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The Nature of Pores in the Skin Layer of Polymeric Reverse OsmosisUltrafiltration Membranes.

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The Nature of Pores in the Skin Layer
of Polymeric Reverse
Osmosis/Ultrafiltration Membranes
Hal Wood* and S. Sourlrajan
Industrial Membrane Research Institute, Department of
Chemical Engineering, University of Ottawa, 767 Louis
Pasteur, Ottawa, Ontario K I N 6N5, Canada
It is assumed that a linear polymer solution may be represented as a suspension of
impermeable macromolecule spheres. In the film-forming procedure, spheres at the
interface form a monolayer and then partially coalesce with each other. Their size,
disposition and degree of coagulation are dependent on the casting composition and
subsequent film-forming procedure.
This ‘interstitial void model’ is applied to Reverse Osmosis (RO) / Ultrafiltration
( U F ) films. Results indicate that an RO membrane skin layer is at least one
monolayer thickness of predominantly close-packed partially coalesced
macromolecule spheres. Variations in the casting conditions influence the surface
morphology and may cause defects in the monolayer, comparable to voids formed by
the surrounding offour or more spheres.
The interstitial void model verifies the existence of a bimodal distribution of pores on
the skin layer of polymeric ROAJF membranes. The general RO membrane
fabrication requirements are that the casting macromolecules be small and packed
closely together at the interface during the membrane forming procedure.
Introduction
Analysis of experimental RO/UF data involving liquid solutions usually indicate
the existence of a bimodal distribution of pores on the skin layer of polymeric
RO/UF
This paper suggests that, for the purpose of membrane
design, these pores may be viewed as arising entirely from the interstitial void
spaces resulting from the size, geometrical disposition, and degree of coagulation
of the polymer macromolecules on the skin layer of such membranes.
Linear polymer solutions and films
Linear polymer solutions may be represented as a suspension of macromolecule
spheres. This is especially true for phase inversion membrane polymers where the
majority of monomer segments of the polymer chain are located at or near the
* To whom correspondence should be addressed.
Developments in Chemical Engineering, Vol. 1, No 1, page 32
33
Polymeric Reverse OsmosisAJZtrafiltration Membranes
surface of the sphere. The following equation may be used to calculate
macromolecule dimensions in relation to the solution composition:6
V = VE = 4nRS 3/3
(1)
The volume of the spherical macromolecule (of radius Rs) is equal to the
product of the volume (v) occupied by a crystal molecule and a swelling factor
(E). In general:
V = 0.507M/gNo
(2)
This simplified equation indicates that the macromolecule dimensions are
mainly influenced by the polymer molecular weight (M) and concentration (g) in
the s ~ l u t i o nA
. ~modification to equation (2) is required if an additive is present,
so that:
V
=:
0.507Map~gNo
(3)
where'-3
[ql' = KM,, a
(4)
From equation (4), the apparent molecular weight (Mapp) is calculated by
relating the intrinsic viscosity of the polymer-solvent-additive solution ([q]') to
the Mark-Houwink constants (K and 01) for the polymer in pure solvent.
Due to solvent evaporation and/or surface tension effects, macromolecules
concentrate at the interface during the film-forming procedure. Their disposition
at the surface is predominantly close packed. Deviations from a close-packed
monolayer are influenced by the casting composition, solution structure, and/or
membrane-making procedure. The macromolecules interpenetrate, or coalesce, to
an extent that is also dependent on the above factors. Only extreme film-forming
procedures cause complete coalescence within close packed interstitial voids. A
subsequent film-forming stage renders the macromolecules frozen and immobile,
and the membrane is ready for use as a separation film.
Modified Poiseuille transport equations are compared to experimental
membrane performance data in order to characterize skin layer morphology in
terms of a porous structure.'" The experimental data indicates that there are
usually two average pore sizes on a membrane surface.ld There are small pores
of mean radius Rbl and standard deviation 01; there are also larger pores of mean
radius Rb2 and standard deviation 02, so that Rbi f 2Ui encompasses 97% of all
possible pore sizes. The ratio of the number of large to small pores (h2) is also
determined from the experimental data, and is a required parameter to predict
membrane performance from the surface morphological constants.
