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Principles of gel chromatography and possibilities for its development.

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Angewandte Makromolekulure Chemie 1 (1967) 150-173 ( N r . 12)
From the Organisch-ChemischesInstitut der Universitat Mainz
Principles of Gel Chromatography
and Possibilities for Its Development
By W. HEITZand W. KERN
(Eingegangen am 17. November 1967)
SUMMARY :
Gel chromatography can be considered as a network-limited partition. This
leads to the conclusion that it is impossible to find a generalizing relationship between the molecular weight and the elution volume using parameters depending
only on the solute.
The preparation of gels with different chemical structure is discussed and possible
methods for the alteration of pore size are described. Investigations of the influence
of the physical and chemical structure on separation and separation efficiency have
shown that the elution volume depends to some extent on the chemical nature, but
the separation efficiency is mainly a function of the physical structure.
ZUSAMMENFASSUNG :
Die Gelchromatographie kann als eine netzwerk-limitierte Verteilung aufgefa5t
werden. Dies fuhrt zu dem SchluB, daD keine normierende Eichbezeichnung
zwischen Molekulargewicht und Elutionsvolumen existiert, die ausschlieDlich von
der gelosten Substanz abhangige Parameter enthiilt .
Die Darstellung von Gelen mit unterschiedlicher chemischer Struktur wird beschrieben, und die Moglichkeiten, die PorengroBe zu variieren, werden diskutiert.
Die Untersuchung des Einflusses der physikalischen und chemischen Struktur auf
die Trennung und die Trennleistung zeigte, da5 das Elutionsvolumen durch die
chemische Natur des Gels beeinflu& wird ; die Trennleistung wird hingegen im
wesentlichen durch die physikalische Struktur bestimmt.
I. Introduction
Gel chromatography has been developed t o a useful laboratory method
for the separation of substances according t o their molecular size. Besides the
expression ,,gel chromatography" this procedure is often called gel permeation
chromatography and gel filtration. Usually the separations are performed as
column chromatography but sometimes also as thin layer chromatography.
The gels used as stationary phases have porous structures. Such structures
may be produced with inorganic and organic polymers. The use of porous
150
Principles of Gel Chromatography
glass1 and silica gels2-4 had been reported, but the most widely used materials
are crosslinked organic polymers which possess, a t least in the swollen state,
such a structure.
11. Experimental arrangement
The practical accomplishment is dependent on the demands of the separation.
I n the most simple case, gel chromatography is performed so that a chromatographic column is filled with the swollen gel, the sample solution is poured
on to the gel bed, the solvent is collected fractionally and the fractions are
individually analyzed. To achieve the optimal separation effect the experimental arrangement should have the following parts (Fig. 1) :
Fig. 1. Schematic representation of
an apparatus for gel chromatography.
1 Solvent reservoir, 2 de-gasser, 3
pump, 4 injection assembly, 5 column,
6 detector, 7 siphon, 8 light barrier.
&I
a
The solvent reservoir ( l ) ,the de-gamer (2) which might be a simple condenser
which is heated with a thermostated liquid. Next comes the pump (3) and the
sample injection part (4). One or several columns ( 5 ) may be used. The detector
system (6) can make use of the spectroscopic properties of the substances in the
UV or visible range. These devices are cheap and insensitive to disturbance,
but they are only applicable if the differences in absorption between solvent
and solute are high enough. Flame ionization detectors have a t present a high
noise level when they are used in liquid chromatography5, but their use should
have a promising future. The differential measurement of the heat effect of
the passing sample is very sensitive but the resulting curve is differential6.
The best detection system a t the present time is a differential refractometer.
From the detector the solvent flows to a siphon (7), which, monitored by a
light barrier (8), when emptied causes a mark to be entered on the recorder
chart.
15 1
W. HEITZand W. KERN
111. Theory
On the elution of a mixture of substances from a column packed with
swollen gel particles, those substances appear first, the molecules of which
are too big to penetrate into the pores of the gel. Their elution volume V E is
equal to the volume of the solvent between the gel grains, the outside volume
VA. Small molecules which enter the pores as easily as the solvent can occupy
an additional volume VI. Their elution volume V E is equal t o VA
VI if we
neglect other effects for the moment.
FLODIN
and GRANATH7 define an apparent partition coefficient KD for the
partition of the substances between the solvent inside and outside the gel
particles. KD is a measure of the availability of the pores and so is no partition
coefficient in its real sense. The values of KD range within the limits of 0 and 1.
