristics.
Furthermore, it woo found that the rela­
tion between them renuino constant only when they arc placed
in nearly tho sane direction from and on tho oano side of
tho source#
A simple circuit is used (Figure Z) which given tho
ratio between the two currente directly with only one read­
ing#
Points A and C are brought to the came potential by
adjusting rc#
Then:
and since 31 and 12 aro proportional to the light Intensi­
ties ill and ttg respectively, the ratio of
to fcg is:
»x - *X*1 J M b .
*8
X2I8 >¥>1
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-6
P h o to tub&"
Beneath Sphere
7o G r'/'d. aF
Ampjj t i e r
" 4-5- v:
■7/
7o
Ground o f
f i er
P h o to tu b e in
D i r e c t Light
Beam,
P h o to tu b e
C ir c u if .
f ig u r e 2
V W W V W V - 1
so, OOOSL
1 8 v:
A r r p J /fte r
0 - 2 5 JD.
C i r c u t t.
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is o constant and cancels out in making c refloation
rector measurement ao follor/s:
Haricotion Factor as
/ocnple n 7ZgEij~~ R % g
\
^Xn2BVi
“b ^ S E !
il2a »
^
The method described above applies to transmission
measurements m well, sinea those also arc mado by talcing
two readings on the sphere wall, one with tho sample in
the light boom, and one without the sample*
For all transmission measurements, and For series of
reflection factor measurements on tho sane sample, R0 a reraaina constant, so that once it io determined only o oinglo
reading is necessary for each measurement*
At first, tho
sphere had a large window three inches in diameter for tho
reflection sample, so that Rg8W varied for each ounplo due
to its effect on tho internal reflections of tlio sphere,
and both Rgsw and H^s had to bo read to dotomine the re*
flection factor#
Reducing tho oiao of tho cample window
to one inch has made the variation in a«„w from ample to
sample negligible without impairing tho accuracy#
Points
a
a null method#
and C ere brought to tho same potential by
That is, the amplifier galvanometer nuot chow
no deflection v;hon 1^
g
Ig ore started flowing by opening
chut ter in the light bcera#
Switches cannot bo used in
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tho circuit because of contact notontielc*
Tho maximum potential drop across EC is about lxlO**s
volt®#
To measure this with an accuracy/ of 0#1 per cent
requires the detection of ladLO*** volts notontial diffcrcnco
between A and C#
Such e potential io eaaily neaoured with
a galvanometer in a lor; resistance circuit, but is possible
in a high resistance circuit only if an amplifier io used#
The amplifier circuit (Figure 3) is o modification of
the dollar balanced elrcuit^5^**^* using a Western
Electric Electromotor vacuum tube (Ho. D904V5), and a
«*1Q
galvanometer of 1x10
amperes per 1x 1 sensitivity* The
vacuum tube has u vory high grid resistance and is well
adapted to measurements in high resistance circuits*
7x11
poorer for the amplifier la supplied by one battery and the
circuit balancoo out tho effect of variation in battery
voltage*
Tho amplifier works well with tho main port of
the circuit unshielded, but it is necessary to shield tlio
electrometer tube und all luado in tho phototube circuit
with grounded shields#
Plate 1 shows the electronictor tube
in its shield can, placed close to tho phototubs beneath
tho sphere9 so that the capacitance to ground of tho grid
land will bo as low as pauGiblo#
Due to this capacitance,
it takes & snail but finite time for tho voltage across A3
to build up$ a longer time than for the voltage aex’osa DC#
Thus there is a voltage difference during the transient
state which gives the galvanometer in the amplifier a kick,
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PLATE
-9 -
W'y.T'.
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-10-
waking it difficult to obtain on exact balance across AC.
The condenser pluced across phototube ilo# C (Figure 8)
tends to equalise the transient states in both phototube
circuits and greatly reduces tho amount of kick*
This method of measurement has three principal
advantages.
First, by essentially making simultaneous
readings of reflected intensity and total light intensity,
tho effect of fluctuations in the source output is elim­
inated*
Second, by measuring directly the ratio of these
two intensities, the error in making simultaneous readings
ia avoided*
Third, by balancing the two phototube
currents before they are amplified, variations in tho
amplification factor of the amplifier do not affect tho
measurements*
In operating the apparatus, it is necooncry to allow
an hour for the electrometer tube to reach thermal
equilibrium before tho amplifier is sufficiently steady
for accurate readings.
A better method is to run the
tube continuously, which i3 fcusiblo einco it draws only
0*27 amperes.
The 3-1 Sunlamp reechos an approximately steady
output in about half an liour* A thermometer placed close
to tho lamp but shielded by esbootoo from its direct raya
gives the air temperature near the lamp*
The- lamp is
cooled and kefft at g constant temperature by a low speed
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-li­
ran*
This I s necessary 3ince not only does the total
output of the Sunlamp vary with temperature hut the
spectral distribution of the radiated energy shifts to
some extent duo to the change in vapor pressure with
temperature of the mercury within the lnrnp^.
This
shift iri spectral distribution affects the measured
reflection factor#
Figure 4 shows the reflection factor
of c particular sample, measured at several lamp temper­
atures#
The usual ambient temperature is 47°C*
3# Testing#
Pigments ore tested dry by packing them in a shallow
steel coll (Plato II}#
Aluminum bronze could not be
peeked in the cell, and was toated by coating a small
panel with a rapid drying datoor resin solution and dusting
it over with tho dry pigment#
Teats mado on basic car­
bonate white lead by both methods differed by only 2 per
cent in reflection factor#
Liquids ere meusurcd in e Gpecially constructed
vitrcosil coll#
Vitrcosil, or fused silica, is, like
quarts, transparent to ultra-violet light*
The cell
(Plato III) consists of a atecl body, A, in which a
lnxlr':s:l/32" polished vitroosil plate is cemented with
oodixun silicatej a coppor spacer, 23, 0*027" thick, which
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12'
65
60
30
35
S u n la m p
40
55
T e tv p e ra tu re
fig u r e 4
*9
O-x) t $
x O -x ft#
x*0-xjxr $
x * 0 -v xr #
xfO-x)zt
\" \\ ^\ v\ \
M u lt ip le
f9
V \\ W
R e fle c tio n s
fro m
Two P a r a / / e /
S u rfa c e s
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provider space fox' tho liquid; a second vitroaoil T>lGtc9
Ct l,,xl,,xl/0,,5 g rubber waciior, D; end o oteol top plttte,
£, with which the entire assembly is clamped together**
There is a clour light path through the coll ©/&» in
cUomofcor*
The cell i*. constructed to be os thin as possible on
the side which is next to the sphere.
For reflection
ncaGurononto, the adapter piste, ]?, coated an its inner
fnce with magnesium oxide, holds the cell in position on
the sphere.
For transmission measurements, the coll is
slid into steel ways which hold it in tiio light been directly
in front of the sphere window*
It 1c customary to use those transmission collo in
such a way that tho transmission of tho coll containing a
solution is compared to tho transmission of tho coll con-*
tuining pure solvent, thus eliminating the effect of the
cell.
In testing oils and solvents this cannot bo dono.
Furthermore, with certain liquids in the coll, tho pci* cent
transmission is great ex* than for tho empty cell,
These
liquids, being almost completely transparent to tho ultra­
violet, ana having an index of refraction greater then
that of air, reduce the amount of light reflected from the
vitreoail-liquid interfaces and so increase the overall
transmission of the cell.
This extreme* case shows tho
necessityanalysing tho effect on transmission measure­
ments of tho multiple reflections from the four surfaces
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-
14 -
of the cell*
It con he eliown (Apiicndirt li) that tho troncniooion
eocfi'icient, tf of tho ratorial in the cell ios
whore K end T arc the measured overull reflection and
tx\nnomission coefficients of the filled coll#
Ccloulotions
on luany samples have shown that t is usually about 10 per
cent larger them T*
taibert*# Law, t«e**^, is used to ol>«*
tain the coefficient “h1* which is ohia'acteristic of tho
liquid and independent of the thiohnesa of tho tdat sample«
Paints are tested by brushing or spraying on 4"x4:n
stool panels which can then be placed in the sanpio position
on tho ophero•
S« Hellability of l;oaauronenta#
For a aeries of teats on successive Uaya of the saiao
sample, the reproducibility obtainable v/lth tho apparetua
v :q c
found to be within 0*2 per cent based on tho incident
Xi£ht.
Since the measurements ere node in a bond 400
Angstroms wide containing oevernl strong mercury linen and
since most materials are coleotive in absorption and reflection in the ultra-violet, tho energy distribution in tho
band will have tm effect on the measured reflection factors#
The characteristics of the moaaixred energy in tho bund
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-15-
wero determined by measuring tlio rospon&e or oooli or tho
two phototubes/ot different wave lengths to tho light from
the S-l Sunlenp, using a quartz monochromator*
Tho Roller
circuit with on input resistance of 14»000 megohms was
used to measure tho phototube currents*
Tho results (Figure
0) fchow that their characteristics are similar, but that
ono phototube has about twice tho current response of the
ot2icr. Tho maximum measured energy in the bond is at 5G24
Angstroms, with the "center c£ gravity” of measured energy
at about the same wave length*
The data shown in Figure 6, together with the data by
15
flames
for the energy output of the S-l, enable the
sensitivity curves of the two phototubes to be determined#
Barnes measured the cnorgy output perpendicular to tho
piano of the leads for the lamp running vcrileully in tho
open, which was its position for the neasuronento for Figure
C» Table 1 gives the calculated sensitivities f;** tho two
phototubes, and Figure 7 shows the agreement between these
calculated results mid the sensitivity curve furnished by
tho tinker for Phototube Ho* 2*
As an independent chock on the results furnished by
this apparatus, Dr# A# 12* Taylor of tho Held Park labora­
tories of the General Electric Company was hind enough to
measure the reflectances of several panels at 5024 Angotroraa
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-18-
Table 1.
Phototube Sensitivity*
•Vavo*.
Relative'
Galv.
Relative
lcnr.tii Jb,‘ncr<-'gr*s-l Beadinr; Sensitivity
Reduced
sensitivity
Phototube tTo, 1
3130
13.5
52
3024
4.4
CD
14.0
0.41
290?
8.54
40
15.8
0.435
2894
0.71
18
25.4
0.70
2804
0.69
25
36.2
1.00
3.80
0.105
Phototube Ho. 2
0,115
3130
13.5
114
3084
4.4
144
32.7
0.442
2907 **
8,54
82
32.2
0.435
2894
0.71
33 {©st. } 30.3
0,41
8804
0,69
51
1.00
0*45
74,0
v/hieh io the moot intone© nurcury lino in tho band
rtoasurad by thin apiHiratuo.
Dr* Taylor used a 4 inch
intecrotiugj sphere, a quarts spectrograph and a quanta
g
sodium T>hotaoloctric cell • Table II io a ooapnriaon be­
tween the reflcctanooa obtained by Dr. Taylor and the
rofleetaneea obtained with tho apparatus described herein*
Tlic’tt£3?eeacnt is oxcclleat when it is considered that one
luoasuronc&t is for ti aiti£le spectral lino and tho other
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-1 9 ~
Table II
Coraparioon of Reflectances.
2hnel
Reflectance for band
Reflectance
aso o -sso o a * _____
54*7
H-5
43*
h -q
41*6
45.
21-10
for a 400 AriGStron band*
The higher reflectance for G-5s,
ond the lonor roflectanoen for the II series panels, obtained
for the hand are tsrobably the result of differencea in tho
spectral absorption curves of these paints.
L further choc!: was provided by duplicating an ultra-
violet paint described by Luckiesh end Uolladay^, their
2-aint "C”. They give its reflection factor as 54.0, and
the value obtained fox' the duplicate v/ith this apparatus
vrao 5 5 . 9 * ’
The reflection factors obtained for pigments arc sub­
ject to an additional error besides that inherent In the
apparatus due to the fact that the iztumov of pocking then
into the cell and leveling off the ourfaco is not entirely
reproducible*
Barytes? for crumple, exhibited a variation
of 1*5 per cent when several successive determination# wore
node on freshly prepared samples.
Consequently, the results
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for the rofXcctGnccs of pigments arc Given only to the
nearest per cent#
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XI. DEVELOP;IHi? OF ULTB/^FIOL2;F PAIET8«
1. Hefleet.ion and ffransmlnslon of Point intertala*
A oystoniatio investigation of the jDoasibilitiea of
caking paints with hieh ultra-violet reflectancoo requires
o loiowloclgo of the ultra-violet behaviour of the notoriels
of which such points night be made*
To this end, the re-
flection factors of white and colored pigmcnto and the
transmission coefficients of olio, reDina and tliinncro wore
measured* All mterinlo aro of cosmoroial erode and purity
unless otherwise indicated.
In Table III arc listed the reflectances for the white
pigments#
They agree qualitatively with the data which
Pfund^o Stuta^2, Luchiesh^**^ end Ctoodeve^ have obtained
for the more common xsigiaants* This is satisfactory when
it Id remembered that the results in Table H i are X‘or the
bond 2800-3200 Angatronu (Figure 6) whereas the data in the
*1 r
.literature with the except ion of acsrc by Luclcicsh
are for
individual lines of the mercury spectrum*
Pfund points out that there is an inverse relationship
between the reflection factor and opacity {i.e. light ab­
sorption) of u pigment, and observes that "The inerta, as a
c3.ass, are much loos opaque, particularly in the short wave
length region”. From u brief study of Table 111, it is
evident that magnesium, sirooniun, silicon, aluminum, lead,
calcium, and barium pigments do not absorb erythccul
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T c b lo I I I *
White I'lgcicaitc*
Picmont
Chemical
Composition
Per (
Hc-flct
Load Free Zinc 0::iclc
ZttO
3
350 Leaded Zino 0;cido
Pbso^, zno
-1
Sine Sulfide
ZnS
C
Titanox B
050 a?i0s»BaS04
6
Lend Titianato
rbl’i03
0
Vituniuia Dioxide
210©
7
Titano;-: G
Ti02, CaSO^
7
Litliopone
acfo Zn3,BaSG4
8
Antimony oniuc-
Gba03
17
Zireoniiim Oxide, Con*I*
<uV0q
41
Celito
3iU0,Zilicatco
45
Baaio Sulfate White Lead
Pb5O4>160 PbO,90 ZhO
48
China Olay
Al©S10»*3H©0*v*
(
*•>
54
Almaimua Caddo
i&.-.Qg
55
Basic Carbonate Viiiito Lead,
Cartel" Process
vr# Pbcoy
59
Gurfcsc
CftC03
01
Basic Carbonate White Lead,
Dutch Prooc&s
750 PbCOs
63
SC
Aluminum Hydroxide
CoCOr*
</
A1s 05.Ho0
Asbestine Puli’)
iig Silicate
67
Barytes
950 Bg 504
68
Commercial Whiting
*•»
67
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Tabic III (Continued).
Pinncnt
Chemical
Goiauooition
1'cr Cent
Reflection.
fillies
SiOo
■’
•QGiittsiua Oxide, heavy,
(Squibb)
LlQO
7<*
Aireordiua Oxide, G«a •
«r0.,
78
Aluraiui.ua Sronsio
Al
80 (eat*
ha£iieaiun Carbonate, U.S.P.,
(/Aallnlrra&t)
k£00<r
81
*-OGttcoiua Carbonate, Ccn’l. l&C0gti!&(on)n
81
“^Gnociua Oxide, licUt,
(Squibb)
L'aO
OS
1'aGneaiuti Oxiclo.
(Baker)
k'cO
83
h'oeacoiuia Carbonate, U.3*F*,
(Coleman & Bell)
k£C0;5
83
i’cGiioaiua Oxide, U.S.Po,
{A’inor L Amend, 33*V3)
L'cO
00
kajvnosiun Oxiclo, freshly
smoked
kfjO
08
ultra-violet appreciably, whereas nine, titanium, and
antimony pier.cntc absorb it to a lores extent*
Airconiua
oxide hue a refractive index of7S#S, hichor than that of
any of the hich reflecting pimento, no that if it con be
obtained in a purer state commercially, it should be the
beet cavorixiG pienant that con bo ucod in on ultra-violet
paint.
A ourpriains foot io the oaull but definite
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
—24
superiority in reflection of the Dutch procoou over the
Carter process wliit© lead, since the Carter process pigment
is \7hito end the Dutch proceoo pigment hue c decided
yelloW-gray cast*
Table IV shows the results for colored pigments#
Although not complete, the list io representative of the
chemical groups’found in colored pigments,
The results
agree well with those of Dtutz^2 for 13024 Angstroms,
Table V lists the absorption coefficients for oils,
thinnersfriers end other liquids, resins, and plastioisers*
Since tho surface reflection from a liquid-air interface is
negligible up to an angle of incidence of 50° from the
normal, it is evident that any liquid or x*osinous material
to be used in a paint, other than volatile thinner, must
have a low absorption coefficient in order that 11gilt m y
be reflected by tho pigment without undue absorption by the
vehicle#
In practice, it has been found that a coefficient
lcoo than GO to 70 is fairly satisfactory*
From Table V-A,
it is evident that no oil will be satisfactory.
