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Determination of Morphological Properties of Swellable Solids by Size Exclusion Chromatography.

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1521 D. J. Cram, J. M. Cram, Science 183, 803 (1974);Acc Chem. Res. 11, 8
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[54] C. D. Y. Sogah. D.J Cram. J. Am. Chem. SOC.98, 3038 (1976).
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100,4569 (1978).
1561 J:M. Lehn. J . Simon, A Muradpour, Helv. Chim. Acla 61. 2407 (1978).
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J. A. Lott. W. Rieman I I I , J. Org. Chem. 31, 561 (1966).
[61]C. Kratchanoo, M. Popova, J. Chromatogr. 37, 297 (1968);C. Kratchanoa,
M . Popooa, T. Obrefenou, N . Ivanov, ibid. 43, 66 (1969);M. Pupova, C Krarchanov, ibid. 72, 192 (1972).
1621 G. Wurff, W. Vesper, R. Grobe-Einder. A. Sarhan. Makromol. Chem 178,
2799 (1977);G. Wulff: R. Grobe-Einsler, W. Vesper, A. Sarhan, ibid. 178,
2817 (1977).
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Prgs, H. Erlenmeyer, ibid. 49, 1621 (1966).
(641 C.H. LochrnirNer. R. W. Sourer, J. Chromatogr 113, 283 (1975).
(651 S Weinstein, F Ferbush, E. GI-Ao, J . Chromatogr. 126. 97 (1976).
1661 V. Schurig. 8. Koppenhofer, W. Burklr. Angew Chem. 90, 993 (1978);Angew. Chem. In1 Ed. Engl 17. 937 (1978).
(671 H . Franck, C J. Nicholson, E. Bayer, J. Chromatogr. Sci. 15, 174 (1977);
Angew. Chem. YO. 396 (1978);Angew. Chem. Int. Ed. Engl. 17. 363 (1978):
J. Chromatogr 146. 197 (1978).
I681 Note added in proof(De7 18,1979):Recent publications onchromatographic
resolution of racemates- e.g. R. Audebert, J. Liquid Chrornatogr. 2, 1063
(1979)(review); V. A . Dauankou, Yu. A . Zolatareu, ibid. 2, 1191 (1979)(further examples of ligand exchange chromatography); W. H. Pirkle. D. W.
House, J . Org. Chem. 44, 1957 (1979)(separation of sulfoxides and 3.5-dinitrobenzoates uia high-pressure liquid chromatography on silica-bound
M Mintas, A. Mannschreck, J. Chem.
SOC.Chem. Commun. 1979, 602 (separation of trans-1.2-diphenylcyclopropane on cellulose triacetate). B. Feringa. W. Wynberg, Rec. Trav. Chlm.
Pays-Bas 97. 249 (1978)(separation of arenes on silica gel impregnated with
( + )-TAPA).
Determination of Morphological Properties of Swellable Solids by
Size Exclusion Chromatographyr**]
By Istvan Halasz and Peter Vogtel"]
Many technically interesting porous solids, e. g. ion exchangers or adsorbents for catalysis, are
swellable polymers, i. e. the pore structure depends on the solvent medium. A method based on
exclusion chromatography, permits determination of the pore size and pore size distribution in
the swollen state.-Size exclusion chromatography, also referred to as gel permeation, gel filtration, or molecular sieve chromatography, is a widely employed method for the separation of
dissolved substances-mostly polymer mixtures-according to their molecular size. Porous solids are used as stationary phase. Conversely, pore sizes and other structural data can be determined by exclusion chromatography. This application requires a series of standards (polymer
samples) of known molecular weight. As a simple and rapid method, it has already proven valuable for such determinations in the case of rigid solids; in the case of swellable solids, this constitutes the sole method by which the pore structure can be characterized: classical methods require dry samples.
1. Introduction
Rigid solids (e.g. silica gels, aluminas) are distinguished by
the fact that their pore structure does not depend upon the
surrounding medium (gas, liquid). The pore structure of
non-rigid solids (e.g. polystyrene-divinylbenzene copolymers, polyacrylamides, dextrans), on the other hand, is a
function of the swelling medium employed.
Organic gels can be obtained by homogeneous or heterogeneous p~lymerization['-~'.
