Post on 01-Nov-2016
www.elsevier.com/locate/jbbm
J. Biochem. Biophys. Methods 56 (2003) 53–67
Comparative evaluation of the swelling and degrees
of cross-linking in three organic gel packings for
SEC through some geometric parameters
Rosa Garcıaa, Clara M. Gomeza, Armando Codonera,Concepcion Abadb, Agustın Camposa,*
aDepartament de Quımica Fısica, Intitut de Ciencia dels Materials, Universitat de Valencia. E-46100 Burjassot,
Valencia, SpainbDepartament de Bioquımica i Biologia Molecular, Universitat de Valencia. E-46100 Burjassot,
Valencia, Spain
Abstract
The size exclusion chromatographic (SEC) behavior of five solvent/polymer systems in three
organic column packings based on polystyrene/divinylbenzene (PS/DVB) copolymer, TSK-Gel HHR,
A-styragel and TSK-Gel HXL, has been compared. All the packings offer similar characteristics (pore
size, particle size and efficiency) but some differences have been found when eluting the same
systems. The different elution behavior observed in both polymeric gels has been analyzed in terms
of their swelling and cross-linking degrees and of the fractal parameters. From the Universal
Calibration plots, values of the chromatographic partition coefficient, Kp, have been obtained and
using some equations previously reported, values of the volume fraction of the network in the
swollen state have been determined for the three sets of columns. Overall, for a given hydrodynamic
volume and solvent-polymeric solute system the fraction of cross-linked polymer in the stationary
phase was ordered according to: TSK-Gel HXL>A-styragel>TSK-Gel HHR. This means an enhanced
swelling degree for TSK-Gel HHR. In general, fractal calculations support the thermodynamic
predictions since both the fractal dimension and the pore size can be ordered as TSK-Gel HHR>A-styragel>TSK-Gel HXL (in 10 of the 15 situations studied). The exceptions can be explained in terms
of strong preferential solvation.
D 2003 Elsevier Science B.V. All rights reserved.
Keywords: Size exclusion chromatography; Swelling and cross-linking degree; Fractal behavior
0165-022X/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0165-022X(03)00072-1
* Corresponding author. Fax: +34-96-386-4564.
E-mail address: rosa.garcia@uv.es (A. Campos).
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–6754
1. Introduction
TSK-Gel (Tosohaas [1]) and A-styragel (Waters [2]) are high performance liquid
chromatography GPC/SEC columns widely used for polymer characterization in
organic solvents. All packings are polystyrene-divinylbenzene (PS-DVB) polymer-
based materials. The Tosohaas manufacturers [1] argued an excellent compatibility of
the new series of PS-DVB columns, TSK-Gel HHR and TSK-Gel HXL, for a wide
range of eluent polarities, from hexane or decaline to piridine, ethanol, dimethylfor-
mamide or trichlorobenzene. Twelve pore sizes are available with a molecular weight
separation range from 102 to several millions (Da). Indeed, the small 5 Am (HHR gel)
and 5/13 Am (HXL gel) particle sizes guarantee high efficiency. According to the
supplier [1], the series HXL are, in general, less swollen that the series HHR in a
given solvent, which suggests a higher PS-DVB chain density or cross-linking degree
for the former.
A-styragel GPC/SEC columns are available in eight pore sizes with effective
molecular weight range between 10 and 108 Da and 5-Am particle size. The
polymeric phase is compatible with both nonpolar and polar organic solvents [2].
In turn, all these polymer-based stationary phases appear as products of similar
characteristics (i.e. mechanical properties, pore size range and efficiency).
In a previous work [3], we have compared two series of columns, TSK-Gel HHR
and A-styragel, in order to analyze specific features of the stationary phase that can
explain some differences observed in the chromatographic behavior of polymer
samples. In fact, it was shown that the cross-linking degree is a crucial parameter
for a high size exclusion chromatographic (SEC) separation efficiency, although it can
also lead to non-desirable secondary effects (higher Kp), such as adsorption of the
polymeric solute to the stationary phase. Thus, it was concluded that a compromise
between these two factors should be attained for high performance in polymer
characterization.
Later on, a comparative study between TSK-Gel HHR and TSK-Gel HXL columns
[4] showed that the highest cross-linking degree was found for the TSK-Gel HXL.
