Reactive & Functional Polymers 68 (2008) 1325–1336

Contents lists available at ScienceDirect

Reactive & Functional Polymers

journal homepage: www.elsevier .com/locate / react

Sulfonation of macroporous poly(styrene-co-divinylbenzene) beads:Effect of the proportion of isomers on their cation exchange capacity

Claudio A. Toro, Raúl Rodrigo, Jorge Cuellar *

Department of Chemical Engineering, University of Salamanca, Plaza de los Caídos 1-5, 37008 Salamanca, Spain

a r t i c l e i n f o

Article history:Received 12 March 2008Received in revised form 16 May 2008Accepted 14 June 2008Available online 21 June 2008

Keywords:PolymerizationSulfonationPoly(styrene-co-divinylbenzene) beadsCation exchange resinsmeta-Divinylbenzenepara-DivinylbenzeneCation exchange capacity

1381-5148/$ - see front matter � 2008 Elsevier Ltddoi:10.1016/j.reactfunctpolym.2008.06.010

* Corresponding author. Tel.: +34 923294479; faxE-mail address: cuellar@usal.es (J. Cuellar).

a b s t r a c t

The influence of the proportions of the meta- and para-isomers of divinylbenzene and eth-ylstyrene in the degree of sulfonation of macroporous poly(styrene-co-divinylbenzene)(poly(ST-co-DVB)) beads has been investigated. The first step in this work was the synthe-sis of poly(ST-co-DVB) beads, with different porous structures, by variation of the propor-tions of cross-linking agent (%DVB) and of the volume fraction of monomers in the organicphase (Fm) of the polymerization mixture. The next step involved transformation of thepolymeric beads obtained into cation exchange resins by means of hot sulphuric acid treat-ment. The quantitative extent of the sulfonation reaction was evaluated by measuring theion exchange capacity (q) of each type of resin. The Design of Experiments (DOE) method-ology was used to study the effects of %DVB and Fm on q and it was found that only the%DVB factor exerted a significant effect on this parameter, its influence being non-linearand negative. To obtain more reliable results, a new set of experiment was performed inwhich the range of %DVB values was expanded, covering from 25% to 80% DVB. The resultsindicated again that the influence of the %DVB factor on q was non-linear and negative;that is, an increase of %DVB in the synthesis process led to a decrease in q. Since this effectcan be thought to be due to the hindered penetration of the sulfonation mixture into thevery cross-linked gel-type nanoparticles comprising the beads, an attempt was made tofind an interrelationship between the specific surface area (SBET) of each type of beadand their q, trying to determine whether the sulfonation was merely a surface process.However, it was found that not only did sulfonation of the surface of the nanoparticlesoccur but also that the sulfonation agent penetrated into their interior. Taking these obser-vations into account, it was suspected that one or more of the isomers present in the com-mercial DVB polymerize in such a way that their sulfonation is not complete. To check thispossibility, the proportion of the DVB isomers and q were correlated The quantitative rela-tionship found indicated that the absence of a completely homogeneous sulfonation ofpoly(ST-co-DVB) beads seems to be due to an insufficient sulfonation of the benzene ringsof the para-isomers present in commercial DVB.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Cation exchange resins are useful in a large number ofapplications, ranging from the exchange of cations for dif-ferent purposes in many industrial and laboratory fields[1,2] (substitution, elimination, isolation, separation,

. All rights reserved.

: +34 923294574.

recovery and concentration of cations) to their use ascatalysts [1–7]. However, since each of these applicationshas different characteristics, the best performance in eachone of them will only be achieved by using cation exchangeresins with properties suited to the application. Theproperties of ion exchange beads, which usually have animportant effect on their performance, are theirstructural characteristics and their type and degree offunctionalization.

Nomenclature

%DVB weight percentage of DVB isomers in the mono-meric mixture

F Fisher statisticFm volume fraction of monomers in the organic

phasep-value level of experimental significance of the testq cation exchange capacity (meq/g dry resin)qm maximum cation exchange capacity (meq/g dry

resin)q̂m predicted maximum cation exchange capacity

(meq/g dry resin)SBET specific surface area, calculated from the nitro-

gen adsorption isotherm (m2/g)t Student statisticx%DVB coded value of %DVB

x%DVBxFm coded value of the %DVB � Fm interactionxFm coded value of FmXm sum of the molar fraction of the meta-isomersXm-DVB molar fraction of the m-EVB in the monomeric

mixtureXm-EVB molar fraction of the m-DVB in the monomeric

mixtureXp sum of the molar fraction of the para-isomers in

the monomeric mixtureXp-DVB molar fraction of the p-DVB in the monomeric

mixtureXp-EVB molar fraction of the p-EVB in the monomeric

mixtureXST molar fraction of styrene in the monomeric

mixture

1326 C.A. Toro et al. / Reactive & Functional Polymers 68 (2008) 1325–1336

Regarding their structural characteristics, ion exchangeresins are usually classified in two groups with majorstructural differences: gel and macroreticular resins. Mostcation exchange resins are manufactured from sphericalpolymeric beads synthesized by the procedure of suspen-sion copolymerization [1,2], using styrene (ST) and divinyl-benzene (DVB) as monomers. DVB is a cross-linking agentthat provides physical strength to the beads. Gel-type res-ins made from poly(ST-co-DVB) beads usually have a DVBcontent below 12% because higher percentages of DVB in-volve a very low swelling capacity and the rate of the dif-fusion processes in their interior is slow [3].

Conversely, macroreticular (or macroporous) cation ex-change resins are synthesized from polymeric beads with avery high proportion of DVB and, owing to their higher de-gree of cross-linking, they have higher mechanical andchemical stability than the gel type. Beads of macroporouscation exchangers are formed by agglomerated nano-spheres arranged in groups (affording a porous structure),their pore size distribution being a function of the synthe-sis conditions [8–13] of the polymeric matrix. The exis-tence of permanent pores allows the entrance of verylarge molecules, or ions, into the beads and a relatively fastmass-transfer rate by diffusion into their interior.