In the former case a pore structure is formed only when the three-dimensional cross-linked
chains in the dry non-porous material become solvated, i. e.
an expanded mesh structure is formed only in the swollen
state. The mean mesh size can be controlled by the crosslinking component. The porosity of the particles, i. e. the ratio of pore volume to particle volume, increases with de-
Prof. Dr. 1. Halasz, Dr. P. Vogtel
Angewandte Physikalische Chemie der Universitat
D-6600Saarbriicken (Germanv)
Part of the Ph. D.Thesis by P. Vogfel, Universitat Saarbrucken 1977.
0 Verlag Chemie, GmbH, 6940 Wernheim, 1980
creasing amount of cross-linking component; at the same time,
however, the mechanical stability decreases. In all cases,
homogeneously cross-linked copolymers are microporous on
swelling (pore diameters 4 <20 A).
In the case of heterogeneous polymerization an inert substance is added to the mixture of mono- and difunctional
components. During the production process a phase separation takes place leading to copolymers which also contain
pores in the unswollen state (permanent porosity). These
"semi-rigid gels are macroporous (pore diameters &>20
In addition, a further increase in porosity can also occur on
The structural data of rigid porous solids-such as specific
surface area O,,, pore volume V,, and pore volume distribution (pore diameter distribution)-can be determined by
classical procedures (BET method, nitrogen capillary condensation, and mercury porosimetry; see e.g.'*]).For gels exclusively displaying swelling porosity, the classical methods
are obviously unsuitable. Though they can of course be used
in the case of semi-rigid materials, the results have only
limited information value.
OS70-0833/80/OtO1-0024 $ 0 2 SO/0
Angew. Chem. I n l . Ed. Engi. 19. 24-28 (1980)
Measurements by the classical methods require special
preparation of the polymer samples, including conversion
from the swollen state into the dry state, thus influencing the
results obtained15]. Moreover, in the case of exclusively macroporous semi-rigid polymers the pore structure is a function
of the swelling agent employed. Finally, the micropores additionally formed o n swelling cannot be determined.
The morphological properties of rigid inorganic solids can
be conveniently determined by a recently described exclusion chromatography (EC)
The new EC method
is simple and fast, leading to results in satisfactory agreement
with those of the classical methods, despite the different and
disputable boundary conditions.
This review will show that the exclusion method is also
suitable for the characterization of swellable solids. The new
method is the only one available so far for the investigation
of swollen gels, i. e. the state in which the material is used in
practice. Here the classical methods fail, for they require dry
2. Exclusion Chromatography-Description
of the
The principles and boundary conditions of the EC method
for determination of the structural data of porous solids have
already been described in detail el~ewhere~'~.
The basic
model concepts of the method will therefore be presented
only briefly here.
When a solvent is passed through a column packed with a
porous carrier, axial transport of the eluent takes place exclusively in the interstitial volume V,. The eluent in the pore
volume V,, of the carrier is exchanged only by diffusion between V,, and V,. For all sample substances, it must be established that they are not adsorbed by the carrier. (This has
been shown, for example, for silica gel as solid phase, dichloromethane as eluent, and polystyrene or benzene as samplel''.) Under these conditions the same applies for the samples on the column as for the molecules of the eluent: they
flow through the interstitial volume of the column and can
diffuse into and out of the pores.
The next condition to be fulfilled is that all sample molecules fully utilize the volume available to them for diffusion,
i. e. that a concentration equilibrium is established between
the "phase" in the pore volume and the phase in the interstitial volume. For samples with small molecules (e.g. benzene)
the whole pore volume in the column is then-as for the eluent-accessible, i. e. this sample is 'eluted with the greatest
possible elution volume.
[*] List of symbols:
molecular weight (weight-averaged molecular weight of polymer)
specific surface area
pore diameter (assuming the pores to be cylindrical); also the exclusion value of a polymer standard
mean pore diameter (for 50% accessible pore volume)
chromatographic elution volume of a test sample
maximum elution volume in calibration series (elution volume of the
standard with the lowest molecular weight)
minimum elution volume in a calibration series (elution volume of
the standard with the highest molecular weight)
pore volume; volume of eluent that has penetrated the pores
specific pore volume. pore volume per gram of the solid
interstitial volume
Angew. Chem.
In[. Ed. Engl. 19, 24-28 (1980)
As the molecular size of the sample material increases the
smaller pores are not accessible, z. e. the elution volume decreases. Finally, for the largest sample molecules the whole
pore volume is inaccessible, and for the elution volume we
The measuring procedure for the determination of the total
pore volume in the column follows from equations ( 1 ) and
If the column is emptied on completion of all the measurements and the mass of the carrier is determined, then the specific pore volume V,,., (referred to one gram of solid) can also
be calculated.