Consequently, a higher separation efficiency due to higher cross-linking degree could
be masked by secondary non-desirable effects in SEC adsorption. So, a compromise
between these two factors has to be achieved.
In this paper, data of volume fraction of the network in the swollen state, /3, of
the coefficient accounting for interactions between the components of the chromato-
graphic system, Kp, fractal parameters and the preferential solvation coefficient [5,6]
have been used to compare the chromatographic behavior of three sets of columns,
TSK-Gel HHR, TSK-Gel HXL and A-styragel. Based on the comparison of these
parameters and their relation with the swelling degree and cross-linking degree on
the gel packings [3] for five solvent/polymeric solute systems in the three packing
gels, we found that the cross-linking degree can be ordered as: TSK-Gel HXL>A-styragel>TSK-Gel HHR. Also, it is evidenced that when changing from one gel to
another, a higher cross-linking or a lower degree of swelling implies a higher Kp
value. However, the fractal behavior parameters depend on how strong the solvation
of the polymer onto the gel is.
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–67 55
2. Materials and methods
2.1. Chemicals used with the chromatographic columns
Chemicals used with TSK Gel HHR and A-styragel columns have been previously
described [3]. Chemicals used with TSK HXL columns are: (a) PBD standards with weight
average molar mass, in daltons, Mw = 920, 6250, 12600, 34000, 60700, 105700, 323000
and 360000 (I = 1.03–1.15) were purchased from Polymer Source (Canada), and (b)
PDMS standards with Mw = 1140, 8100, 33500, 123000 and 188000 Da (I = 1.06–1.23)
were supplied by Polymer Source, (c) Tetrahydrofuran (THF), benzene (Bz), toluene (Tol)
and 1–4 dioxane (Diox) of chromatographic grade from Scharlau (Barcelona, Spain) were
used as solvents or eluents.
2.2. Viscometric measurements
An automatic AVS 440 Ubbelohde-type capillary viscometer from Schott Gerate
(Hofheim, Germany) at 25F 0.1 jC was used to perform viscometric from measurements,
as previously described [3].
2.3. Chromatography
AWaters liquid chromatography instrument with refractive index detector was used for
SEC experiments, as previously described [7–9]. Three sets of columns connected in
series (each one of 7.8 mm ID� 300 mm) based on a PS/DVB cross-linked copolymer
have been compared: (i) three TSK-Gel HHR from Tosohaas, Tosoh (Tokyo, Japan), (ii)
three A-styragel (Waters) and (iii) three TSK-Gel HXL from Tosohaas, Tosoh. Their
packing characteristics as particle size, nominal pore size, pore and total exclusion
volumes (Vp and V0) and molar mass separation range are summarized in Table 1.
Table 1
Column packing characteristics
Commercial
name
Gel packinga Pore sizea Particle
size (Am)aEffective Mw
rangeaV0
(ml)
Vp
(ml)
VT
(ml)
TSK-Gel HHR cross-linked G2500 5 200–40000 16.40b 21.00 37.40c
copolymer G4000 5 1000–600000
PS/DVB G6000 5 10000–4� 106
A-Styragel cross-linked 103 A 15 200–30000 17.70b 18.10 35.80c
copolymer 104 A 15 5000–600000
PS/DVB 105 A 15 50000–4� 106
TSK-Gel HXL cross-linked G2500 5 200–40000 17.07d 16.63 33.70e
copolymer G4000 6 1000–600000
PS/DVB G6000 9 10000–4� 106
a Supplied by the manufacturer.b Determined with a PS standard of high molar mass (Mw = 2700000).c Determined with small molecules such as Tol or Bz in THF.d Determined with a PS standard of high molar mass (Mw = 3800000).e Determined with small molecules such as Bz in THF.
Fig. 1. Universal calibration plots for different systems eluted in the three columns: (a) TSK-Gel HHR, (b)
A-styragel and (c) TSK-Gel HXL.