With regard to the degree of functionalization, thetransformation of poly(ST-co-DVB) beads into cation ex-change resins can be accomplished by several methods,the one most widely used (in the case of strong cation ex-change resins) involving the sulfonation of polymericbeads by hot concentrated sulphuric acid [1,14–20]. Thisgives rise to an aromatic electrophilic substitution reactionand sulfonic acid groups are incorporated to the aromaticrings. The degree of sulfonation, and hence the exchangecapacity, is an important feature of cation exchange resinsbecause in exchange and catalytic operations [21–23] theirperformance depends on this parameter. Cation exchangecapacities, which are usually measured [1] through H+/Na+ exchange, depend only slightly on the degree ofcross-linking of the polymer. Thus, in the case of polysty-rene, a mono-sulfonation of each benzene ring in the poly-mer results in a exchange capacity of about 5.4 meq/(g dryresin in the H+ form), whereas, for poly(ST-co-DVB) resins

with 50%, w/w, cross-linking, the exchange capacity shoulddecrease to approximately 4.7 meq/g owing to the increasein the molecular weight of the polymeric structural unit.However, in practice, reported experimental cation ex-change capacities vary widely and are usually in the1–5.4 meq/g range, gel-type resins showing the highestvalues [22–25], while most macroporous resins have lowervalues. Depending on the conditions of the sulfonationreaction, such as temperature, the degree of cross-linking,the reaction time and the size of the beads, different ex-change capacities can be achieved [26–31]. Nevertheless,the differences between gel and macroporous resins inthe values of this feature cannot always be explained interms of the above different conditions of the sulfonationreaction and neither do they seem to be due to the differ-ent molecular weight of the polymeric structural unit inthe case of beads with different degrees of cross-linking.

Since a low capacity is usually assumed to be due to aincomplete sulfonation of the benzene rings caused by hin-dered diffusion of the sulfonation agent into the beads, sev-eral studies [22–24,29–31] have attempted to search for arelationship between the cation exchange capacity of theresins, or their catalytic activity, and some of the factors re-lated to their manufacturing process. From the results ofthose works it may be deduced that the degree of cross-linking, the porosity, and the type of DVB isomers do havesome type of influence on the resulting exchange capacityof cation exchange resins. Despite this, although the useful-ness of these kinds of materials in principle depends ontheir cation exchange capacity, there is lack of quantitativestudies addressing the real effects of such factors.

In light of the above, here we were prompted to seekquantitative information aimed at facilitating the designof processes for the synthesis of resins with predeterminedproperties. Thus, in this work we report the results of thesynthesis of a set of polymeric beads made with very dif-ferent structural characteristics, together with the resultsconcerning their degree of sulfonation. In particular, theobjectives of this research were (a) to determine the fac-tors, or variables, involved in the process of synthesis ofthe polymeric matrix that have a significant effect on thefinal cation exchange capacity of the resins, and (b) to find

C.A. Toro et al. / Reactive & Functional Polymers 68 (2008) 1325–1336 1327

a quantitative interrelationship between those significantfactors and the final cation exchange capacity of the resinssynthesized. Then, the first step in this work was the syn-thesis of poly(ST-co-DVB) beads, with different porousstructures, by changing the proportions of cross-linkingagent (%DVB) and of the volume fraction of monomers inthe organic phase (Fm) of the polymerization mixture. Ina second step the polymeric beads were transformed intocation exchange resins by means of hot sulphuric acidtreatment. The degree of sulfonation was evaluated bymeasuring the ion exchange capacity (q) of each type of re-sin. The design of experiments (DOE) methodology wasused to study the effects of %DVB and Fm on q, and someinterrelationships have been obtained through the analysisof the results by multiple linear regression.

2. Experimental

2.1. Materials

2.1.1. Synthesis of polymeric beadsThe monomers to be polymerized were styrene (ST,

99%) and two types of commercial DVB (DVB, containing55% and 80% DVB isomers respectively, the remainderbeing 3- and 4-ethylvinylbenzene), all of which were sup-plied by Aldrich (Madrid, Spain). The initiator, benzoyl per-oxide (BPO, 70%, remainder water) was supplied by Aldrich(Madrid, Spain) and was used as received. The inert diluent(porogen) was n-heptane (HEP, synthesis grade), obtainedfrom Panreac (Barcelona, Spain), and the suspension agentwas poly(vinyl alcohol) (PVA, with a weight-average molarmass of 88,000 and a degree of hydrolysis of 88%) from Ac-ros Organics (Geel, Belgium). Both were used without fur-ther purification. Deionised water was employed toprepare the aqueous solutions.

2.1.2. Sulfonation of the beadsThe poly(ST-co-DVB) beads were swollen in dichloro-

methane (DCM) and sulfonated with concentrated (95–98%) sulphuric acid, supplied by Scharlau (Barcelona,Spain). Silver sulfate, used as catalyst, was supplied by Pan-reac (Barcelona, Spain), and was used as received.

2.2. Synthesis of polymeric beads procedure

Macroporous poly(ST-co-DVB) beads were prepared bythe suspension polymerization technique, using HEP as theporogen. BPO was used as the initiator, and the suspensionagent was PVA. Prior to polymerization, ST and DVB werefirst washed with a 10% aqueous NaOH solution to removethe inhibitor (p-tert-butylcatechol) and then with deion-ized water until neutralization was achieved. The reactionwas performed in a 500-mL three-necked round-bottomedjacketed glass reactor fitted with a mechanical stirrer, acondenser, and a thermometer. To obtain different struc-tural characteristics, the beads were synthesized from or-ganic mixtures with the DVB and porogen proportionsshown in Table 1. The details of the polymerization proce-dure have been reported previously [13]. Most of micro-particles obtained had a size between 150 and 200 lm.

2.3. Polymeric bead sulfonation procedure

The transformation of the macroporous polymericbeads into strong cation exchange resins through their sul-fonation was accomplished following the usual procedurefor the sulfonation [1,14–20] of polystyrene beads: the pre-cursor macroporous poly(ST-co-DVB) beads were function-alized to convert them into cation exchange resin in 250-mL, three-necked, round-bottomed glass reactorsequipped with mechanical stirrers, reflux condensers, andthermometers. The reactors were loaded with 100 mL ofsulphuric acid (95–98%) and heated to 75 �C in a polyethyl-ene glycol bath. Then, 0.02 g of silver sulfate, as a catalystfor the sulfonation reaction, was added to the reactorsand the mixture was stirred to dissolve the solids. Follow-ing this, a sample of macroporous beads (about 1 g), previ-ously swollen in DCM (30 ml) for 4 h at room temperature,was slowly added to the reactor. Since sulfonation pro-gresses with time, the mixture was kept at 75 �C for suffi-cient time for a steady value of the cation exchangecapacity to be reached. After the reaction time, the mixturewas sequentially: (a) poured into a beaker placed in afreezing water bath to quench the reaction; (b) dilutedslowly, by drop-wise addition of deionised water with aperistaltic pump; (c) vacuum-filtered in a Büchner funnelto recover the solid products, which were washed withdeionised water to completely remove any possible resid-ual acid. Finally, the resins were vacuum-dried at 40 �Covernight. To achieve the maximum degree of sulfonationunder the operation conditions, for each type of micropar-ticle sulfonation experiments were performed at differentreaction times and the cation exchange capacity was mea-sured; that is, the sulfonation kinetics were determined.