A substance with KD = 0 is totally excluded from the gel. Substances with
KD - values between 0 and 1 are partly excluded.
Therefore V E is given by
+
VE = V A
+ K ~ V. I
&-values larger than 1 are often reported in the literatures-10. This effect
is commonly explained in terms of adsorption phenomena. But even in this
case the peaks are quite symmetric. As the adsorption isotherm is not linear
a t higher concentrations (leading to unsymmetrical peaks) these results should
be explained in terms of partition as we will discuss later. As DETERMANN~~
has pointed out, the inner surface of a gel is extremely high, this will lead to
linear adsorption isotherms over a large concentration range. So it seems that
M
'\
\
300.103
152
-
\\\
Principles of Gel Chromatography
the problem is merely a matter of definition. I n some cases, however, KDvalues are observed which are smaller than expected from consideration of
molecular size**93 121 13. This effect has been called ,,negative adsorption",
but this concept has no physical significance.
The quantities t o be correlated in gel chromatography are the molecular
weight and the elution volume. Plotting the logarithm of the molecular weight
versus the elution volume, v E, an approximately linear relationship results.
This dependence was repeatedly confirmed using proteins ; the molecular
weight of unknown proteins can thus be found.
Fig. 2 shows a plot of literature values collected by DETERMANN14.The results
of separations of proteins on different types of Sephadex (G 25, G 50, G 100)
are compared. The individual types of Sephadex differ in the degree of crossinking as well as in their average pore diameter and their pore size distribution.
I n order to be independent of the column used VE/VA is plotted instead of VE.
The usual characteristic quantity for the separation behaviour of a gel is its
excluded molecular weight (Me). We will define the excluded molecular weight
as that molecular weight which is obtained when extrapolating the log M
versus v i - curve t o V E = VA. The simple relationship between log M and V E
allows a rapid determination of the molecular weight distribution of a
polymer. The time necessary for one determination ranges between 4 and 24
hrs. Using a commercially available differential refractometer, the recorder
deflection is proportional to the just eluted concentration, which means the
recorder diagram is easily converted into the distribution function. Fig. 3
shows the integral distribution curve for a poly(styrene) obtained by different
fractionation procedures. The agreement is satisfactory.
Fig. 3. Integral distribution
curve of a poly(styrene)
determined by different fractionation methods according
60 MEYERH0FFl5.
o column elution at con-
stant temperature, BAKERWILLIAMS;
curves A and B
are from gel chromatography
using different types of gels.
l;:lT96
0.4
Q /
500
1000
1500
~ . 1 0 - 2500
~
Fig. 4 shows corresponding curves for a poly(ethylene) investigated by
TAKAGI~~.
The differential distribution shows a similar shape but the quantitative agreement is not satisfying.
The reason for these results could be : the method is relatively new and the
basic investigations which have been performed up to now are too scarce. So
153
W. HEITZand W. KERN
-
3
Fig. 4.
Distribution curves of a poly(ethy1ene)determined by gel chromatography
- x- x - x - and by column elution - . - - according t o T A K A O I ~ ~ .
-
we attempted t o clarify the process of gel chromatography with the aid of
model compounds. The basic assumption in the equation of FLODIN
and
GRANATHis that the elution volume V E is exclusively determined by the
availability of the gel to the different compounds. This caused intensive
research t o find a generalizing function which is valid for all polymers for a
given pore sue distribution. Since the availability of the gel depends on the
molecular size it seems likely to find such a normalizing function in the equation
R = f ( v x ) (R = radius of gyration). But the investigations of MEYERH0FFl7
show that this function has no normalizing character. Fig. 5 shows a plot of
Elution data of different polymers on
the same poly(styrene)gel according to MEYERR O F F ~ ~R
, = radius of gyration: 1. cellulose
trinitrate 2. poly(methy1methacrylate) 3. poly(styrene)
Fig. 5 .
v&mU
90
154
103
110
la
130
Principles of Gel Chromatography
radius of gyration versus elution volume. Poly(methy1 methacrylate), poly(styrene) and cellulose trinitrate were separated on the same poly(styrene) gel.
Each of the 3 polymers has its own curve.
All these considerations presume that the interactions between the gel and
the substances to be separated are always the same. The framework of the
gel is considered as a completely inert support material which contains the
solvent in its pores. Only then does the pore size distribution exclusively
determine the value of the elution volume.