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–6756
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–67 57
To avoid concentration effects [10] on the elution volumes, Ve, all solute samples were
injected at four concentrations and extrapolated to zero concentration. The elution
behavior has been presented in terms of the assumed ‘‘universal calibration’’ curves made
by plotting the hydrodynamic volumes, Vh (as logM [g]) versus Ve. The five systems
assayed were: THF/PBD, Bz/PBD, Diox/PBD, Bz/PDMS and Tol/PDMS. In the hydro-
dynamic volumes, range here studied all the ‘‘universal calibration’’ plots were lineal (with
correlation coefficient, R2>0.998) (Fig. 1).
3. Theory
3.1. Cross-linking and swelling degree
Since the SEC experimental data are frequently extrapolated at /2!0 (/2 is the volume
fraction of polymer solute in the mixture solvent(1) + polymer solute(2) + polymer gel(3))
the accurate equation [3] that evaluates the chain density or cross-linking degree per mole,
m/NAV0, of a polymeric gel in SEC, can be simplified to the following expressions:
mNAV0
¼ /5=33
12� v
13
V1
!ð1Þ
or for the swelling degree:
/�13 ¼ V
V0
¼ NAV0
m
12� v
13
V1
!#3=5264 ð2Þ
being m the average number of chains in the network, NA the Avogadro’s number, V1 the
molar volume of component 1, v13 the Flory interaction parameter between solvent(1) and
polymer gel(3), V the volume of swollen gel, V0 the volume of dry gel and /3 =V0/V the
volume fraction of the network in the swollen state. As can be seen from Eq. (1), for a
given solvent (V1 and v13 constants) when /3 increases the cross-linking degree m/V0 also
does if (1/2� v13)>0; whereas from Eq. (2), for a given gel packing (V0/m) constant) andfor the same V1, as the eluent better solvates, the network, v13 will be lower and the
swelling degree will increase. Furthermore, simplified Eqs. (1) and (2) allow to approx-
imately evaluate either the cross-linking degree m/V0 or the interaction parameter v13, ifpreviously the swelling degree, /3
� 1, has been experimentally calculated in the swelling
equilibrium procedure [7–9,11].
3.2. Fractal surfaces
It has been suggested that porous materials used in size exclusion chromatography,
SEC, are surface fractals [12]. This was tested for diverse gels through data on SEC of
biopolymers with negative results for classical gel materials as sepharose or sephacryl,
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–6758
and with positive results for the more efficient gels TSK SW and TSK PW [13,14]. Size-
exclusion was the principal mechanism governing macromolecule separation in the
above gels, as in the present case. We have shown previously the fractal activity [15] of
polar inorganic gels [16–18] and of theoretical apolar organic gels [4] with additional
secondary effects such as partition and adsorption. It seems worthwhile to analyze the
fractal nature of the present materials (TSK-Gel HHR, A-styragel and TSK-Gel HXL) and
its variation with eluent and polymeric solute nature since, for example, the adsorption
of macromolecules on gel surfaces is also a process sensitive to the fractal dimension Df
[19]. Magnitudes important in fractal theory as applied to SEC are KD and R. KD is the
total distribution coefficient [4,6] of a polymeric solute and it is related to its elution
volume, Ve, through:
KD ¼ Ve � V0
Vp
¼ Ve � V0
VT � V0
ð3Þ
where Vp, V0 and VT are pore, total exclusion (or interstitial volume) and total volume of
the column, respectively.
The radius of the equivalent hydrodynamic sphere, R, defines the hydrodynamic radius
of macromolecular solutes and can be calculated according to the Einstein equation:
R3 ¼ 30M ½g�1022pNA
ð4Þ
from intrinsic viscosity measurements, [g]. In the above equation, M stands for molar mass
of sample and R values are in A if [g] are in ml g� 1.
As suggested by Brochard [12], KD is related to the fractal dimension, Df, of the surface
of pores through:
KD ¼ 1� R
L
� �3�Df
ð5Þ
with L standing for pore size. From the above equation, a linear relationship between lnR
and ln(1�KD) [14] is attained,
lnR ¼ 1
3� Df
lnð1� KDÞ þ lnL ð6Þ
which allows evaluation of fractal characteristics of gel surfaces from elution data of
solutes of diverse sizes.
3.3. Average pore radius of the gel
Different thermodynamic affinities for the polymer as well as for the gel are found in
the chromatographic experiments depending on the solvent [16]. Thus, partition and/or
adsorption can play a fundamental role in the elution mechanism.