The interstitial void model of membrane surfaces
The magnitude of an interstitial void in a monolayer of spheres is dependent on
the sphere radius and the packing arrangement of the spheres. Interstitial void
dimensions at the equator of the surrounding spheres may be determined from
geometry considerations. The total, or cross-sectional (xs) void area may be
calculated and compared to a circle of equal area. An inscribed (ins) radius, the
distance between the center of the interstitial void to the point of closest approach
of a surrounding sphere, may also be determined from geometry. Figure 1
illustrates some representative interstitial void spaces.
34
Hal Wood and S. Sourirajan
Shaded area i s equal to t h e
area of a c i r c l e of radius:
Figure 1 Void spaces between various arrangements of spheres.
The geometric void spaces may be determined for monolayers of
macromolecules, where the sphere radius is made equal to Rs. The magnitude of
interstial voids in monolayers of partially gelated macromolecules depends on the
macromolecule size and their disposition at the interface, and also on the degree
of interstitial coagulation that occurs during the film-forming procedure. The
inscribed geometric void dimensions are useful parameters to determine the extent
of interstitial coagulation in semi-gelated macromolecule monolayers.
From Figure I and geometry considerations, rc ins (i.e. the inscribed (ins)
radius (r) between closely (c) packed macromolecule spheres, of radius Rs) may
be determined from the following equation:
Polymeric Reverse Osmosis/Ultrafiltration Membranes
35
Rs/rc ins = (2/3112 - 1)-' = 6.464
(5)
The cross-sectional (xs) void area between closely packed macromolecules
(represented by a circle of equal area, of radius rc xs) may be determined from the
following equation:
RS/r, xs = [(3'12 - ~ / 2 ) / x ] - ' /=.~ 4.414
(6)
The inscribed and cross-sectional void areas between squarely (s) packed
macromolecules may be estimated in a similar manner:
Rs/rs ins = (2*12- I)-' = 2.414
R&
xs
(7)
= [(4 - ~ ) / n ] - ' /=~ 1.913
(8)
Representative circular void areas of radius r6 and rg, formed by spheres
missing from a closely or squarely packed array, respectively, can also be
determined:
Rs/I'6 = [(6.3'12 - 2X)/K]-1'2
5
0.874
(9)
Rs/r8 = [( 16 - 3n)/~]-'/~
= 0.69 1
(10)
The hydrodynamically-impermeable solution macromolecules at the interface
approach a crystalline state during the membrane-making procedure. It is assumed
that all permeate transport through the membrane skin surface monolayer occurs
between the partially coalesced paracrystalline macromolecules. Therefore, the
surface morphological constants of a membrane are related to interstitial void
spaces that originate i n the semi-gelated monolayer of the precursor
macromolecule spheres. Note that Rs and the magnitude of the geometric void
spaces are inherent in the casting composition. The geometric void areas,
described in Figure 1 and equations ( 5 ) to (lo), may be compared to the surface
morphological constants in order to relate the casting conditions to either the
resultant porous structure or the performance of the membrane skin layer.
Equations (5) to (10) show that the geometric void spaces are linearly related
to the sphere radius. Therefore, Rs/Rbi ratios are useful for determination of the
disposition and extent of coalescence i n surface monolayers of macromolecules.
The following analysis illustrates the general applicability of the interstitial void
model.
Analysis
According to the interstitial void model, RO membranes are made from solutions
of small-radius macromolecules. Macromolecules at the surface pack closely
together and coalesce with each other to some extent before the gelation stage in
the membrane-making procedure. Rbl and 01 from the modified Poiseuille
equation are related to voids between close-packed macromolecules. Rb2. 02 and
h2 originate from voids formed by the surrounding of four or more
macromolecules.
General analysis
The relationship between Rbi and Rs for particular values of Rbl and Rb2 is shown
i n Figure 2, for various RO/UF film-forming mixtures and their resultant
Hal Wood and S. Sourirajan
36
80
0
0
40
30
20
10
50
0
pore radius, Rbi ( A )
Figure 2 Macromolecule radius and pore radius comparisons for RO/UF
membranes.
Symbol
Polymer
PA
PA
PA
PES'
CA
Reference
I
2
3
4
5
wings on data points are of length 2a1.Non-shaded (open) data
points are Rbl values. Shaded (solid) data points rue Rbz values.
60
Polymeric Reverse Osmosis/Ultrafltration Membranes
37
membranes.ld Included i n Figure 2 are the interstitial void dimensionmacromolecule radius relationships, as given by equations (5) to (10). As shown
in Figure 2, the value of Rs is small (from 28 to 73 A) in these RO/UF solutions.