Actually the interactions between the gel phase and a substance entering it
must not be the same as those with the pure solvent. This leads to a substancespecific partition of the compounds between the interstitial volume VA and
that part of the gel volume available to the molecules, let us call it
OL'VI.
Decisive for the transport of the substance in the column is the partition
number G
which is equal to the partition coefficient times the ratio of the volumes
vA/a VIThe polymer network limits the gel phase for the individual solvated substances according to molecular size.
Thus gel chromatography is considered as a network-limited partition and
it can be described with the well known equations for partition processes.
The separation efficiency of a column is expressed as the number of the
equivalent partition steps n (the plate count). The maximum of the elution
curve can be evaluated16 as
Introducing the value of G (equ. (2)) we get
VE =
n
(4)
and for large values of n we find an equation similar to that of FLODIN
and
GRANATH(equ. (1))
For the mean deviation 6,which is the distance between the inflection point
and the perpendicular in the maximum, we have
155
W. HEITZand W. KERN
We may eliminate VA
by equation (3) and so obtain
1
(J=-
]I=
vE.
(7)
The theoretical plate count is
The theoretical plate count can easily be obtained from the elution volume and
the base width of the peak as b = 4 u and so
(y).16.
2
n=
(9)
For values of n larger than 500 the elution volume is within the limits of error
independent of theoretical plate count. A change in theoretical plate count, as
could be caused by higher flow rates, has nearly no influence on VE . The peaks are,
however, drastically broadened. If the theoretical plate count drops from 10000
to 1000 VE is altered by 0.1 yo but u grows by 300 yo.
The pore size and its distribution measures the random coil of the molecule,
so that the molecular weight dependence of the elution volume is mainly
governed by the factor a. The interaction with the gel and the thus caused
partition prevents a generalized function between V E and the radius of gyration R.
The influence of the partition coefficient on elution volume is mainly of
a substance-specific nature. The partition coefficient may also give rise to a
small molecular weight dependence as expressed by the BRONSTED’
equationlg
log K = E - P ,
RT
where P is the degree of polymerization and E is the difference in energy of one
monomer unit of the solvated substances in both phases.
Became of the exponential relationship in this equation an undisturbed
separation according to the principles of gel chromatography can only be
expected if E is sufficiently small.
Our knowledge of the structure of the gels is too scarce for quantitative
description. To a first approximation a gel can be considered as a polymer
solution. But a t least in the case of macroporous gels we have a concentration
gradient towards the center of the pores. The dense polymer wall is covered
156
Principles of Gel Chromatography
with linear or slightly crosslinked polymer molecules of different sizes (Fig. 6).
The BRONSTEDequation will, a t present, merely give a qualitative description of the effect. The given model (Fig. 6) allows the suggestion that VA
may, in some cases, be dependent on the solvated polymer (differences of
some tenths per cent).
Fig. 6. Model of a macroporous gel with decreasing concentration of the “polymer solution” towards the center of the pore.
IV. The stationary phase
a ) General modes of prepration
The given equations lead t o the supposition that it is impossible to solve
all separation problems having only one gel. This was one of the reasons why
the behaviour of different gel systems during gel chromatographic separations
was studied.
The stationary phase in gel chromatography is a material with a porous
structure. A swollen, statistically crosslinked polymer has such a porous
structure. I n order t o obtain good flow characteristics for the column, the
polymer particles should have a spherical shape. Thus the most suitable mode
of preparation is that of suspension polymerization.
To prepare a crosslinked polymer one can either start with a linear polymer
and crosslink this in a subsequent reaction - an example is the preparation of
Sephadex - or one may copolymerize a monovinyl compound with a divinyl
compound. I n the latter case the amount of divinyl compound determines
the crosslinking density and consequently its excluded molecular weight. I n
the unswollen state these gels have, of course, no porosity. I n the case of
styrene/DVB gels, with 1 yo of crosslinking compound, an excluded molecular
weight of about 3000 is obtainable. The amount of divinyl compound also
determines the swelling character of the gel. As crosslinking density decreases
the swelling is greater and the mechanical stability in the swollen state decreases.
Columns which are packed with such highly swelling gels are impenetrable to
the solvent after short use. With S/DVB-gels the limit of practical use is
reached if the amount of divinyl-compound is decreased to about 0.1 yo.This
is equivalent to an excluded molecular weight of about 10 0o0.