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–67 59
In the network-limited partition and network-limited adsorption mechanism proposed
by Dawkins and Hemming [20], the equation, which relates retention volume, Ve, to
average pore radius is:
lnðVe � V0Þ ¼ � R
rþ ln
2Kp
r
� �ð7Þ
Kp is the distribution coefficient for solute partition between stationary and mobile
phases (if Kp = 1 there is no retention and solutes will separate solely by steric exclusion)
and r is the average pore radius of the gel.
4. Results and discussion
4.1. Chromatographic data
Fig. 1 compares the universal calibration (u.c.) curves obtained with PBD and PDMS in
three different eluents and with PS in THF, for (a) TSK-Gel HHR,(b) A-styragel and (c)
TSK-Gel HXL columns. As seen, some differences arise for the different systems solvent/
polymer in the same gel, and also differences arise for the same systems solvent/polymer
in different type of columns. In order to better explain the observed elution behavior, we
have chosen three values of the hydrodynamic volumes (M[g] =Vh = 106, 107 and 108
mlmol� 1), which are representative of the most effective mass separation range in the
columns being evaluated. The elution volumes, Ve, for non-ideal SEC (when secondary
mechanisms such as adsorption appear) are given by [3,5]:
Ve ¼ V0 þ KDVp ¼ V0 þ KSECKpVp ð8Þ
where KSEC is the size distribution coefficient for ideal SEC. The KSEC data obtained with
a reference system (THF/PS) as is usual [3] for the three types of packings are gathered in
Table 3. With values of V0, Vp and KSEC compiled in Tables 1 and 2 and experimental Vedata, Kp values can be easily determined from Eq. (8) for the five chromatographic
systems at the different values of Vh, 106, 107 and 108 ml mol� 1 and are given in Table 3.
The comparison of Kp data in the three packings reveals, in general, except for the Diox/
PBD system, that the lower adsorption effects (lower Kp values) occur in TSK-Gel HHR.
This evidence could be attributed to different density or cross-linking degree in the three
gels. To confirm this hypothesis, we next proceed to measure thermodynamically the
cross-linking degree.
Table 2
Values of KSEC (PS/THF) for the three hydrodynamic volumes selected in the three sets of columns
Vh (ml mol� 1) TSK-Gel HHR A-styragel TSK-Gel HXL
106 0.251 0.403 0.267
107 0.170 0.272 0.152
108 0.088 0.140 0.037
Table 3
Values of Kp, /3, Df, L and r for the different systems studied in the three columns at the three hydrodynamic volumes selected
Gel packing Vh = 106 ml mol� 1 Vh = 10
7 ml mol� 1 Vh = 108 ml mol� 1 Vh = 10
6, 107, 108 ml mol-1
Kp /3 ( gchrA ) /3 ( gchr
B ) Kp /3 ( gchrA ) /3 ( gchr
B ) Kp /3 ( gchrA ) /3 ( gchr
B ) Df L (A) r (A)
THF/PBD
TSK-Gel HHR 0.981 3.4� 10� 2 2.8� 10� 2 0.966 3.4� 10� 2 2.8� 10� 2 0.935 3.4� 10� 2 2.8� 10� 2 2.86 446 197
5.6� 10� 5 5.6� 10� 5 2.1�10� 4 2.1�10� 4 1.7� 10� 4 1.7� 10� 4
A-styragel 1.006 3.4� 10� 2 2.8� 10� 2 0.992 3.37� 10� 2 2.8� 10� 2 0.958 3.37� 10� 2 2.8� 10� 2 2.73 403 170
9.6� 10� 5 9.6� 10� 5 2.05� 10� 4 2.05� 10� 4 1.8� 10� 4 1.8� 10� 4
TSK-Gel HXL 1.307 3.74� 10� 2 3.15� 10� 2 1.515 3.67� 10� 2 3.09� 10� 2 3.013 3.69� 10� 2 3.16� 10� 2 2.78 402 153
Bz/PBD
TSK-Gel HHR 1.205 7.69� 10� 2 5� 10� 5 1.160 7.68� 10� 2 5.69� 10� 2 1.038 7.68� 10� 2 1.7� 10� 4 2.84 507 183
5.10� 10� 5 5.7� 10� 2 1.2� 10� 4 2.1�10� 4 1.1�10� 4 5.8� 10� 2
6.49� 10� 2 6.48� 10� 2 6.48� 10� 2
A-styragel 1.293 7.69� 10� 2 5.7� 10� 2 1.298 7.69� 10� 2 5.7� 10� 2 1.325 7.69� 10� 2 5.7� 10� 2 2.63 428 180
6.5� 10� 2 6.5� 10� 2 6.5� 10� 2
TSK-Gel HXL 1.873 7.82� 10� 2 5.79� 10� 2 2.466 6.59� 10� 2 5.8� 10� 2 6.727 6.58� 10� 2 5.8� 10� 2 2.72 686 234
6.57� 10� 2 7.82� 10� 2 9.5� 10� 4 7.82� 10� 2
R.Garcıa
etal./J.