2.4. Resin characterization

The morphology and topography of the resins beforeand after the sulfonation process were studied by scanningelectron microscopy (Zeiss DSM 940 scanning electronmicroscope (SEM)). The presence of sulfonic groups onthe polymer surface was also checked by X-ray energy dis-persive (EDX) analysis.

The quantitative extent of the sulfonation reaction wasevaluated by measurement of the ion exchange capacity ofeach resin, using the standard procedure for polystyrenecation exchange resins [1,20], summarized as follows.The sulfonated particles were first treated with an excessamount of 1 N HNO3 to ensure complete loading of the res-ins in the H+ form. The material was then washed thor-oughly with deionized water to eliminate the excess ofnitric acid. Then, a known amount of wet particles wasplaced in a 250 mL Erlenmeyer flask containing an excessvolume of a 0.1 N NaOH solution, and this was allowedto stand overnight. Of the supernatant solution, 25 mLwas back-titrated with a 0.1 N H2SO4 solution, using phe-nolphthalein as indicator, and the exchange capacity (q,meq/g dry resin) was determined from a mass balance. Ineach case, the titrations were repeated three times. Thedry-weight fraction of the wet resins was determined fromthe weight loss of the resin samples at 110 �C for 15 h in anoven.

Table 1Experimental design: factor levels, values of the response, and effects

Experimentnumber

Factors and interaction Response, qm

(meq/ g dry resin)SBET

a

(m2 g�1)%DVB Fm %DVB � Fm

Real values Coded values Real values Coded values Coded values

E1 25 �1 0.5 �1 1 3.56 100.0E2 55 1 0.5 �1 �1 2.38 430.8E3 25 �1 0.7 1 �1 3.48 50.3E4 55 1 0.7 1 1 2.22 342.2E5 25 �1 0.5 �1 1 3.62 106.9E6 55 1 0.5 �1 �1 2.41 426.2E7 25 �1 0.7 1 �1 3.35 53.4E8 55 1 0.7 1 1 2.50 338.6E9 40 0 0.6 0 0 2.64 304.8E10 40 0 0.6 0 0 2.73 292.0

Effects on q �1.125 �0.105 0.070

a Experimental SBET values from García-Diego and Cuellar [13].

1328 C.A. Toro et al. / Reactive & Functional Polymers 68 (2008) 1325–1336

2.5. Design and analysis of experiments

The preparation of cation exchange resins requires thesynthesis of polymeric matrices followed by their function-alization via sulfonation. Since the synthesis conditions(factors) seem to exert a relevant effect on the final cationexchange capacity of the resins (response), here the designof experiments methodology [32,33] was chosen as a firsttool for the development of this work because of its useful-ness in the determination of the existence of cause–effectrelationships. To apply this methodology, a sequence ofsteps must be followed.

2.5.1. Problem identificationDifferent potential applications of cation exchange res-

ins require the use of resins with appropriate structuraland functional characteristics, the cation exchange capac-ity being a very important property because of its influencein operations involving separations and/or catalysis. In thissense, macroporous cation exchange resins usually have alow cation exchange capacity in comparison with gel-typeresins, but few studies have been undertaken to elucidatethe cause(s) of this. Accordingly, since the control of thisfeature is important, the aim of the present investigationis to contribute to the understanding of the interrelation-ships between the factors involved in the processes ofmanufacture of these resins and their final cation exchangecapacity, by determining which of the factors, or variables,brought into play in the manufacture of these resins havethe most relevant effects on the final cation exchangecapacity, and also, by quantifying such effects.

2.5.2. Factor identificationSince in the manufacture of cation exchange resins

there are two clear steps (synthesis of the polymeric ma-trix and sulfonation), the variables (factors) involved ineach step can affect the final results. While the effects oftemperature, the reaction time and bead size in the sulfo-nation step can be readily understood, it is in the first stepwhen the structural characteristics of the beads aredecided, and these structural characteristics appear to af-fect the final ion exchange capacities in a way hithertonot fully explained.

Research carried out up to date to determine the influ-ence of the synthesis conditions on the structural charac-teristics of the polymeric matrices has indicated that themain factors with a significant influence are the type andproportion of porogen and the proportion of cross-linkingagent [13,34]. Factors such the polymerization tempera-ture and the type and proportion of catalyst have lesseffect.

Thus, to obtain beads with different structural charac-teristics, the weight percentage of DVB isomers in themonomeric mixture (%DVB, w/w) and the volume fractionof the monomers in the organic phase, or monomeric frac-tion, (Fm, v/v), were considered as the factors that shouldbe varied in order to study their effects on the final cationexchange capacity.

2.5.3. Level identificationAt this stage, it is necessary to select the values (levels)

of the factors at which the experiments are to be run. Sinceseveral earlier works [8–13] have identified the range ofvalues of the %DVB and Fm that would permit the synthesisof macroporous beads, the levels for the DVB concentrationand monomeric fraction were chosen within that range.Thus, the values of %DVB selected were 55% and 25% forthe high and low levels, respectively. Regarding the mono-meric fraction, Fm, the values were 0.7 and 0.5 for the highand low level respectively. In principle, it was consideredthat these ranges of values were sufficiently wide to unveilthe influence of the structural characteristics in the finalcation exchange capacity of the resins.

The research was initially planned as a bifactorial de-sign, with only four experiments (experiments E1–E4 inTable 1). These first four experiments were then replicated(experiments E5–E8) in order to obtain an estimate of theexperimental error and a more precise estimate of the ef-fects of the factors on the response. Additionally, two cen-tre points were also included in the design (experimentsE9 and E10 in Table 1) with a view to checking whetherthere was curvature in the effects. The results of this setof experiments indicated the appropriateness of carryingout additional experiments. The operation conditions of anew set of experiments (experiments E11–E22) are givenin Table 2.

Table 2Additional experiments: factor levels and response values

Experimentnumber

Factors Response, qm

(meq/ g dry resin)SBET

(m2 g�1)%DVB Fm

Real values Coded values Real values Coded values

E11 25 �1 0.6 0 3.71 102.0E12 25 �1 0.6 0 3.62 108.6E13 30 �2/3 0.6 0 3.20 138.4a

E14 30 �2/3 0.6 0 3.30 142.7a

E15 40 0 0.5 �1 2.74 363.3E16 40 0 0.5 �1 2.81 357.4E17 55 1 0.6 0 2.38 439.0a

E18 55 1 0.6 0 2.40 434.8a

E19 60 4/3 0.5 �1 2.10 ndb

E20 60 4/3 0.5 �1 2.04 ndb

E21 80 8/3 0.6 �1 1.78 524.1a

E22 80 8/3 0.6 �1 1.85 492.1

a Experimental SBET values from García-Diego and Cuellar [13].b Not determined.