Refined
castor oil is possibly an exception, but, when made into a
drying oil by dehydration, it io unsatisfactory.
Table V-B showo that the common driers cannot bo used
except in minute amounts*
However they need not be used at
oil since the oils themselves ore unsatisfactory.
Bony of
the common solven 3 have low ubsorption coefficients, so
that they can be used to tost resln3 in solution.
Casein is
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
Table IV*
Colored Pimento.
Pi^iont
Per cont
neflootion
Solfaot Shy Blue
1
Chinese Blue [A Prussian Blue)
2
C*
O
Pera Toner Dari:
O
Toluidine Tonor
tv
ht. Para Toner
tv
Copper Carbonate
i>
n
Graphic Red Li (Pithoi Bed Toner)
2
Llaplco Yollov; Lonon
2
Chrorao Yollov; Bed*
3
I-iolybdato Orange
3
Cadniuni Sulfide
3
£ine
3
-ronato
G. P* Chronc Oranc/j Dari:
5
Chroraiuia 0:;iclo
S
Rose lahe
5
Alinarlno Laico
3
Persian Gulf OrdLde (Iron oxide)
5
lithcrco
6
Subllnod Blue Lend
10
Ultra I.iarine Blue
no
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
Table V-A
Ultra-Violet Absorption of oils*
Absorption .
Coefficient (in *).
‘Aoterial
Oitieica Oil
Infinite
China v/ood Oil
l.CxlO4’'
Heat Boiled linaoed Oil
l.GxlO2
P-Qfinod Pcrilla Oil
1*0x10°
Alkali Ecfincd Linseed Oil
1.5x10s
Heat Bodied Bonilla Oil
1*0x10s
Special Dehydrated Castor Oil
Alkali Hefined Soya Buan Oil
Dehydrated Castox* Oil
20
Cootor Oil* Ccnfl*
^
tlofinod Castor Oil
^
Table V-2
Ultra-Violet Absorption of Thirmers Driers and other Liquids.
Hatoriel
Absorption *
Coefficient (in )
6# Cobalt 1'iuodex
Infinite
C>j llmcunose Kuo&ex
Infinite
Lead IiUodex
Acetone
1*8x10
X*2xl02
Sulfate v/ood Turpentine
70
Casein Solution
57
Mineral Spirits
44
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
Table V-3 (Continued)*
Absorption *
Coefficient (in )
Material
Solveaso Ho* Z
ZQ
Commercial Zylol
£4
Toluone
9*5
Butanol
9.2
Bthyleno Bichloride
3.9
Glycerine
3*5
Absolute Alcohol
1#1
Distilled Water
0.4
found to be only moderately absorbent.
Luckieeh
has pro-
pared paints with reflectances as high as 34 per cent with
casein as binder*
The resins were tested in solution#
In calculating
tho absorption coefficients of the resins from the coeffi­
cient for tho solutions, a modification of Beer’s law was
used.
It was assumed that the absorption coefficients are
additive in proportion to the relative volume of each
component, and that the volumes of resin and solvent ore
additive in solution.
Those assumptions'are as accurate as
the datu warrant, since the thickness of the material in
the cell is Known only to two figures#
Table V-c shows
that the natural resins have very high absorption coeffi­
cients*
Of the synthetio resins, urea formaldehyde,
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission
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R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
nitra-colluloso lacquer, ethyl cellulose, the notliacrylotc
ectorsfl and vinyiite are lov; in absorption*
Urcm-formeldo-
hyde, howeverj mist be baked, and it is well known that
nitro-ccllulonc deteriorates upon exposure to ultra-violet
radiations*
Table V-D shows the absorption coefficients of
plcsticiscro used with ethyl cellulose and the methacrylates*
Tho results on the Dow Plaoticiaors are interestins in view
°f tJioix' structures (Figure 8)*
Tho substitution of torti-
butyl croups in para position on trlphcziyl phosphate
decreases the absorption slightly*
The substitution o£ one
phenyl group by c diphenyl group increases the absorption
tremendously, but the substitution op a second has no
further effect#
The explanation of this effect is a subject
Tor further investigation, but has no direct bearing on this
work* y
3.* .Ih.’onertlos of ainnlo Paints: Two Oaaponcnt Systems*
L typical paint formula is very couple;:, and m y in­
clude several plononto raid Tillers, one or mono oils or
varniahoc, driers and thiimsro*
This complexity io tho re­
sult oi* the modification of on originally simple formula in
oi’der to give tho paint various desirable properties ouch
ao brusfcabllity, lac!: of settling, high hiding powor, and so
forth*
Oinco this v;orfc Is an investigation of the posaiuil-
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
°n
y..-0
■P=o
T rip h e n y l
P h o s p h a te
(k = 20>
V
v . v o ^o.
■':
0/ 0
0
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p-o
p=o
T )o w
.
; P l a s t i c j ? e r .?
Dow
P l a s t i c izer t
{k.= ia>
:*■ \
■P y ■
;
' j ■ o, ,.o •
- .V !
*
-.^o- y
p io
D o w P l a s t i c iz e r No,5
C M 1.2 • \ 0 X)
\*
Dow
P l a s f tcizer N o . 6
(k=i.2-i0';
.
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
ity of new types o f p o i n t which will reflect ultra-violot,
end since in complex systems it is a i m mat to difitiuguish
the properties o f the individual components, the simplest
possible systems of pigment end vehicle were studied first#
Since- surface reflection at the vehicle-air interface
can account for but a small part of tho reflection of a
paint, reflection must result chiefly froxa repented reflec­
tion and refraction of tho light by tho pigment particles
with tho find result that tot light which io not absorbed
onergoa from the paint film as reflected light#
It io evi­
dent then that, among other properties, it io desirable that
both pigment and vehicle possess low absorption in order
that tho maximum amount of light may be returned from the
film#
neglectine the effects of refractive index and par­
ticle cine, a high reflecting pigment will havo a low
absorption coefficient#
"Therefor it was decided to prepare a number of prelim­
inary simple pointa to test the truth of the above conclu­
sions} also, in slightly more complicated systems, to observe
the effect of varying one component at a time#
I/Tom these
teats the combinations of picment and resin which would
prove satisfactory were determined#
"Then, after satisfact­
ory pleatioizer composition and content had been determined
for each resin, trial paints were milled and compared, and
tho correct pigment volume per cent determined*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The preliminary points were ground by hand in a mortar
end pestle with an appropriate thinnex4, and brushed to a
heavy film on steel panels#
I/o effort was made to control
exactly the pigaent volume pex* cent, as its effect and
correct value wore not known, mid only the general effects
of pigment and vehicle were desired#
Table VI is c complete
tabulation of the points ground by mortar and pestle#
Tho combinations of a single pigment with c single oil
or resin show that both a high rof1eating pigment and a
vehicle with a loiv absorption coefficient arc necessary in
ox*dor to produce a paint v?ith a high reflection factor*
This i3 olcax’ly shown in Table VIJ which shows the relation
of reflection factor to vehicle absorption end pigment in­
flection, and which is a retabulation of part of Table VI#
Another feet, not so obvious, is illustrated by this table,
namely that those white pigments whiclt arc used as iuerts
and fillers in paints reflecting visible light, bohave in
somewhat the some manner in paints reflecting ultra-violet
light#
In other tvords, "inert" piaaonts, which are auteriala
with refractive indices for visible light so close to those
of most oils and resins that their particles arc inefficient
reflectors and refractors, also have refractive indices in
the ultra-violet comparable to those of the- resins#
Thus,
dry*silica powder reflects 71 per cent, but immersed in c
urea-fonaeldehyde resin reflects only about 25 per cent;
whereas dry white lead reflects 62 per cent and immersed in
/
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
—SC**
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V-7746 XJreatom~9 rosin
aol*n.(k»2S)
05
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Acryloia
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Clear nitro­
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lacquer*
(k*40}
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j 57
....
Urea-foria.
roain Dolfn.
(1»03)
3Q
Hosyl #227-8
(fcsci)
Bthyl Cellu­
lose {1;«75)
Alkali Re­
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Glyceryl
Phtkalate
Varnish A
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40
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9
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
-40-
ux^a-foxmaldehy&c resin refloats about 40 per cent#
Most or tho light reflected from c paint is not reflect"
cd from tlio surface, but has traveled a variety of paths of
different lengths through tho point* a certain amount having
been, absorbed along each path before it emerges as reflected
light#
That light which dooa not appear as reflected light
has been absorbed#
A moan light path can bo defined* such
that if nil the light traveled that path, the same fraction
would have emerged as reflected light#
the refractive indices of the two ma
:;inee tho ratio of
~ials at on interface
determines tho degree of bending of light rays paasing
through it, one would expect tliat the larger the ratio of
refractive indices of pigiacnt ond vehicle* the sharper would
bo the average curvature of the light paths through a paint.
Sharper curvature ueuno shorter light paths, and consequent­
ly, for the same absorption coefficients, leas total absorp­
tion and wore reflection for larger refractive index ratios#
A dry pigment can be thought of ac a paint with no vehicle
for theco considerations of reflected light#
The effect on reflection of varying tho relative pro­
portions of nicwent end resin was determined for basic car­
bonate white Icqu and for augneoiun carbonate with Acryloid
8-7 oa vehicle (Figure 9)#
It can bo shown (sac Appendix C)
that from those curves one can calculate very approximately
tho mean light path through tho dry pigment, L0, and tho
absorption coefficient of the pigment,
prdviuGd one
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
knovfo the absorption coefficient of tiio rosin*
The necm
light jiGtho end absorption coefficients for the ttto pia**
.'.enta* ealeuia tod in this cay* are givun in Table VIIIo
Table VIII*
/.baoi'ption of Pigment0 *
Absorption
hean light
lothp. n
vO-
\+aLw
I&eneoiua Carbonate
0*01
B d Co white Load
0.002
Coefficient,
20
200
hhgncsiun carbonate paintc attain half their muxinun reflec­
tion footer at a tkiclaicsa of about 0*001 inches*
If the
light paths ere considered as ccni-circlcoj this would
correspond to a mean light path of about 0*000 inches for
films of infinite thickness*
Thun tho calculated mean light
path xg of oho I’iglit oz’dor of magnitude*, since the actual
light paths would be erpccted to bo more irregular and
longor than ac-ni-oiralotje
5* Proportles of 2 1 m lc Paints* MThree. Conponent Syatcna*
So for* only paints containing a sir.gic pigment have
boon considered#
Since it is often desirable to incorporate
norc than one pigment in a paint cither for economy* for
improvement of film properties* or for tinting* throe
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
component oyat eras were also investigated*
Figure 10 Qhoxia the effect o» reflection of varying
the'proportions of an inert typo pigmentf aurfo~3 and e
moderate hiding pigment v;hito lead, in nr. feryloid paint*
Figure 11 cho’
.vr. the effect on reflection ox different proportions of rmgneaiua earbenafco,, «l«o on Inert typo pigment*
and white leads in t\.*o different vehicles*
The tv;o vehiclea,
teryiorUI end V«7?d05 have about tho cane absorption eoef£3>
cicnto®
Tho separation boteccn the too curves chore the
effect of uiffercnccu in total pigment concentration at each
pigment ocliposition s higher reflectances accompanying higher
Pignent concentre11one *
Figures 12 and 15 ehow the effect of addition of
colored pi
paints*
carbonate and white lead
A d would bo expoctad from Table IV5 or.mil amountc
of colored pignonb dopraoo the reflectance a great deal*
Tho rate of depression is aoncvdiat more rapid with tho
im&noBiun earbonata than with tho white Icou ,ainfcc* end in
the ease of ultra marine blue it is much more rapid*
This
may bo explained by the fact; that due to the- longer light
path through nucuosiun carbonate painto, colored pigments
con remove a larger amount of light in these paints then in
vrhito load paints*
Tho effect of the addition of increasing amounts of
aluminum bronuo on the reflection factors of magnesium
carbonsto end white lead paints is illustrated in
R eproduced w ith perm ission o f the copyright owner. F urth er reproduction prohibited w itho ut perm ission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
^
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
'•’ Ob*'*
Ficuro I d •, fhenu curveo indicate that the aluminum bronso
first ciopi'oeaoD the reflection factors much og do tho
colored pigL'.cntCj i-uc tiicn rnlcca it GGuin*
Tho color of
tho 2'jaintG ranees from white to a dull cvoy at the minimum;;
and beyond tho minimum the; paint a become more and more
metallic in e;:*yonranoo*
..luininura bronze :lo a metallic piGi.icmi;, with flei; thin
par tic.Lea „
it uifi'c-i'O from tho white pifsdcntc {Table III)
in that each par t i d e transmits practically no iip.ht s but
reflects a lor me i'raotioru whereas each particle or c v/hite
pirxicnt transmit a a lur,;>o fraction, but reflects only a
omnll fraction of the iidit incident upon it*
It appcarc,
then, that the action or tito aluminum bx*onne at lo?i concen­
trations in due largely to tho opacity or its particles,
end at higU concentrations is duo principally to thoir
metallic ref1cotions *
In order to obtain o more definite picture of its
action.; aacuno that the aluminum bronze act a as a 100 per
cent absorbing pigment mined with the white pigment, deduct
the effect oi’ tiiio mixture from the reflect;ion of occli
paint, and ascribe tho balance to metallic reflection from
tho aluminum bronze particles*
Figure 15 siiov/s the semo
curves rcplottod with log reflection factor os ordinate*
The pigment mixture absorbs itore light as the percentage of
u l u m i n m bronzo ia increased*
Thio increase in absorption
lo exponential, due to U m b e r fc*s Law, so that tho effect of
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5 8 -
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R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
-50-
the mixture can now be represented by a straight lino
tangent to each curve at zero per cent aluminum bronze.
Figure 10 shown the difference between each curve end its
tangent plotted against per cent oX’ aluminum bronze« Both
curves con be approximated by the cane straight line pass­
ing through the origin and the point eo per cent reflection,
100 per cent aluminum bronze.
This straight line represents
the metallic reflection from the aluminum bronze. /»s one
night expect, it is directly proportional to the volume
pox* cent of aluminum bronze present in each paint, inciieat­
ing direct reflection from the particles at the surface#
Since it is the diffuse reflection factor which is boing
measured, it is not necessary that these particles be
oriented parallel to the surface.
v
From the lex*go decrease in reflection factor on addi­
tion of analI amounts of colored pigment, it would socm that
an ultra-violet paint will have to bo either dead white, or
at most a very light Pint*
aluminum bronze, however, pro­
vides ail interesting exception*
The left branch of each
curve provides e aeries of grays with a fairly high reflec­
tion factor and without tho objectionable metallic lustre
of an aluminum paint.
This suggests addition of colored
piOacnta to these grays to produce subdued colors together
with moderate ultra-violet reflectance.