157
W. HEITZand W. KERN
If higher excluded molecular weights are desired the gel should be prepared
by a heterogeneously crosslinking polymerization. This process involves a phase
separation during polymerizatjion20.
The polymerization is performed in the presence of an inert compound.
This compound must be soluble in the monomer mixture and must be removable
after polymerization. To the forming polymer this added compound may be
a solvent or nonsolvent. Even another linear polymer may be added. The
principles of this procedure may be transformed to polycondensation reactions
as shown by LANOHAMMER,
who precipitated silica gel in the presence of
poly(vinylalcohol)4.
Let us look a t a single polymerizing droplet in a suspension polymerization :
it consists of the monovinyl compound, the divinyl compound and the inert
solvent. Because of the large amount of crosslinking agent and the dilution,
we have an increased number of intramolecular crosslinking steps beside the
normal intermolecular crosslinking steps. As a result, highly crosslinked nuclei
originate which are only slightly swellable. This leads to a phase separation.
We now have highly crosslinked solid particles in the polymerizing droplet
which grow together in the course of the polymerization. Depending on the
solvent power of the inert compound and the copolymerization parameter it
might well be that a t first, a very loose network is formed, to which dense
centers became attached. This means that phase separation may occur before
or after the gel point of the system is reached. The cavities between the parti-
excluded
diluents, parts / 100 parts of gel
molecular weight
M,
60 toluene
30 toluene, 30 diethylbenzene
60 diethylbenzene
45 toluene, 15 n-dodecane
30 toluene, 30 n-dodecane
15 toluene, 45 n-dodecane
10 toluene, 50 n-dodecane
40 diethylbenzene, 20 isoamyl alcohol
20 diethylbenzene, 40 isoamyl alcohol
13.3 diethylbenzene, 46.7 isoamyl alcohol
60 isoamyl alcohol
*
7 x 103
x 104
1.2 x 104
1 x 105
3 x 105
2 x 106
2 x 103
3.6 x 103
8 x 106
1010
extremely high
“styrene” is a mixture of styrene and ethylvinylbenzene.
158
1.5
Principles
of
Gel Chromatography
cles or the dense centers are filled with inert solvent which becomes poor in
monomer. A polymer results which is porous even in the unswollen state. By
choosing a suitable inert compound it is possible to produce any pore size.
Tab. 1 shows a collection of excluded molecular weights as obtained by
MOO RE^^. Styrene was copolymerized with 30 yo Divinylbenzene in the
presence of different solvents or non-solvents. Solvents like toluene or diethylbenzene raise the excluded molecular weight to about 10000 to 15000. Replacement of part of the toluene with n-dodecane gives excluded molecular
weights of more than 1 million. The last example of this series - addition of
10 parts of toluene and 50 parts of dodecane - shows a phenomenon which may
often be recognized when preparing such gels. With decreasing quality of the
solvent the excluded molecular weight first increases but then drops drastically. Apparently, the microscopic phase separation has changed to a macroscopic one. Same observations were made with poly(methy1 methacry1ate)gels
and poly(viny1acetate) gels. By use of higher alcohols as nonsolvents excluded
molecular weights up t o 1010 and higher are obtained. Such high excluded molecular weights are not limited to poly(styrene gels), as we could also produce
gels with this pore size with methyl methacrylate and vinyl acetate. Gels with
excluded molecular weights higher than 107 have not been investigated in detail. The separation of viruses22 and the size determination of pigments as well
as in dispersions are most interesting problems and work in this area is promising.
b) The gels
The most important applications of gel chromatography are : the separation
and purification of naturally occurring compounds, especially proteins which
are performed in aqueous systems and the fractionation of polymers which is
accomplished, in most cases, in organic solvents. We may divide the gels into
hydrophilic and lipophilic gels.
Besides some polystyrene samples we used the oligomers given in Tab. 2 as
solutes for the separations.
1. H y d r o p h i l i c g e l s
Among the gels swelling in water, by far the most known are the crosslinked
dextran gels commercially available under the trade mark Sephadex. Water
soluble dextrans are crosslinked in water with epichlorohydrin by treatment
with alkali. The concentration and the molecular weight of the dextran, and
the amount of epichlorohydrin are the factors which determine the pore size of
the gel. The highest excluded molecular weights available are 500 000 for proteins.