C.A. Toro et al. / Reactive & Functional Polymers 68 (2008) 1325–1336 1329

2.5.4. Response identificationAs indicated above, the usefulness of resins in exchange

and catalytic processes often depends on their degree ofsulfonation, which is usually expressed in terms of theircation exchange capacity. Accordingly, this parameterwas chosen as the response to be studied, the objectiveof this being to study the relationships between thisparameter and the operating conditions during beadsynthesis with a view to contributing to the design of pro-cesses aimed at the synthesis of resins with predeterminedproperties.

3. Results and discussion

3.1. SEM and EDX analyses

The morphology and topography of the resins were in-spected by SEM. The spherical morphology and smoothtopography of the macroporous beads can be seen in theSEM micrographs shown in Fig. 1.

Complete sulfonation of the inner part of the beads maybe affected by problems of diffusion if the reaction time isnot long enough. In our experiments to check whether thesulfonation had reached the centre of the beads, some ofthem were fractured and examined by dispersive X-rayanalysis (EDX). A SEM micrograph of a halved cation ex-change bead is shown in Fig. 2a, while Fig. 2b shows thesame particle analyzed by EDX, depicting the homoge-neous distribution of the points with sulphur. Finally,Fig. 2c shows the EDX spectrum.

The results for the rest of the beads also indicated thatthe sulfonation had reached the centre of the beads.

3.2. Cation exchange capacity

Regarding the effect of the factors on the response, inorder to facilitate the interpretation of the quantitative re-sults, the levels of the factors were coded, assigning a valueof �1 to the low level and a value of +1 to the high level ofthe range studied for each factor, by means of the codingequation:

xj ¼nj � nj;center

nj;max � nj;centerð1Þ

where xj are the coded values, and nj, nj,center and nj,max arethe real, the centre real, and the maximum real values ofthe range studied for the j factor, respectively.

The values of the plateau in the sulfonation kineticcurves (Fig. 3) were taken as the maximum cation ex-change capacity, qm, for each type of resin and these values,for all experimental runs carried out, are listed in Tables 1and 2. The tables also show the values of the specific sur-face area, SBET, for each type of bead.

3.3. Effects of synthesis variables on the cation exchangecapacity

From the values of the responses for the first set ofexperiments (experiments E1–E10) given in Table 1, the ef-fects of the factors and their interaction on the cation ex-change capacity were calculated using the Yatesalgorithm [33]. These values are given in the last row of Ta-ble 1, showing that the %DVB factor has the most impor-tant effect, followed in importance by the Fm factor, andfinally by the %DVB � Fm interaction. The variations inthe response value, when the factors change from thelow level to high level, are shown in Fig. 4. The factor hav-ing the straight line with the highest slope is the one withthe greatest effect, while the line with the lowest slope cor-responds to the factor with the smallest effect. Thus, the ef-fect of %DVB is the most important and is negative; that is,the highest value of the response occurs at the lowest level(25% DVB) of the factor.

This behaviour is also a common experimental findingin the case of gel-type beads, and is usually explained asbeing due to the difficulty encountered by the sulfonationagent to penetrate into very cross-linked polymericstructures.

After the effects had been calculated, an analysis of var-iance (ANOVA) was applied to the experimental results ofqm (experiments 1–10) with a view to establishing the sta-tistical significance of the influence of the factors, and the

Fig. 1. SEM micrographs of the macroporous beads from experiment 1 (E1): (a) shape, (b) roughness of the surface and (c) detail of external surface.

1330 C.A. Toro et al. / Reactive & Functional Polymers 68 (2008) 1325–1336

existence of curvature in the effects. The results of the AN-OVA, shown in the Table 3, give the values of the F statis-tics and their corresponding p-values for each source ofvariation studied (factors, interaction, and curvature).

From the values calculated for the F statistics, it may beconcluded that within the range investigated the %DVB isthe only factor that has a significant effect on the response.Moreover, this influence is not linear because the value ofthe F statistics for the curvature is higher than the tabu-lated value (F0.05,1,5 = 6.61), where 0.05 is the level of sig-nificance; 1 is the degree of freedom of this source ofvariation, and 5 is the degrees of freedom of the error.

Having found from this first set of experiments thatonly the %DVB factor had a significant effect on the re-sponse, its influence being non-linear, it was decided toperform a new group of experiments with the aim of veri-fying the non-significance of the effect of the Fm factor andalso of obtaining an empirical model capable of predictingthe values of the response for a broader range of values ofthe factors with greater accuracy.

In this new set of experiments, the value of Fm = 0.7was not used because the microparticles synthesized withthis small proportion of porogen were sometimes found tobe partially agglomerated. Regarding the %DVD factor, itsrange of values was expanded, this time covering from25% to 80% DVB. The new values of both factors are givenin Table 2, and this table also shows the values of the re-sponse. A graphic plot of the values of the factors in allthe experiments performed in this work is given in Fig. 5.

3.4. Correlation between maximum cation exchange capacity,qm, and synthesis variables

In this new step, a multiple linear regression analysis[33,35] was applied to all the values of qm, shown in Tables1 and 2, to search for a response surface model able to pre-dict the maximum cation exchange capacity of the resinsas a function of the values of the %DVB and Fm used intheir synthesis, within the range of our experimentalconditions.

Fig. 2. Inner structure of the cation exchange resins synthesized from the macroporous poly(ST-co-DVB) beads obtained in experiment 2 (E2): (a) SEMmicrograph of a halved bead, (b) EDX analysis of the same bead, and (c) EDX spectrum.

Fig. 3. Variation of the cation exchange capacity, q, with the reaction timefor experiments E11(s), E18 (h) and E21 (e).

Fig. 4. Plot of the effects of each factor on the qm response.

C.A. Toro et al. / Reactive & Functional Polymers 68 (2008) 1325–1336 1331

Taking into account that the curvature was found to besignificant, in a first attempt a model including quadraticterms was fitted to the data.

q̂m¼2:83�0:609x%DVB�0:0226xFmþ0:0522x%DVBxFm

þ0:099x2%DVB�0:0123x2

Fm

R2¼0:973; R2adj¼0:965 ð2Þ

Table 3ANOVA applied to the analysis of the effects

Source of variation Sum of squares Degrees of freedom Mean of squares F p-value

%DVB 2.5313 1 2.5313 234.59 0.00Fm 0.0220 1 0.0220 2.04 0.21%DVB � Fm 0.0098 1 0.0098 0.91 0.38Curvature 0.1040 1 0.1040 9.64 0.02Error 0.0539 5 0.0108 – –

Total 2.7211 9 – – –

Fig. 5. Factors and levels used in the experiments carried out in the (s)first and (h) second set of experiments. The coded values in this figurecorrespond to those used in the multiple linear regression analysis.