Paints P-115 and P-11G, which represent tho combination
of 25 and 50 per cont ultra marine blue respectively to
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
aluminum bronze, show very little color and little loos of
metallic lustre*
Paint P-117, however, which ia a mixture
of aluminum bronze, ultra marine blue end white lead, 1r a
eky bluo with practically no metallic lustre#
The presence
of the aluminum bronze ia indicated by a slight sparkle in
the surface and by the high ultra-violet reflection factor
of 40 per cent#
Thus it appears that a colored ultra-violet
paint containing both aluminum bronze and white pigments
can be produced with a moderate ultra-violet refleotanco#
4# UnpiAmontcd Films#
The general behaviour of piement-resin combinations
with ^regal’d to reflection has been investigated, but little
attention has boon paid to tho physical properties of the
film produced, except for the rough observetiona that a
film is brittle, tough, hard or soft, adheres well or pools*
The properties of its film are important for a practical
paint*
They are principally dependent on the properties of
the vehicle and on th e proportion of pigment to vohiolo*
Hence it is logical to study tho properties of unpiguented
films, before proceeding further with the otudy of ultra­
violet paints#
The possible rosins for uua in un air drying paint for
ultra-violet service have been shown to be ethyl cellulose,
vinylite, end the methacrylates*
Strain, Kcnnelly onu
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
18
Dittnar
liuyo determined the compatibilities of the
aothccrylctea for a number of plootioiserc*
Information
on plaoticisora for ethyl cellulose and vinylite v;as fur~
hialied by the Dor/ Chemical Company*
Dace end Hauppi*^ iiave
also Given valuable information on tho action of several
plusticizers on ethyl cellulose®
Plaoticizoro v/itk hich
absorption coefficients v;erc eliminated from conoideration
by use of the dote of Table IVD*
Tricreoyi phosphate v;ac
eliminated because of its toxicity*
Tho various possible compatible combinations of rooin
and plasticiser wex’e made up in solution at oovarnl concern**
trations between 0 and 40 per cent plcsticizor content and
flowed out on steal panels*
After thorough drying, they
v/ere examined for toughness, hardness, brittleness, anti
adhesion*
The combinations examined v:eres ethyl cellulose
with triphenyl phosphate, tripropionin, Dow Plasticisor no*
80 Dow Plasticiser Ito* 7, and vinylite; nothyl mothaci’ylato
with triphcnyl phosphate, n**butyl d-tcrtrato, end tripro*pionin; isobutyl methacrylate with tripropionin, butyl
stearate, n-butyl d-tartrntc, triphcnyl phosphate, Dow
Plasticiser Ho# £, Dow Plasticiser lio# 7, and vinylite; and
vinylito with Dovr Plastioisor no® 7e Vinylite, although a
resin, air dries to a soft film, and acts as a piacticizor
in ethyl cellulose with which it is compatible up to about
30 per cent vinylite*
All methyl methaoryiu t;c filns peel readily*
Of the re*-
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w ith o u t perm ission.
mein itiQ eombinations» four Give Good films#
They arcs
ethyl cellulose with '10 per cent bow V’laoticiscr ho• V;
ethyl cellulose with 20 nor cent vinylite3 isobutyl
mothaorylato with IS per cent butyl stce.ruto 5 a;id isobutyl
methacrylate with SO p e r cent Dow rlcoticiaer bo0 2 «
35# Milled Paints#
Tho above Tour combinations of renin end plenticinar
produce satisfactory implemented filtaa#
Thoir action when
combinecl with piclient, and tho bent proportion of pigment
to vehicle must next be considered*
Although preliminary
observations of hand-ground paints indicated that tho re-*
flection factor of a combination of two pigjr.cnto did not
exceed thut of the better of the* twos combinations of pig­
ments were used because of possible desirable offoots of
mixed pigments on filn propei'ties*
for those studies* paints wero milled in a ball mill
so that a better and more uniform Grinding of the pigment
into the" vehicle would be obtained*
6
The mill used was a
inch diameter porcelain boll mill with 5/8 inch porcelain
balls*
It was rotated at 00 r*p#n*
Tho composition and
reflection factors of tho several paints thus Ground ore
listed in Table IX* The thinnera used were toluene for tho
methacrylates and an 80-20 toluenc-nlcohol mixture for tho
ethyl cellulose*
Unless otherwise indicated, all paints
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-G 7 -
wore ground for 70 hour5 , After grinding, tlie pointc wore
filtered through cloth and c portion uao thinned and sprayed
on 4,«x4w steel panels to a heavy ccat.
G-l, G-2 , and 0 3 show tho effect on reflection factor
of tho more intimate grinding of the mill us compared with
grinding by hand.
If their reflection factors arc compared
with those in Figure 11 for 100, 0 ana 79 per cent magnesium
carbonate (by volume), it will be noted that the acre
thorough grinding of the mill produces a email decrease for
white load, e slightly greater decrease for the mixture of
white lead ana maGncoiUEi carbonate, and a very large doorease
for magnesium carbonate.
In paints 0 4 through 07, 0 mixture of white lead and
laogacoiun
<jQrb0nctc was used oa tho pigment in tasking tho
action of the four good rcsin«*plostioincr combinations when
pigmented and tho effect of varying the pigment volume per
cent in tho dried film,
hach paint served cm o base grind
to which the proper amounts of roain-plasticisor solution
were added to give pigment volume poreontogoo ranging from
50 to 25."
Figure 17 chows the effect on the reflection factor of
reducing the volume of pigment in the paint film#
The
reason for the difference between tho curves for the ethyl
cellulose paints and the curves for the isobutyl methacry­
late paints is not clear, especially in view of the fact
that tho former rcoin^plnsticiscr combinations huve higher
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
""Oy***
absorption coefficients than the latter*
Then too. O C P
which la an ethyl cellulose paint containing both plant;!**
c iz o v s present in 0*4 and C*~S, behaves lilce tho methacrylate
painta® Further* 0-4 and G-5 are ’’flat” at all pigment
volumes* uhereaa G-G* G-7 end 0 8 are slightly cLosoy at
pigment t'olunes below 40 pier coat*,
It is evident fron Figure 17 that*, whatever the reason
nay be* ethyl cellulose Is somewhat superlor to isobutyl
methacrylate for tho purpoooo of an ultra-violet paint 9 and
that it is advantageous to keep the pigment volume p a r cent
as high as possible*
The limit to the pigment volume v;hich
can be used is sat by the physical strength of tho film; the
washer the film which can be tolerated* the higher is tho
pigment volume which cun be used and the higher the reflec­
tion factor which can bo attained*
Semination of th o films showed that a pigment volume
between 40 and 50 pen cent would bo satisfactory*
Tho films
adhered better and ware tougher at 40 per cent; were less
adherent and more brittle at 80 per cant*
Howover the 00
par cent films compared favorably with standard intorlor wall
finishes*
The filns containing ethyl cellulose wore loco
brittle and nore cohesive than thoco containing methacrylate*
G-8* containing ur/plc.cticiucr both vinylite and Dow Plactioizcr No* 7, was no better than G-4 or O S in film quality,
and lower in ultra-violet reflectance*
simple formulations wore adhered to*
lienee tho more
Four reasons suggest
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
~vo~
v e n /'h
the choice of ethyl cellulose os the basic
for ultra­
violet paints: it elves higher reflectance films; it pro**
duces a truly "flot" finish; it produces o slightly better
film; c?;d it is also, at the present bine, lass expensive*
The determination of the optimum combination of pie*
nents is not 00 oinple as the choice of the beet resin,
since factors other than absorption are important; end the
beat combination has not yet been determined*
white lead
is the only pigment which has lou ultra-violet absorption
ana which does not act as on inert; and consequently one
should try to include it in any formulation because of its
reduction of the thickness necessary for hiding*
zirconium
oxide would bo still bettor because of its high refractive
Index and !o:? absorption, if it could bo procured commer­
cially in a moro puro state end at a reasonable coot*
As a beginning of a more careful study of pigment
combinations than was made with the preliminary paints,
three ethyl cellulose pointc were ground with white lead,
magnesium oxide and mcgnosium carbonate, respectively, e.s
Pigaewt (0-9, 0-10, Oil: Tablo XX}* These throe paints
r/ei’O mixed in the proper’ proportions to produce luiov/n volume
ratios of tko three piemonto*
i’he total pigment volume per
cent remained constant, since ell three paints wore formu­
lated at 40 pc-r cant pigment volume*
Theseymixtures were
thinned and oprayed to a thick coat on steel panels, and
their reflection factors measured*
1’ho results are
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
presented in Figure 18. u triangle diagram with the constant
reflection contours sketched in*
A surprising result is tho
lov? reflectance of the magnesium o;;ido paint* and the dc«
croaae in reflectance on addition of white lead to magnesium
oxide*
In amount3 up to So per cent by volume, magnesium
carbonato and n.'gnesium oxide
ora
equivalent in their effects
on the reflection of white lead paints.
There is a difference in reflection between painto of
tho same composition in Figures 17 and 18*
The volume per­
centage of nagnoaiun carbonate In the pigment in 0 4 i3 71*5
pei* cent* At 40 per cent total pigment volume, 0 4 has c
reflectance of 55*0 (see Figure 17), which comparc-s with u
reflcotance of 42 for c paint of the same composition
according to Figure 18#
similarly, G-19, v/ith 50 per cent
magnesium oxide, has a reflectance of 51*0, which comperes
with a reflectance of 45 per cent for a paint of the same
composition according to Figure 1G*
Those differences are
much larger than tho possible errors in reflection measure­
ments*
Therefor» for those three pigments, a higher re­
flection is produced when two pigments ora ground together
into u paint tlmu when each pigment is ground into a
separata point and the paints nixed*
There are several possible reasons r/hy those differences
occur#
It is shovm later (111*2) that theso paints consist
ill pai’t of clusters or
°f particles, end that
those’clusters ore the more effective portion of the pigment
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
in reflecting light*
Palute ground separately and then
nixed woulu contain two types of elur.ter each :~ado up from
but n single type of pigment particle#
it nay bo that in
grinding two pigments together, clusters containing both
pigments uro l'omcd and that theno conplo: clusters oro
more cffoctive in reflecting light than the oinplc cluotorn*
Another possibility is that no complex cluster's ore fomad,
but that the simple clusters arc destroyed to a greater ex­
tent when only a single pigment is ground at e tine tlian
i7hen
t;v;o are ground together*
unknoviiie
The correct explanation is
Its determination is a problem in itaolf, and was
not considered in this study«
/mother important fact brought out by the points c o o
prising Figure 16 is that saints containing mixtures of two
pigments form films with bettor physic*.1 properties than
single
pigment paints*
Thus, the magnonlura oxide end
magnesium carbonate paint films orach, on drying, whereas
white lead paint films shot? a tendency to peel*
The- mixtures
of white lead with either tiagnoaiun oxide or carbonate
formed paints which neither eracl:ed nor peeled*
These results indicate- that 0 pigment formulation of
about CO per cent by volume of wi.it0 lead ■nd the balance a
mixture of narnosiim ccrbouuto and r.iagnecium oxide* with 45
to 50 per cent pigment by volume in the dried fiin should bo
satisfactory*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
«y/u.
C» Exnoonre Tests*
An ultraviolet reflect Inc paint will, in service, be
submitted to prolonged exposure to ultraviolet radiation*
It must/ therefor, be dc ./trued to maintain its h ii:k reflec­
tivity ao lone aa possible*
Although thut li^ht which is
reflected from a point cannot affect it, the 30 to 50 per
cent tfiioh is absorbed may be converted into heat and pasaod
off without further effect, or it nay cause a photochemical
reaction with a possibly deleterious action on the point
film or its reflectivity*
Hence oxpocuro toetc are necessary
in order to ascertain the behaviour of the paints undez* the
conditions of use*
The four types of paint, G-4, 0-5, G«G, and G-7, reprosentins the four satisfactory rcsln-plcnticisor combinations,
and cl30 G-9, 010, and G-21, repro3sr.tinc a cinclo reoinpleotioizer combination milled v.’ith three different picneiito,
wore exposed to o strong ultraviolet source*
Duplicate
panele of each paint wore kept in an envelope cs o control*
Tho panelo v/orc placed IS inches from a Cooper-ilewitt mer­
cury arc rated at 0*4 osaneroo at 200 to 250 volts*
,.since
the Cooper-Hewitt arc has a quarts envelope, each panel v;ac
protected with a cheat of 1/16 inch Coi’e:; 0 class so that
the radiation reachinc tho paint corresponded approximately
to that emitted by tho S~1 Junlump, particulcrly in the cboence of radiation less than 2000 Angstroms in wave length*
Tho Corex clans sheets were copareted fron the panels by a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-75-
cardboard spacer around the edge, with c snail vent left
open to provide ventilation*
Table X is a comparison of tho energy output of the
Coopar-llcwitt arc and the 3-1 Sunlamp, in microwatts per
era2 at a distance of SO cm {12 inches).
The data on the
output of the"Cooper-Hewitt arc ore by McAllister20, roughly
corrected to a distance of 30 era by tho inverse square loo*
Tho data on the output of the 3-1 Sunlamp running opon are
by Barnes*2, similarly corrected to a distance of 30 era*
The data on the 3-1 Sunlamp in its roflector arc by Taylor2*
and have been converted from tho ratio of energy output in
reflector to energy output in open, using Barnes * data#
Tho
intensities of the ultra-violet linos from tho CooporHewitt «ro are 10 to 20 times the intensities of the lines
from the S-l,
sothat
the 24
day exposure inthose toots io
approximatelyequivalent to a year*a service one foot frorj
an 3-1 gunlaup*
Tho effect of ultra-violet radiation on the reflection
factors of tho exposed panels and of acing without irradia­
tion on tho standard panels io shown in Figures 19* 30 and
21«
The email initial differences in reflection between
standard and exposed panels lo due to the fact that some of
those panels were not sprayed to effectively infinito thick­
ness*
Figures
19and 20 3 how that both tho othyl cellulose
and the isobutyl iuethucrylato points which did not contain
a Bov; plusticizor increased almost 20 por cent in reflectance
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
—70—
Table X*
Comparison of Cooper~Hev7itt Arc and S-l Sunleiup*
:
.
’/Qve<*
length
2
Pnerrey Output (Iiicromttto pox* cm at SO era) .».
Vortical
s-1 sunTanpTrerDQnd. to lea del
Coonor-Hewltt Are
In open
In^ji'cflcctor
6008
37
6234
13
G780
2240
108
5401
1890
91
4916
67
4350
1610
100
4047
955
64
3900
40
4
3GS4
8880
193
3341
256
12
3130
1770
150
795
3028
926
49
286
2967
479
28
151
2925
65
2894
174
8
40
2804
368
8
37
2752
115
Continuous:
2500-3200
Proot* none
7
3200-4000
°
"
50
4000-7600
u
"
0320
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
■■gMjgi
ISilRilI
liifisM
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Reproduced with permission
of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-Bo­
on exposure, whereas the puinto containing either resin
with a Dot; Plactieiser decreased 25 end 50 per cent at first
on exposux’e and tlien Gradually increased to a reflectance
almost as high as tho unopposed standard panels*
It is evi­
dent that it is the Dot? Plasticiner which causes this
transient deterioration*
The standard panels were kept in the d ark in envelopes
except fox* tho five minutes necessary to determine eaoh
reflectance*
They show a slight deere; so in reflectance
with ago*
Figure 21 shows tho influence of each of the three
different pigments on tho deterioration caused by Dow
Plusticiscr No* 7 in ethyl cellulose paints*
The reaction
occurs with ell three end io greatest with magnesium oxido*
Evidently the Dow Pleatieisers undergo a photochemical
reaction when irradiated with ultra-violet*
In o~der to
make certain that this is the case, a sample of Dow Plaoticisscr ho* 2 was pieced in the vitrcosll cell uood for trans­
mission measurements*
Tho cell was thon placed in tho
light been in tho apparatus and irradiated continuously with
the 0-1 Ounlemp for 52*5 hours#
measured periodically*
Its transmission was
Figure 22 shows the variation in its
absorption coc:.'.‘,\oient v;ith duration of exposure*
Its be­
haviour in quite nimilur to that of the paints* an Initial
rapid increase in absorption followed by a doorcase.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
jilflflll
R eproduced with perm ission o f the copyright owner.
Further reproduction prohibited without permission
—02—
Following its irradiation, the sample woo loft in the cell
in the dark for three doyo*
at tho end of that tine* ito
absorption wae found to have decreased to 80#9 in*2-, almost
its initial valuo*
The reaction of these Don Piaaticinoro oloo causes
paints containing them to yollow badly after, but not during,
exposure, so that their use in any ordinary paint v/hioh may
be occasionally exposed to ultra-violet, for example summer
sunlight, ic not advisable#
Furthermore, it is not necessa­
ry, since the 'increase in reflectance of tho paints not
containing them io an uncxpectod cfi'ect very much to bo
deaired#
Other Hoquiraments#
The studies ao far indicate that a point V7itk good
ultra-violet reflection can bo made by uaing ethyl cellulose
uud vinylite as vehicle and white lead v.ith come magnesium
oxido end magnesium carbonate os pigment#
The requirements
of reflection end poi'munence which this typo of point lias
boon designed to meet arc the primary ones which tiny ultra­
violet paint nuat fulfill and hence they were considered
first#
Uomvc-r there are added requirements which uro im­
portant and should be mentioned#
Tims o paint for interior
use should have c high reflectance for visible light; should
bo oleanable, bruahable, non settling and non-poisonous#
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*>83*"
The requirement of high reflectance in tho visible
nccme to be automatically uaticfied by o good ultra-violet
paint, since moot materials with low ultra-violet absorption
huvo Ion visible absorption end are non-selcctlve.
Figure
23 is c spectral reflectance curve fox' a panel of paint G«5
made on a Hardy Speotrophotonctcr tlircugh the courtesy of
His
Iir Taylor at tho Hols Pari: Laboratories of General
Kleetric*
This same panel had on ultra-violet reflectance
^of 34*7 at the tine the tost v/as made*
An ultra-violot paint should be able to bo cleaned in
ouch a v?ay as to remove any ultra-violet absorbing X’iln of
Greece and dirt which nay collect upon it, anu so retain its
LicL reflectance#
Its solvent formulation should bo adjust**
able so that it cun be brushed or opruyod on a surface#
Settling, which is rapid in these px'ocont formulations,
should bo ovorcomo without impairment of ultra-violet re­
flectivity, in order to produce a stable- product*
/.nd the
Uoe of white lead, because of Its poisonous nature, chould
be carefully considered*
:v Other Factors AffoctinK Reflection. Factor*
In this ctuuy of the possibility of mahing Paints which
reflect largo percentaloa of incident ultra-violet light,
attention has been focused chiefly on the tv/o controlling
factors, the transparency of the vehiclo and of the pxgcient#
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Howovor, there have been indications that otnor factors
nay also bo important.
