Quantitative effects of synthesis conditions on oil absorptive properties of oil gels based on...

Quantitative Effects of Synthesis Conditions on OilAbsorptive Properties of Oil Gels Based onEPDM/4-tert-Butylstyrene

Bo Wu,1,2 Mei H. Zhou2

1Department of Polymer Material and Engineering, Donghua University, State Key Laboratory for Modification ofChemical Fiber and Polymer Materials, Shanghai 201620, People’s Republic of China2College of Environmental Science and Engineering, Donghua University, Shanghai 201620, People’s Republic of China

Received 7 June 2007; accepted 12 November 2008DOI 10.1002/app.29674Published online 13 February 2009 in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: The oil absorption properties of porous poly-meric gels are dependent on their synthesis conditions. Inthis work, we have investigated whether it is feasible to finda quantitative relationship between the synthesis conditionsof porous poly(EDPM/4-tert-Butylstyrene) gels and theirbehavior in the kerosene absorption through a factorialdesign of experiments. For this purpose, a series of such oilgels have been synthesized in toluene with various divinyl-benzene (DVB) and EPDM contents. The kerosene absorb-ency and kerosene-absorption kinetics of oil gels weredetermined. Finally, empirical models correlating the synthe-

sis conditions with the kerosene absorbency (Qeq) and kero-sene-absorption kinetic constant (K) were calculated; it wasobserved that lower the DVB concentration and higher theEPDM fraction in the monomeric mixtures, the higher thekerosene absorbency. With regard to the kerosene-absorptionkinetics, the largest K value was achieved with the lowestDVB concentration and the highest EPDM fraction. VVC 2009Wiley Periodicals, Inc. J Appl Polym Sci 112: 2213–2220, 2009

Key words: oil gel; factorial design of experiment; oilabsorption; absorption kinetics; response surface

INTRODUCTION

The oil pollution of marine becomes more and moreserious because of the development of petroleumindustry and the marine oil transportation. One ofthe methods to solve this problem is using oil sorb-ents, such as silica gel,1 zeolites,2 active carbon,3 andnatural and synthetic polymers.4–10 Some of themhave proved to be highly efficient.

A critical step in the sorption processes is thechoice of the most suitable absorbent for a specificseparation problem. It is desirable that the absorbentshould have a high absorption capacity, fast oil-absorption rate, good absorption selectivity of oilover water, convenient shipping and storage, lowerdensity compared with water to float with or with-out oil absorbed, chemical stability.5 In this respect,polymeric absorbents have proved to be useful inthe absorption of oil or oil-like solvents and, in par-ticular, porous oil gels based on rubber have beenintensively researched to investigate the influence of

the synthesis conditions on the structural character-istics and oil absorbency, previously.6,7 However, tothe best of our knowledge, there are no works thathave reported the quantitative relationships betweenthe oil absorbency of oil gels and their synthesis con-ditions, nor have we found any information aboutresearch focused on the quantitative influence of thesynthesis conditions of oil gels on the absorptionkinetics, which would provide very valuable infor-mation for the design of oil gels.Taking this into account, in this work, a series of

porous oil gels based on EPDM/4-tert-butylstyrenewere synthesized with several divinylbenzene (DVB)and EPDM concentrations through a factorial designof experiments with the goal of finding quantitativerelationships between the oil absorptive propertiesof oil gels and DVB and EPDM concentration, whichfacilitates the synthesis of oil gels with predeter-mined absorption properties, and these quantitativerelationships should be considered as a reasonablestarting point in the choice of the most appropriateabsorbent for a specific absorption process.

EXPERIMENTAL

Materials

4-tert-Butylstyrene (tBS; Aldrich Chem, USA) andDVB (Fluka, USA) were each extracted with a 5%

Journal ofAppliedPolymerScience,Vol. 112, 2213–2220 (2009)VVC 2009 Wiley Periodicals, Inc.

