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Polymer Testing 29 (2010) 119–126

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Polymer Testing

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

Material Properties

Evaluation of the polymer–solvent interaction parameter c for the systemcured polybutadiene rubber and toluene

A.J. Marzocca*, A.L. Rodrıguez Garraza, M.A. MansillaUniversidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Fısica, LPMPyMC, Pabellon 1, Ciudad Universitaria Buenos AiresC1428EGA, Argentina

a r t i c l e i n f o

Article history:Received 13 August 2009Accepted 26 September 2009

Keywords:Polybutadiene rubberTolueneFlory–Huggins interaction parameterCrosslinkingSwelling

* Corresponding author.E-mail address: marzo@df.uba.ar (A.J. Marzocca)

0142-9418/$ – see front matter � 2009 Elsevier Ltddoi:10.1016/j.polymertesting.2009.09.013

a b s t r a c t

One of the most popular cured rubbers used in industrial applications is polybutadienerubber (BR) and frequently its network structure, in the cured state, is studied by means ofswelling in a solvent. Normally, toluene is used as solvent in this test. In order to estimatethe crosslink density from the equilibrium volume fraction of rubber in the swollen state,the correct evaluation of the Flory–Huggins interaction parameter c is necessary. This workcovers the swelling behaviour of two types of cured BR in toluene. The rubbers used havesulphur and accelerator in their composition and were vulcanized at 433 K at differenttimes in order to obtain several network structures and crosslink densities. The crosslinkdensities were evaluated from uniaxial stress-strain data measured at room temperatureand analysed in the frame of the conformational tube model. Using this information andthe swelling measurements in the frame of the Flory–Rehner relationship, a relationshipbetween c and vr, the polymer volume fraction at equilibrium (maximum) degree ofswelling was established for the cured BR/toluene system. It was found that c is nota constant but depends on the crosslink density of the sample.

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1. Introduction

Polybutadiene, BR, is one of the most popular rubbersused for technological purposes mainly in elastomericblends. The major use of BR is in treads and sidewalls oftyres. Cured BR imparts excellent abrasion resistance andlow rolling resistance due to its low glass transitiontemperature, Tg. BR also has a major application as animpact modifier for polystyrene and acrylonitrile-buta-diene-styrene resin (ABS) [1].

The low value of Tg is a consequence of the low vinyl-content in the molecule. The vinyl content increases the Tg

of the BR by creating a stiffer chain structure. Vinyl alsotends to crosslink under high temperature conditions and,in consequence, polymers with high vinyl contents are lessthermally stable than low-vinyl polymers. In the vinyl

.

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units, the double bonds are pendent of the main chain, andthis fact produces special properties of high vinyl polymers.

Although vulcanization takes place by heat and pressurein the presence of sulphur, the process is relatively slow.The addition of small amounts of accelerators speeds up thecure reaction. The quantity and kinds of crosslinks formedduring vulcanization are determined by the relativeamounts of accelerator and sulphur used in the compoundformulation, and also by the time, temperature and pres-sure conditions in the cure process.

Swelling of rubber compounds is an important tech-nique used for the determination of crosslink density. Themolecular weight of the network chain between crosslinksfor a phantom network, Mcs, is given by the Flory–Rehnerrelationship [2,3]

Mcs ¼ �rð1� 2=fÞV1

�v1=3

r � 0:5vr

�lnð1� vrÞ þ cv2

r þ vr(1)

A.J. Marzocca et al. / Polymer Testing 29 (2010) 119–126120

where r is the unswollen rubber density, f the functionalityof the crosslinks, vr the volume fraction of polymer at theequilibrium (maximum) degree of swelling and V1 themolar volume of solvent; c is an interaction parameterbetween the polymer and the swelling agent known as theFlory–Huggins interaction parameter. The knowledge ofthis parameter is fundamental in order to obtain a correctestimation of Mcs. The polymer–solvent interactionparameter c is expressed as a series expansion in powers ofthe polymer volume fraction vr as

c ¼ c1 þ c2nr þ c3n2r þ. (2)

where the coefficients c1, c2, ., are functions of molecularcharacteristics and temperature [4,5].