159
W. HEITZand W. KERN
A second hydrophilic gel which is commercially available is prepared by polymerization of acrylamide with methylenebisacrylamide. I n this case the highest
excluded molecular weights are approximately 400 000, however this gel has
the disadvantage that it swells to 70 ml/g dry substance. Working with such a
gel creates some technical problems. By copolymerization of vinyl acetate with
divinyl compounds which are not easily hydrolyzed and subsequent hydrolysis
of the vinyl acetate part, we could produce another hydrophilic gel. If we use
butandiol divinylether, a gel which is extremely resident t o hydrolysis results.
2. O r g a n o p h i l i c g e l s
The preparation of organophilic gels was the real starting point of our studies
on gel chromatography. At that time nearly nothing was known about the use
of organophilic gels, so it was logical to use the existing experience with dextran
gels and to convert the commercially available Sephadex by chemical reaction
to an organophilic gel. By reaction of Sephadex with isocyanates we obtained
urethane modified types of Sephadex. These gels swell in many organic solvents.
Fig. 7 shows the attempt to separate a mixture of oligourethanes with isocyanate modified Sephadex.
Fig. 7. Separation of a
mixture of oligourethanes
(cf. Tab. 2) on Sephadex
G-25 modified with isocyanate. Column 8x1600
mm, solvent : ethylene
chlorohydrine, 1 dodecaurethane, 2 decaurethane,
3 hexaurethane, 4 tetraurethane.
The oligourethanes were prepared from hexamethylene diisocyanate and diethylene glycol. The elution occurs - according to the principles of gel chromatography - in the sequence of decreasing molecular weight. Methyl methacrylate
crosslinked with ethylene glycol dimethacrylate is also suitable for gel chromatographic separations. The use of methyl methacrylate gels was first described
by DETERMANN24. Fig. 8 shows a separation of polystyrene and some oligophenylenes using a methyl methacrylate gel crosslinked with 0.1 yo ethylene glycol
dimethacrylate. The eluting solvent was chloroform.
By copolymerization of vinyl acetate with a suitable crosslinking agent we
obtained gels which can be used for separations in organic solvents. As cross160
Principles of Gel Chromatography
Fig. 8. Separation on a
copolymer of methyl methacrylate with 0.1 wt. - yo
glycol
dimethecrylate.
Solvent : CHC13, column
4.1 X40.5 em; 1poly(styrene), 2 p-deciphenyl
(VII), 3 p-quinquiphenyl
(IV), 4 m-bitolyl (I) (see
Table 2).
linking agent we usually use divinyl ethers or divinyl esters. Fig. 9 shows the
separation of poly(styrene) and some oligophenylenes with a vinyl acetate gel
crosslinked with 1 yo butandiol divinyl ether.
1
Fig. 9. Separation on a
poly(viny1 acetate) gel a)
a t 5OOC. b) a t 23°C.
1. Poly(styrene), 2. p-deciphenyl (VII), 3. p-sexiphenyl (V), 4. p-quaterphenyl (111),5. m-bitolyl
(I);column 2. 1 x 1lOcm.
Solvent: THF.
I
I
lo0
m
a0 vdurne (crn3)
161
W. HEITZand W. KERN
THF was used as solvent. The separations were performed a t 23 and 50 "C.
The differences between the two curves are small but well beyond the limits of
error.
The use of crosslinked poly(styrene) gels became common mainly through
Fig. 10 shows it separation of some oligophenythe investigations of
lenes by use of a poly(styrene) gel prepared by copolymerization of styrene
with 2 % divinylbenzene.
Fig. 10. Separation of some methyl substituted oligophenylenes on a poly(styrene)
gel (2 yo divinylbenzene). Solvent: THF, column 4 x 150 cm.
1 sedtiphenyl (IX), 2 deciphenyl (VII), 3 octiphenyl (VI), 4 sexiphenyl
(V), 5 quinquiphenyl (IV),6 quaterphenyl (111),7 terphenyl (11),8 bitolyl
(I),9 benzene.
Fig. 11. Separation of oligoethylene glycols
HO--[CHZCHZO]~-H
using a poly(styrene) gel. Solvent :THF, columnl. 1 X 200 cm.