These .*ro the physical propertied
of the pignont und the influence of the fclUaaiucs of the
applied film on reflection factor.
Tho importance of the: ratio of tho refractive indices
of pigment and vehicle3 in the dried film, Jiao been pointed
out ulreudy an being Important* since it controls the
possible bonding of light by each paptxolo and so is a
factor determining directly the thickness of paint necessary
for high reflection end the affect o f addition of opaque
pigments.
The effects of tho particle :rise of a pigment*
its degree of wetting by tise vehicle* und tho purtiolc
arrangement within the paint may aloo bo important # The
relation between tne roflootion factor of o film and its
thickness bus a direct bearing on tho hiding power and
economy of a paint as well aa the mxiiaun rofloctr-nco ob­
tainable frca it.
Theso factors are also of importance in
paints de-signou for visible service* and will now be con­
sidered in more detail.
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••80**
in .
x ira n re iic a
op
? lG :;i;irr p flo r a r c m s .
1. Particle Gi^oT
The overage size end the distribution of sizes of tho
particles of a pigment ere important in determining the
amount of light scattered by it and heneo its reflecting
power#
This dependence of scattering on particle size is
particularly critical when the particle diameter io approx­
imately the wave length of the light being scattorod.
22
Shoulejkin
has calculated the redial distribution of
soattored light around particlos of various diameters from
the general form of &ie*8 equations for the scattering of
electromagnetic waves by dielectric spheres#
He finds that
for particles very snail compared to the wave length of the
light the amount of light scattered bach is equal to that
scattered in the direction of the incident lightj and that
ns the particle size is increased the amount scattered bach
decreases, until, for particles large compared to tho wave
length of the light, it is the amount calculated by the laws
of optics. Ho concludes that "There la, therefor, a smooth
continuous change from the scattering of light to its re­
flection and refraction”*
Caaperaon2^, using lile’a and Shouldjkin’s theories, has
calculated the absorption coefficients and the intensities
of the diffuse scattered reflection for various particle
diameters, save lengths of incident light, and ratios of
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•67
refractive indices of particles and dicpcroing noaima*
He
finds that "...there is, for each particle radius, a wuv©
length for which the absorption at constant concentration is
a maximum*
The position of these maxima is shifted more and
more toward tho long wave length spootruxa for larger partide"*
At the maximum, the particle diameter is approxi­
mately two thirds the wove length#
The literature on tho experimental relations botv/oon
particle size and the scattering of light by amohos, solo,
P4—°7
and dilute suspensions is extensive ' ~ • Agreement with
Uie*s and Rayleigh^ \ Tories is not found, as a rule,
nevertheless all results indicate that the particle oiso,
in certain ranges, critically affects their ability to
soatter and reflect light.
Three general means are available for determining the
particle size and size distribution of pigments: tho cedimentation method; the light absorption method; and tho
photomicrographies method*
Tho sedimentation method hao
many variations, but all depend on Stofceo* Luv; for the
calculation of size*
OQ
By the uao of the ultra-contrifugoJ ,
very small particle aizos can be determined*
Stuts end
Pfund22 use the percentage light transmission in tho vinibla
band by a suspension of fixed concentration to determine
particle size, and Gamble and Barnett^ use a similar method
in the infra-red.
The method is only applicable to fairly
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-88uniform pigments with average particle else leas than tho
wave length of light available*
It is a relative method
and requires a separate comparison with other methods for
each pigment#
The photomiorographic method io direct, but
may Involve sampling errors*
Its lowor limit ia approxi­
mately the wave length of"light used#
Kuhn®^ describes a
method using the ^ciss-l'homa blood corpuscle counting
chamber*
32
Green
describes an accurate method based on
Photographing the pigment after dispersing it on c glass
elide, end points out the distinction between true particles
and aggregates, and the importance of eliminating the letter
by the proper dispersing procedure*
Because of the critical effect oi‘ tho particle q Iz q cn
reflection end hiding power found with some pigments in the
visible range, an effort wan made to discover whether the
particle size of the pigments uood An ultra-violet paints
lias on important effect on their ultra-violet reflection#
The photonicrographic nothod wac used in examining the par­
ticles*
Preliminary examination showed aagneciuxa oxido to
be the only pigment, of the throe used, v;ith many psx'tioloo
approaching the oritical range in size#
Tlio difference in
reflection between the commercial magnesium oxide powclero
and the smoked deposit (fublc* III) may bo due to the exist­
ence of many more
tides in the critical range in tho
smoked form, as well us to a lack of purity in the commercial
fora#
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permission.
-B O -
Two forms of magnesium oxiue poivdcr arc* available,
"light" end "heavy", of which the light bulks much larger«
In lino with the reasoning above, the reflection factor
measurements (Table ill) suggest that the light form has
the sncillcr particle size since it hw> tho larger reflec­
tance#
Two paints nor© ground, 0 1 7 and O l O (Table IX) t
identical except that one contained the heavy mid the other
the light fora of magnesium o:d,do* AO might be expeetGd,
O l G had a larger ultra-violet reflectance'tiiun 017.
Yot,
photomicrographs of these tvjo points (Plote V) at first
glance seem to indicate that G-X8 lias the larger particles#
This Vrw first intimated by the fact that M O
filtered
through cloth slower tfcun 0 1 7 and also settled faster to a
looser sediment• Closer examination o f the photomicrographs
shows that those 3nrgc purticloo ore actuully clusters or
aggregates of many small particles#
Also, perticloa email
enough to be in the critical range for ultra-violet scatter­
ing and reflection uro just bolov; the limit of visibility of
a raioroooops using visible light* so that they do not appear
021
the photomicrographs#
Hence it io uncertain whether the
observed difference In reflection is duo tu particle size or
to some othor effect#
In the cose of paints 0-1, 0-8 and
03, it was observed (p* 67) that tho effect of grinding in
the mill was to produce & reflection factor below th a t of
paints of identical composition gx-ound by hand, tho diiforwnce
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being greatex* tlie grcntei* the proportion of magnesium car­
bonate to white lead*
'fhoee differences cannot be due to
differences in tho particle sizes of the pigments, but must
bo due to the better dispersion obtained in tho mill, ao
that it is likely thot tho difference between G-17 and G-18
is due to the different degrees of dispersion in the two
paints os indicated by the many more largo clusters of
particles in G-18 as shown In tho photomicrographs*
2* Particle structure or Aggregation*
In order to compare the effect of particle structure
alono'(l*e* the clustering of a rnuabor of individual parti­
cles into an aggregate), examine the photomicrographs of
the magnesium carbonate paints, G-10a, in the ground form,
and G-10bv in the unground form (Plates VI end VII)*
flies©
points era identical except that G-10a was ground 70 hours
as usual and G-lOb was rotated in the mill for tho come
length of time, but without balls#
Plate VI was mo do from
tho paints diluted 5il with a resin solution of tho same
Viscosity and composition as that used in making tho painta#
Plate VII was made from tho paints diluted 80 il in tho 3an©
way#
Slides were prepared fron the diluted paints by plac­
ing one drop on a clean slido, and spreading it out with the
edge of another*
This procedure wgo found to produce a
uniform dispersion of tho paint on the slide without
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-ft .
W
i-md-
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destroying the ocs^ccato etructuro boing investigated#
Tho
other photomicrographs prooouted here were similarly pre­
pared from paints diluted au indicated.
The photomicro­
graphs wore nude by transmitted light#
The reflection factor of G-lQa is 32 per cent* while
that of G-lOb, the unground foita* ia G4 per cent.
The
difference i3 evidently due to tho difference in number
and size of the aggregates as shown in the photomicrographs#
notice that some of the aegi’ecates are perfectly blaoJ:9
indicating that they are reflecting practically all the
light#
Other smaller aggregatca are leos opaque and tho
fact that they arc made up of a number of small transparent
particles can be seen#
Single particles aro those with a
clean line border and a clear center on the photographs#^
That the difference in reflection is duo to tho
presence of aggregates is very reasonable 3ince in this case
the paints are otherwise identical and tho aggregates are
dispersed on Grinding*
figure 24 shows tho decrease in re­
flection factor which occurs as the grindiUG tirae io in­
creased and tho aggregates uro graducdly dispersed by tho
action of the ball mill*
Table SI shows the results of a
count of tho ratio of number of aggregatac to number of
single particles in tho ground and unground puints, made on
the photomicrographs*
Such o count cannot bo considered
accurate since tho very small particles do not show on tho
plates and are therefor not included; and booouso there ore
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ll»5|U
i l i H I i i f i l l
M255 52SIS
Reproduced with permission of the copyright owner.
iitlUfi
-go*
Stable X I
m m g & L jG£h*&
Point
Dilution
G~10a
sa
G^lOa
50a
G~10b
8a
M.0b
soa
Leas
10 microns
I'l*cction
CJrVot'er than
10 microns
05
.001
.0007
.007
•04
.008
borderline cooes whero It is not definite nhothor a group
of particles Is an oQcjVocjato o r a naturally occurring
coincidence of particles,
nevertheless* it makea more
Quantitative the conclusions already reached#
The large
difference between the ground and unground paints is in the
larger aggregates, end* as is evident from the photographs,
they ore the ones which tu*o moot effective in reflection#
There appears to be a decrease in tho aggregate count on
dilution, but it is snail and errors in the count and in
sampling may account for it.
Plates V end V2II shov; that aggregate structure occurs
uloo in magnesium oxide and white load paints, suggesting
tho possibility that it may occur in all typca of paint.
The Question naturally arises, then, whether tho presence of
aggregate structure will affect the light reflection from
other points oo markedly as it does in the case oi* magnesium
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*•98-
carbonate, because if it does it establishes the condition
that dispersion of the pigment in paint manufacture should
be kept to the minimum necessary to produce a smooth film.
A hint as to tho answer io provided by paints G-l, G-2,
and G-3, which, as hau been pointed out, show an .increasing
drop in reflection factor from that of the hand-ground pre­
liminary paints with increasing proportion of magnesium
carbonate to white lead a3 pigment.
Grinding or mixing with
a mortar and pestle is approximately equivalent to long
churning without bolls in a mill, arid in fact does not pro­
duce as smooth o product#
Therefor theoe drops in reflec­
tion ere similar to that desci*ibed for G-10, end 2iereafter
the hand-ground preliminary paints will be referred to as
unground*
Table XII shows the effect of grinding in rela­
tion to the approximate refractive indices of pigment end
vehicle| for three pigments.
The refractive indices are for
visible light, and so are only approximate for comparison
with ultra-violet reflection data#
It is eviiWc that, as
the ratio of refractive index of pigment to vehicle in­
creases above one, the effect of grinding'on reflection
factor decreases rupidly#
Honce ono will expect the pres­
ence of aggregate struoture to bo affective in increasing
light reflection only in the case of inert typo pigments
whioh have low refractive indices comparable to thoso of the
common vehicles#
Thus, contrary to the usual manufacturing
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—90—
Table XII.
Pifsasnt
Vehicle
Refractive Index
Pimerit Vehicle
Reflection Factor
cbound
Unground
HgCOg
Ethyl Cell. 1.5-1.54
Dow Ho# 7
1.5
52
64
KgCOg
Acryloid
1.5-1.54
1.5
36
CG
fcgO#C.P.
(Baker)
Ethyl Cell#
Dow o 7
1.74
1.5
47
70
ttGQfhvy*
Ethyl Cell#
Dow NO. 7
1.74
1.5
35
55
(Squibb)
L&O, It#
(Squibb)
Ethyl Cell#
Dow Ho# 7
1.74
1.0
70
73
B«G# Ml.
Lead
Acryloid
£.0
1.5
31
52
b«g« m .
Lead
Ethyl Cell#
Dow Uo. 7
2.0
1.5
55
II #
5Q-G0 (e
procedure of disperainG the pigment as thoroughly as possi­
ble, inert type pigments may bo made much more valuable by
deliberately creatine an QGGrcgato structure within paints
containing them, improving their light reflection end hiding
power#
Little decrease in reflection on grinding is ob­
served in the case of light magnesium oride, because, al­
though ground at the came concentration in the sano viscosity
resin solution os the heavy Wcuenium oxide* it made o point
so
viscous that the grinding action of the bollo v;;:s de­
stroyed#
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\lh n t causes the effectiveness of aggregate structure,
end in what ways it can be cheated or maintained within a
paint, are questions which have not yet been answered
satisfactorily#
The importance 01* refractive index with
respect to the effectiveness of aggregates, as shown in
‘fable XIX, suggests tho explanation that there is aone air
within each aggregate, thus making the low refractive index
pigments much more affective than if every jmrticle were
surrounded by vehicle, end making the higher refractive in**
dex pigments also more effective, but to a nuch lesser oxtent,
Whether or not this explanation ia correct is not yet
known,
nevertheless, whatever the correct explanation may
be, aggregates are important in promoting higher reflectances
from paints containing inert pigmentBe
It may bo that
aggregate structure is Involved in the higher reflectances
obtained when two pigments are ground together into a paint
rather than separately.