A complete review about the interaction parameter ofcrosslinked networks and star polymers was published byHorta and Pastoriza [6]. McKenna et al [7,8] studied theswelling behavior of cured natural rubber in good and poorsolvents and the authors found that the Flory–Hugginsinteraction parameter is dependent on the crosslinkdensity. Hergenrother and Hilton [9] performed a studywhere the change in c as a function of the volume fractionof rubber was established for hydrocarbon rubbers swollenin heptane. For sulfur cured SBR and peroxide cured SBR,they proposed a relationship of the form c¼ aþ bln nr

where a and b are constants. In a recent paper, the changeof c with the crosslink density was calculated in the case ofthe system SBR/toluene [10].

In the case of cured BR, there is enough information inliterature about the swelling behaviour in differentsolvents. Some of these values are summarised in Table 1. Itis interesting to note that c depends on the microstructureof the polymer. Toluene is one of the solvents frequentlyused to analyse the swelling behaviour of cured elastomers,however in the case of cured BR there is no informationabout how the Flory parameter changes with polymervolume fraction vr. If the molecular weight of the networkchain between crosslinks is known, it will be possible torelate c with vr using eq. (1).

In several research works, uniaxial stress-strain data ofSBR, NR and BR vulcanizates were analysed in the frame ofthe conformational tube model developed by Heinrich etal [21–29]. The model allows a proper separation ofcrosslink and constraint contribution to the mechanical

Table 1Values of the Flory–Huggins interaction parameter c for cured BR withdifferent solvents. (a) high cis content, (b) medium cis content.

c Solvent Reference

0.34 Toluene 11, 120.47 Toluene 130.21 Benzene 140.265 Benzene 150.325 Benzene 160.36 Benzene 170.463 Decane 150.542 hexadecane 150.37þ 0.52 vr Ciclohexane 180.45þ 0.35 vr (a) n-Heptane 190.37þ 0.52 vr (b) n-Heptane 190.428þ 0.535 vr (a) n-Heptane 200.330þ 0.638 vr (a) Benzene 20

behaviour and gives a reliable determination of themolecular mass between two crosslinks connected bya polymer chain, Mcs.

The objective of this paper is to obtain the dependenceof the Flory parameter c with volume fraction vr for twotypes of cured poybutadiene with different cis content intheir microstructures when they are swollen in toluene atroom temperature. For each compound, several crosslinklevels are obtained by vulcanization at 433 K and changingthe time of cure. The values of Mcs were estimated bymeans of uniaxial stress-strain tests analysed in the frameof the tube model. Therefore, c can be evaluated by meansof eq. (1).

2. Theory

The tube model for crosslink networks assumes that dueto the topological constraints, the motion of the chain isessentially confined in a tube-like region made of thesurrounding polymers. For uniaxial deformation, Heinrich etal [21] presented a relationship between stress s, and strain e,based on a tube model considering moderately crosslinkedrubbers, where the reduced stress is expressed as

s�l� l

�2� ¼ Gc þ Gnf ðlÞ (3)

with

f ðlÞ ¼ 2l

0:5b � l�b

b�

l2 � l

�1� (4)

where l is the expansion ratio (1þ e) and b describes therelaxation of the deformed tube in the deformed state to anundeformed tube corresponding to the equilibrium state. Theparameter b ranges between 0 and 1. b z 1 was found to berelevant for almost complete converted unswollen well-con-nected networks made from long primary and crosslinkedchains [21]. Gc and Gn, represent the crosslink and theconstraint contributions of the modulus respectively and theyare connected to the molecular parameters of the polymer.

The entanglement junctions act as transient ‘‘cross-links’’, restricting the slippage of chains during deformationunder applied stress. Gn is expressed in terms of themolecular parameters by [21]

Gn ¼kT

4ffiffiffi6p b

2nst

�lst

do

�2

(5)

with

do

lst¼ a

�nstl3

st

��1=2 (6)

where lst the length of the statistical segment, nst is thesegment number density, do the fluctuation range of a chainsegment. k and T are the Boltzmann’s constant and theabsolute temperature respectively.