162
Principles of Gel Chromatography
The solvent was THF. The methyl substituted oligophenylenes which were
separated have 1 6 , 1 0 , 8 , 6 , 5 , 4 , 3 and 2 p-connected benzene rings. Benzene
was also separated.
i
a
2
3
Y
Y
3
Fig. 12. Separation of paraffins ClonHzon+z using a poly(styrene) gel. Solvent: toluene (9O"C), column 2.4 x 100
em.
G
I
qo
'
3
'20
'10
"
L
I I
1%
2CO
250
300
volume ( c m 3 )
4m
The separation of oligoethylene glycols using a poly(styrene) gel is another
example (Fig. 11).Only the polymerization degrees 36,27, 18 and 9 were present in this mixture. THF was the solvent.
The separation of paraffins is demonstrated in Fig. 12. 1,lO-Dibromodecane
was condensed with an excess of sodium. The reaction mixture was hydrolysed
and that part which was soluble a t 70 "C in toluene was separated. Here the
peaks correspond t o the paraffins with 10,20,30,40,50,60, 70 carbon atoms,
CsoHl62 is barely recognizable.
V. The partition eflect
We have a t our disposal a series of chemically different gels and we are able
to investigate the influences on separation and separation efficiency which are
specific to these gels. I n order to show that gel chromatography can be consi163
W. HEITZ
and W. KERN
Tab. 2.
Molecularly homogenous oligomers used for the separations.
M = molecular weight.
a) oligophenylenes ( / = methyl)
formula
I
M
I
182
I1
258
I11
362
IV
438
V
542
VI
723
VII
903
VIII
1082
IX
1444
164
Prircciples of Gel Chromatography
*
d = phenylisocyanate, 50 = diethylene glycol, h
(c. f. KERNet al.23). ( 5 0 h ) ~ =
&~
= hexamethylene
diisocyanate
H[-OCHZCHZ~CHZCHZ~CONH(CH~)~NHCO]~OCH~CH~~CHZCHZOH
dered as a network-limited partition, we have separated several series of oligomeres (Tab. 2) on different gels but under the same experimental conditions.
Oligophenylenes with up to 16 p-connected benzene rings, in addition diololigourethanes prepared from hexamethylene diisocyanate and diethylene glycol
were used. Another series of oligomers differ from the just described oligourethanes only in endgroups. The hydroxyl end group of the diololigourethanes
were reacted with phenylisocyanate. For these series of oligomeres the log M
versus V E relationship had been determined in the same solvent, a t the same
temperature but using different gels. Fig. 13-16 show curves for the separation
on a poly(styrene) gel, an isocyanate modified Sephadex, a poly(methy1 methacrylate) gel and a poly(viny1 acetate) gel.
Comparing substances with the same molecular weight, the sequence of elution on poly(styrene) gel is: First the diololigourethanes, then the urethanes
with phenylurethane endgroups and finally the oligophenylenes. With modified
Sephadex oligophenylenes and oligourethanes with phenylurethane endgroups
are eluted simultaneously, oligourethanes with hydroxyl endgroups were eluted
last. With poly(methy1 methacrylate) gel and poly(viny1 acetate) gel tirst the
oligophenylenes and then the oligourethanes are eluted as opposed to poly(styrene) gel, the sequence is just reversed. As all separations were performed under
the same conditions (same temperature and same solvent) the molecular parameters of each substance are always the same. So the differences found are t o
be related to the gels. Differences in mean pore diameter can only cause a displacement of the curves in the same sense. The relative displacement of the
curves with respect t o each other is caused by differences in interaction of the
substances with the gel.
165
800
xxx)
1x0 vE(ml)
'
1403
.
Fig. 13. poly(styrene) gel;
10'
50
60
70
,
80
,\
v,(ml)
1M
a
see Table 2 .
Fig. 13-16. Elution data in THF at 25°C; 0 (curve 1) methyl substituted p-oligophenylenesa; h (curve 2) oligourethanes d(50h),50da;
(curve 3) dioligourethanes (Soh)&*
I
Fig. 14. Sephadex modified with phenylisocyanate;
Principles of Gel Chromatography
VI. The separation efficiency
One of the unsolved problems in gel chromatography is the separation efficiency. This range of ideas creates questions like : Are we really working under
optimum conditions in gel chromatography? Is it possible to perform the separations in minutes or even faster? Are theoretical plate counts of 10 000, 20 000
or 100000/m column length to be realized?