Correspondence to: B. Wu ([email protected]).Contract grant sponsor: State Key Laboratory for

Modification of Chemical Fibers and Polymer Materials,Donghua University, Shanghai, China; contract grantnumber: 0601.

aqueous sodium hydroxide solution and water,dried over anhydrous sodium sulfate, and distilledunder reduced pressure before use. Benzoyl perox-ide (BPO; Aldrich Chem) was recrystallized from amethanol solution. EPDM, having ethylidene norbor-nene as a termonomer (Aldrich, ethylene/propylene¼ 50/50, Mn ¼ 50500, Mw ¼ 102000, Mooney Viscos-ity ¼ 85), and all other chemicals were used asreceived.

Polymerization

The EPDM/tBS copolymers were prepared in aque-ous suspension polymerization using toluene asdilution, mixing together with BPO initiator 1 wt %.The weight percentage of DVB concentration inmonomeric mixture and the monomeric fraction ofEPDM (Fm) in EPDM/tBS mixture were varied. Tohinder coalescence and break-up of droplets in thecourse of polymerization; gelatine, tricalcium phos-phate, and sodium dodecylsulfate (SDS) were usedas suspending agent at a certain ratio. The ratio oforganic phase to water phase was 1 : 5.

In a 250 mL four-necked reaction flask fitted witha variable mechanical stirrer, thermometer, nitrogengas inlet, and reflux condenser, the suspensioncopolymerization reaction was started at 40�C, and5�C was elevated every hour up to 80�C. Thecopolymerization and crosslinking reactions takingplace in the monomer-diluent droplets result in theformation of beads having a glassy, opaque, ormilky appearance, the resulting copolymer beadswere then filtered and washed with hydrochloricacid and hot water orderly, and then dried under avacuum at 60�C until to a constant weight. The dilu-ent, the residual monomers, and the uncrosslinkedcopolymers were removed by extracted with tetra-hydrofuran and n-hexane in a Soxhlet apparatus,finally they were dried under vacuum at 60�C untilthe weight was constant.

Oil-absorption test

Oil-absorptivities of oil gels were determined byASTM (F726–81)11: 0.1 g gel was put in a stainlesssteel mesh (4 � 4 � 2 cm3), and immersed in kero-sene. The swollen gels were taken out at regulartime intervals, wiped superficially with tissue papergently, weighed on a balance and replaced into thesame bath. This procedure of swelling and weighingwas continued until the sample achieved a constantfinal weight. The equilibrium oil absorbency ofcrosslinked polymer gel Qeq can be calculated

Qeq ¼ We �W0

W0(1)

where W0 is the initial weight of the sample and We

is the weight at equilibrium.

Design and analysis of experiments

To perform the research reported here, the design ofexperiments methodology was followed.12–15 Thisprocedure allows one to determine if interactionsbetween the factors occur and to obtain quantitativecause-effect relationships. Use of this methodologyrequires the following steps:

Problem identification

The aim of this work was to study the quantitativeeffect of the synthesis conditions (factors) on the oilabsorptive properties of the product obtained(responses). The advantage of knowing these rela-tionships is that it facilitates the synthesis of oil gelswith predetermined absorptive properties.

Factor identification

Previous experimental findings have revealed thatthe DVB concentration, the EPDM fraction, and thesolvating power of the porogen have a critical effecton the oil absorptive properties of gels. The effectsof the concentration and type of initiator and the po-lymerization temperature are less pronounced. Thiswork focused on the study of the effects of the DVBconcentration and EPDM fraction. Accordingly, theother reaction conditions remained the same in allexperimental runs carried out.