The parameter a allows the connection of the modulusGn with the plateau modulus Go of the uncrosslinked bulkelastomer. This relation was proposed as

Table 2Microstructure and density (rp) of the polybutadiene studied in this work (as provided by the supplier).

Polymer cis-1,4 content (%) trans 1,4 content (%) vinyl content (%) Mn (g/mol) Polydispersity Degree of branching rp[g/cm3] GoN [MPa]a

BR (Buna CB-25) 97 2 1 130,000 2.6 15 0.91 0.698BR (Buna CB-55) 38 51 11 125,000 1.3 < 5 0.91 0.856

a Data evaluated from our DMA tests.

A.J. Marzocca et al. / Polymer Testing 29 (2010) 119–126 121

a ¼ 3:04ðGn=GoÞ1=2 (7)

Gc is related to the molecular parameters [21]

Gc ¼ AkT�

nc �2rNA

ðf� 2ÞMn

�(8)

f is the functionality of the crosslinks, nc the network chaindensity, Mn is the number molecular weight and NA is theAvogadro’s number. The parameter A is a microstructurefactor which depends on the ratio between the fluctuationrange of a crosslink, dc, and the end-to-end distance Rc ofa network chain. This parameter is defined as [22]

A ¼ 1� 2f

"1�

2Kexp�

K2�

ffiffiffipp

erf ðKÞ

#(9)

with

K ¼�

3f

2

�1=2dc

Rc(10)

The end-to-end distance of a network chain, Rc, isexpressed by

Rc ¼ lst

�Mcs

Mst

�1=2

(11)

The molecular mass between two crosslinks connectedby a polymer chain is defined as [22]

Mcs ¼ð1� usÞMco

ð1þ 2McoMn

� (13)

where Mco¼ rNA/nc, us is the sol fraction of the sample andnc is obtained as a result of Eq. (8).

3. Experimental

3.1. Sample preparation

The rubber compounds used in this work were preparedwith two types of commercial polybutadiene provided by

Table 3Compound Formulations in parts per hundred of rubber (phr).

Sample 1 Sample 2

BR (97% cis) 100 –BR (38% cis) – 100Zinc Oxide 5Stearic Acid 2Antioxidant 1.2Accelerator (TBBS) 1.0Sulphur (S) 1.5

Lanxess: Buna CB-55 NF and Buna CB-25. Buna CB-25 isproduced by neodymium catalysis. It has a high cis-1,4content and presents long chain branching. Buna CB-55 NFis a lithium grade with linear structure and a low degree ofbranching. The differences in the microstructure of theseisomers, the molecular weight, polydispersity, degree ofbranching and density of the polymers, as provided by thesupplier, are included in Table 2.

The samples were prepared with the compoundformulations indicated in Table 3. In this research, the curesystem based on TBBS (N-t-butyl-2-benzothiazole sulphe-namide) and sulphur was used. The compounds weremixed on a laboratory mill, and the torque curves obtainedwith an Alpha MDR 2000 rheometer at 433 K are shown inFig. 1.

Normally, the level of cure, q, can be evaluated from therheometer curves by means of the relationship

q ¼ st � sl

Ds¼ st � sl

sh � sl

where sl and sh are the minimum and maximum torque ofthe rheometer curve and st is the torque at time t of the test.

From these curves, several times were selected forpreparing cured samples, at the cure levels showed inTable 4. The objective was to have different crosslinkdensities in the cured samples.

Samples in the form of square sheets with sides of150 mm and a thickness of 2 mm were cured in a mould at433 K in a press at the cure times that are given in Table 4.The samples were cooled rapidly in ice and water at the endof the curing cycle. The densities of the samples (r) aregiven in Table 4.

Fig. 1. Curves of torque as a function of the time at 433 K for BR compoundswith 38% cis and 97% cis. The circles show the selected times for curing thesamples for uniaxial strain-stress tests and swelling tests.

Table 4Cure time, cure level, density of the cure samples, sol fraction us andvolume fraction, vr obtained from swelling measurements using eq. (14),for the both BR compounds.