1332 C.A. Toro et al. / Reactive & Functional Polymers 68 (2008) 1325–1336

In Eq. (2), q̂m denotes the predicted value of the cationexchange capacity and the terms x%DVB, xFm and x%DVBxFm

represent the coded values of %DVB, Fm, and their interac-tion, respectively. Likewise, x2

%DVB and x2Fm are the coded

quadratic terms that provide the curvature to the model.The value of the coefficient of multiple determination, R2

of this model is close to 1, indicating that the regressionmodel fits the experimental data well. However, the ad-justed coefficient of multiple determination, R2

adj, suggeststhat non-significant terms could have been included inthe model, because their value is insufficiently close to R2.

To determine the significance of the regression, ANOVAwas applied to the model and the results are summarizedin Table 4. The p-value for the F statistic of the regressionis close to zero, indicating that at least one of the fiveregressor variables contributes significantly to this qua-dratic model.

However, the test for the lack of fit is significant, mean-ing that this quadratic model is not adequate to explain theexperimental data because the F statistic calculated ex-ceeds the tabulated value (F0.05,5,11 = 3.20) where 0.05 isthe level of significance; 5 represents the degrees of free-dom of this source of variation, and 11 refers to the degreesof freedom of the pure error.

In light of the above, a test of the significance of theindividual regression coefficients was performed. The val-

ues of the t statistic and the corresponding p-values areshown in Table 5.

The regression coefficients are statistically significant,with a level of significance of 0.05 if the absolute valuesof their t statistics are higher than t0.025,16 = 2.47, where0.025 is the half-value of the level of significance and 16represents the degrees of freedom of the residual error.Therefore, since the t statistics for the regression coeffi-cients of Fm, %DVB � Fm and Fm2 are smaller than 2.47,the regressor variables xFm, x%DVBxFm, and x2

Fm can be elim-inated from Eq. (2). After these regressor variables hadbeen eliminated, the experimental data were subjectedagain to multiple linear regression analysis and the follow-ing simplified quadratic model was obtained:

q̂m ¼ 2:807� 0:628x%DVB þ 0:099x2%DVB

R2 ¼ 0:975; R2adj ¼ 0:972

ð3Þ

The value of R2 is close to 1, indicating that the regres-sion model fits the experimental data well. Moreover, inthis case, R2

adj is close to R2, meaning that non-significantterms had not been included in the model. Also, to deter-mine the significance of the regression, ANOVA was ap-plied to the model; the results are summarized in Table 6.

The p-value for the F statistic of the regression isclose to zero, indicating that at least one of the two regres-sor variables contributes significantly to this quadraticmodel. Regarding the test for the lack of fit, since the Fstatistic calculated does not exceed the tabulated value(F0.05,3,15 = 3.28) it can be affirmed that the model givenby Eq. (3) fits the experimental data well and that it canbe used to predict qm at any value of the %DVB factor with-in the range studied. The significance of the individualregression coefficients was also checked and all of themwere found to be statistically significant.

The final model, represented by Eq. (3), again indicatesthat the influence of the %DVB factor on cation exchangecapacities is non-linear and negative; that is, an increasein the proportion of DVB in synthesis process leads to a de-crease in the cation exchange capacity of the final resins.

As mentioned in Section 1 of this work, this effect hasbeen observed in earlier studies [22–24,31]. Poinescuet al. [31] described the synthesis of cation exchange resinsby sulfonation of poly(ST-co-DVB) beads with SO3 andstudied the influence on the cation exchange capacity ofseveral reaction parameter (proportion of SO3, degree ofcross-linking of the beads in the range from 1% to 18%,and the time and temperature of sulfonation) and foundthat the higher the %DVB in the beads, the lower the cationexchange capacity of the resins obtained. Also, the studies

Table 4ANOVA applied to the first quadratic model

Source of variation Sum of squares Degrees of freedom Mean of squares F p-value

Regression 7.8202 5 1.5640 117.21 0.000Residual error 0.2135 16 0.0133 – –Lack of fit 0.1436 5 0.0287 4.52 0.017Pure error 0.0699 11 0.0064 – –

Total 8.0337 21 – – –

Table 5Statistical significance of the regression coefficients of the quadratic modelgiven by Eq. (2)

Predictor t p-value

Constant 60.42 0.000%DVB �19.71 0.000Fm �0.62 0.541%DVB � Fm 1.46 0.164%DVB2 4.68 0.000Fm2 �0.23 0.819

t0.025,16 = 2.47.

Table 6ANOVA applied to the best quadratic model

Source ofvariation

Sum ofsquares

Degrees offreedom

Mean ofsquares

F p-value

Regression 7.7595 2 3.8798 347.57 0.000Residual error 0.2009 18 0.0112 – –Lack of fit 0.0725 3 0.0242 2.82 0.075Pure error 0.1285 15 0.0086 – –

Total 7.9604 20 – – –

C.A. Toro et al. / Reactive & Functional Polymers 68 (2008) 1325–1336 1333

of Ahmed et al. [24] indicate that the cation exchangecapacity of poly(ST-co-DVB) resins decreases when thebeads are manufactured with high proportions of DVB.They also found that the exchange capacity depends onthe porosity of the beads, a maximum being reached whenporosity is in the 0.3–0.4 ml/g range, owing to the fasterdiffusion of the sulfonating agents through the intercon-nected permanent pores in the beads. With a similar endin mind, Coutinho et al. [22,23] synthesized poly(ST-co-DVB) cation exchange resins and studied the influence ofcertain copolymer synthesis parameters in their exchangecapacity and in their catalytic activities. After studyingthe behaviour of the resins, with different degrees ofcross-linking and different types and proportions of poro-gen agent, those authors found that the resins with thehighest swelling in water (that is, resins with the lowestdegree of cross-linking) also showed the highest cation ex-change capacity. They explained this assuming that in thecase of the most cross-linked structures there was hin-dered access (during measurement of the exchange capac-ity) of the water solution to the sulfonic groups.Conversely, the resins with the highest proportion of DVBexhibited the highest catalytic activity, which was ex-plained as being due to the more porous structure of theresins made with a high proportion of DVB, thus permit-ting easier access of the reaction mixture to the active sites.However, in those works [22,23] the authors failed to men-

tion the degree of sulfonation of the beads; they only stud-ied the exchange capacity, measured by the exchange H+/Na+, and attempted to explain their findings in terms ofthe hindered penetration of the ions into highly cross-linked polymeric structures. The work of Struck and Wid-decke [36] also explored the sulfonation of macroporouspoly(ST-co-DVB) beads. In this case, the aim was sulfona-tion of only the surface of the beads. The results wereexplained in terms of the inhomogeneity of the cross-link-ing density; cross-linking density varies within the micro-particles, being high at the centre and very low at thesurface. The inhomogeneities were found to depend onthe synthesis parameters; in particular on the proportionof DVB in the copolymer. According to that work, the beadsreally consist of nanoparticles fused together to formagglomerates with spaces between them, forming a porousnetwork, which affords access of the sulfonation mixtureto the centre of the beads. Thus, the sulfonation occurs firston the surface of the nanoparticles located on the outer-most part of the beads and progresses down the pores intothe centre of the beads at a rate that depends on the size ofthe pores. Once sulfonation of the external surface of thenanoparticles has been completed, the sulfonation pro-gresses towards their interior with the reaction time. How-ever, in that work no study about the influence of thedegree of cross-linking was reported.