Attempts to describe the procedure of gel chromatographic elution theoretically were made by v I N K 2 5 and by L A U R E N T
VINK
~ ~ . calculated the shape of
the peak numerically with the aid of a computer. LAURENT
simulated the process of gel chromatography with a series of electrical analog circuits. Both procedures lead to similar results. Fig. 17 shows the elution peak with increasing
flow rate. With higher solvent flow rates the curve became more and more unsymmetrical and the maximum is displaced to lower values.
b
Fig. 17. Theoretical elution curves of substances with the same partition coefficient
but different equilibrium factors E (according
to LAURENT~~).
t
-
C
3
a) E = 1, b) E
=
0,52,
C) E =
0.14.
tvnj
Such a behaviour is not to be realized under normal experimental conditions.
But it should be emphasized that these effects can be verified under extreme
conditions (very high flow rates).
Both considerations have as a common basis that one starts with a fixed
number of partition steps. The key problem is to find a quantitative description
of the theoretical plate count. Previously we considered gel Chromatography as
a special kind of partition chromatography. So an obvious approach is to check
theories which were developed for other partition processes, especially for gas
chromatography. A statement about the separation efficiency in chromatography was made by VAN DEEMTERB7 and by GIDDINGS~~.
As the separation
167
W. HEITZand W. KERN
efficiency is strongly influenced by the particle size of the stationary phase,
reduced quantities are introduced. We define
where, H is the height equivalent t o a theoretical plate, d, is the diameter of
the gel particles in the swollen state, v is the linear elution velocity, D is t'he
diffusion coefficient of the solvated substances, h reduced plate height, v reduced velocity.
The dependence which is t o be expected according to VAN DEEMTER
may be
formulated as follows
h = a +b/v + c v .
(11)
a - describes the influence of the regularity of the packing. With good packings it
is in the vicinity of 2.
b -reflects the peak broadening, caused by diffusion; of course this term will
vanish with increasing velocities.
c - originates in non-equilibrium conditions; it probably consists of 2 parts:
1. The lack of equilibrium in the exchange process, 2 . The none-equilibrium in
the mobile phase itself.
If 2. holds the c-term will not vanish even if we have no exchange process, e. g.
if we elute a substance on a column filled with glass beads or on the elution of
substances which are totally excluded from the gel.
According to the classical VAN DEEMTER
equation the separation efficiency
may be approximated over a fairly large range of velocities by a linear relationship. At a reduced velocity of 100 we should expect a reduced plate height of
10. According to GIDDINGSa flat, bent curve is to be expected. Thus an increase
of the flow rate should not cause an appreciable reduction of the separation
efficiency. This fascinating idea caused our work on separation efficiency31.
Both theories predict a minimum, which means an optimum flow rate exists
which is dependent on the substances being separated. The normalizing quantity is the diffusion coefficient.
Fig. 19 shows the results for the system poly(viny1 acetate) gel (crosslinked
with 8 % butanediol divinylether)/THF/methyl substituted oligophenylenes.
A single curve results which was independent of particle size and the substances. At a reduced velocity of 100 we find a reduced plate height of 11 which
is in good agreement with the expected value. At slow flow rate the reduced
plate height decreases to 2, i. e. the height of one theoretical plate is about twice
the diameter of the gel particles.
I n gel chromatography the substances are eluted in the sequence of decreasing molecular weight. As the diffusion coefficient increases with decreasing
168
Principles of Gel Chromatography
12
-
10
-
h
8-
Fig. 18. Reduced separation efficiency according
VAN DEEMTER
and
GIDDINGS (from GID-
to
7
DINGSz9).
Fig. 19. Reduced separation efficiency for
the system poly(viny1
acetate) gel (crosslinked with 8 w t . -% butanedioldivinylether)/
THF /methyl substituted oligophenylenes.
0
-
dp
= 0*0191
d, = 0.0382 em
2,
a,
= 0.0191
= 0.0382
20
'
40
benzene,
60
v
Bo
1W
120
160
160
190
203
m-bitolyl(I), A quaterphenyl (111),
A
cm x
quinquiphenyl (IV),
octiphenyl (VI)
em j0
molecular weight, the reduced plate height w i l l become smaller and the separation efficiency will be better. This is the reason for the well-known phenomenon
that in gel chromatography the peaks of the substances which are eluted last
are too narrow compared with the peaks which appear first if a partition process with constant plate count is assumed.