Therefore, the corresponding geometric void spaces are also small, if
macromolecules are not missing from the surface array. This ensures a relatively
high solute-separation efficiency, even if there is little interstitial coagulation.
From Figure 2 for RO membranes made from aromatic polyamide or cellulose
acetate solution^,^^^'^ Rbl is smaller than rc xs. These values of Rbl (from 3.1 to
7.5 A) are comparable to close-packed partially coagulated interstitial voids.
Similarly, the corresponding Rb2 values (from 17 to 56 A) are comparable to
square, or larger packin arrangements. Note that h2 has a value very close to zero
for most data
The membrane surfaces are then composed of
predominantly close-packed partially coalesced monolayers of their precursor
macromolecule spheres.
Figure 2 shows that the magnitude of Rbl for polyethersulfone membranes4 is
approximately rs ins,indicating that the surface macromolecules are not
predominantly close packed. Although the macromolecule dimensions are small,
these are UF and not RO membranes.
Figure 2 illustrates the general applicability of the interstitial void model for
various RO/UF membranes. The geometrical void dimensions provide the link
between the various membrane design parameters, i.e. the casting composition/
structure, membrane-making procedure, and the resultant film surface
morphology and performance.
Aromatic polyamide membranes
Some of the experimental data points in Figure 2 are for various aromatic
polyamide (PA) polymer - inorganic additive - dimethyl acetamide (DMAc)
solution compositions.' From Figure 2, for these membranes, all values of Rbl are
less than rc ins.The average RS/Rbl ratio is 10, which indicates there is a good
degree of interstitial coagulation between the closely packed macromolecules. The
large pores are comparable to the smallest possible defects, i.e. voids formed by
the surrounding of square-packed spheres. Corresponding to the above monolayer,
NaCl rejection capability is greater than 96% for almost all these membranes.
Some RO membrane surfaces may be characterized by just one mean pore
radius.' This indicates that the size and/or number of larger pores in these skin
layers are too small to significantly influence membrane performance.
Consider other data available for various PA-DMAc-CaC12 compositions.2
From Figure 2, the Rbl values are much smaller than rc ins.The average RS/Rbl
ratio is 9, indicating a considerable degree of coalescence amongst the closely
packed macromolecules. The corresponding values for Rb2 may generally be
compared to square-packed voids. The NaCl separation ability for these
membranes is usually greater than 95% when Rb2 is less than rs xs. However, an
excess of CaC12 in the casting solution strongly affects Rb2 and can increase h2.
The large voids which occur in membranes made from high CaC12 concentration
solutions, approach the size created by a macromolecule that is missing from a
close packed array. Salt rejection decreases by more than 20% if Rb2 becomes
much greater than rs x s .
The membranes discussed above''2 were made from a PA polymer with a
molecular weight of slightly over 30,000 g gmol-', and a 15 minute solvent
evaporation period. Membranes can also be made from lower molecular weights
38
Hal Wood and S. Sourirajan
of PA in DMAc-CaC12 solutions, with a 9 minute solvent evaporation stage.3 A
decrease in M (and therefore Rs) and the solvent evaporation period adversely
influences the disposition of the macromolecules at the interface, and their
subsequent degree of interstitial coagulation, as shown in Figure 2. The magnitude
of Rbl is approximately equal to rc xs when M is very low. The corresponding Rb2
value is approximately equal to that created by a sphere missing from a
square-packed array. As M increases, Rs increases and interstitial coalescence
increases. As M approaches 30,000 g gmol-', Rbl and Rb2 become smaller than
rc ins and '6, respectively. The disposition and degree of coalescence of the surface
macromolecules approach that of membranes made with a 15 minute solvent
evaporation stage. Therefore, Figure 2 shows that the effect of M on the PA
surface structure is greater than the effect of the decrease i n the solvent
evaporation period.
Data for the various molecular weights of PA3 in Figure 2 illustrate the
practical significance of the interstitial void model for RO/UF membrane analysis.
Note from Figure 2 that Rbl and Rb2 remain essentially constant, independent of
the PA molecular weight used to fabricate the membranes. However, Figure 2 also
shows that RS/Rbl and Rs/Rb2 significantly increase as the value of M increases.
Using the interstitial model, an increase in M will increase the surface uniformity
and skin structure integrity, thereby increasing the overall solute separation ability
of the membrane.