Level identification

In this stage, the range of values of the factors (lev-els) must be selected. In an earlier work, we identi-fied in a general manner the range of values of theDVB concentration and EPDM fraction that leads tothe production of porous oil gels. The values investi-gated by us were chosen within this range. Thehighest level for the DVB concentration was 15%.The research was initially planned as a two-facto-

rial design, with only four experiments, designatedDesign I. These first four experiments were thenreplicated (experiments 5–8) to obtain an estimate ofthe experimental error and a more precise estimateof the effects of the factors on the response. The realvalues of the levels investigated in Design I arethose corresponding to the points depicted with atriangle in Figure1. The design matrix of Design I isgiven in Table I, which also shows the order inwhich the experiments were performed. This runorder was determined in a randomized way becausethe statistical study of the results requires that theobservations be independently distributed random

2214 WU AND ZHOU

Journal of Applied Polymer Science DOI 10.1002/app

variables. To facilitate the interpretation of theresults, the real values of the levels were coded byassigning a value of �1 to the low level and a valueof þ1 to the high level of the range studied. Addi-tionally, since a potential concern in the use of two-level factorial designs is the assumption of linearityin the factor effects, two center points were alsoincluded in the design with a view to checkingwhether there was curvature. These center points,corresponding to experiments 9 and 10 of Design I,are also shown in Figure 1.

Since it was found that the oil gels obtained at thelow level of EPDM content were rigid, a new centraltwo-factorial design, designated Design II, wasplanned using higher levels for this factor. More-

over, a broader range of the DVB concentration wasconsidered in this new set of experiments to enlargethe studied region. Again, 10 experiments were per-formed in this design, corresponding to four experi-ments of the two-factorial design (experiments 11–14), another four experiments to replicate them(experiments 15–18), and two center points (experi-ments 19 and 20). The values of the levels investi-gated in Design II correspond to the points depictedas squares in Figure 1, and the design matrix isshown in Table II.

Response identification

Because the most important items used for evaluat-ing a absorbent are absorptive properties. Therefore,the oil absorbency and oil absorptive rate were cho-sen as responses. Both responses were correlatedwith the synthesis conditions through multiple linearregression analysis.

RESULTS AND DISCUSSION

Oil absorbency

Taking one gel sample from each pair of replicatesfor oil absorption test, the kerosene absorbency isshown in Figure 2. It is observed that the oil absorb-ency of the gel increases with the larger fraction ofEPDM, which can be explained that EPDM is macro-molecular and oleophilic soft monomer, whereas tBSis rigid monomer, and thereby addition of EPDMcontent in polymerization can reduce the oil gel’srigidity caused by phenyl group in tBS structure.The more EPDM content, the looser structure ofpolymeric gel, and more solvent can be held. Addi-tionally, the oil absorbency decreases with increasingDVB concentration. This is because an increase inthe amount of a chemical crosslinking agent causesthe formation of a denser network of the copolymer

Figure 1 Factor levels used in the experiments carriedout in Design I and Design II. The coded values in this fig-ure correspond to those used in the multiple linear regres-sion analysis, which are designated as the Global codedscheme. The shaded region indicates the application rangefor the correlations obtained.

TABLE IDesign Matrix and Values of Theresponses for Design I

Experiments

Factors and interaction

Responses%DVB Fm %DVBFm

No. Run order Real values Code values Real values Code values Code values Qeq (g g�1) K (min�1) R2

1 3 5.0 �1 0.4 �1 þ1 18.56 0.043 0.9732 4 15.0 þ1 0.4 �1 �1 7.37 0.030 0.9663 1 5.0 �1 0.6 þ1 �1 22.624 2 15.0 þ1 0.6 þ1 þ1 11.14 0.042 0.9835 6 5.0 �1 0.4 �1 þ1 18.106 7 15.0 þ1 0.4 �1 �1 7.707 5 5.0 �1 0.6 þ1 þ1 21.75 0.044 0.9758 8 15.0 þ1 0.6 þ1 þ1 10.489 9 10.0 0 0.5 0 0 15.36 0.042 0.98310 10 10.0 0 0.5 0 0 14.92Effects on Qeq �11.08 3.56 �0.29

EFFECTS OF SYNTHESIS CONDITIONS OF OIL GELS 2215


and reduces the chain length between crosslinks,which reduces oil absorbency.