The elution volumes (V,) of the remaining samples lie, according to the above mentioned, between V,,,,, and V, ,,".
If the sample molecule is assigned a n exclusion value (4)
then a plot of V, against 4 corresponds to the residual sum of
the pore volume frequency. The exclusion value 4, [A] thus
describes the diameter of the smallest pores which are accessible for a molecule having a molecular weight M , . Obviously, all pores with diameters greater than 4, are then likewise
accessible. The exclusion values of the samples employed are
listed in Table 1. In the case of polystyrene (PS) samples the
I#I [A] = 0.62 M" 5 9
Table 1. Pore diameter assigned to standard (sample molecule). (PS= polystyrene, the number indicates the molecular weight.)
PS 600
PS 2100
PS 4000
PS 10000
PS 20800
PS 36000
PS 1 1 t o o o
PS 200000
PS 498000
PS 867000
PS 2610000
PS 3700000
was assumedl'l; in the case of the alkylbenzoyl samples the 4
values correspond to the length of the extended chains['].
From the residual sum of the pore volume frequency a mean
pore diameter of 4socan be assumed for 50% accessible pore
Assuming homogeneous, cylindrical and continuous pores,
the specific surface area O,, of the solid can be calculated
from the specific pore volume Vp,s [cm3/g] and the mean
pore diameter (pso [A]:
3. Experimental
The measurements were carried out on a simple apparatus
for liquid ~hromatography1’~.The units comprised a pump
(Type M 6000, Waters Associates, Milford, Mass. USA); a
sample loop injector (Rheodyne Type 7120; Kontron Technik GmbH, Eching bei Munchen, Germany), a UV detector
(254 nm) of our own construction, and a differential diffractometer (Type R 401, Waters).
With this apparatus the pore structure of the following
polystyrene-divinylbenzenecopolymers was investigated:
1. Bio beads SX 12 (BioRad, Richmond, Calif, USA),
2. Styragel 60, 100, 500, and 1000 (Waters),
3. PSDVB B1 to B4 (Farbenforschung Lewatit, Bayer AG,
Leverkusen, Germany).
The first five copolymers are commercially available and
are well-known stationary phases for exclusion chromatography. The first material is homogeneously cross-linked, the
Styragels are heterogeneously cross-linked. The samples B1
and B4 were kindly supplied by the manufacturer. The average particle diameter of these materials is between 10 and 60
Fm. As sample substances we used polystyrenes of various
degrees of polymerization and narrow range of molecular
weight distribution as well as various alkylbenzenes (MerckSchuchart, Hohenbrunn bei Miinchen, Germany). The eluent employed was dichloromethane. The samples were dissolved in the eluent (ca. 10 mg/g); ca. 1 Fg of sample per
gram of solid in the column was used.
To avoid any misunderstanding it must be pointed out
once again that the standard substances employed as samples
were linear polystyrenes dissolved in dichloromethane; the
swellable solids, however, were copolymers of styrene and
divinyl benzene.
Stainless steel tubes with a nominal internal diameter of 4
mm were used for the columns. The column length (between
30 and 100 cm) was so chosen that at least 300 theoretical
were obtained for benzene as sample. The columns
were packed by a modified balanced-density methodf7’.For
a 100-cm column, ca. 4 g of copolymer was pre-swollen in 30
mI dichloromethane for ca. 12 h (CHzC12has a greater density than the copolymer!). Before packing the column a further
14 ml of CHzClz and 40 ml of tetrahydrofuran were added.
The suspension was stirred, transferred to the packing vessel
covered with a layer of 40 ml T H F to prevent mixing and
then with CH2C12.Dichloromethane was used as pressure liquid. Packing was carried out a flow rate of ca. 3 ml/min.
The columns for the measurements were also operated with
CH2C12,but also proved to be stable on changing the solvent.
All measurements were carried out at room temperature and
a flow rate of 1 ml/min. (A detailed account of the evaluation of SEC measurements for the determination of structural data is given in r7.81.)
4. Results and Discussion
Figure 1 shows semilogarithmic plots of the elution volume of a sample as a function of the molecular weight M for
five polystyrene-divinylbenzene copolymers. These plots can
be regarded as graphical representations of the measuring
procedure. The further the curves are shifted to higher molecular weights the greater is the mean pore diameter 4 5 0 of
the solid. The difference in elution volume between the samples with the smallest and those with the largest molecular
weight corresponds to the pore volume V,, in the column [see
eq. (311.