The preceding observations indicate that a PA membrane surface is a
predominantly close-packed partially coalesced monolayer of the precursor
macromolecule spheres. The performance of a PA membrane is dependent on the
size, disposition and degree of coagulation amongst the surface macromolecules.
These factors are influenced by the casting conditions.
Polyethersulfone membranes
The values of Rs for two polyethersulfone (PES) solutions in pure N-methylpyrrolidone (NMP) can be calculated from equation (2), and compared to surface
data4 for the resultant membranes. From Figure 2, Rbl f 201 encompasses
square- packed and semi-gelated close-packed voids. The values of Rb2 are close
to that which is produced by a sphere missing from a square-packed array.
Figure 2 reveals the possibility of a trimodal distribution of pores in a PES skin
layer. Figure 2 shows that PES surfaces deviate considerably from a close packed
formation, therefore, these materials act as UF and not RO membranes.
Cellulose acetate membranes
Using available data,5b78Rs for a batch 316-type cellulose acetate (CA) solution
is estimated to be about 3 5 . 2 8, and may be compared to the surface
morphological constants5c of a resultant membrane. From Figure 2, after the
membrane is treated in a hot water bath at 82OC, Rbl and Rb2 have approximately
the values of rc xs and r6, respectively. Since the value of h2 is 0,001, this CA
surface may be compared to a predominantly close-packed macromolecule
monolayer. Deviations from close packing occur when macromolecules are
missing from the array.
Polymeric Reverse Osmosis/Ultrafiltration Membranes
39
Relevance to membrane fabrication
Relationships can be established between casting conditions and resultant
membrane performance. The interstitial void model is a template that provides a
physical explanation for such relationships. The surface morphological constants
are compared to values of Rs. The interstitial model predicts that variations in the
casting conditions cause changes in the size, disposition and degree of coagulation
amongst surface macromolecules, ultimately influencing the final porous structure
of the membrane skin layer.
Some initial general conclusions concerning design aspects of RO/UF
membrane surface formation may be drawn from the results presented in Figure 2:
(a) Skin layer formation is strongly dependent on the polymer type.
(b) In general, RO membranes are formed because the surface macromolecules are
small, and become predominantly close-packed.
(c) Coalescence amongst close-packed macromolecules generally increases if
changes in the casting composition cause an increase in Rs.
(d) Larger pores may be formed by the surrounding of 4 or more surface
macromolecules, their origin and degree of coalescence are strongly
dependent on the casting conditions.
Membrane design
The flux and separation ability of a membrane can be determined from the casting
conditions by comparing R s values to the surface morphological constants.
However, the membrane must first be made and tested, before its performance
characteristics can be predicted. Relationships between R s and the surface
constants can be used for design purposes, revealing the effect of the casting
conditions on skin layer formation. These relationships are used to determine the
required casting conditions for a desired membrane performance, and the
performance can be predicted without first making and testing the membrane.
Equations (1 1) and (12) below illustrate that relationships can be made between
R s and the surface constants. The following relation is obtained for
PA-DMAc-LiN03 data: I
Rs = 5.MARbl
+ 11.134
(1 1)
where Rs is varied by changing the PA and/or LiN03 concentration in the casting
solution. The quantity ARbl is equal to (rc xs - Rbl). The correlation coefficient
for equation ( 1 1 ) is 0.9975. The relationship for PA-DMAc-CaC12 data2 is:
Rs = - I . I2ARb2 + 57.53
(12)
where 0.3 grams of CaC12 are added per gram of PA. Then Rs is varied by
changing the PA concentration in the solution. The quantity ARb2 is equal to
(rs xs - Rb2). The correlation coefficient for equation (12) is 0.97.
The number of pores per membrane area
A practical advantage of the interstitial void model is that the number of pores per
membrane area (n) can be counted. For example, n may be calculated for flow
through monolayers of close-packed macromolecule spheres from the relation:
fl
= 3-"2/Rs 2
(13)
Equations (6) to (10) show that Rs should be small in RO casting solutions,
so that the inherent geometric void spaces are also small regardless of the
40
Hal Wood and S. Sourirajan
subsequent degree of interstitial coagulation. Equation (13) shows that for flux
optimization, the number of pores per unit area is maximized when Rs is
minimized. Macromolecule dimensions are then of prime importance for
membrane design considerations.
Estimates of the parameter n can be used to approximate an effective pore
length from a modified Poiseuille equation. The present equations involving RO
transport may then be simplified. Note that the interstitial method of analysis can
be used for design purposes, regardless of the validity of the assumptions in the
model.