Sample Cure time [s] q r [g/cm3] us vr

1 555 0.10 0.941 0.0305 0.0976690 0.50 0.941 0.0289 0.1443780 0.75 0.943 0.0281 0.1776960 0.90 0.942 0.0263 0.1843

1800 1.00 0.944 0.0247 0.17912 775 0.30 0.932 0.0386 0.1473

825 0.50 0.933 0.0379 0.1667950 0.75 0.938 0.0336 0.2060

1130 0.90 0.939 0.0319 0.20041850 1.00 0.939 0.0297 0.1918

A.J. Marzocca et al. / Polymer Testing 29 (2010) 119–126122

3.2. Dynamic mechanical measurements

It was necessary to measure the plateau modulus GoN of

the uncrosslinked bulk polymers to solve eq. (7). Thisevaluation was made by using a Rheometrics DMA IV inthe traction mode in the frequency range between 0.01and 150 Hz. Measurements were performed in theisothermal mode at 293, 273, 253, 223 and193 K andapplying the WLF relationship. In order to obtain themaster curves it is necessary make use of the reducedvariables at a reference temperature To, which wasselected as 293 K. The correction in the density of therubber due to this change with temperature must beconsidered [31]. In this paper r(To)/r(T)¼ 1þk(T� To) wasused, where k is the volumetric thermal expansion whichwas taken as 7.5�10�4 K�1 for BR [32].

The master curves of the storage modulus E0, lossmodulus E00 and loss tangent (tan d) as function of the

Fig. 2. Master curves of high cis (97%)BR at 293 K. (a) Storage

angular frequency can be observed in Figs. 2 and 3 for bothBRs. It is known that high cis BR crystallizes at around 240 K[27], and the WLF method can only be applied at temper-atures above this. In the case of an amorphous polymer, aslithium grade BR, the WLF method is applied at tempera-tures above the glass transition.

The plateau shear modulus is obtained from the plateaumodulus Eo

N by considering that G¼ E/2(1þ n) with thePoisson’s ratio n¼ 0.49 for rubbers. The value of Eo

N is equalto the storage modulus E0 at the frequency where tan d is ata minimum in the plateau zone [30] (i.e.,Eo

N ¼ ½E0�tand/minimum). The values obtained for GoN are

included in Table 2.

3.3. Tensile tests

ISO 37:2005 type 1 samples for tensile tests were cutfrom the cured sheets. Stress-strain curves were measuredwith an INSTRON 4201 at room temperature at a deforma-tion rate of _e ¼ 6� 10�4s�1. A load cell of 50 N was used toobtain good sensitivity. Strain was measured by means ofa large deformation extensometer (INSTRON XL) with20 mm gauge length. The stress-strain curves wereobtained for the three different samples of a given sheetand the average curve was calculated. The standard devi-ation in stress of the three tests was less than 0.015 MPawhile for the strain it was insignificant.

3.4. Swelling tests

Two samples of 16 mm diameter were cut with a diefrom the cured sheets for each compound. The discs wereallowed to stand in pyridine for 16 h at room temperature.

c

b

a

modulus E0 , (b) Loss modulus, E00 , (c) loss tangent, tan d.

c

b

a

Fig. 3. Master curves of medium cis (38%) BR at 293 K. (a) Storage modulus E0 , (b) Loss modulus, E00 , (c) loss tangent, tan d.

Fig. 4. Stress-strain data and fit curves according to eq. (3) for samples ofcompound 1, high cis (97%)BR, cured at 433 K at different times.

A.J. Marzocca et al. / Polymer Testing 29 (2010) 119–126 123

Then, they were continuously extracted in acetone for 24 h(ISO 1407:1992) and dried. us was evaluated and it is givenin Table 4.

Each sample was completely immersed in pure toluene,in a sealed glass bottle, at room temperature until equi-librium swelling occurred. Normally this process takesmore than 48 h. When this step was completed, thesamples were removed from the bottles, the excess toluenefrom the surface of the samples was wiped and the swollenweight immediately measured.