Q I ~ O ~ B B a5
208 35
198 86-
l e Iy
Fig I . Elution volumes V, of the standard substance on five commercial poiystyrene-divinylbenzene copolymers. Eluent: dichloromethane; flow rate: 1 ml/min.
Standard substances: see Table 1. Solids (copolymers): + BioBeads SX 12; A.
0 . 0. 0 Styragel 60. 100. 500. 1000.
The integral pore distribution curves are reproduced in
Figure 2. The measurements from Figure 1 were so recalculated that the portion of the accessible pore volume V,, is
plotted on the ordinate and the exclusion value (pore diameter) of the sample on the abscissa. From this plot the
mean pore diameter 4 5 0 can be taken for 50% accessibility of
the pore volume; the steeper a curve is, the narrower is the
corresponding pore distribution. Figure 2 shows that the
Fig. 2. Sum of residues distribution of the pore diameters (integral distribution
curve) for the five copolymers in Fig. 1 (for explanation see text).
samples measured cover the whole range of pore sizes of interest between 10 and 1000 A. It should be pointed out
that-as a result of standardization-no information can be
gained from Figure 2 about the absolute size of the pore volume. From the specific pore volume Vp,sand the mean pore
diameter 4 5 0 , the surface area of the swollen copolymer in
the column can be estimated according to equation (5). Decisive for the use of swellable copolymers is the magnitude of
the surface area or pore volume referred to the volume of the
Angew. Chem. h i . Ed Engl. 19, 24-28 (1980)
vp I%!
swollen gel. The data in Table 2 are referred to the volume
and not the mass of the solid; a knowledge of the packing
density makes possible the calculation of these quantities.
Table 2. Pore volumes V,,, mean pore diameters dsoand surface areas 0 referred
to the volume of the swollen gel o f some swellable copolymers.
sx 12
Sty 60
sty 100
s t y 500
s t y loo0
In Figure 3 the elution volume is plotted as a function of
the molecular weight of the sample for four heterogeneously
cross-linked PSDVB copolymers manufactured by Bayer
AG (Farbenforschung Lewatit). The integral pore distributions derived from these according to the EC method (unbroken line) and according to classical mercury porosimetry
(broken line) are shown in Figure 4. The most important
data can be taken from Table 3.
Fig. 4. Sum of residues distribution of the pore diameter (integral distribution
curve) according to the EC method (-) and according to the mercury porosimetry method (---) (measurements by the manufacturer). a)-d) PSDVB copolymers Bl-B4.
is found to be smaller and the pore volume per grain of solid
larger than in the mercury porosimetry measurements. Further, in Table 3 it is shown for sample B1 how strongly the
Table 3. Pore volumes and mean pore diameters +sr,. The pore volume was calculated from apparent and true density.
Manufacturers data
Total pore
EC measurements
[a] Prepared with methanol. [bj Swollen in THF, then THF removed. [c] Dried.
The different results afforded by the two methods are not
surprising, since the classical measurements were carried out
on dry material and the EC measurements on swollen material. In the EC method the swollen porosity (micropores) is
also measured. Thus it would appear reasonable that in the
chromatographic measurements the mean pore diameter +so
data determined by classical methods can depend on the
preparation of the sample prior to carrying out the measurements.
5. Summary
An exclusion chromatographic method can be used for determination of the structural data of swellable solids. Pore
volume, pore distribution, and surface area of swollen materials are measured by this method and reproduce the conditions prevalent in the solids as they are used. This is illustrated by polystyrene-divinylbenzene copolymers of different
porosity and having different mean pore diameters. It is suggested that the pore volume and surface area be referred to
in terms of the volume of the swollen material, as is usual in
When suitable combinations of sample material and eluent are found, it should also be possible to investigate solids
which are swollen in different solvents.
019 ma8
208 36
Fig. 3. Elution volumes V, of the standard substance on four polystyrene-divinylbenzene copolymers from Bayer, Leverkusen. 0,
A , 0+ PSDVB-copolymers
B1-B4. For conditions see Fig. 1.
Angew. Chem. Ini. Ed. Engl. 19, 24-28 (1980)
We thank the Deutsche Forschungsgemeinschaft for financial support of this work. W e are especially indebted to Dr. P.