Biochem
.Biophys.
Meth
ods56(2003)53–67
60
Diox/PBD
TSK-Gel HHR 1.265 4.46� 10� 2 2.45� 10� 2 1.364 4.56� 10� 2 2.57� 10� 2 1.659 4.56� 10� 2 2.59� 10� 2 2.84 648 294
A-styragel 1.636 4.44� 10� 2 2.43� 10� 2 1.853 4.63� 10� 2 2.63� 10� 2 2.490 4.58� 10� 2 2.62� 10� 2 2.49 509 189
TSK-Gel HXL 1.056 4.14� 10� 2 2.07� 10� 2 1.004 4.32� 10� 2 2.29� 10� 2 0.628 4.27� 10� 2 2.24� 10� 2 2.80 278 103
Bz/PDMS
TSK-Gel HHR 1.246 0.232 0.137 1.244 1.5� 10� 4 0.137 1.243 0.232 0.138 2.81 430 181
7.0� 10� 5 7.0� 10� 5 1.5� 10� 4 1.3� 10� 4 1.3� 10� 4
A-styragel 1.077 0.232 0.137 1.043 0.232 0.137 0.962 0.232 0.138 2.66 317 136
1.6� 10� 4 1.6� 10� 4 3.1�10� 4 3.1�10� 4 2.7� 10� 4 2.7� 10� 4
TSK-Gel HXL 1.557 0.233 0.139 1.886 0.233 0.140 4.257 0.233 0.1397 2.70 355 123
TOL/PDMS
TSK-Gel HHR 1.097 0.233 0.263 1.095 0.233 0.263 1.103 0.233 0.263 2.84 455 188
0.139 0.139 0.139
1.0� 10� 4 2.0� 10� 4 1.0� 10� 4
A-styragel 1.061 0.233 0.263 1.089 0.233 0.263 1.181 0.233 0.263 2.71 400 168
0.139 0.137 0.137
TSK-Gel HXL 0.999 0.352 6.7� 10� 6 1.000 0.352 1.5� 10� 6 1.001 0.3509 2.8� 10� 6 2.80 265 93
R.Garcıa
etal./J.
Biochem
.Biophys.
Meth
ods56(2003)53–67
61
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–6762
4.2. Cross-linking and swelling degree from chromatographic and thermodynamic data
We have recently developed [5,8] some relationships between the distribution coef-
ficient, Kp, and the thermodynamic interaction functions, which allow to obtain the gel
volume fraction involved in the chromatographic separation process, /3:
ln Kp ¼ � V2
V1
/3gAchr ð9aÞ
ln Kp ¼ � V2
V1
/3gBchr ð9bÞ
where gchrA = 1� g12� g13 + g23 + gT and gchr
B = 1� g12� g13 + g23� (/2–/1)gT, when
/2! 0 are complex interaction functions that take into account all the binary and ternary
interactions between the three components of the system [5,8]. Values of the binary g12,
g13 and g23 and the ternary gT interaction functions composition dependence for the
different systems studied have been obtained previously from phase separation experi-
ments [5,8]. Values of these complex expressions, gchrA and gchr
B , as a function of /3 are
gathered in Table 4 for the systems studied.