The volume fraction vr was calculated based on thefollowing equation

vr ¼Wd �Wf

�r

Wd �Wf

�rþ ððWs �WdÞ=rsÞ

(14)

where Wd is the weight of the sample after swelling anddrying, Wf, the weight of the non extractable filler in thesample, Ws, the weight of the swollen sample and rs thedensity of the solvent (0.8669 g/cm3 for toluene). The ISO247:2006 method was used to evaluate Wf.

4. Results and discussion

The plots of s – l for both BR gum mixes cured at 433 Kare given in Figs. 4 and 5. These figures show the experi-mental data and the fitted curves according to eq. (3)considering b¼ 1. As can be observed, the fitting of thecurves to the data is excellent. The model parameters Gc

and Gn are given in Table 5. The error in the determinationof Gc and Gn was less than 1�10�3 MPa.

Using eq. (7) with Go and Gn, the values of a were esti-mated for the different samples and they are given inTable 5. The values obtained are in the range of thoseexpected for elastomers [23].

From the values of Gc and Gn, information on theparameters of the network structure can be extracted. Forthe estimation of the parameters associated withconstraint, it is necessary to know the value of the Kuhn’sstatistical segment length, lst, for BR. This value was takenfrom literature [33] being lst¼ 0.76 nm for high cis-poly-butadiene lst¼ 0.96 nm for medium cis-polybutadiene.

Fig. 5. Stress-strain data and fit curves according to eq. (3) for samples ofcompound 2, medium cis (38%) BR, cured at 433 K at different times.

A.J. Marzocca et al. / Polymer Testing 29 (2010) 119–126124

Using eqs. (5)–(13), all the parameters involved in thetube model were obtained following the methodologygiven in references [24,25]. These values are given inTable 5 for each compound analysed. In both compounds,the minimum value of the molecular weight of the networkchain between crosslinks, Mcs, is in the cure level between0.90 and 1.00. It is also interesting to note that the fluctu-ation range of a chain segment, do, which is related to thelateral dimension of the tube, has its highest value for thecompound with highest degree of branching.

nc, the network chain density, is related to the crosslinkdensity of the samples. Then, from Table 5, the samples ofthe compound with high cis structure (sample 1) presenthigher crosslink density than those of the compound withmedium cis structure (sample 2) at similar cure level. Thisfact contradicts the rheometer curves where the compoundwith medium cis structure shows the highest maximumtorque and, normally, a higher torque is expected whenmore elastically active crosslinks are present in thecompound. This result can be used as evidence showingthat the linear structure and a low degree of branching ofthe lithium grade BR improve some mechanical properties,such as the maximum torque and the modulus, comparedwith neodymium grade BR.

The rubber volume fraction, vr, was evaluated by meansof swelling in toluene using eq. (14). These values are givenin Table 4 for the two compounds cured at different times.The correspondence between vr and the corresponding Mcs

values are plotted in Fig. 6.

Table 5Parameters of the tube model obtained for both BR compounds.

Sample Cure time [s] Gc [MPa] Gn [MPa] a do [nm]

1 555 0.091 0.185 5.90 2.78690 0.382 0.440 3.83 1.80780 0.419 0.466 3.72 1.75960 0.404 0.380 4.12 1.94

1800 0.339 0.380 4.12 1.942 775 0.247 0.659 3.46 1.55

825 0.326 0.612 3.60 1.61950 0.363 0.648 3.49 1.56

1130 0.364 0.612 3.60 1.611850 0.282 0.653 3.48 1.56

To fit the experimental data to eq. (1) and eq. (2), theLevenberg-Marquardt chi-square minimization was usedwith a program provided by Origin 7.0 software (Microcal)which uses nonlinear least squares fitting [34]. The trun-cation of the series in eq. (2) at the second term is satis-factory for most purposes [5] and was adopted in thisresearch. V1 (toluene)¼ 106.29 ml/mol [35] was used inthis calculation.