M. Lange and Dr. A . Meyer, Farbenforschung Lewatit, Bayer
AG, Leverkusen for supplying some copolymers and the data
f o r these compounds.
Received November 14. 1979 [A 302 IE]
German version: Angew. Chem. 92, 25 (1980)
[ I ] J. C. Moure, J. Polym. Sci. AZ. 835 (1961).
121 W. Heirr, Angew. Makromol. Chem. 10, 115 (1970).
131 W Heitr. Angew. Chem. 82,675 (1970). Angew. Chem. In1 Ed. Engl. Y, 689
( 1970).
141 S. J. Gregg. K. S. W. Sing: Adsorption. Surface Area and Porosity. Academic
Press, New York 1967.
151 F. Mnrlinola: Der EinSdt%von Kationenaustauschern in der heterogenen Katalyse. Informationsschrift der Bayer AG, Leverkusen 1975.
[6] I. Halusz, K. Martin, Ber. Bunsenges. Phys. Chem. 79, 731 (1975).
171 1. Halasz, K. Martin, Angew. Chem. 90, 954 (1978); Angew. Chem. Int. Ed.
Engl. 17, 901 (1978).
181 1. Halusz, P. Vogte!. R. Croh. 2 Phys. Chem. (Frankfurt a m Main) 112. 235
191 H. Engelhurdt: High Performance Liquid Chromatography,Springer, BerlinNew York, 1979.
A Model of Hydrogen-Bonded Liquids
By Werner A. P. Luck"]
Dedicated to Professor Gustav Kortiim on the occasion of his 75th birthday
The orientation defect model can be used for quantitative estimates and for understanding
the properties of H-bonded liquids, such as water and alcohol. The defect concentrations can
be determined by vibrational spectroscopy, and the applicability of the approximation procedure derives from considering H-bonds as chemical equilibria. Possible extensions of the simple model are critically discussed.
1. Introduction
1.1. Statement of Problem
A model has recently been described for nonpolar liquids
with spherically symmetrical van der Waals forces"'. Whether attraction or repulsion prevails is determined by the intermolecular distance. This model''' would remain incomplete
if it were not possible to formulate extensions accounting for
dipolar forces with attractive or repulsive effects depending
upon the orientation of the molecule.
Orientation-dependent interactions of this kind are especially pronounced between protons of acidic groups (e.g.
OH, NH) and lone pairs in H-bonds. The properties of Hbonded liquids are determined by two partition functions,
viz. of the distances and of the angles; they cannot yet be described exactly. In view of the importance ofjust such liquids
in biochemistry, colloid chemistry, and large areas of chemical technology, it appears pointless to wait for an exact solution o f this problem. For the chemist, too, a bird in the hand
in generally worth two in the bush. Having a particularly
high concentration of strong H-bonds, water is particularly
suitable for a simplifying approximation. On the basis of the
model for water on the one hand and nonpolar liquids1']on
the other, a wide scale of liquids can be envisaged taking account of the relative contribution of H-bonds (hydrophilic/
hydrophobic balance = HHB). Yet more parameters would
have to be considered for metallic and ionic melts.
1.2. Hydrogen Bonds
ture Tcl'l. The T, of nonpolar substances is approximately
proportional to the square root of the molecular weight or
the sum of the number of electrons 2,(Fig. 1). H-bonds increase T,. On the other hand, the relation
T,(C,H2,+ ,OH)- T,(C,+4H2(n+5Jis found to apply for
n 3 2. The effect of an alcoholic OH group thus corresponds
k KI
The intermolecular pair potential of nonpolar molecules
can be characterized approximately by their critical tempera-
Prof. Dr. W. A. P. Luck
Fachbereich Physikalische Chemie der Universitat
Auf den Lahnbergen, D-3550 Marburg (Germany)
0 Verlag Chemie, CmbH. 6940 Weinheim, 1980
x Alkyner
0 Cnbn+lOH
0 CnH,,+,COOH
4 Cvcloalkanes
Noble gases
Fig. 1. Critical temperature as a function of the root of the sum of the numbers of
electrons Z, of all the atoms of a molecule. T, is raised by the presence of Hbonds in carboxylic acids, alcohols, and H 2 0 .
Angew. Chem. In/. Ed. Engl. 19, ZX-41 (IYHO)
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solids, properties, swellable, determination, size, exclusion, chromatography, morphological
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