The separation efficiency shown in Fig. 19 is, unfortunately, not found with
all systems. Fig. 20 shows the reduced separation efficiency for the system poly(styrene)gel/THF/methyl substituted oligophenylenes. Also in this case the
influence of the particle diameter could be eliminated as can be seen in the
curve €or m-bitolyl. A skrong dependence on the substances were obtained;
169
W. HEITZand W. KERN
each substance has its own curve. This dependence on the substance may have
two causes : either it is caused by the chemical nature of the gel, i. e. differences
in interactions, or by the crosslinking density, i. e. the hindrance of diffusion
in the gel.
I
20
0
40
W
80
ino
120
Fig. 20. Reduced separation efficiency for the system poly(styrene)gel (crosslinked
with 10 wt. -yo divinylbenzene)/THF/methylsubstituted oligophenylenes.
benzene, V m-bitolyl (I), A quaterphenyl (111)
Vp
= 0.0169 cm, v Jp = 0.0153 cm, V ip= 0.0413 om.
ap
Investigations with poly(styrene) gels of different crosslinking density showed
that the dependence of the separation efficiency became smaller with decreasing crosslinking density. With 2 yo divinylbenzene the reduced plot shows
practically no dependence on the substance. The curve corresponds exactly to
that for vinyl acetate gel in Fig. 19. The investigations of vinyl acetate gels of
different crosslinking density show the same behaviour as poly(styrene) gels.
This shows that there is no influence on the separation efficiency of the chemical nature of the gel if the crosslinking density is low. It is probable that the
curve found for low crosslinking densities represents the highest obtainable
separation efficiency.
Fig. 21 shows the separation efficiency in the range of the minimum. Thus
an optimal flow rate exists in gel chromatography, which is dependent on the
substance ; the diffusion coefficient is the normalizing factor. With benzene we
obtain a t the minimum H/dp-values between 4 und 5 , i. e., the theoretical plate
height is equivalent t o 4 or 5 times the particle diameter. The optimal ratelm
170
Principles of Gel Chromatography
I
I
2
6
6
10
8
Fig. 21. Reduced separation efficiency at slow, reduced flow rates for the system
poly(styrene) gel (10 wt.-% divinylbenzene)/THF/methyl substituted
oligophenylenes. d, = 0.00238 om, benzene, m-bitolyl (I),A quaterphenyl (111).
column length and the theoretical plate count t h a t we obtained or that are t o
be expected for benzene are collected in Tab. 3.
Tab. 3. Optimal experimental conditions for gel chromatographic elution of benzene on a poly(styrene) gel crosslinked with 10% divinyl benzene. Solvent: THF.
t,,t-Time of elution/m column length, n,,t-theoretical plate count/m
column length.
d, (mm)
0.17
t o p t (h)
Pa)
calcb
noptfound
calcc
1250
1580
1560
a
calculated for vd,/D
b
H/d, = 5
0.09
12
2200
16OOd
2800
=
2
0.45
6
4400
4800
5500
0.024
3
8 300
10000
10400
C
d
0.021
3
9500
10500
11900
0.01
(1.38)
20000
25000
0.005
(0.6a)
40000
50000
H/dp = 4
Different technique of column packing.
A reduction in particle size reduces the optimal time of analysis and raises
the theoretical plate count. A gel of a particle size of one hundredth of a mm
will have an optimum value of 1.3 hrs. Polymers have a diffusion coefficient
which is 1-2 orders of magnitude smaller than benzene, i. e., the optimal time
of elution is 1-2 orders of magnitude higher and thus not easy to realize. Columns which are well packed show a reduced plate height of 4 t o 5 for benzene
a t the minimum. With these values we calculated the theoretical plate counts/m
column length. These data correspond well t o the values experimentally
found over the whole range of particle diameters. The highest plate count/m
column length we have obtained until now is 10500.
171
W. HEITZand W. KERN
These results give reasons for the suggestion that it should be possible to
come t o column systems which generate plate counts of some hundreds of thousands; however, it is highly improbable that it will be possible to separate two
neighbouring polymer homologs of high molecular weight. To a first approximation gel chromatography measures the size of the molecular coil. So the increase of the separation efficiency should reach a limit which is determined by
the dimensions of the statistical coil and not by experimental refinement.
Thanks are due to Drs. Coupek and Ullner for their help in these investigations.
Support o f this research by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.
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13
14
15
16
17
18
19
20
21
22
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