Absorption kinetics

The oil-absorption kinetics of oil gels is shown inFigure 2, where Qt plotted versus time. Because allthe gels have different structural characteristics as aresult of their different synthesis conditions, thecurves of the absorption kinetics differ from somegels to others. More careful scrutiny of the curvesreveals that the rate of approach to equilibrium issmaller for the gels synthesized with the highestDVB concentrations. However, before attempting toestablish a quantitative inter-relationship betweenthe absorption kinetics and the synthesis conditionsfor all the gels, it is necessary to collect further infor-mation about the mass-transfer processes that partic-ipate in the global absorption process.

It is well known that the absorption of kerosenecan be described in terms of a three-step mechanism,which contains three steps16: (1) A short initial stageof a high absorption rate due to the solvation of thenetwork chains; the main driving force of this pro-cess is the change in the free energies of mixing andelastic deformation during expansion of the network;(2) a longer stage of a constant, slow absorption ratedue to the resistance of diffusion into the pores onaccount of the pore structure and dimensions; and(3) a third stage of a plateau value because ofabsorption saturation.

The first-order kinetics equation is commonlyused to describe the experimental absorption rate,which is directly proportional to the oil absorbencyat any given time before the maximum or equilib-rium absorption (Qmax) has been reached. If Qt is theoil absorbency at time t, (Qmax � Qt) is the unreal-ized absorption of oil medium. If K is the absorption

kinetic constant which is dependent on the synthesisconditions of gels, then17:

dQ

dt¼ KðQmax �QtÞ (2)

which integrates to:

lnQmax

Qmax �Qt¼ Kt (3)

From eq. (2), the relationship between Qmax and Qt

can be obtained:

Qt ¼ Qmaxð1� e�KtÞ (4)

The kinetic curves calculated from the eq. (4) areplotted in Figure 3, where they can be comparedwith the experimental kinetic data for each gel. Itmay be observed that most of the experimentalkinetic data are situated on the theoretical curves,indicating that the first-order absorption kinetics isable to describe the mass-transfer process adequatelythrough the gels.A rapid look at the values of K for each gels

allows us to corroborate in a quantitative way thepreliminary qualitative findings achieved frominspection of the location of the experimental kinetic

TABLE IIDesign Matrix and Values of the Responses for Design II

Experiments

Factors and interaction

Responses%DVB Fm %DVBFm

No. Run order Real values Code values Real values Code values Code values Qeq (g g�1) K (min�1) R2

11 11 3.0 �1 0.5 �1 þ1 18.76 0.048 0.97212 12 15.0 þ1 0.5 �1 �1 9.3213 15 3.0 �1 0.7 þ1 �1 19.63 0.051 0.96814 12 15.0 þ1 0.7 þ1 þ1 6.83 0.040 0.98315 17 3.0 �1 0.5 �1 þ1 17.5016 18 15.0 þ1 0.5 �1 �1 11.87 0.033 0.96817 13 3.0 �1 0.7 þ1 þ1 20.2518 14 15.0 þ1 0.7 þ1 þ1 6.1019 19 9.0 0 0.6 0 0 13.6220 20 9.0 0 0.6 0 0 12.77 0.043 0.978Effects on Qeq �10.51 �1.16 �2.97

Figure 2 Kerosene absorbency of gels in Design I (a) andDesign II (b).

2216 WU AND ZHOU


data in Figure 3: the gels synthesized with the high-est concentrations of DVB show the smallest rate ofapproach to equilibrium and, hence, have the lowestK values.

Factorial designs of experiments

After experiments 1–10 of Design I were performed,the oil absorption test was conducted. From the val-ues of this response for each type of gels, listed inTable I, the effect of the factors and interaction Qeq

was calculated. The values of the effects of both fac-tors and their interaction are reported in the last rowof Table I.