Conclusions
The porous structure of an asymmetric membrane is determined by the size,
disposition and degree of coalescence of surface macromolecules. These variables
are controlled by the film-casting solution composition and membrane-forming
procedure. An RO membrane surface is a monolayer of predominantly
close-packed partially coalesced macromolecules. The possibility of a bimodal
distribution of pores on a membrane surface is a reflection of the disposition of
the macromolecules at the interface. The correlation of Rs and surface
morphological values (similar to Figure 2), together with the corresponding
details of the membrane-forming conditions, offers a means of tailoring specific
skin morphology in polymeric RO/UF membranes.
Acknowledgements
Hal Wood wishes to thank the NSERC for partial support of this work. Special
thanks to T.D. Nguyen for his helpful comments and suggestions.
Nomenclature
Polymer concentration in the casting solution
Ratio
of the number of large to small pores per area of
h2
membrane surface
Mark-Houwink constant for polymer in pure solvent
K
Polymer molecular weight (g gmol-')
M
Polymer apparent molecular weight (g gmol-') in a solution
containing an additive
n
Number of pores per membrane area
Avogadro's number (6.023 x
molecules gmol-')
No
Mean pore radius of the ith distribution of pores in a
Rbi
membrane surface
Mean
radius of small pores in membrane surface
Rbl
Mean radius of large pores in membrane surface
Rb2
'c ins Inscribed interstitial void radius measured at the
equator between close-packed spheres
rc xs Radius of a circle of area equal to the cross-sectional
void area measured at the equator between close-packed
spheres
rs ins Inscribed interstitial void radius measured at the
8
Polymeric Reverse OsmosisLJltrafiltration Membranes
41
equator between square-packed spheres
Radius of a circle of area equal to the cross-sectional
void area measured at the equator between square-packed
spheres
Hydrodynamic radius occupied by a solvated polymer
molecule
Volume occupied by a crystalline polymer molecule
Hydrodynamic volume occupied by a solvated polymer
molecule
Expansion factor to account for the swelling of a
polymer molecule when in a suitable solvent
Polymer-solvent-additive solution intrinsic viscosity
Mark-Houwink exponent for polymer In pure solvent
Standard deviation of the small-pore mean radius
Standard deviation of the large-pore mean radius
References
1 Nguyen, T.D., Matsuura, T. and Sourirajan, S. 1987. Effect of nonsolvent additives on
2
3
4
5
6
7
8
the pore size and pore size distribution of aromatic polyamide RO membranes. Chem.
Eng. Commun., 54, 17-36.
Nguyen, T.D., Matsuura, T. and Sourirajan, S. 1987. Effect of the casting solution on the
pore size and pore size distribution of resulting aromatic polyamide membranes.
Chem. Eng. Commun., 97,351-369.
Nguyen, T.D., Chan, K., Matsuura, T. and Sourirajan, S. 1985. Viscoelastic and
statistical thermodynamic approach to the study of the structure of polymer film
casting solutions for making RO/UF membranes. Ind. Eng. Chem. Prod. Res. Dev.,
24(4), 655-665.
Lafreneire, L., Talbot, F.D.F., Matsuura, T. and Sourirajan, S. 1987. Effect of
polyvinylpyrrolidoneadditive on the performance of polyethersulfone ultrafiltration
membranes. Ind. Eng. Chem. Res., 26,2385-2389.
Sourirajan, S. and Matsuura, T. 1985. Reverse osmosis/ultrafiltrationprocess principles.
(a) Chapter 4; (b) p.462,465; (c) p.563. Available from Division of Chemistry,
National Research Council, Ottawa, Canada, K I A OR6; NRCC No, 24188.
Rudin, A. and Johnston, H.K. 1971. Predictions of viscosities of concentrated polymer
solutions. J. Paint Tech., 43(559), 3 9 4 7 .
.Wood, H. and Sourirajan, S. 1991. The effect of additives, solvent type, and polymer
concentration on macromolecule dimensions. J. Appl. Polymer Sci., 43( l), 21 3-217.
Johnston, H.K. and Sourirajan, S. 1974. Viscometric behaviour of concentrated cellulose
acetate solutions. J. Appl. Polymer Sci., 18, 2327-2338.
Received: 5 September 199 1 ; Accepred: 17 February 1992
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