On the other hand, to investigate the influence of the molar mass (or polymer solute
size), M, on Kp we plot lnKp against V2/V1 (being Vi the molar volume of component i, 1
solvent and 2 polymeric solute) obtaining a good linear dependence for every system.
From these plots, and according to Eq. 9a and b, the slope should be independent of M and
equal to either �/3gchrA or �/3gchr
B [5]. From the values of these slopes and the interaction
functions gchrA and gchr
B (Table 4), we obtain the values of the gel volume fraction, /3,
involved in the chromatographic process at the three selected hydrodynamic volumes for
every system in the three types of columns packing [3]. The obtained values of /3
(positive and real solutions) are gathered in Table 3 where, in general, it can be seen that,
as the average mean (except for Diox/PBD system) /3 values are ordered as follows: /3
(TSK-Gel HXL>/3 (A-styragel)>/3 (TSK-Gel HHR).
Moreover, for every solvent and polymer molar mass used in this work, the second
virial coefficient, A2, of PS is positive at room temperature [21]. The second virial
coefficient can be related to the solvent/polymer (gel) interaction parameter, v13, as:
A2 ¼ v23
V1
12� v13
, being v3 the specific volume of PS. Since A2>0 for solvent(1)/PS(3) (PS
simulates the gel matrix), it yields that (1/2� v13)>0 for every system here studied. So, as
/3 values here obtained (Table 3) are very small, we can assume that (1/2� v13)>0 and
consequently the cross-linking degree can be ordered according to the /3 values found for
Table 4
Values of the chromatographic functions, gchrA and gchr
B for the ternary systems studied
System gchrA gchr
B
THF/PBD/PS 0.05� 1.47f3 0.05–1.84f3 + 2.09f32
Bz//PBD/PS 0.33� 5.08f3 0.33–6.29f3 + 8.89f32
Diox/PBD/PS 0.05� 1.12f3 0.05–2.17f3 + 5.40f32
Bz/PDMS/PS 0.13� 0.56f3 0.13–1.44f3 + 3.60f32
Tol/PDMS/PS � 0.26 + 0.73f3 � 0.26 + 0.73f3� 2.26f32
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–67 63
the three gel packings, that is: m/NAV0(TSK-Gel HXL)>m/NAV0(A-styragel)>m/NAV0 (TSK-
Gel HHR).
With respect to the fractal behavior, Fig. 2 shows the plots of lnR against ln(1�KD)
(Eq. (6)) for all the systems in the three columns all of which yield good linear
relationships. Values of Df and L obtained from the slope and ordinate, respectively, are
compiled in Table 3. Values of Df are always close to the numerical value of three,
Fig. 2. Plot of lnR against ln(1�KD) for different solvent/polymer systems in the three columns packings: (a)
TSK-Gel HHR, (b) A-styragel, and (c) TSK-Gel HXL.
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–6764
indicating a large pore density or knots of the network probably due to the highest cross-
linking degree found in these modern gel packings in contrast with lower values of Df
found in former ones [15].
Fig. 3 depicts the plot of ln(Ve�V0) against R (Eq. (7)) for every system in the three
columns studied. All these plots are lineal and values of the average pore radius, r , are
gathered in Table 3. Values of r are always smaller than half the value of the pore size,
L, as expected. Moreover, for every system solvent(1)/polymer(2) when changing from
Fig. 3. Plot of ln(Ve�V0) against R for different solvent/polymer systems in the three columns packings: (a) TSK-
Gel HHR, (b) A-styragel, and (c) TSK-Gel HXL.
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–67 65
one column packing set to another, the variation of r is practically parallel to the one
observed for L that supports the obtained results. To investigate how the magnitudes
compiled in Table 3 (/3, Kp, Df, L and r ) are related with the different gel packings
employed; Table 5 depicts the relative variation of these parameters for the different
systems studied in the three sets of columns. For instance, for THF/PBD, /3 and Kp
increase while L, r and Df decrease by comparing TSK-Gel HHR with A-styragel and with
TSK-Gel HXL. However, going from A-styragel to TSK-Gel HXL, L does not change.