From these results, it may in principle be concludedthat the %DVB has a negative influence on the cation ex-change capacity, although such influence appears to bemodulated by the porosity of the particles. The influenceof the %DVB has been suggested to be due to the hinderedpenetration of the sulfonation mixture into the highlycross-linked gel-type nanoparticles comprising the macro-porous beads. However, although the experimental sulfo-nation conditions were given in those works, nothing ismentioned of studies aimed at determining the minimumreaction time necessary to attain beads with the maximumcation exchange capacity at the reaction temperature em-ployed. Nevertheless, taking into account that an insuffi-cient time of sulfonation affords beads with a capacitylower than the maximum at the reaction temperature, itis possible that the above conclusions are not correct.

Accordingly, in order to establish reliable quantitativecause-effect relationships we first determined the sulfona-tion kinetics of all of the particles studied in this work;some of them are shown in Fig. 3. As can be observed,the shape of the curves varies depending on the %DVB,but in each case a flat plateau (maximum cation exchangecapacity, qm) can be attained. Additionally, the existence ofa flat plateau in the kinetic curves indicates that there is noformation of sulfones with time.

1334 C.A. Toro et al. / Reactive & Functional Polymers 68 (2008) 1325–1336

3.5. Relationship between SBET and the cation exchangecapacity

Since macroporous resins are highly cross-linked, andsince there is a porous network that (as suggested in someof the works cited above) is used by the sulfonation agentto penetrate into the interior of the beads, it could bethought that, owing to the difficult penetration of the sul-fonation agent into highly cross-linked structures, sulfona-tion would occur only on the surface of the nanoparticlesforming the beads. Whether this is the case, the degreeof sulfonation should be proportional to the specific sur-face area (SBET) of the precursor beads (last column in Ta-bles 1 and 2). To check this, the values of the maximumcation exchange capacity were plotted vs. the SBET of eachtype of bead. As seen in Fig. 6, the higher the SBET, the lowerthe exchange capacity, indicating that not only sulfonationof the surface of the nanoparticles occurs, but that sulfona-tion also reaches their interior.

Having determined that sulfonation was not merely asurface process; a second conjecture was that the degreeof penetration of the sulfonation into the nanoparticlesmight be a function of the degree of cross-linking of eachof them. This could be possible if it is assumed that theDVB monomers polymerize first, because they are morereactive than the styrene monomers. In this case, the coreof the nanoparticles would be formed by highly cross-linked DVB and the outer region of the nanoparticleswould be made of polystyrene, with only a small degreeof cross-linking, which could be easily sulfonated. If thisis so, the higher the %DVB, the lower the cation exchangecapacity would be. However, such an explanation cannotbe considered adequate because in fact it is possible to ob-tain ion exchange resins from polymeric beads made with100% DVB. Although in this latter case it could still be pos-ited that the nucleus of the DVB nanoparticles would bemore densely cross-linked that their periphery, someauthors, working with gel-type resins [29,30,37], haveattributed the differences in cation exchange capacities to

Fig. 6. Values of qm vs. the SBET of the precursor polymeric beads.

the presence of DVB isomers in the polymerization mix-ture, and this was the hypothesis explored here.

3.6. Correlation between the proportion of isomers and qm

Commercially available DVB is a mixture of m-divinyl-benzene (m-DVB) and p-divinylbenzene (p-DVB), togetherwith a substantial amount of m-ethylvinylbenzene (m-EVB) and p-ethylvinylbenzene (p-EVB). Table 7 shows thecompositions of the commercial 55% DVB and 80% DVBused in the present investigation.

Some previous works [29,30] have addressed the sulfo-nation of gel-type beads made with styrene and with pureDVB isomers, in which the effect of m-DVB and p-DVB iso-mers on the kinetics of the polymerization and sulfonationwas studied. In contrast, other authors [38] have only stud-ied the polymerization kinetics of pure DVB isomers. Thus,Wiley and Venkatachalam [29,30] synthesized gel-typecation exchange resins from polystyrene cross-linked (2%,4% and 8% w/w) with pure m-DVB and pure p-DVB, observ-ing that the beads made with styrene and p-DVB were sul-fonated (at 100 �C) faster, and at higher levels, than thosemade with the meta-isomer. They concluded that takinginto account the differences in the reactivity ratio valuesin the copolymerization of styrene with each isomericDVB, the overall effect appears to be that the copolymeri-zation of styrene with p-DVB will result in a structure witha tightly cross-linked nucleus to which long chains ofpolystyrene are attached and in which much more purepolystyrene may be imbedded. In comparison, thepoly(ST-m-DVB) copolymer would be expected to have astructure in which the cross-links are more widely distrib-uted than in the poly(ST-p-DVB) copolymer, and presum-ably, less pure polystyrene is formed in the last stages ofthe polymerization. Later [37], the same authors reportedthat sulfonation kinetics depends on the swelling agentused, because the swelling agent retained in the beadsprobably renders the reaction sites more or less inaccessi-ble to the sulfonating agent. They found that, when thebeads were swollen in dimethyl sulfoxide or in ethylenedichloride, the para-cross-linked copolymer was sulfo-nated more rapidly. Nevertheless, since in those worksonly gel-type resins (with very low %DVB) were studied,the difference in the exchange capacities of resins madewith different isomers was very small.

Moreover, Nyhus et al. [38] carried out a study of thekinetics of the polymerization of pure m- and p-DVB andfound that m-DVB polymerized at higher rates thanp-DVB in the presence of toluene and 2-ethylhexanoic acid,the monomer conversion, at the visual gel point, beinghigher for p-DVB than for m-DVB.