Within the range of values of the factors studiedin Design I, it was observed that the %DVB factor isthe key factor influencing the Qeq response nega-tively: an increase in the DVB concentration resultsin a considerable decrease in the Qeq response. The

effect of the Fm factor on the response is, by contrast,less important and is positive (i.e., the higher theEPDM fraction, the higher the Qeq). Regarding theinteraction of the factors, and considering its nega-tive effect on response, we can state that the higherthe %DVB, the lower the Qeq and that this effectbecomes more pronounced as the level of Fmdeclines.After the effects were calculated, an analysis of

variance (ANOVA) was applied to the experimentalQeq results to establish the statistical significance ofthe influence of the factors, their interaction, andcurvature. The results are shown in Table III.ANOVA gives the values of the F statistics and

their corresponding P values for each source of vari-ation studied (factors, interaction, and curvature).From the values calculated for the F statistics, it maybe concluded that both factors, except for their inter-action, have a significant effect on the Qeq responsewithin the range investigated and that this influenceis linear because the value of the F statistics for cur-vature is lower than the tabulated value, F0.05,1,5 ¼6.61, where 0.05 is the level of significance, 1 is thedegrees of freedom of these sources of variation, and5 is the degrees of freedom of the error. Further-more, the ANOVA indicates there is no evidence ofinteraction between the factors in the response overthe region of exploration.Likewise, in the second factorial design, Design II,

experiments 11–20 were run, and the Qeq responsewas calculated for the oil gels thus obtained. Fromthe values of this response, the effects of the factorsand interaction were determined; they are shown inthe last row of Table II. When the values of theeffects of the factors and interaction are scrutinized,it can be seen that the %DVB factor has the greatesteffect on the Qeq response within the range studied.This effect is negative and, therefore, the higher theDVB concentration, the lower the Qeq. Interestingly,the effect of the Fm factor on the response is also

Figure 3 Curves of the kerosene-absorption kinetics ofgels. The symbols represented experimental data, andsolid lines were calculated with the first-order kineticsequation [eq. (4)].

TABLE IIIANOVA Tables for Designs I and II

Design Source of variation Sum of squares Degree of freedom Mean square F P

I %DVB 245.75 1 245.75 1445.58 <0.001Fm 25.42 1 25.42 149.53 <0.001%DVBFm 0.17 1 0.17 1.00 0.366Curvature 0.29 1 0.48 2.82 0.250Residual error 0.85 5 0.17Total 272.48 9F0.05,1,5 ¼ 6.61

II %DVB 220.71 1 220.71 227.54 <0.001Fm 2.69 1 2.69 2.77 0.157%DVBFm 17.64 1 17.64 18.18 0.008Curvature 0.55 1 0.55 1.20 0.485Residual error 4.87 5 0.97Total 246.46 9F0.05,1,5 ¼ 6.61



negative. This means the optimized EPDM fractionis 0.6.

Also in this case, as in Design I, the statistical sig-nificance of the effects of the factors, their interactionand curvature, was calculated by applying ANOVAto the experimental data of Design II. The results arealso shown in Table III and indicate that %DVB andinteraction between %DVB and EPDM fraction havea significant influence in the response, and this influ-ence is linear because the value of the F statistics forcurvature is smaller than the tabulated value F0.05,1,5¼ 6.61, where 0.05, 1, 5 have the same meaning asbefore.

The values of the effects of the factors and theirinteraction are not the same in both designs. Thiscan be explained considering that these valuesdepend on the amplitude of the range of the levelsof the factors studied and that, in this work, this am-plitude was different from one design to the other. Itcan be noted that in Design I, both factors except fortheir interaction have a significant effect on theresponse, whereas in Design II, EPDM fraction hasno significant influence on the response. This is con-sistent with the previous conclusion that the maxi-mum EPDM content is 0.6.