These questions deserve further
study*
\
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—101**
XV. F i m TillOKNSSS M iD 11XDIIIG i ’0/321.
X. Theoretical delations.
Hiding power ia defined no the area covered by a unit
volume of point when the paint film just obliterates o beckground of specified contrast, usually block end white of
some specified brightnesses, and is obviously on important
quantity, since it expresses the economic value of e paint,
so far as hiding is concerned#
Depressed oa area per unit
volume, it is readily converted into an equivalent rilm
thickness, and measurements of hiding power are essentially
measurementa of the film thickness at which obliteration
occurs#
Obliteration occurs when the difference in tho re-*
fleetanooc of the paint film over tho contrasting areas be­
comes less than the minimum difference detectable by the
human eye,
Tho experimental determination of hiding power
io difficult because tho variation of reflection vvith film
thickness is very slight at the hiding thiclsiesB, permitting
considerable latitude in fixing the exact hiding thickness#
Consequently a number of attempts have been node to derive
a theoretical expression relating the light reflection of a
film of light dispersing material to its thickness, so that
the experimental determinations from which hiding power will
be calculated can bo nude in regions whore the film thick­
ness is more critical#
Tho first attempt was made by Itollott®®*
He does not
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-102—
define hie use of tho term hiding explicitly, but appears
to moon the ratio of the reflection of o paint film at a
Given thickness'to its maximum reflection (ct infinite
thickness)*
Ho observed that if a paint had a hiding of
50 por cent at a certain thickness, it had a hiding of about
75 per cent ot twice the thickness, 07*0 nor cent at three
times the thickness, and so on*
Ho then assumes that the
paint film is divided into a series of unit layers of un«
specified thickness and that hiding io o geometrical func­
tion of thickness*
‘
X’licso assumptions lead to the equation:
S a l - (1-G)a
(1)
where s is tho hiding of n unit layers and o io the hiding
of a single layer*
Rhodes and Fonda
assume the paint film to bo divided
into layers of thicluicso equal to tho average diameter of
the pigment particles, and that each layer transmits ct
fraction f of the light inoidcnt on it and reflects a
fraction U* fhen, concidoririG the multiple reflections of
the light between tho first two and subsequent layers, they
derive the cxpreooions
V Dn= (V B1> [3^]2(n‘1)
(8)
whore 33 y 33 and B- ore the brightnesses (reflectances) of
U
«
A
an infinite thickness, of n layers, and of one layer
respectively*
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*•103**
Haliett’a equation can bo put in the fora:
3n ~ % ~ ^(1*0 )n »
since 3 is defined
(3)
Hiiodea end Fonda’s equation
go
differs essentially in the mm.11 correction tern 13^ for the
reflection t o n the surface layer4 Their equation (2) can
bo rewritten:
(4)
This is e relatively simple equation which fit3 reflection**
thiefcneao data fairly well#
However, their derivation is in
error in the handling of nultiple reflections beyond the
first two layers#
A correct derivation, based on tho samo
assumption's, is Given in Appendix D#
Tho correct analysis
does not Give o ouramabl© finite aeries, as was obtained by
Hhodes and Fonda, but Gives a recursion formula which can
bo solved#
The solution, not correoted for surface reflec­
tion, is:
1-BJJO
w
This equation, which neglects surface correction, diffora
from M
essentially in the additional torn in the denomi­
nator, Giving larger values of
for tho same value of Bu*
'5*5
2Jofcrowa3;iu assumes that liglit flu:; la dininiehod
oscponontially v;ith penetration into g body, in deriving an
expression relating the reflection factor of a mixture of
powders (at infinite thiohn©33) to the reflection factor0
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of tho component powders at infinite thickness*
he gives no justification for this aoounption*
However
His expres­
sions, if Integrated for n finite rather than an infinite
thickness, give o dependence on thickness similar to equation
(5), but with different constants*
Smith**® assumes that the transmission and reflection
of light by diffusing films
incidence*
isindependent of the angle of
By considering the symmetrical cose of light
sources on both sides of tho film, and using matrix algebra,
he obtains expressions Involving the reflection and trans­
mission of the film and hyperbolic functions of the film
thickness*
These expressions can be transformed into an
equation for reflection very similar to equation (5}j
(6)
where B is tho reflection of a film of thickness t, I: is a
characteristic constant of tho material and r ic the maximum
value of IU
If the number of layera, n, in equation (G) be
replaced by its equivalent film thickness, equations (G) and
(6) arc identical*
Tho importance of this derivation is
the simplicity of tho aocumptionc involved s no layer
structure of tho paint film io required, and no assumption
us to tha dccroanc in light intensity through the film io
nooessary*
Smith goes on to derive an expression for the “absolute
hiding power” of a film, which he defines as
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~xos~
Yrtiero
cmd Jg arc the reflection factors over contractias
areas of reflection factor 1 end 0 respectively*
To do
this, he rocordc tho background as a oourca of light at the
beck side of the film of relative intensity equal to the
product of tho transmission of tlio film and tho reflection
of tho background, and proceeds as in his first analysis*
However* this is only a first approximation, since it neglects
subsequent multiple reflections between the film and thu
background, end hence hie recults on hitting power arc
approximate*
Kewish^ assumes uniform cubical pigment partiolos
oriented in planes of thickness equal to the edge length of
the particles, no light absolution by liquid or pigment,
and light4incident normally on the surface*
By considorinG
the probabilities, for a givon number of pianos n, that
different numbers of particles will bo lined up beneath
each othor, and applying the law of multiple reflections for
a series of reflecting planes, he obtains an expression
Giving tho reflection from a vaint film n luyors thick as
c series of n terns*
aura this sericc*
To unto, it has not boon possible to
However, he has shown (Figure 25) that it
can be expressed approximately by ecu ation (8) (hio equation
S, Fleur0 25), but only when x , the reflection of tho unit
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Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
-107-*
particle, is large*
This is cm interesting result;,
do
it
indicates that paints nay foliar the usually observed fora
of reflect ion-tkioluicsa curve only when tho pigment parti**
cles arc distributed in a non-uniform nunnor,
go
thut tho
unit particle for the above typo of derivation is really a
cluster of x^rticlco with a largo unit reflection*
However
too much weight should not be given this observation, since
no light absorption is assumed and since tho experimental
curves arc fitted by equations, such as Guith°s, which are
derived without reference to the distribution of the parti­
cles except that it be reasonably uniform*
The -writer, with tho aid of Dr» Taylor*, hue derived
a relation equivalent to (0 ) in a more direct fashion than
Smith, by considering the requirements which any functional
relation between reflection and thickness must satisfy*
Only two ccflMnptiona ticod bo made regarding tho paint film,
both of which 'oro tacitly m d o in every derivation*
ono la
that the film is uniform to the extent that any small, but
finite, volume of it will contain pigment in the sqeo con­
centration and behave toward light in the caraj manner as any
other small volume*
The other 1c that either the angular
distribution of tho light penetrating to any depth in tho
filia is tho acme, or tho action of tho film on light ia
independent of the angular distribution*
Tho detailed
* Dr* W# C« Taylor, I&thewaties Dept*, Univ. of Cincinnati#
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-103derivation io pyoccnted i n Appendix 3-1#
Briefly, 1»he
xiotkod its to divide tlio film arbitrarily into two layers
by an imaginary piano, and consider tho multiple reflections
between then which moke up tho reflection froa tho ant ire
filuu The requirement io then imposed that the roflection
must ho tho oano whether tho thinner or tho thicker layer
io on top#
This loads to a linear fi'aotioual relation be­
tween tho reflection factor of tho film and the reflection
factors of tho two layers*
A special linear fractional
transformation then transform thic relation into one whose
solution is readily soon#
Tho result, not corrected for
surface reflection. :isi
n «
xll-e"*1*)
l-r^o6
vhero R io the reflection factor at a filn thichnoaa t,
r ifi the maximum value of Zls and a in a characteristic
constant#
The two assumptions involved in this derivation ob­
viously cannot hold exactly for very thin filiac; of tho order
of ono pigment 2>article thick, end hence equation (V) cannot
3d
bo expected to be correct for tliin filuu* However Tolnnn
has found, for aiaohoa and silica suspensions, a strict proportionality botwaen'tho strength of tho TyMall boon and
tho concentration over a wide ranee of concentration; and
Kowish has ohown3^ tlvat for very thin films the light re­
flection should bn proportional to the thickness, neglecting
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—X00«
correction for surface refleoticm*
v/ith this in nindp it io
interesting to observe -hat the relation (7) also gives a
reflection proportional to thiclaiooo for esall thiclaicoono*
anC\ co io probably valid over the entire range of thioh®*
nossea*
In Append!:: E-2* tho nocoennry corrections aro nodo
fey reflection at the ourface of the filn, and tho conations
end
constanto are arranged for fit tine to ospcrinentnl data#
Tho brief survey herein of the literature 011 reflection*
thickness relationships indicates a v:iue van^.c in the ncaninc attached to tho torn hiding power*
In Append!:: 13-55
hiding power io defined in. accordance! with the a* S* T« U*
definition* and the related quantity hiding thickness io
oloo defined*
Tho correct nethod for dctcxnining; the hiding
thiefcneos froa tho ref1 cction-thickncea relation io outlined*
end it la shown that it depends on tho reflectances of tho
contrasting boeJegrotmfl it in desired to hide and on tho
value chosen for tlio photometric sensibility of the eye*
The hiding thiclmoos io found to vary inversely as the curvoturo constant a*'and to be a function of l/rf tho reciproeel of the nantan possible reflection from u filn*
Itanatocl:'*0 states without derivation tho approniimto
relation
-n
®
J ii-oC
(a)
Xor tho transaiaoion at ths hiding thickncca* where h in
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
-110-
the leaot perceptible contrast, H end oC two tlio rcfloctaneoo
of tho contrasting arceto to be hidden, and <* io 0130 tho
maximum reflectance of tho paint*
This equation neglects
all multiple reflections*
8.
Ssncrisental Results.
•tA
Rhodea and Fonda
obtained reflcction-thlckneas curves
for paints made from a nunbor of white pigments end inorto
ground with linseed oil*
They found good agreement with
their formula, equation (8 ), except for sine oxide paints*
31no Oxide gave higher values for intermediate thicknesses
than could bo fitted with their formula, and they attributed
this to the agglomeration of tho sine oxide particles*
Tho
exact equation {7} should fit this case better, and at the
same time give fair agreement, with their other results*
Khodoo and Starr‘S found tho rofloctlon-thieloiGos rela­
tion, (S), also valid for paints made by adding omall
amounts of carbon black, pruooiun blue and aluminum powder
to white linseed oil paints*
nollullen and Ritchie^ give o refleetion-thicfcncso
curvs obtainod with u recording spectrophotometer, but make
no attempt to fit an equation to it*
Figure 26 chows the
fit which can bo obtained with equation (7) to their curve*
tfaachfun.^ has measured tho transmission of paint filno
on glass plates at various thicknesses*
Although he did
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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not ucc a sphere to gather oil the diffusely transmitted
light 9 ho obtained most ox* It by placing his cylindrical
photoelectric cell so that it touchod the bach of tho plute*
Equation (13) s Appendix E, oxprooseo tho transmission of
tho filta in terms of the some constants which ere used in
the reflection relation*
as
This equation is:
(9)
T ~ (1
l~rMe^ r r
One would e xpect it to fit Men chain’s results* and Figure 27
shows the fit of this equation to his dota for two different
white paints*
It is evident that the functional relations derived in
Appendix JS fit the experimental data well for reflection of
visible light#
Two questions then arise*
tions hold for ultra-violet reflection?
Do thcna rela­
And what ere tho
relations between tho constants a and r ar.d the properties
of tile individual materials comprising tho film?
Erom
practical experience, one would expect that both o and r
would increase with increase in tho ratio of refractive in­
dices of pigment and vehicle, and that increase in the absorption coefficient of pigment or vehicle would decrease v#
The nature of these relationships is not known, and experi­
mental worl: to discover them would bo worth while#
Tho scope* of such work in so groat that tho solution of
only a snail part of the problem could bo attempted here*
It wan decided to Investigate the offset of tho absorption
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
gnsssm
kti*5e
I
S
l
i
mm
w
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m
mm
Wu
W L,
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8
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l i B
i l i l
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-114coefficient of the liquid, end by making reflection footox*
readings in the ultra-violet to determine whether the re**
floction-thiclmcGri curves follow tho ouc;o lev/ in the ultra**
/K:
violet es in the visible region* l-ftgncsiua carbonate was
chosen u3 the pigment for these toots because its lone mean
light path should make the effect of vehicle absorption
larger end because it requires a relatively thick filn to
reach maximum reflection, thus making the measurements of
thickness nore accurate*
The scries of inethaarylate estei*
resins was chosen for the series of vehicles because tliolr
physical and chemical properties ore similar and they differ
chiefly in thoir ultra-violet absorption coefficients*
The series of paints, G-18 to (>-16, was ground, each at
40 per cent pigment volume*
Tho pigment for each was taken
from the some sample of mogncoiuo carbonate#
The resin of
each m o dissolved in tho caxio amount of solvent*
Kaeh
paint was ground PA hours at 90 r#p*m# in tho sane mill with
the same set of balls#
The paints wore sprayed on steel panels coated with a
baked black finish* whose solid vehicle has a refractive
index very nearly tnnt of the methacrylates, so that reflec­
tion from the background would be negligible # Tho panels
v/oro mucked during spraying so that only an area 1 1 / 2
inches square would bo covered, und o more uniform film
would be obtained*
The weight of paint applied was obtained
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•‘’lit**
by wolcUiaa tho psnels boforo spraying ftnd after the paint
had dried, and iron this weight a relative filn thickness
wae calculated fron tho specific Gravities of tho component
materials*
The results obtained for each paint ore displayed
graphically In Figures 28 anil 29 togctho? with the curves,
of the form derived in Appendix 02 * wliioh havo been fitted
to the rocultc for each paint*
Tho results for 0 1 2 scatter
badly and cannot;be fitted accurately with c curve. This is
due to tho fact that the rosin of 0 1 2 , methyl notheorylato*
although apparently v;oll dissolved in its solvent* nliioh v/as
toluene cuid cellosolve, tended to forn un air emulsion in
the spray cun and to leave tho cun in fibrous eobocb-lika
strands.
Thus nuch air was trapped in the applied films
with tho effect of Increasing their reflection factors duo
to the increased bonding ox’ light at tho vohiclc«air interfacan created within the filn.
This effect is quite similar
to that suggestGd as tho explanation for the cffuetivoncos
of ae$?ogatea with inert piGEieuts* and might pouoibly bo
developed as a neons of improving the reflection from paints
containing inert pigments.
Since tho amount of air trailed
in this way in the 0 1 2 panels will very for each panel
sprayed, the reflection factors of such panels cay differ
widely.
For 0 1 4 the last point, at a film thickness of 0.02
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission
118inches> is low.
This is due to the feet that films ao
thick as this dry very slowly so that the pigment 1ms a
chance to settle, creating c film with & non-uniform oom o~
sition*
Thus the principal assumption in the derivation of
the reflect! on-thiokness relation is violoted, end a differ-*
ent reflection factor is the result*
This condition is al­
most impossible to ovoid in spraying thick filno with paints
of the loequer type, since each succeeding coat tends to
redissolve the film already applied*
The fit of the calculated curves to the results indi­
cates that tho derived reflection-thicknesa relation also
holds in the ultra-violet region*
The constanta a, 8 0, and
r employed in7fitting curves to tho results i’or the five
paints, together with the absorption coefficienta of the
rosins, and their densities end refractive indices as given
by Strain*®, arc tabulated in Table XIII*
Table XIII*
hofleetlon-fhiekncBS Curve constants*
faint
Hbr#
Curvature
Constant
maximum
Surface
Kefl##Hrt 2tefl**r ,A.
.(Af&L
Vvbs* 1
Coeff
he sin
iioirr*
Index
Density
0-12
*06
•390
1180
48«6
1*490
1.19
0-13
*07
#246
425
40.5
1*485
1.11
0—14
•036
•356
605
24*8
1*484
1.06
0-15
•04
•320
628
21.6
1*483
1.05
G—16
•05
•308
642
20*0
1.477
1.02
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
~119~
Excluding tho values for 0 *1 2 , for tho reasons given
above, tho curvature constant is found to decreoae with in­
crease in absorption coefficient oT the rcoin and with de­
crease in tho rofructivc index ratio of pigment and rcoin*
The ncxinun reflection, r, however, does not vary in o
uniform manor with any of the indicatod variables, cboorption coefficient, refractive index or density*
Since it has
been shown to v/hat o largo extout aggregates can affect the
reflection factor of raagiiosiun carbonate points, it is
possible that this factor woo tlic controlling one in thc30
tests, obscuring the effects of rosin absorption*
Tho diff­
erences in viscosity between tho resin oolutiono used in
0 1 5 to G~16 are negligible, 00 that viscosity differences
probably did not offoot the dispersion in the mill*
But
differences in tho wotting of tho particles by each resin
could affect the dcgi’ce of dispersion of the aggregates by
the alll, especially if tho vie?/ ia tahen that aggregates
contain enti'apped air*
In this connection, it may also be
pointed out that the difforcxicec between ethyl cellulose and
ioobutyl loothaoryloto points shown in figure 1 ? may be duo
to better wotting of the pigmont by tho latter resin*
tfhould
wetting measurements substantiate this supposition, it
would account for the difference in gloss which was noted,
since it has bean shown that addition of wotting agents to
1
40
vehicles which wot the pigment poorly can improve the gloss*
Poorer wotting of tho pigtoent by the ethyl cellulose would
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
••iso**
provide the opportunity of occluding some air in tlio film,
particularly since tho pigment volumes ore high, with the
result of higher reflection because of the refractive index
effect#
Although the presence of air in tho paint film is
only definitely known in the case of tho cprayed G-12
panels, which showed higher reflection factors^ it is inter­
esting that it also provides a consistent explanation of the
case above and of the effectiveness of aggregates as well*
This explanation, however, is entirely speculative and
further research on this particular subject should be
valuable *
This work on refleotion-thiclmess curves is preliminary
and shows tho need of more experimentation of this type with
careful control of all variables.
white lead, which is not
aggregates, is indicated.
30
For this, tho choice of
sensitive to the presence of
Tho offoct of refractive index,
light absorption, particle siac and particle structure of
pigments on the constants a and r, as v/ell as the effect of
vehicle absorption, should be studied#
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
-1221"
V. StftSlARY.
1* The development of paints reflecting up to 70 per
cent in the ultra-violet is described.
The four stages of
development ore (1 ) testing of reflection or transmission
of ell possible j)aint materials to select thcso suitable5
(3) nixing ond testing of the oimplect possible combinations
of pigment and vehicle to determine ouitablo combinations;
(3 ) determination of low ultra-violet absorption rosinplastioizer combinations which form goad films 5 end (4)
'accurate milling of the most likely paint formulations end
testing then for reflection end deterioration.
8#
For this purpose* on apparatus woo developed which
measures accurately tho integrated reflection factors and
the transmission coefficients of substances in tho band from
2800 to 3300 Angstroms.
This apparatus balances out fluctu­
ations in source intensity, and its readings are independent
of tho amplification of its amplifier.
3. An e::uot method of taking into account tho multiple
reflections in an absorption cell is derived#
4. A method is derived by which approximate values for
the absorption coefficient of 0 pigment and tho length of
tho mean light path through it can bo obtained from tho
variation in reflection with pigment concentration in paints,
at very high pigment eoiicontrutions*
5. Tho effect of pigment properties and pigment
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
structure ic discussed, and tn*- Oroat importance of on
nCSTCGQtG structure in improvise the reflection of points
containing inert pi^onto is demonstrated*
0* The theoretical relation botwuon tiio reflection and
the t ici:noso of
l
film is discussed in the light of the
v/orh of other investigators*
-v functional derivation of
such a relation is mu do on the basis of tuo reasonable
assumptions, and a beginning is mule on tuo study of tho
connection between the constant a of this relation and '--lie
physical properties of pi^iiont and vehicle*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-12S-
AciaffluLKDrrFimr.
The writer is grateful for the counsel and advice of
Dr. T, Goller, Dr. F* F. Ileyroth and Dr. P. J. Flory of tho
Basic Science Research Laboratory and for the aid of Dr. w.
C* Taylor of the L'athematics Department , University of
Cincinnati.