Overall, from the inspection of Table 5, we can say that over the 15 situations studied for
the five binary solvent/polymer solute systems when changing from TSK-Gel HHR to A-styragel, from TSK-Gel HHR to TSK-Gel HXL and from A-styragel to TSK-Gel HXL
columns, the behavior of /3 is the same to that observed for Kp. Moreover, we have seen
that an increase of /3 always implies an increase of the gel cross-linking degree, m/NAV0,
and so an increase of Kp. This is due to the fact that the higher the cross-linking degree, the
higher the quantity of active residues in the network knots coming from the synthesis of
the gel (the chemical derivatisation procedure can lead to more support active sites), and so
more polymeric solute–gel interactions and larger values of Kp. On the other hand, an
increase of either /3, Kp or m/NAV0 should imply a decrease of L, r or Df. As the gel
becomes more cross-linked, irregularities on the surface gel packing for a given solvent–
polymer solute system will be lower. This reasoning is fulfilled in seven systems and
partially in three of the 15. However, there are five exceptions for which L, r or Df do not
fulfill the predicted trend. These systems are: (i) Bz/PBD from TSK-Gel HHR to TSK-Gel
HXL, and from A-styragel to TSK-Gel HXL; (ii) Diox/PBD from TSK-Gel HHR to TSK-Gel
HXL, and from A-styragel to TSK-Gel HXL; and (iii) Bz/PDMS from A-styragel to TSK-
Gel HXL. For Bz/PBD L, r and Df should decrease but they increased. This trend can be
interpreted by keeping in mind the strong increase of Kp in both situations, larger than in
the systems where L, r and Df evolve in the usual way. This implies a strong preferential
Table 5
Comparison of chromatographic and fractal parameters for the different systems between the three columns
System Kp /3 L r
THF/PBD TSK-Gel HHR! A-styragel z z # #TSK-Gel HHR!TSK-Gel HXL z z # #A-styragel!TSK-Gel HXL z z = #
Bz/PBD TSK-Gel HHR! A-styragel z z # #TSK-Gel HHR!TSK-Gel HXL z z z zA-styragel!TSK-Gel HXL z z z z
Diox/PBD TSK-Gel HHR! A-styragel z z # #TSK-Gel HHR!TSK-Gel HXL # # # #A-styragel!TSK-Gel HXL # # # #
Bz/PDMS TSK-Gel HHR! A-styragel z z # #TSK-Gel HHR!TSK-Gel HXL z z # #A-styragel!TSK-Gel HXL z z z #
Tol/PDMS TSK-Gel HHR! A-styragel = = = =
TSK-Gel HHR!TSK-Gel HXL = z # #A-styragel!TSK-Gel HXL = #
The symbols indicate an increase (z), a decrease (#), and no variation (=) in the magnitude when going from the
first column set to the second one.
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–6766
solvation of the polymer onto the gel packing [5,6] and this could influence on the
unexpected increase of L, r and Df. For Diox/PBD when changing from one gel packing
to another, L and r decrease although they should increase. This behavior can be explained
by considering the high decrease of Kp in both systems which causes a strong decrease of
the preferential solvation of the polymer onto the gel packing [5,6] and induces an
unexpected decrease of L and r .
Finally, we can conclude that the values of /3, m/NAV0, Kp, L, r and the preferential
solvation parameter onto the gel for each system shed light on the different elution
behavior of the five solvent/polymer systems studied in the three chromatographic
packings which are in principle very similar.
5. Conclusions
The elution behavior of five solvent/polymer solute systems eluted in three sets of
chromatographic packing based on PS/DVB copolymer and similar particle and pore
sizes has been studied. Parameters like volume fraction of the network in the swollen
state or volume of dry gel/volume of swollen gel, coefficient accounting for secondary
effects as interactions between the different components of the chromatographic
system, Kp, pore size, L, average pore radius of the gel, r , fractal dimensions and
preferential solvation parameter have been determined and related. The comparison of
the parameters obtained in the different columns gives additional information on the
properties of PS/DVB based supports for SEC, which can be useful for polymer
characterization. The highest cross-linking degree or lowest swelling degree, obtained
in TSK-Gel HXL, is a crucial magnitude to achieve a good separation efficiency by
SEC but it can also lead to major secondary effects like adsorption of the polymeric
solute to the stationary phase.