These results indicate that the rate of polymerization ofeach isomer may change, depending on the solvent or

Table 7Isomeric composition in percentages of the two types of commercial DVBused in the experimentation

%DVB m-DVB p-DVB m-EVB p-EVB

55 37.52 14.82 37.86 9.8180 57.36 22.45 12.68 7.51

C.A. Toro et al. / Reactive & Functional Polymers 68 (2008) 1325–1336 1335

whether styrene is present in the polymerization mixture.In any case, it appears certain that if the rate of polymeri-zation of the isomers of DVB and EVB are different and thisdifference affords beads and nanoparticles with differentstructural characteristics, which in turn leads to differentcation exchange capacities, it should be possible to find arelationship between the proportion of each type of iso-mers in the polymerization mixture and the final degreeof sulfonation.

In this sense, taking into account the lack of completemono-sulfonation of the benzene rings, our startinghypothesis was that one or more of the isomers presentin the commercial DVB would polymerize in such a waythat their sulfonation could be incomplete. If this is thecase, by means of the statistical analysis of our results con-cerning cation exchange capacities it should be possible todetermine which of those isomers, at the reaction temper-ature, the sulfonation agent was unable to penetrate.

To perform the statistical analysis, as the dependentvariable we used the maximum exchange capacity of eachtype of bead, and as independent variables the molar frac-tions of the different isomers involved in the polymeriza-tion (Table 8). These were designated: XST, Xm-DVB, Xp-DVB,Xm-EVB and Xp-EVB. Following this, a multiple linear regres-sion was performed in search of a suitable correlationamong the values of qm and the molar fractions of all thecompounds. Since in this first attempt the result was notsatisfactory, the molar fractions of the compounds weregrouped in all possible combinations and, in each case, alinear regression analysis was performed. The best correla-tion found was as follows:

q̂m ¼ 3:45� 8:91Xp þ 2:36X2ST þ 2:12X2

m

R2 ¼ 0:990; R2adj ¼ 0:988

ð4Þ

where XP is the sum of the molar fractions of the para-iso-mers; Xm is the sum of the molar fractions of the meta-iso-mers, and XST is the molar fraction of styrene.

Table 8Molar fraction of the different isomers involved in the polymerization

Experiment XST Xm-DVB Xp-DVB Xm-EVB

E1 0.6015 0.1510 0.0596 0.1492E2 0.0000 0.3788 0.1496 0.3745E3 0.6015 0.1510 0.0596 0.1492E4 0.0000 0.3788 0.1496 0.3745E5 0.6015 0.1510 0.0596 0.1492E6 0.0000 0.3788 0.1496 0.3745E7 0.6015 0.1510 0.0596 0.1492E8 0.0000 0.3788 0.1496 0.3745E9 0.3205 0.2574 0.1017 0.2545E10 0.3205 0.2574 0.1017 0.2545E11 0.6015 0.1510 0.0596 0.1492E12 0.6015 0.1510 0.0596 0.1492E13 0.5118 0.1849 0.0731 0.1829E14 0.5118 0.1849 0.0731 0.1829E15 0.3205 0.2574 0.1017 0.2545E16 0.3205 0.2574 0.1017 0.2545E17 0.0000 0.3788 0.1496 0.3745E18 0.0000 0.3788 0.1496 0.3745E19 0.2943 0.4065 0.1591 0.0880E20 0.2943 0.4065 0.1591 0.0880E21 0.0000 0.5759 0.2254 0.1248E22 0.0000 0.5759 0.2254 0.1248

The value of the coefficient of multiple determination,R2, is close to 1, indicating a good fit of the regression mod-el to the data. The R2

adj coefficient is very close to R2, whichconfirms the absence of non-significant terms in themodel.

In this case, ANOVA was also applied to check the ade-quacy of the model. The results, shown in Table 9, indicatethat at least one of the variables contributes to the model.Also, the test for the lack of fit, with a p-value of >0.05 re-vealed that the model given by Eq. (4) was adequate for theprediction of the values of the response within the range(25–80% DVB) of variables studied.

The model represented by Eq (4) indicates that the sul-fonation of styrene and m-isomers occurs to a similar ex-tent while, in the case of the p-isomers, the negativevalue of the regression coefficient suggests that, at theoperation temperature used here, their sulfonation doesnot take place at all, or only does so to a slight extent.Moreover, this negative value denotes that the presenceof the p-isomers in the polymerization mixture to some ex-tent prevents the subsequent sulfonation of the styreneand of the m-isomers.

These results are consistent with the rules concerningthe effects of substituents on the regioselectivity of elec-trophilic aromatic substitution. In the case of meta-iso-mers, in the benzene rings there are two alkylsubstituents that are ortho and para directors, whosedirecting effects reinforce each other. Thus, sulfonation ofmeta-isomers should take place at reinforced positionswhich are ortho to one alkyl chain and para to another.The ortho position between the two alkyl chains is alsoactivated by the two substituents, but is less reactive be-cause it is more sterically hindered. Conversely, in the caseof the para-isomers there are no positions with accumu-lated activating.

Additionally, taking into account that the sulfonationagent is a polar compound and that the polymeric matrix

Xp-EVB Xm Xp q (meq/g dry resin)

0.0387 0.3002 0.0983 3.560.0970 0.7533 0.2466 2.380.0387 0.3002 0.0983 3.480.0970 0.7533 0.2466 2.220.0387 0.3002 0.0983 3.620.0970 0.7533 0.2466 2.410.0387 0.3002 0.0983 3.350.0970 0.7533 0.2466 2.500.0659 0.5119 0.1676 2.640.0659 0.5119 0.1676 2.730.0387 0.3002 0.0983 3.710.0387 0.3002 0.0983 3.620.0474 0.3678 0.1205 3.200.0474 0.3678 0.1205 3.300.0659 0.5119 0.1676 2.740.0659 0.5119 0.1676 2.810.0970 0.7533 0.2466 2.380.0970 0.7533 0.2466 2.400.0521 0.4945 0.2112 2.100.0521 0.4945 0.2112 2.040.0739 0.7007 0.2993 1.780.0739 0.7007 0.2993 1.85

Table 9ANOVA applied to the best correlation between the values of q and the molar fraction of isomers

Source of variation Sum of squares Degrees of freedom Mean of squares F p-value

Regression 6.2654 3 2.0885 475.83 0.000Residual error 0.0614 14 0.0044 – –Lack of fit 0.0006 1 0.0006 0.13 0.726Pure error 0.0608 13 0.0047 – –

Total 6.3269 17 – – –

1336 C.A. Toro et al. / Reactive & Functional Polymers 68 (2008) 1325–1336

is hydrophobic, penetration of the sulfonation agent intothe polymeric matrix requires – as an a priori condition –that the matrix must become polar through its sulfonation.Thus, if the sulfonation of para-isomers did not to takeplace, the structures formed with this isomer should beimpermeable to the sulfonation agent, which would notbe able to attack the meta-isomers or the styrene possiblyenclosed in structures surrounded by para-isomers either.This effect could explain the negative influence of thepara-isomers in the degree of sulfonation of the beads.