IIo is indebted to Professor E. 1C. Wore and Hr*
J. A. ileachom of The Sherwin-v/illiams company, and to Lir. D.
A. ICohr, Hr. 11. w'« Fasig, Dr. J. 1.1. Purdy end Dr. U. u.
Kewish of The Lowe Brothers Company for their interested
assistance and odvice*
Tho cooperation of Dr. A. H. Taylor
of tho Lighting Research Laboratory of the General electric
Company is appreciated.
Acknowledgement is due The Lov:o Brothers company for
its sponsorship of the Cooperative Graduate Research
Fellowship which has made this research possiblo.
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
-
184-
RKFKRi&ICBS.
1» Luckicah,
and Holladay, L. L., Fundamental units and
terms for biologically-effoctive radiation, J. 0 . 3* A.
23, 197 (1933).
2. Gumpner, Phil* Mag., 3g, 61 (1893).
3* Taylor, A* H#, Tho Measurement of Reflection Factors in
the Ultra Violot, J. 0. S. A,, 21, 776 (1931).
4* Pfund, A* H., Some Optical Properties of White Paint
Pigments in the Ultimo Violet Spectrum, Proc. An* Soc*
Test* Mat*, £3, II, 369 (1923).
5* Taylor, A* II*, A Simple Portable Instrument for Measuring
Reflection and Transmission Factors in Absolute Units,
Trana* I. E. S., 15, 811 (1920)*
6*
Rosa, E* B* and Taylor, A* II*, Theory, Construction mid
Use of the Photometric latest. vj.ng sphere, B* S*
Scientific Paper, Mo* 441*
7. Taylor, A* H*, Tho Measurement of Brythemal Ultra Violet
Radiation, d** 0* 8 * A*, <33§ 60 (1932).
8*
soller, '.Valter, Balanced Electron Tube Circuits, U* 8 *
Patent Mo* 2104211*
9* Goller, Walter, Ono Tube Balanced Circuit for D* C*
Vacuum Tube Amplifiers of Very Small currents, Rev.
Soi. Inst. J5, 416 (1932)*
10* Penick, I). B., Direct Current Amplifier Circuits for Use
with the Electrometer Tube, Rev. Soi. Inst., <1, 115 (1935).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-125-
11. Foroytho, Barnes and Easley, Characteristics of a Hew
Ultra Violot Lamp, «T, 0 . a. A., 21, 50 (1931).
12. Stuta, G. F. A.| Observations of Opeotrophotoiaetrie
Ueasurcsacntu of Paint Vehicles and Pigments in the
Ultra Violet, J. BTank. Inat., 200, 87 (1925).
13. Darnea, B« T.f spectral Distribution of Energy Radiated
from a Hew Type of Tungsten Mercury Arc, Physical
Her., 36,
1468 (1320).
14. Pfund, A* II., Come Optical Properties of white Paint
Pigments in the Ultra Violet Spectrum, Proc. Am* Soc.
Teat* Uat., 25, XI, 369 (1925).
15# Luckiesh, II., Spectral Reflectances of Common Materials
in the Ultra Violet Region, J * u* 3. n., and Rev. soi*
Inat., 13, 1 (1929).
«#
16* luekieoh,
iU
and Holladay, L. L., Paints for Reflecting
Biologioally-effactive Radiation, j* Frank. Inat#, 212.
787 (1931).
17, Goodeve, C. P., The Absorption Spectra and Photo-sensi­
tising Activity of VJhito Pigments, Trans. Faraday
£3, 340 (1937).
18* Strain, 1). E«, Kennelly, R. G. and Dittmar, II. R.,
Methacrylate Resina, Ind. Ens,g# Chon. 31, 382 (1939).
19. Bass, 8 , L , and Kauppi, T. A., Evaluation of Ethyl
Cellulose Plcoticiscrs by Load-elongation Curves, Ind.
Eng»g. Client., 2£, C76 (1937).
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
20* McAlister, E, D#, Absolute Intensities in the Visible
end Ultra Violet Spectrum of e Quarts Mercury Arc,
Smithsonian rdsoellaneous Collections, 87, IIo. 17 (1935).
21, Taylor, A. H.f Ultra Violet Radiation from tho Sunlight
(Typo S—1) Sunlamp, J « 0# S. A#, SI. SO (1951).
22, Shoulejkin, Was., Scattering of Light by V ery Bis Col­
loidal Particles, Phil* lias, 48, 307 (1924).
23, Casperaon, Torbjorn, The optics of White Sols. I. Theo­
retical Derivation of tho Absorption Coefficients,
Kolloid 2,, 60, 1D1-9 {1932} J II. The Diffuse scattered
Reflection, Kolloid 3., 65,
162-70 (1933)
24, Tolman, Ryeroon, Vliet, Gerko end Brooks, Relation Be­
tween the Intensity of the Tyndall Beam ond Concentra­
tion of suspensions and Smokos, J, Am, Chem. Soc., 41,
300 (1919),
2*5, Patterson, H. S„ and Gray, P*. v;*, The Scattering of
Light by the Individual Particles of Smokoc, i'roo. Roy#
Soc. (London), Alls. 518 (192G).
26. Gurevich, Luefcinskii and Mikhailov, The Dependonoo of
the Scattering of Light in Aerosols on Particle size
and on Wave Length, Kolloid A., 60, 24-34 (1932)#
27, Tezak* Do, The Relation Between Absorption and scatter­
ing of Light by White Sols, Kolloid A,, 74, 10-28 (1936).
28. Colloid Symposium Monograph, Vol. Ill, p.260*
29, stutz, G. lr* A* and Pfund, A. H*, A Relative Method for
Determining Particle Sizo of Pigments, Xnd. Eng’s*
fihem. 19# 51 (1927).
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
~127~
20* Gamble, I)*. L. end Dai'notfc, C»
scattering in tho Hear
Infra-Red - a Reacure of Particle Size and Oise Distri­
bution, Ind. Hng» Chen., Auul. BG., £, 210 (1927)*
21* Kuhn, von Curt* On the Value of Counting Fine Grained
Substances, Xoltschrift fur /.nceuandte Chcnic, 26,
126 (1915).
32. Green* 2I», A Photonforographic Method for the DoSemina­
tion of Particle Size of Paint and Rubber Pigacnts. J.
Frank. Inst** 192, 627 {1921)*
22* Hullott* R* L», Hiding Pov;or of white i'lgaenta, Froo.
An. Soc. fest« Hat., 22, 11, 023 (1922j.
24* Rhodes, F* IU and Fonda,
Factors Determining tlio
Brightness anu opacity of \7hite Paints, lnd* £ng. Chen.,
10, 130 (X92G).
22. Pakrowoki, G. In on tho Reflootion Properties of Complex
System, *• Phyoik, 47, 6QS~902 (1920) *
36. Smith, I’e, She Hiding Pox/er of Diffusing Hodia, Trans*
Optical
Ooe. (London)„ 22P 130 (1931-32).
27. Kcuiaii, R. V/*, Reflection and Transmission of Light by
Faint Filna, Louc Ilvothex-o I*. H« 456, 4th supp., 4-14-39«
30. nonstock, IU F., Tho o p a c ity of Paints, J. Oil Colour
Chen. Assoc., 20, 2-3<- (1937)*
39, Rhodes, P. II. and 3tarr, J. V., Reflection Factors of
VJhite Paints j, 2nd. Hug. Chon?, 21, 396 (1929).
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
—128—
40* LiOliulXen* E. w. end Ritchie, E* J ♦, I?cw Uses for a Re­
cording Spectrophotometer, Official Digest of tho Fed­
eration of Paint end Varnish Production Clubs, 174#
11? Ukr* 1938} *
41* Ilecicham, J. A., Light Reflection from Fainted Surfaces,
Jin. Paint J *, 23, 23 (Oct.
1930)*
42* Pickett, C. F., The Effect of Pigment Concentration on
tho Gloss of Enamels, Official Digest of the Federation
of Feint and Varnish Production Clubs, 18V, 310 (Jun.
1939).
OTHER REBdm&CFS.
Apparatus.
Hardy, A. C«, A Hew Recording Spectrophotometer, J. o* s* A.,
25. 303 (1933)«
Koller, L* R. and Taylor,
a
* II.# Cadmium ikicuQsium Alloy
Photo-tubes, J. 0* O# A*,
, 104 (1938).
Reflection Measurements? Metals and Pigments.
Coblentz, V/* U«, Ultraviolet Reflecting Povjcr of «luninua
end Several Other Hotels, B„ S. Jour. of Res., 189a
Fob. 1939.
Ilulburt,
0,, The Reflooting Power of Iietaln in the Ultra
Violet Region of the Spectrum, Aatrophyo, J. 42, 205,
(1915).
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
-1 2 9 -
Preston, J. S., The Reflection Factor of Kceneaiua aside,
Trano* Optical Soe. {London) , 81. 15-35 (1929-130) •
Gtutn, G. F ? A*? The Testing of Paint Picmonto for Trans­
parency to Ultra Violet Radiation, J * Prank* Inst•, 202«
89 (1926)«
Taylor j A. 11., Reflection Factors of Various lleterialo for
Visible and Ultra Violc-t Radiation, J. 0 * S. A#, 24,
192 (1954)*
Taylor, A* H* cnu Ftards, Funlus D.s Ultra Violet and Light
Reflect in" Properties of Aluminum, J. 0# £>. A*, 21,
077 (1951)c
Transmission Heaourementa.
Duvey, Duncan anu uiggan, Absorption of Ultra Violet Light
by Luoquor Films, Phya* uev«, 55, 1425 (1980)5 Ind.
Eng# Chen*, 25, 904 (1981)»
Gamble, lu L» and Gtuta, G. F.
a
.& Ultra 'violet Light Tranc-
mission Characteristics of Gome cyntiietio Resina, Ind.
Eng. Chen., 21, 350 (1929).
Stutz, G« P.
a
., Absorption of Ultra Violet Light by Paint
Vehicles, Ind. Eng. Chesu, 19, 897 (1987).
Reflection of Paint3 .
Gamble, D* L*, Light Reflecting Characteristics of Points,
Ind. Eng. Chwa., 84, 875-81 (1932).
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
-130-
Gardner, IU A., Illumination from Point, Point, Oil end Drug
Bev*, £ 8 , Ho* 23, 8 (1919)«
Mallctt, H*
The- Bffect of Certain Point Palma on Ultra
Violet Light, Proo* An. 3oc* Test# lu it-», 23, II, 379
(1923)c
L’oiiUllen, ii# J»s Ritchie, ji* J e and Bullard, u L», Deter­
mination o f Hiding Power by the Jx>ectrophotometer,
Official Digoat of tho federation of Paint and Varnish
Production Clubs, 187* 272 (June 1939)<*
Mew, G* P ,3 Radiation and Paint, J. Oil and colour CLem#
Aaaoc.* 19, 136 (1936),
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
APPEHDICK9*
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
-1 3 2 -
Appcndix A.
Theory of Integrating gphero >
X, Absolute Reflection Heaourenents.fAfter gunpncr, Taylor,
and others)•
Assume the inner surface of tho sphere to bo a perfect
diffuser, so that light reflected from it obeys tho cosine
low#
That io, (Figure 30-1),
vox &
®iiC **
where
(1)
is the intensity of light reflected in the direc­
tion a C, and &c is the intensity of light reflected in tho
direction AO, when light io incident or. the point
If S0
a
#
Wie intensity of the light reflected normally,
tho intensity in the direction AC at c will be:
$0
cos 9
AC
The intensity normal to the surface at C, duo to reflection
from A will bo:
8^
a $0 coo £
Cos 9
nnnw O
(2)
AC
However,
HT ss Ha coo 9
(5)
Hence
*0 ■ 90 C°sS&
s Ho
(SdCOS«}“ 4a'"
(4)
Thus, since a is the radiuu of tho cnhcro, and constant, the
intensity at any point 0 Inside the sphere duo to tho first
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F ig u r e
3 0
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w ith o u t perm ission.
-1 5 4 -..
reflection from
a
will be the sane*
Xn other words* each
portion of the inner surface will illusiinoto uniformly
each 'other portion*
Consider non tho sphere roflcctoaetcr#
Tho light been
enters tho sphere through a snail openii'Si and strikes
either tho oiunplo or the sphere wall depending on how tlia
sphere is turned*
Let
r ~ reflection ratio of sphere coating, l»o* ratio of
oil reflected light to incident light#
P ss reflootion ratio of sample«
&nh®as area of sphere *
Consider first the esse where the light is incident
on the sphere well (Figure SO-I}*
tion fro&
Due to the first rail ac­
a,
tlio intensity at any point C on the sphere
H«)C
surface will be ftr f) , where $ ie the fc.tog-ity ofAincident
4na*
light, since the sphere ie equally illuminated from A#
This
will also bo the intensity at l*$ due to the first reflection#
The second reflection from all points C to p can bo
evaluated go follows*
From any unit area of the sphere, tho
intensity at P duo to second reflection will be gr > r . ♦
dfiriAkira1
^
Proa tho entire sphere surface, the intensity at V duo to
the second reflection will be
fo...
Similarly the intensity duo to tho
gyP
r ..
4 va^
9r
dire^ *'
thirdreflection will be:
, Sioainc UP c11 *ilc aultiplo reflections, tho total
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-1 3 5 -
intensity at P ias
Sp sc for
(1 t
* rs * » « «)
(5)
4tru^
Since r la loss than one, the series own be cuiiaed9 anti'
Sp " f4tra
~ 2 * i-x*
tO)
Bow co.uaIdor the case shore tho light is incident on
the sample (Picure 30«II)*
It Is not necessary to assume
that reflection from tho sample obeys the
ooainc lav/* Let
£ and 4>be polar coordinates ivith origin at D, and ?(&»f) be
the function representing the distribution of refloated
li^lit from the sample*
Then, tho reflection ratio a is
TT Iti
B mjfflM) W &
(7)
0 i
The intensity due to first reflection ut uny point C
will bo
I £(£,<?}
Due to the oorcon between B and P#
this first reflected li&ht does not reach .■* 1'he intensity
due to tho second reflection at ? will bo9 because of
equation (7): / f ®
o o
*
47ia
fartx*
The intensity due to the third reflection at P will be
O
‘
SET
r
.W ** a aitt4ua" 4ira"
4,m"
SuiiBias “P all tho nultlplc rofleotiona, tho total intensity
ut P is:
«£ «alE„ U t
A
Aira*
*
»8
* • * *> sSS-«.JE^TTd*1'
<8>
Comparing equations (0) and (8 )# it io seen that
S. s ®
SP
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(0)
-1 3 6 -
Thio is tho ratio of intensities which i3 measui’ed
in on experiment by measuring the ratio of she phototube
currents when the sphere io in the two positions*
.Equation
(9) shows that such a reflection measurement is independent
of the reflection factor of
the sphere surface*
2* Error due to Holes and sample*
In this derivation, the effects of holes in tho sphere
and of low reflection fuctor samples huve boon neglected*
The error duo to them can be found readily if tho sample
and sphere wall aro assumed to obey the cosine law*
Lot
b bo tho area of sample esrpooed in the sphere, and o bo the
area of holes in the sphere.
Considering first light incident on tho sphere wall at
A, the intensity at any point C due to tho first reflection
from A will be, no before, Or » The intensity at X5 due to
4ira“
tho second reflection will, however, now be:
X47raw
L
J
*■* 4 n a *
sfcSi
T “
~ '
4taM
♦ c -
{1 0 }
(1 1 )
Similarly, the intensity due to the third reflection will be
Summing up all the multiple reflections, the total
Aim4
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* "1 5 7 * *
intenoity at P is:
~
2
I* *
* x-
>
*
• « .)
. . ., «
&
_
2 T _
(lg)
Considering light incidont on tlic samplo, tho intensity
at ony point C due to the first reflection free* B is gR
ter2
This first reflection does not reach P because of tho
Screen*
The intensity ut P due to the second reflection is
gR
nous
4ira2
rl47ras-b-o) «■ nb ] _ gBgi* * Similarly, the
47TQ2
J = 4ira“
third reflection will Give
gRr8
« SUDaaine up all the
g W 5''
multiple reflections, tho total intensity at P duo to’light
incident on tho sample 1st
« ! « S & l U * * r - * r ct'-* • • o i m i S L ^ & i
4™*4-ira*2 1 -r*
us)
If one now takes the ratio of the intensities, from
equations (IB) and (13), ono obtains:
(fit
-&.» ra
(14)
h
Thus the factor j , defined by equation (11)„ is tho
approximate correction for holes and for low reflectance
samples*
The correction factor J io unity (i*e« no correc­
tion) only wlien the sample has the sane reflection as tho
sphere wall, and there are no holes in the sphere*
requirement o«n be achieved practically#
neither
Hence, in order to
keep the correction factor as near one as possible, the area
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-1 3 8 -
of holes end the area of somple c;;posocl must be hopt os
small ac possible*
Tho correction will always bo larger
for smaller values of sample reflectance, and the measured
Io w /.
reflection factor will always be slightly i?#gn#
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—1 3
3—
Appendix B,
Analysis of Transmission Cell.