Acknowledgements
Financial support from Direccion General de Investigacion (Ministerio de Ciencia y
Tecnologıa) under Grant No. MAT2000-1781 is gratefully acknowledged.
References
[1] Catag. Teknokroma. (electronic address available is comercial@teknokroma.es).
[2] Catag. Millipore-Waters. (electronic address available is www.waters.com).
[3] Garcıa R, Recalde IB, Figueruelo JE, Campos A. Quantitative evaluation of the swelling and crosslinking
degrees in two organic gel packings for SEC. Macromol Chem Phys 2001;202:3352–62.
[4] Gomez CM, Garcıa R, Abad C, Campos A. Comparison of the chromatographic behavior of two organic gel
packings for SEC through the swelling and crosslinking degrees. Chromatographia [in press].
[5] Garcıa R, Gomez CM, Figueruelo JE, Campos A. Thermodynamic interpretation of the SEC behavior of
polymers in a polystyrene gel matrix. Macromol Chem Phys 2001;202:1889–902.
[6] Garcıa R, Gomez CM, Abad C, Campos A. An analysis of the concentration effects on elution volumes
trough the preferential solvation parameter in two SEC packings. Macromol Chem Phys 2002;203:2551–59.
R. Garcıa et al. / J. Biochem. Biophys. Methods 56 (2003) 53–67 67
[7] Gomez CM, Verdejo E, Figueruelo JE, Campos A, Soria V. On the thermodynamic treatment of
poly(vinylidenefluoride)/polystyrene blend under liquid – liquid phase separation. Polymer 1995;36:
1487–98.
[8] Gomez CM, Figueruelo JE, Campos A. Evaluation of thermodynamic parameters for blends of polyether-
sulfone and poly(methyl methacrylate) or polystyrene in dimethylformamide. Polymer 1998;39:4023–32.
[9] Gomez CM, Figueruelo JE, Campos A. Thermodynamics of a polymer blend solution system studied by gel
permeation chromatography and viscosity. Macromol Chem Phys 1999;200:246–55.
[10] Berek D. In: Wu C-S, editor. Column handbook for size exclusion chromatography. London: Academic
Press; 1999. p. 445–57.
[11] Gomez CM, Garcıa R, Figueruelo JE, Campos A. Theoretical evaluation of Kp in size-exclusion chroma-
tography from a thermodynamic viewpoint. Macromol Chem Phys 2000;201:2354–64.
[12] Brochard F. Some surface effects in porous fractals. J Phys 1985;46:2117–23.
[13] Brochard F, Ghazi A, le Maire M, Martin M. Size exclusion chromatography on porous fractals. Chroma-
tographia 1989;27:257–63.
[14] le Maire M, Ghazi A, Martin M, Brochard F. Calibration curves for size-exclusion chromatography.
Description of HPLC gels in terms of porous fractals. J Biochem 1989;106:814–7.
[15] Porcar I, Garcıa R, Soria V, Campos A, Figueruelo JE. Porous fractal gels: secondary effects in SEC. J Non-
Cryst Solids 1992;147–148:170–5.
[16] Campos A, Soria V, Figueruelo JE. Polymer retention mechanism in GPC on active gels, 1 polystyrene in
pure and mixed eluents. Makromol Chem 1979;180:1961–74.
[17] Figueruelo JE, Soria V, Campos A. Polymer retention mechanisms in GPC on active gels, 3 poly(dime-
thylsiloxane) and poly(methyl methacrylate). Makromol Chem 1981;182:1961–9.
[18] Mori S. Secondary effects in aqueous size exclusion chromatography of sodium poly(styrenesulfonate)
compounds. Anal Chem 1989;61:530–4.
[19] Avnir D, Farin D, Pfeifer P. Chemistry in noninteger dimensions between two and three: II. Fractal surfaces
of adsorbents. J Chem Phys 1983;79:3566–71.
[20] Dawkins V, Hemming M. Gel permeation chromatography with crosslinked polystyrene gels and theta
solvents for polystyrene 2. Separation mechanism. Macromol Chem 1975;176:1795–813.
[21] Lechner MD, Steinmeier DG. In: Brandrup J, Immergut EH, editors. Polymer handbook. 3rd ed. New York:
Wiley; 1989. p. VII-128.