Comparative evaluation of the swelling and degrees of cross-linking in three organic gel packings...

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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: [email protected] (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.



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,


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.


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.

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ods56(2003)53–67

61


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


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.


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.


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.


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.

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mailto:[email protected]

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Comparative evaluation of the swelling and degrees of cross-linking in three organic gel packings...

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