Fitting a response surface to Qeq

To enable the prediction of the Qeq at any combina-tion of levels of the factors, a multiple linear regres-sion analysis was applied to fit a response surfacemodel to the 20 experimental results. Initially, amodel including quadratic terms was fitted to thedata despite the results in Design I, II indicated bothfactors, their interaction, and the curvature were notall significant. The regression coefficients of a sec-ond-order response surface model were estimatedby the least-squares method,15 affording the equa-tion

Q_

eq ¼ 16:0� 5:60x%DVB þ 0:05xFm � 0:76x%DVBxFm� 0:52x2%DVB � 2:10x2Fm (5)

where Q_

eq denotes the predicted value of the Qeq

response and the terms x%DVB, xFm and x%DVBxFmrepresent the coded values of %DVB, Fm, and theirinteraction, respectively. Likewise, x2%DVB and x2Fm arethe coded quadratic terms responsible for the curva-ture of the model. In this case, the coded scheme fol-lowed is designated Global, as indicated in Figure 1.

The usefulness of the model was checked byapplying ANOVA to the regression equation. It wasdetermined that at least one of the five regressorvariables contributed significantly to the model.However, the test for the lack of fit of the modelindicated that this quadratic model was notadequate to explain the experimental data. Hence, a

higher-order model incorporating cubic terms wascalculated

Q_

eq ¼ 15:9� 15:0x%DVB � 6:35xFm � 2:85x%DVBxFmþ 0:07x2%DVB � 5:10x2Fm þ 9:62x2%DVBxFmþ 0:93x%DVBx

2Fm

þ 10:1x3%DVB � 0:96x3Fm (6)

Again, in this case, the ANOVA for the signifi-cance of the regression was performed to check theadequacy of the cubic model, and it was observedthat at least one of the nine regressor variables had anonzero regression coefficient. The test for the lackof fit of the model indicated that this quadraticmodel was adequate to explain the experimentaldata. Therefore, the next step, to determine whichregressor variables contributed significantly to themodel, was to test the significance of the individualregression coefficients. Their t statistics and theircorresponding P values are reported in Table IV.The regression coefficients were statistically signif-

icant, with a level of significance of 0.05 if the abso-lute values of their t statistics were higher thant0.025,10 ¼ 2.228, where 0.025 is the half-value of thelevel of significance and 10 represents the degrees offreedom of the residual error. Therefore, since the tstatistics for the regression coefficients of %DVB%DVB, %DVBFmFm, and FmFmFm were smaller than2.228, the regressor variables x2%DVB, x%DVBx

2Fm; and x3Fm

could be eliminated from eq. (6), then the experi-mental data were subjected again to multiple linearregression analysis, the following reduced cubicmodel was obtained

Q_

eq ¼ 15:8� 14:8x%DVB � 5:69xFm � 2:52x%DVBxFm

� 4:62x2Fm þ 10:4x2%DVBxFm þ 7:75x3%DVB ð7Þ

Since eq. (7) is a different model from eq. (6),another new ANOVA was performed to determinethe significance of the regression. The ANOVAresults are summarized in Table V.

TABLE IVStatistical Significance of the Regression Coefficients of

the Cubic Model for Qeq Given by Equation 2

Term t P

Constant 43.35 <0.001%DVB �9.36 <0.001Fm �5.00 0.001%DVBFm �6.88 <0.001%DVB%DVB 0.13 0.897FmFm �8.10 <0.001%DVB%DVBFm 5.42 <0.001%DVBFmFm 1.40 0.191%DVB%DVB%DVB 5.89 <0.001FmFmFm �0.72 0.490t0.025,10 ¼ 2.228

2218 WU AND ZHOU


In this case, the P value for the F statistic of theregression is smaller than 0.001, indicating that atleast one of the six regressor variables contributessignificantly to the reduced cubic model, as men-tioned before. Furthermore, the coefficient of multi-ple determination, R2, is close to 1, meaning that themodel fits the experimental data well. In addition,the adjusted R2 statistic, R2

adj, is close to R2, whichconfirms that nonsignificant terms have not beenincluded in the model. With regard to the test forthe lack of fit, since the F statistic calculated doesnot exceed F0.05,3,10 ¼ 3.71, it can be said that thereduced cubic model given by eq. (7) fits the experi-mental data well and that this model can be used topredict Qeq at any value of the %DVB and Fm factorswithin the region studied. The significance of theindividual regression coefficients was also tested,again showing that all of these coefficients were stat-istically significant.