1. Transmission of materiel in Cell#.
The tronamiaeion cell is composed, essentially, of two
vitreosil plates with space between for tho material to be
tested*
The two surfaces of caoli vitreooil plate can be con­
sidered, for this analysis, as one composite surface, which
reflects a certain percentage of tho light striking it.
cell ccn then be represented (Figure 5}
go
The
an absorber trans­
mitting g fraction "t” between two surfaces each reflecting
a fraction f,xn* If we let
x
sat
tho fraction of light reflected from the two
surfaces of each vitreosil plate,
H « tho total reflection from the coll (measured),
t * the fraotlon of light transmitted by the mat­
erial in the cell,
Tss the overall transmission of the cell (measured),
we canwrite the total reflection
from the coll as tho infi­
nite series:
H
mm
dp
m
x ♦ (l-x)Vx * ( l - x ) W *r . * .
ft
X 4 (l~X)23CtS (1 ♦ X2t2 ♦ x*t4 ♦ ..e)
This can be summed, since xnt2 is less than one, whence
11 « * ♦ ll»*jrx»*
1 -art2
_ x(l * t2 <» axtT)
*"*
1 -x^t2
(i)
Similarly, we can v/rite tho overall transmission of tho
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-1 4 0 -
c$ll
03
the infinite series:
2 *a ^ j* (l-x}~t 4 (l~;ic)2x2t3 ♦ (l«oc}2 x4 tS 4 »«*
s: t(l-0C}2 (l 4 X2 t2 4 X^t^ 4 #»« )
whence, since a^t2 is loos then one,
In order to eliminate x and solve for t, note that
equations {1 } end (3) can he combined to give:
B = s ♦ xtT
or
x
"
R
1 4 tO*
/r,*
Substitute for x in equation (1) from equation (5):
R~
r
»i ♦ t2 **
2Rt2
if
jt‘
' 7 r z r m ! r ; m'm
;*'mm
(1 4
w
Clear of frootions;
(Ifti*)2- R2 t2 w {l4tT} (l*t2) - 8 Bt3
Multiply out and rearrange:
ft3 4 (l~2R4R2 ~T2 )tS 4 (T~2 ?)t sc 0
Divide through by tTs
t2 4 (1 -SR7n a- 1 3) . t - 1 a 0
ivhenco, solving for t:
* = - ndgik!
,
4 /N a f e g f * i
(4)
g« Rcfrootivc Index of Kateriol in Cell»
Let us consider in detail a single vitreosil plate,
assuming that it absorbs no light*
If ws define the
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-1 4 1 -
follov/ina cto:
c\ ss the fraction of li^ht reflected fron the
vitroooil«*air interface,
b a tho fraction of light reflected fron the
vitrooail«liquid interface p
t i f z tho v ofractive index of vitrcocil,
2i j m
the refractive index of notorial in cell,
then
x * a a (i-a)sb * {l~a)‘
\b^ ♦ ••• a a ♦ b(l»o)8
TvTau
and
:e~abr » n •* b •* gab
xihanco:
b ac
g «■» a
l-ga-tax
/r \
' '
a con bo calculated fron jfrcsnol'a Lav;;
t?
(i —<»^
\nJSl7
x con be calculated fron R and T by equationo (5) and (4) •
Hence b can be calculated fron equation (5)#
ilao, fron:
li’csnol^ hav;:
f
b
nyiSr
co that
con bo calculateds
UL -
+ Ih)
ITjW^T
(0J
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-1 4 2 -
I’liua tho refractive indcr of the raatci'iGl bolng tooted
can bo determined approximately from (G) if it is Imoivn
whether it io larger or smaller than that of the vitreosil
in the ultra-violet.
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-1 4 3
Apuondix C*
Calculation of Pigment Absorption*
Figure 9 ohov/s tho decrease in ultra-violet reflection
factor with increase in the volume ratio of vehicle to pig­
ment, for two pigments* It is aeon that, for small volume
in +Ue.
I 05 av> i'fK *w of +v» c
v effect io*\
t a-cto*
ratios, the decreaoeAis proportional to tho volume ratio#
Since a reflection factor lose than one represents uboorption by tho reflecting material, it is reasonable to ascribe
this decrease in reflection to absorption by the vehicle#
If this is so, one should bo able to calculate, from tho
rute of decx*eace and the absorption coefficient of the vehi­
cle, the length of a nc-nn light path through the paint, and
therefrom tho absorption coefficient of the pigment#
one
must liiako several assumptions, however, which render the
results only approximate#
Let
If * ratio of xrolumo of vehicle to volume of pigment,
R * reflection factor at a volume ratio V,
R0« reflection factor of dx*y pigment (V*0),
3c * absorption coefficient of paint,
3c^« absorption coefficient of vehicle,
V
absorption coefficient of pigment,
L * length of the moan light path through the
paint, not including distance traveled
through eir between particles, defined
by the equation R * e ' f h u s reflection
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-1 4 4 -
ic hero represented cc the roGult o£
absorption. according to^Lanbex't’c Lor/,
and no tnls equation io oloo a defini«*
t-ion of \ u
In other v/ordo, of all tho
light paths pooclblo through the paint,
the zioon light path, L : io that ono
which. if traveled by all tho light,
would give the obaervou reflection
factor. Ho
Lv“
that portion of L contained in vchiclo»
L_~
that portion of L contained in picmant*
LQ~
length of the r.:can light path through
Jr
the* dry pigment (\r«0 )*
n a
tho number of pigment particleo along
tiio mean path L.
For email valueo of V, each curve of Figure 0 can be
represented by u straight line whose equation is:
In H « la Hq ~ v;V
where «r io
V*Q*
q constant
(1)
o^proaaing tho dope oftho oux-vc at
Equation (1) can be rewritten:
It a V " V
(8 )
Consider o cubical particle of edgelength d, covered
by a very thin uniform coating of vehicle of thiofcnesu b*
Tlien, for this particle:
V X5
_ MM
ca2b
- Cb
wmm— mm pym
d°
-
(3)
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-1 4 5 -
JSquation (5) a l s o holds for r. ophorical particle#
Assume iiict tho follov/in.; appro:cir.ations hold:
1# L approaches
as V approaches 0#
This io strongly
suggested by the smooth transition fron point to dry pig­
ment for nceneciun carbonate#
The typo of pa chins of the
particles aill not affect this asmmption nutorially,
since L and L0 do not include tho distance traveled through
nir between particles#
2« Tho particles ore of unifora cine, and tho nunber of
particles, n, in the near, light path remains the sane as
7 upnroachea 0* so that LY,-L„* This can ordv bo true for
if
O
very snail values of 7 :d!on the vehicle surrounds each
particle v/itli u thin coat and ;/ir still fills the spaces
+•
between particles*
5* When 7 io snail, the vehicle surrounds each x'urticle
with o uniform coat*
4# Tho thicknesses of the paint films tested for reflection
are great enough oo that ell light paths aro included in
reflection ccaourcnants, and tho films isay be considered
go
effectively infinite in thickness#
The accompanying diagram represents the mean light
path otraichtened out, with the pigment Qnd vehicle paths
separated# £rou this diagram, it io evident that, with the
U----------- L 0 = L p —
—
$
---
- - 'Ht
~>jzb* |*—
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-1 4 6 -
anoiniptions above 9
end
n
H0o ^
(4 )
r
*a c~kPL°
(G)
Equatiac P from equations (2 ) and (4),
yjV
n r*
is k\-(£bu)
v ; *— i " v»
~Z2Z*&o
(6 )
IT
Substituting For b rx’ccx equation (0 )P
tf JJJ ICyXl Vd, Itr* m 2 ^
e— ■*tz “*TT*.... ***,;".
Y
5
i>
5
{*75
v''
Substltutlxic £or Zq t o n oquation (5)*
w ~.j£{----—k... -In o.
8
\ l;
)
/8 j
wi
P
k
or
- bx. In nn
I> ■» J r . P.
, .
(0)
liquation (7) can bo rewritten:
Lo s |S
(1 0 )
Sr
Equations (9) and (10) ai’o the desired results.
It
nuot be rerxerxbored that they ore only approninato duo to the
assumptions involved, and caii probably Give only a*dor or
laaGnitude X’esults*
Bor tha curves ox’ FiGuru 9, fcy-SO.
For
inc{yie3 ium carbonate, \?*G.1£7 and -In ho*0#225, rroci which
I»0 »Q#Q1 inches and k^niiQ in**^.
-In H *0,461, fron which
For white lead, wso.024 and
Lj bQ9QQ& inohoa and J:o*209
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-1 4 7 -
Armendix D«
Derivation on Abodes and Fondafs Assumptions.
L'ohing the sane asaurt tiona as Rhodes and Fonda, con­
sider the paint film as a series of superimposed layerc each
reflecting a fraction l\ and transmitting n fraction T of the
incident light*
Consider now the multiple reflections be­
tween the n**1 layer and the n-1 layers beneath it, much as
.
in Ai>pcndix B:
% s «* ® w *
* » w « w *
- h * V i *2 a ♦
where
* ...i
(a
and 33^^ denote the reflection from n and n-1
layers respectively.
Since
is loss than one, (1} can
be rewritten as:
3^ « h t y /
n *( r W W i
**%***
(2)
1 - nBn-l
Let
Bn as ft * On
(g)
1 * aOn
where a is a constant and Gn is a function of n, related to
Bn as shown in (3)*
a ♦
<hx
1 + aGn “
Substitute (3) in (S):
H ( X v a V x)
(l^aO^)
♦ (T3" H g ) ( a ^ x )
U)
- B(a^Gn-l)
Solve for Gn i
G^asiRag-a*K»a (Tn-H2 )) + (Ra-a^lto^-R8) ^ !
{1-Ra-Ra-a^(T2- ^ )) ♦ (a-K-e^R-aCfy-R^))Gnwl
In order to make the relationship between Gn and Gn„^ simple,
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Then:
2Ha
0,1 ■
-
S>
0
T* ~ B- «
l-2 Hu - * * ( & & )
G“ -l
(7)
Sinoo a, T, and K arc constants, this can be rewritten,
°a»EVi
<e>
where JC is a constant*
0a
The solution of (8 ) la
s OS*
(0)
where C is on arbitrary constant*
Equation (3) then
becomes:
1“ '
In order to evaluate K, substitute for u2 from
equation (6 ):
2
~
0
0
2
+l»a ((
1
)
-Z'tfT
a
*
*
9
K will bo less than ono if
T8~1 *R8 2 (TS-a2 Ha£~Ii2 -l) - SHS
(18)
or if
4tl2 2 (^-H 2 )(TS-H2-1 ) - Ss ♦ a8 ♦ 1
or if
4HS 2 (T2~R2~1)2
(^)
This inequality, ( 1 3 can be shown to be true, for,
since ther*
.o always some absorption,
TI 1 - R
UWr)
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-1 4 9 -
and
T2 £ 1 - 2 K * H 2
or
8R
/ 1 * R2- T 2
and
4B2/, (1*H2«T2 )^ ss (T~-l-?t2 )2
(ID)
IIouco K ia lees than ono 8 provided tho film 2ian some ab­
sorptions and one can then Brito:
rj-n m e**kn
shero k ia a positive constant« Then
( 16)
Oft as
l^Ce"**
Bn must approach
the ultimate or cc::imuu reflection, no
n approaches infinity, so that
Bu s fc
(17)
Bn must equal 0 when n*0 , eo that
or
0
*» - 3 ^
(1 C)
The final roaulbf aftor substituting for a and C, is then:
Bn *. Rd {X- o'131)
r r 'lie-’w —
„ 0,
1191
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•1 5 0 -
A p p o n d i s IS#
Film Thickness and Hiding Power.
1. Rcflectlon-Thiokncsa Curve Derivation*
In order to derive the functional relation between the
reflection factor of a filn and its thicknese, one need calse
only two aasumpV one*
They arc:
If. The notorial composing the film io of uniform
composition throughout*
II* hither the angular diatribution of the pone**
trating light in the onmo at any depth in
the film; or the reflection of light by the
film at any depth is independent of the
angular distribution*
Let
B(t) be the fraction of light reflected from a film of
thickness t,
T(t) be the fraction of light transmitted by a film of
thickness t*
Consider e film of thickness t divided by an imaginary
plane into tv/o layers of thicknesses t-^ and
tr>#
Because of
the assumptions above, tho reflect ion end tranomiosion of
tile lower layer can bo expressed by tho sumo functions R and
T, where tho light incident on the lower layer is that trans­
mitted through tho upper layer*
For brevity, denote R(t^)
by R1# T(tx) by Tx, il(t)SR(t^ts) by Hl2> and oo forth#
Talcing account of multiple reflections in a manner analo­
gous to that used for tho transmission coll (Appendix b),
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-1 Sl­
one obtains for
the infinite norieo:
The series can be sunned* olnoe ft*IU £ 1:
(1)
l-P^B*
i /.«
1
« R-jBo
i.j
By syxnetry,
(2 )
Equating these two values of u^,>5
H2 * iili'l - Hjfif - Hi * n3l| - H?fls
Dividing by KjBog cn^ rearranging,
Equation. (3) states that a function of layer 1 dLone is
equal to a function of layer 2 alone» Since the thiohnesses
t, and t„ are arbitrary; this function must be a constant,
i*
K, characteristic of tho notarial composing tho filn, oo that
w
TJhen t* 0 9 1 Too *0 , H approaches a lauxinun value r, and then
Ksr*i
r
«•>
Substituting for Tj in equation (1) by equation (4),
(C)
1
- IkR,
tn M
In order to solve the functional relation {*>), let
(V)
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-1 5 2 -
whero S(t) is a function or t to be dotcriained*
Equation
(G) beccness on cubatitutins (7);
)(1—rsp )4(r—Sg){X-rS^-Kfr-s^){3>*So)
1~p 3^«->
(l-r3^)(i«.rr>o) «• (r-3^) (r*3g)
Solving £or
<j^0 ^
) {1-rSo)♦ (r~3o}
{x’-s^J^rCl-rs^} (l*»rs^)
‘»r(r-31)(r-3o)
)ii-rSn)♦ r l r ^ p { I-r3J
£}
^rKjr-G^}(r-3o)
""
Coliccl*ins t2rns 9
QjLg « (r+r*ftr*W»y* )-(l^r^Kr^r^r^ ?(3;j*3*>)♦ (r l r - K - r *»
(~l*r^+rLVr *-Krb)* (x*~r~r~r
){3^**32 )* (^ ♦ l + r ^ r ^ K r }S;jS,
or.
pgg (1-Kr*r“)- (l~Ky»r*?(at^ )*(3g-ft»rs)aisg
{•‘l+Sp^Kr^)«-ir(l-Kr^r**)(3^*3»>)*■•*(
)
G^s^
2*ott
,OJ
equation (5)3
1
~ Kr * r* *« 0
(9)
Substituting equation (9) in equation (8 )f
s12 _ (3r-r-l/r-r5)n^2
opi)
11
■•?— z— *------— x*
(XO)
llccept for the trivial solution S»0 ; equation (1 0 ) aim
ba aatiafied only by an exponential relation of the lorn
s(t) « r < f at
(1 1 )
whore a in u oonatant, characteristic of the nafccriul op tho
i’ila#
Equation (7) non bacowoas
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-155-
.~ut
>*51 —at
l~re
uhcre the subscript p reform to the paint i’iln o f thiehnoso
t 6 v;ith ao correction for aurfccc tfefJLoction©
I n order that
tiay approach 2? ao t becomes infinite, u must bo a positive
constant, thus justifying the necutivo sign In tho opponent*
The tranraiauion of the film ia obtained by substitute
ing equutions (.Is) end (5) in equation (4): ’
sp s> 1 1 ~ (s^) s ik s f ^ X
* ^ ( W *)8
( l - r V 08)
~>/(l-arS+l
(l-i-V**)3
.
x - rV ^ '
or.
5*
^ ^ t ■r 4-lv>^Z cL
) ..
p — .c..—
1 ** r e
(13)
Equations (IS) end (15) cun be expronacd very conoicely
by mfcin& the nubatitut ion, v/hero s ic a constant:
rce~s
(14)
They then becoitoi
il
mm,
e *g~<rat)
0
♦at/s -at/s
/ _h> 7
,
and
a> _ 0 "“t/,2 (i-*"2“)
p *
— 1-
o°-»"8
ppst/sq^o-ar/s
Those can now be expressed in terms o f the hyperbolic
functions as follows:
fl n alnh (at/2 )
»
a ^ is w a i
(X5)
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2* Correction
for
surface
■*H»iHI.*■!
u#«»**»Iwmm
i m H.m w mi Ml»Effects.