The model given by Eq. (4) permits the design of syn-thesis processes of cation exchange resins with a verybroad range of degrees of sulfonation, which may be veryuseful in certain processes. Thus, taking into account thatthe affinity of the resins for water depends on the degreeof sulphonation, in some catalytic processes such as esteri-fications, where one of the reaction products is water, itcould be convenient to use resins with a low degree of sul-fonation with a view to facilitating the desorption of water.

4. Conclusions

Under the operation conditions used here (75 �C), thequantitative model obtained indicates that the lack ofcompletely homogeneous sulfonation of poly(ST-co-DVB)beads seems to be due to a insufficient sulfonation ofthe p-DVB and p-EVB isomers involved in the polymeriza-tion mixture. These findings are consistent with thedirecting effects of the two alkyl substituents in the ben-zene rings, which in the case of the meta-isomers exert areinforcing effect on certain positions of the benzenerings that facilitates the sulfonation process at those posi-tions. In contrast, in the case of the para-isomers, thedirecting effect of each substituent occurs on differentpositions of the benzene rings and hence there wouldbe no positions with a reinforced effect. Apart from thelack of sulfonation of para-isomers, the observed negativeeffect of the %DVB on the values of q could be explained ifsome proportion of the styrene and meta-isomers wereenclosed during the polymerization into structures coatedwith non-sulfonated para-isomers. In these cases, sincethe para-isomers are non-polar the sulfonation agentwould be unable to penetrate into the interior and thestyrene and meta-isomers enclosed in these structureswould remain unsulfonated.

Acknowledgments

This work was supported financially by the Ministeriode Educación y Ciencia (MEC, Spain). Furthermore, the

authors thank Banco Santander Central Hispano for schol-arship granted at one of them.

References

[1] K. Dorfner, Synthetic Ion Exchange Resins, in: K. Dofner (Ed.), IonExchangers, Walter de Gruyter, Berlin, 1991, p. 328.

[2] F. Helferich, Ion exchange, McGraw Hill, New York, 1962.[3] A. Chakrabarti, M.M. Sharma, React. Polym. 20 (1993) 1.[4] G. Gelbard, Ind. Eng. Chem. Res. 44 (2005) 8468.[5] V.M.T.M. Silva, A.E. Rodriguez, Chem. Eng. Sci. 61 (2006) 316.[6] D.C. Sherrington, Catalysis by Ion-exchange Resins and Related

Materials, in: P. Hodge, D.C. Sherrington (Eds.), Polymer-SupportedReactions in Organic Synthesis, Wiley, Chichester, UK, 1980, p. 157.

[7] P. Hodge, Organic reactions using polymer-supported catalysts,reagents or substrates, in: P. Hodge, D.C. Sherrington (Eds.),Synthesis and Separation Using Functional Polymers, Wiley,Chichester, UK, 1988, p. 43.

[8] J.R. Millar, D.G. Smith, W.E. Marr, T.R.E. Kressman, J. Chem. Soc.(1963) 218.

[9] J.R. Millar, D.G. Smith, T.R.E. Kressman, J. Chem. Soc. (1965) 304.[10] K. Dusek, J. Seidl, J. Malinsky, Collect. Czech. Chem. Commun. 32

(1967) 2766.[11] K.A. Kun, R. Kunin, J. Polym. Sci. 6 (1968) 2689.[12] I.M. Abrams, J.R. Millar, React. Funct. Polym. 35 (1997) 7.[13] C. García-Diego, J. Cuellar, Ind. Eng. Chem. Res. 44 (2005) 8237.[14] N.E. Topp, K.W. Pepper, J. Chem. Soc. (1949) 3299.[15] D. Reichenberg, J. Am. Chem. Soc. 75 (1953) 589.[16] I.M. Abrams, Ind. Eng. Chem. 48 (1956) 1469.[17] F.P. Regas, Polymer 25 (1984) 249.[18] W.R. Carroll, H. Eisenberg, J. Polym. Sci. Polym. Phys. 4 (1966) 599.[19] F. Kucera, J. Jancar, Polym. Eng. Sci. 38 (1998) 783.[20] C. Martin, J. Cuellar, Ind. Eng. Chem. Res. 43 (2004) 475.[21] C.N. Rhodes, D.R. Brown, S. Plant, J.A. Dale, React. Funct. Polym. 40

(1999) 187.[22] F. Coutinho, R.R. Souza, A.S. Gomes, Eur. Polym. J. 40 (2004) 1525.[23] F. Coutinho, S.M. Rezende, B.G. Soares, J. Appl. Polym. Sci. 102 (2006)

3616.[24] M. Ahmed, M.A. Malik, S. Pervez, M. Raffiq, Eur. Polym. J. 40 (2004)

1609.[25] M.D. LeVan, G. Carta, C.M. Yon, Adsorption and Ion Exchange, Perry’s

Chemical Engineers’ Handbook, McGraw Hill, New York, 1999. p. 16.[26] James S. Fritz, James N. Story, J. Chromatogr. A 90 (1974) 267.[27] James S. Fritz, Philip J. Dumont, Luther W. Schmidt, J. Chromatogr. A

691 (1995) 133.[28] Thomas K. Chambers, James S. Fritz, J. Chromatogr. A 797 (1998)

139.[29] R.H. Wiley, T.K. Venkatachalam, J. Polym. Sci. Polym. Chem. 3 (1965)

1063.[30] R.H. Wiley, T.K. Venkatachalam, J. Polym. Sci. Polym. Chem. 4 (1966)

1892.[31] I. Poinescu, A. Carpov, M. Dima, Rev. Roum. Chim. 11 (1966) 573.[32] G.E.P. Box, W.G. Hunter, J.S. Hunter, Statistics for Experimenters: An

Introduction to Design, Data Analysis, and Model Building, Wiley,New York, 1978.

[33] D.C. Montgomery, Design and Analysis of Experiments, Wiley, NewYork, 2001.

[34] O. Okay, Prog. Polym. Sci. 25 (2000) 711.[35] N.R. Draper, H. Smith, Applied Regression Analysis, Wiley, New York,

1998.[36] M. Struck, H. Widdecke, Angew. Makromol. Chem. 235 (1996) 131.[37] R.H. Wiley, T.O. Ahn, Y. Kamath, J. Polym. Sci. Polym. Chem. 6 (1968)

1414.[38] A.K. Nyhus, S. Hagen, A. Berge, J. Polym. Sci. Polym. Chem. 37 (1999)

3345.