Scrutiny of the regression coefficients of eq. (7)reveals that high Qeq can be obtained by decreasingthe DVB concentration and that this influencebecomes more marked as the EPDM fractionincreases. The presence of quadratic and cubic termsimplies that there are stationary points in this rela-tionship. In the contour plot of eq. (7), as illustrated

in Figure 4, it may be observed that a maximum Qeq

of 24.26 g g�1 should be obtained when operatingwith a DVB concentration of 4.14% and a EPDMfraction of 0.60.

Correlation between the absorption kinetics of thegels and their synthesis conditions

After it had been observed that there were differen-ces in the absorption kinetics of the gels because oftheir different synthesis conditions, it seemed appro-priate to investigate whether there was a quantita-tive relationship between the characteristics of theabsorption kinetics and the operating conditions(values of % DVB and Fm).Accordingly, to search for a correlation suitable

for predicting the amount of kerosene absorbed atdifferent times on several different oil gels, as afunction of their synthesis conditions, the modelgiven by eq. (4) was chosen as a starting pointbecause of its good fit to the experimental kineticdata.Taking into account that, in eq. (4), K has been

shown to be dependent on the synthesis conditions,this term was substituted by a second-order polyno-mial in the following manner:

Qt ¼ Qmaxf1� exp½�ða0 þ a1x%DVB þ a2xFm

þ a3x%DVBxFm þ a4x2%DVB þ a5x

2FmÞt�g (8)

where x%DVB and xFmrepresent the coded values

of %DVB and Fm, respectively (see Table I). To fiteq. (4) to the kinetic data, multiple nonlinearregression techniques were used. The regression

TABLE VANOVA for the Significance of Regression of the Reduced Cubic Model of Qeq Given by Equation 3

Source of variation Sum of squares Degrees of freedom Mean square F Tabulated F P

Regression 518.45 6 86.04 161.88 F0.05,3,16 ¼ 2.92 <0.001Residual error 6.94 13 0.53

Lack of fit 1.22 3 0.41 0.72 F0.025,3,16 ¼ 3.71Pure error 5.72 10 0.57

Total 525.39 19R2 ¼ 0.987 0.987R2adj ¼ 0:981 0.981

Figure 4 Contour plot of Qeq (g g�1) according to thereduced cubic model given by eq. (8).

TABLE VIRegression Coefficients of Equation 8

Regresson coefficient Value 95% confidence

a0 0.04114 0.00142a1 �0.00668 0.00086a2 0.00382 0.00101a3 0.00175 0.00111a4 �0.00102 0.00190a5 �0.00006 0.00166

R2 ¼ 0.957



coefficients (a0, a1,. . ., a5) were estimated with theLevenberg-Marquardt algorithm, and the valuesobtained are shown in Table VI, together with their95% confidence intervals.

For the regression model to be stable and statisti-cally valid, the confidence intervals must be smallerthan the respective values of the regression coeffi-cients (in absolute values). In this case, the 95% con-fidence intervals for the regression coefficients a4and a5 are larger than the values of the regressioncoefficients themselves. This may indicate that theseregression coefficients are not needed. Therefore, theregressor variables x2%DVB and x2Fmwere eliminatedfrom eq. (8), resulting in the equation

Qt ¼ Qmaxf1� exp½�ða0 þ a1x%DVB

þ a2xFm þ a3x%DVBxFmÞt�g (9)

When the regression analysis was performedagain, the values of the regression coefficients of eq.(9) were determined. These values are given in TableVII, where the 95% confidence intervals are alsoshown. It can be observed that the 95% confidenceintervals are much smaller than the values of theircorresponding regression coefficients after a4 and a5are removed. Despite the correlation coefficient, R2,is not enhanced to close to 1, all this indicates thatthe model given by eq. (9), with the values shown inTable VII, is statistically valid and stable and, hence,suitable for reliably predicting the kerosene-absorp-tion kinetics of these gels.