*Hul
l■#*»>i»u
Up to thio point, the reflection ut tho surface of tlic
filn and the reflection at tho interface between tho filn
and its supporting ourl'aco have been neglected*
Multiple
reflections will of course take place botwean these aurfaqos
£iid the body of the filn, vZZlvi LilX&'b 1)c conoidcred#
The re­
flection at the interface io important when considering tho
ability of a filn of finite thickness to hide a background
of varying reflection factor#
In tho experiments here con­
ducted on filn thickness, tho films wore sprayed on a back­
ground of baked'black cuariel whose vehicle has a refractive
index so clone to that of the paints beinj: tooted that the
reflection factor of the interface is negligiblee Henco
only the surface reflection need bo considered#
The multiple reflections between surface end film ccn
be summed exactly as for tho cacc of two layers of tho film*
Equation (1 ) then becomes:
* «
bJLitz &%.- no.j 1*. i
- v v
»
.
m
1 “ V p
where now
Rp 5, reflection
of paint film, neglecting surface
effect, equation (15),
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-1 5 5 -
t> w raflootion rector of aurfaoo,
I*0 jm.l*»ii0 kj trancnisoioa factor of surface*
For a filn of infinite thickness:
H «„ = -i0 * r(l~2 ii0)
>«» ».«i 1»»4>i*
r»w m**
f*lQ \
1 ~ rn0
For a filn of thickness approachinc zero, R will approach
R0« This is a definite value for caoh cxporinontal ourvo
which can be easily detorainod since tho rofleotion^thickncsa curve is linear at very snail thicknesses and can be
extrapolated to aero thickness*
By substituting equation (Is) in {!?), 0110 obtains;
11 ~ (V"gr3 o*g* *
(1-rH0 )
j19j
+ rCi^-iOe"0*
SZlnlnatins r between equations (10) and (19)8 one obtains:
„
adUriU-... * | f % 2 U L k & J . i m
Hb 1 -aHo*^;^
L
U-B 0 }2
ri....... , rT - r.. „
l - s V ^ o 8^
, ^
a
),1G~ftt
J e
(p0.
(ii*rB0)
[n0 j;i2 R0 *B4 HJ-(H^-H„aO-0*
*
»'» «MI i l
.
U J
(x-sn0«»C)B«J'4
Rearranging,
jh- e~at'
E " 3~ ^
I + k ~ -"***
(31)
Cj. 6
where
^ ■ (1-Bo) U-IU-flnU-lU
(b b )
)(SRQ«*Rcto**Rpiiab)
and
C2
*» ^i^+aRpR
2 Ro*Hoo*HQflt
•Cc
(23)
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-1 5 C-
fho U 3U01 problem is to fit equation (Cl) to the ex­
perimental date end deternlno tlic constants e and 1^*
for
this purpose, it can bo rov;rittens
-at_ Cid^-H)
CtJ-*ull
“
An v;ao pointed out nboi'e, K0 la readily determined*
t24*
H^can
be estimated Quito closely if the data include points at
Knowing n0 and a trial value of Roc,
large film thickness*
one calculates
and Cn»
Thon ono calculi tea, for each
value of* R, tho expression on the right side oi- equation
(C4)» If this expression is thon plotted on ocmi-log paper
against t, a straight lino will result if R*, lias been
correctly chosen*
Tho dope of this line will bo tho con­
stant, &•
„
0p
f
-,r
-t*U«."t"
nidinc thicknesses hero defined us the film thickness
|> 1%4v#
and hiding power^ao the aroa covered by >
U M f w j ------------------------- --------------------------- — «<__ \
tmit volume of the paint at tfe-iti thickness,\which is neces­
sary to make insensible to tho oye tho difference botwoon J
Jbwo contrast in^surfaceo beneath tho filn*J"*Thot is, the
differenco in rofleotion factor of tho paint film over a
low reflectance and a high reflectance background must be
juat loos tlian the "least perceptible contract” or "photomotrie sensibility" of the eye*
Thus, no matter what rola-
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-1 5 7 -
tionships arc used, any determination of hiding power ia
arbitrary to the extent of the value used for the least
perceptible contrast.
Lowry52*1 measured tho photcmotrie
sensibility aB/B, where B is the brightness, of a number
of observers at different field brightnesses.
lie found
that it varied with, the field brightness, with q minimum
value of 1*37 per cent at 25 nililonberta.
accepted value
w
qo2per
cent,
Previously, the
dodetermined
by Ionic end
Erodhim^*3.
As a first approximation, tho ourfoce reflection from
tho filn will be neglected in calculating hidinc power.
This is reasonable, since nQ will bo the same for the same
paint over different backgrounds• Lot
bo the reflectance of tlio paint film over a
background of reflectance L,
bo tho reflectance of tho paint film ovor u
background of reflectance D /, L,
k bo
the leant perceptible contrast*
Then, adopting equation {1} to this case,
•31. 13. Li* Lowry - Tlio Photometric Sensibility of the Bye and
tho Precision of Photometric Observations* J.O.G.A.
2J., 132 (1931).
132. P. G. Hutting - Outlino of Applied Optics, p.120 (1912).
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-1 5 8 -
i‘he condition for tho hiding thickncsG iu then:
k = B c i =
1 -
t
e
X
«
!
^
)
w >
uh
The most extreme case of hiding io when L~1 and B«0 *
Equation (27) then becomes;
k as 3. -
s ,------------------------ (2 0 )
n+srsir
b -r ^ m t
Substituting for R and f from equations (12) ami (13),
k . , ___________ o"at(i^ ) 8
,__________________
r U - s ^ K i - r V * * } 4 c T ^ U - r 8 )3 ~ r * ( W « i )3
or
*
m
—
ir-xUi*EiV!L_
* * U - r 3)#*** „ A * a *
(20,
Ihio 1b a quadratic equation in e"K*i. kiiu., alnee r and a
are known froia tho reflection^thickncss curve, can be
solved numerically for o~a* and t*
If the characteristics
of tlio background to be hidden are known, that ic if L and
D are known, substitution from equations (12) and (13) is
made directly into equation (27) * The x’csult will in
General be a cubic equation in o"u^ s from which the hiding
thickness can bo determined#'
It ia evident from equation (29) that, if tho valuo cf
k lias boen decided on, the hiding t&Lckncss depends on both
r and a#
For two paints having the sumo maximum rofleotanoa,
V<l/u
r, who hiding thicknesses will be inversely
their & constants#
a-s
its& z &s & S z ElFSsr
For curves having tho ecmo curvature
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
159-
conotnnt a*, the .hiding thickness decreasac as r increases
from almost aero to nearly one,
This can be seen most
easily by using equation (1 2 ). choosing a value of
nearly 0 (say, 0 *0 0 } cad computing ^§^*100 *
percentage
decrease bolor/ tho maximum*
In evaluating a paint for brightness and hiding ponor
fron the experimental constants a and r, therefor, r cay
be taken as a direct,mcasure of brightness,, and the larger
tiie constants a and r tho hotter tlio hiding power#
This
docs not contradict the knovm fact that addition of a black
or colored pigment to a r/hitc raint docx'caccs the brightness
and increases the biding power (see, for example, the nork
of iUiodoa and Starr
}, for such an addition will increase
a faster than it decreases r, so that the hiding thickness
will decrease*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T. II. 4SG
Gth oiipp.
9 - 0 - SO
v s m z., of "wS'.v ?actors i^i/Ju-jcrim tig, foai^-noii
^rav-vioiis? light m fahits".
U.
Kewioh
"Somo Faotorc Influencing the Reflection of Ultra-violet Light by
Fainto'1 is a report by l>. i• bilcoc!: covoring tho e::col3ent v.-orI: that ho
has carried out in tho problem of developing r. paint having high reflection
in tlio near ultraviolet. In rovicv/ing this report, c. tabulated ctatemont
of tlio things that Yiilcoch hue accomplished trill first bo given, than a
diccuccion of tliogo acccmnliciimcntn, and finally a criticism of tho report.
Lict of Things Accomplished
1. Tho development of tv precision iicthod for measuring roflection and
trciicniaaioii of ultraviolot light.
Zm Tho improvement of the prccioion of the hitograting cphoro by tho uco
of a smaller vrindov; for tlio sample.
3. Tlio derivation of equations by ncano of which correction can bo ruado
for tho effect of holes in tho sphoro.
4. Tlio derivation of equations csccntial to tlio accuracy of transmission
coll measurements.
5. Tlio aottsercncnt of rcfloctancoo of a largo nunbor of pigments, end
absorption cocfficiont3 of a large number of tliinncre, oilc, rooino,
drlore, and plaaticiscra*
G. Tlio measurement of tho effect of additions of aluminum bronco to viiito
pigmmito and tlio v;orI:ing out of cn ozcplanation for tho unusual rticultc.
7. The discovery that larger eggrcgato size loadc to greater reflection,
end that tho creation of on aggreguta ctruoturo with incrto iiaprovcs
thoir ability to roflcct light and thoir hiding poiror.
0. Tlio devclopi-ont of pigment combinations for ono or tv;o pleasing tints
of high ultraviolot I’eflactcnco.
9. The development of eoveral paints which havo eatiofootory roflootarco
and film characteristic a and v;hich retain tlioir roflectanoo properties
after prolongod oxpoauro to ultraviolot light.
10. The derivation of equations for determining from transmission coll
measurements on liquids thoir refractive indices for ultraviolet light.
11. Tho dorivatiou of equations for determining mean light path through
end absorption cocffioionts of pigments.
12. Tlio derivation of aquations relating reflectance to thichiecs of paint
filno.
blccusoion
Undoubtedly tho greatest contribution which biloocl; has nndo ic tho
precision, method v;hicli lio has developed for measuring reflection and tramsrricclon. By using tv/o photocells, tho cfx’ootc of variation in tho intensity
of tlio light souroo arc eliminated, end by a direct balancing of potential
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2*
in tlio ohototubo circuits before amplification, tho effect of variationo
In anplifxaation ax’o eliminated* Other methods either do not oliniuato
variations in tlio source, or oleo require a com.plicatod cystcr. of rotating
prismo to split tho light into two beams of equal intensity* In ilcocIc*c
method tho precision is attained with relatively ino:cpcnsivo equipment*
Tlio importance of thic contribution ic not ccntorod eololy in tlio ncaovtronont of ultraviolet* By tho uso of otlior photocells tho nothod can bo
easily cntoncled to tlio measurement of visible light* hero a great itmgo
of uso bocancc appiu’cnt, for e;camploi meaouremcnt of glosa by r,*casurinr
tho intensity of roflection at various angles* accurato comparison of tlio
effectiveness of flatting agonto, accurato measurements of hiding power
and opacity, oolor comparisons by tho uso of filtcrc or monoaliromatio
light sources - in other v;ordo a whole nxngo of properties that v/o havo
no fanilitioc for measuring at tho present tino* Tho practical value of
cuch measurements in research, production control, and technical develop­
ment is obvious*
Tho development of tlio accurato equations for coll trancmiccion,
although essential to tho development of an ultrai'iolct-rofleeting paint,
may bo of oorr.ov:hat lose practical value to us* ;hoy arc ocacntiol to tho
accuracy of any transmission coll measurer,ante*
Tho othor equations which, have been derived are at present of a
rather more theoretical t)ion practical interest* Tho equations on neon
light path, absorption coofficient of pigments aid x'oflcctraico vc* film
thickness fora a workirt^ basic for any fundamental investigation of hiding
power*.
Tho discoveries as to tho effects of aggregate else arc of great
practiced, valuo end open up a wide field for investigation*
firconiivi o::ic1o is ir/oorcotiug as a nor; pigment possibility*
As several white and tintod paints of high ultraviolot reflectance
and satisfactory filn properties have been developed, tho original purpose
of tho work has been accomplished* Tho work widen remains to bo carried
out is tho adjustment of solvent bolanco so that tho paints will havo
satisfactory working chars.ctericticc* Tho tendency toward cnooscivo
cottling also nuoh bo corrected* Tlio working out of tlio first of thcco
problems depends almost ontirely or. tlio uses to which tho paints arc put,
and on tho methods of application* Tho proliniuary problem lioro, thon,
is one of calcs investigation. Various possible usos which havo been
suggested for ultraviolet-reflecting paints arc:
1, In hones or office buildings in connection with illumination
containing ultraviolot light* Walls nay bo painted with on ultraviolct-rcflooting paint, or papered vdtlx a paper coated with an
ultraviolot-rcfleoting
naint.
*—» *
»
8* In hospitals which maintain rooms in whinh tho air line boon
sterilised by means of ultraviolot light*
3* In noat packing houses v;hioh aro using ultraviolet light for tho
rapid curing of neat*
<•* ’
.Vcotinghouco io manufacturing a "literilnno" for uso in provonting
nold and bactorial growth in rcfrigoratorn* A coating of high
ultraviolet roflcction would bo essential to tlio efficient uso
of ouch lamps*
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
S. -nito paintc having high rdtraviolct reflectance havo .pearly
porfcct rcflcctaiico in tlio visible. Tho paintc nay find cm o
use in cacoa wlicre Jiigh iilu;iinating efficiency if: desired.
Criticism
.fhoro arc no unfavorable criticisms to bo nndo otliox* thon to point
out a feu vilnor correct.lone in tcrninolcgy and mathematics*
n. 152.
It would cocn that the terminology hero could bo considerably
improved by using the t o m "illumination'1 instead of "intensity
normal to tho surface"*
p. 134. In the cccond paragraph the statement is i-.ado iliat ’’ - the
Intensity at any point C on the sphere curface will bo
Cr ,
*1 a.v
vixcro S ic tho intensity of incident light, - • .. vary narrow
incident been of light of a given intensity would i:ot illuminate
the point c to tho gana e:ctcnt ac a larger bean of tlio ccno
intensity, lienee incorrect tcmc are fcoing unod. a hotter
abatement would bo ‘f ~ tho iliunination at any point c on tho
sphere curfaco v;ill bo Fr vhoro V is tho flun of incidoat.
4 c.{;
light, .la*: is a power factor and roprosex.tu tho total
quantity of incident light pox* seoancl (intensity tiroes crooo
sectional area).
p. ISO. It night bo a little smoother u;>n*onch to consider tho effect
of a oinglo holo in tlio sphere end thon point out that the
effect of the sn.Tiplo would be that of a holo of area (r~R)b m
v
p. 137.
Tho equation for a single holo is -
JUL
o
(j m _ _ \-.
If tho dicnotcr of tlio cphox»o is 253.4 cm. (10 in.) thon tlio
error in dotornir&iig I? by oinply taking, tho ratio of Gp to Cp
idll be c/2030. In ordor for tlio ciTor of naasurcrcnt to bo
leas than 0*1*2 the area C. must bo loco than 2.03 cq. c:n.
However, it would not bo rxecoccary to hold tho area of C to
this voluo, cinco tlio correct vultio of K can bo obtained by
menus of tho dbovo equation* To do thic tho area of tho liolo
tJirough v/hlch tho boon enters, as woll ao tl:o effect of the
phototube opening would havo to bo known, bitico it ic tlio
ratio of C5p to ffp tliat ic aotually noanured, noglect of thoco
corrections leads to slightly lov.’or values of P., co tliat it
nay bo said that tlio rcflootanccs that Vfilcook hao obtained
oro slightly low, rather tlicei olightly high as ho lias indicated
on page 130.
p. 143, - lino 4. - chould read
tho dcoroaco in tho lorarltto of
tho rofleotion factor ic proportional to tlio volusio ratio"*
p, 140* Tho assumptions given aro x*oaconablo, and within thoco
assumptions tho derivation Ic correct*
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4,
p. 140.
Equation (11) should read -
K‘a
E
(lioto that tlio firct two torsio in tlio denominator aro cauarcd.)
This correct statement of tlio equation rorcovoo any doubt os
to tho validity ox* inequalities (12) a n d (lo) and tho quoction
narks aro unnecessary.
P* 157
Hidin:; --•ov?or
h hotter ctatcacsit of tho firct ccntcnco in the paragraph io:
“Hiding thickness of a paint is hero defined as tliat filn thickness
v.iiioli io necooeury to naloo insouciblo to tho cyo the differc-nco
between two contrasting surfaces beneath tho filn, cnu hiding
pcrr.'sr io horo defined as tlio aroa covered by unit volusto of tho
paint at hiding thickness.
p« 1G0
Equation (20) should read
K « 1 - (l-K)R
KVf«-Ra
„
(Goto tlio nogativo oign in tlio donor;linator 'of tho firct
fraction.)
p. 158.
IScxfc to last lino. " - tho hiding thiclaieoaoc v.-ill bo
invoroely proportional to tlioir a constants.” This statement
is not truo in a strict ccnco, b*ut ic approximately true.
}.. .. hcr.vich
COPIESt
L’liF
Mil
J?JP
GEL
Pile
Extra
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