From the values of the regression coefficientsobtained, it can be deduced that the fastest absorp-tion is achieved when the gels are synthesized withthe lowest DVB concentration and biggest EPDMfraction, at which the oil gels may exhibit the highestproportion of pores.

CONCLUSIONS

Porous oil gels based on EPDM/4-tert-butylstyreneusing toluene as diluent have been synthesized. TheDVB concentration and the EPDM fraction in the re-active mixture were varied to study their effects onthe oil absorptive characteristics of the gels, namelythe kerosene absorbency and kerosene-absorption

kinetic constant. The experiments were plannedthrough a factorial design of experiments and usingthis procedure, together with multiple linear regres-sion analysis, quantitative relationships (empiricalmodels) between the synthesis conditions and theseoil absorptive characteristics were obtained. Thesemay be of use for determining suitable compositionsof polymerization mixtures for obtaining poly(EPDM/tBS) gels with predetermined oil absorptiveproperties. The quantitative relationship foundbetween the synthesis conditions and the keroseneabsorbency indicates that the smaller the %DVB andthe higher EPDM fraction, the higher the keroseneabsorbency.With regard to kerosene-absorption kinetics, the

first-order kinetic model proved to be a reliablemodel to explain the experimental kinetic data, andit was therefore used to calculate the kerosene-absorption kinetic constant (K) through nonlinearmultiple regression analysis. In this case, it wasobserved that the fastest absorption was achievedwith the lowest DVB content and highest EPDMfraction. However, it is necessary to take intoaccount that any change in the oil medium involvesa change in the type of oil-gel interaction andchanges in the viscosity. Therefore, since the modelsgiven in this work were obtained with kerosene, anysignificant change in the oil medium will introduceinaccuracies in the predictions.

References

1. Hrubesh, L. W.; Coronado, P. R.; Satcher, J. H. J Non-CrystSolids 2001, 285, 328.

2. Meininghaus, C. K. W.; Prins, R. Microporous MesoporousMater 2000, 35, 349.

3. Stenzel, M. H. Chem Eng Prog 1993, 89, 36.4. Choi, H. M. J Environ Sci Health Part A 1996, 31, 1441.5. Jang, J.; Kim, B. S. J Appl Polym Sci 2000, 77, 914.6. Zhou, M. H.; Cho, W. J. Polym Int 2001, 50, 1193.7. Zhou, M. H.; Cho, W. J. J Appl Polym Sci 2002, 85, 2119.8. Zhou, M. H.; Cho, W. J. J Appl Polym Sci 2003, 89, 1818.9. Atta, A. M.; Arndt, K. F. J Appl Polym Sci 2005, 97, 80.10. Atta, A. M.; El-Ghazawy, R. A. M.; Farag, R. K. Polym Int

2005, 54, 1088.11. ASTM.Standard Method of Testing Sorbent Performance of

Adsorbents E1, F726; ASTM: West Conshohocken, Pennsylva-nia, 1993.

12. Himmelblau, D. M. Process Analysis by Statistical Methods;Wiley: New York, 1970.

13. Box, G. E. P.; Hunter, W. G.; Hunter, J. S. Statistics for Experi-menters: An Introduction to Design, Data Analysis, and ModelBuilding; Wiley: New York, 1978.

14. Draper, N. R.; Smith, H. Applied Regression Analysis; Wiley:New York, 1981.

15. Montgomery, D. C. Design and Analysis of Experiments;Wiley: New York, 2001.

16. Kangwansupamonkon, W.; Damronglerd, S.; Kiatkamjorn-wong, S. J Appl Polym Sci 2001, 79, 504.

17. Yao, K. J.; Zhou, W. J. J Appl Polym Sci 1994, 53, 1533.

TABLE VIIRegression Coefficients of Equation 9

Regression coefficient Value 95% confidence

a0 0.04114 0.00058a1 �0.00682 0.00070a2 0.00373 0.00085a3 0.00185 0.00094

R2 ¼ 0.953


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