Two fitting curves, one for each compound, are plottedin Fig. 6. For the sample with high cis content the function

c ¼ 0:19þ 1:13nr (15)

was obtained. In the case of the sample with medium ciscontent the function

c ¼ 0:22þ 1:16nr (16)

was obtained.Considering the errors involved in both equations,

a unique relationship for both BR can be considered as

c ¼ 0:20þ 1:22nr (17)

A widely used equation to calculate c, based on theHildebrand solubility parameters, is

c ¼ cb þV1

RTðds � drÞ2 (18)

where ds and dr are the solubility parameters for solventand polymer respectively, R the molar gas constant and Tthe absolute temperature. cb is the entropic contribution[36].

Considering ds (toluene)¼ 18.2 (MPa)1/2 [37], dr (BR)¼17.15 (MPa)1/2 [38] and cb¼ 0.34� 0.08 [39], and replacingin eq. (18), a value of c¼ 0.39� 0.08 at 293 K isobtained. The behaviour of eq. (1) considering thesevalues of c is included in Fig. 6 and, as can be observed,the fit of the experimental data is poor.

As it was shown, the molecular weight between cross-links in both cured BR compounds in the dry state wasdetermined from uniaxial stress-strain measurementsanalysed in the frame of the conformational tube model.Furthermore, the polymer volume fraction at equilibrium(maximum) degree of swelling was obtained by means ofswelling measurements in toluene. The Flory–Rehnerrelationship, eq. (1), allows us to link both variables directlyand to find the polymer–solvent interaction parameter c

for each one of the studied samples.

Mco [kg/mol] nc [nm�3] Rc [nm] A Mcs [kg/mol]

18.424 0.031 9.17 0.842 13.9184.635 0.122 5.04 0.792 4.2024.220 0.135 4.82 0.787 3.8514.167 0.136 4.80 0.750 3.8135.151 0.110 5.30 0.785 4.6567.891 0.071 6.73 0.903 6.7365.846 0.096 5.88 0.868 5.1445.271 0.107 5.91 0.863 4.6985.215 0.109 5.59 0.855 4.6606.917 0.082 6.36 0.891 6.043

Fig. 6. Experimental values of r/2 Mcs versus volume fraction of rubber inthe swollen state vr, for cured BR of high and medium cis content. Linescorrespond to the Flory–Rehner equation.

A.J. Marzocca et al. / Polymer Testing 29 (2010) 119–126 125

The crosslink density in a 4-functional network isdefined by [40]

mcs ¼r

2

�1

Mcs� 1

Mn

�(19)

The values of c plotted versus mcs are shown in Fig. 7. Atfirst approximation a linear regression can be established,i.e.:

c ¼ cu þ a1$mcs (20)

and following McKenna et al [7,8], cu is the value of theuncrosslinked rubber at dilute solution limit for a good

Fig. 7. Dependence of c on crosslink density, mcs, for cured BR of high andmedium cis content. The lines correspond to the linear regression of the data.

solvent and at the limit of miscibility for poor or non-solvents, and a1 is a parameter that depends on the kind ofsolvent used in the swelling test.

Eq. (20) was used to fit the data of Fig. 7 and the value ofcu¼ 0.23� 0.02 and cu¼ 0.30� 0.07 were obtained forhigh cis BR and medium cis BR respectively. Therefore,these values could be assigned to the Flory–Hugginsinteraction parameter for the uncured BR/toluene systemfor each chain structure. In the case of sulphur cured BR theresulting values of c are dependent on the crosslink densityof the rubber.

5. Conclusions

This research leads to the following conclusions:

1. The tube model for crosslink networks was successfullyused to analyse uniaxial stress-strain measurements fortwo different types of cured polybutadiene, preparedwith TBBS(accelerator)/sulphur and vulcanized at 433 K,at several cure levels.

2. The interaction parameter c is not constant when therubber is swollen in toluene. In this case, c is a functionof volume fraction of rubber, vr, which changes with thecrosslink density of the cured compound and the type ofstructure of the molecules.

3. The molecular weights between crosslinks, obtained bymeans of stress-strain data analyzed in the frame of theconformational tube model, were used for the calcula-tion of c. At first sight, a linear relationship between c

and the crosslink density mcs is proposed and for uncuredBR/toluene a value of cu¼ 0.23� 0.02 andcu¼ 0.30� 0.07 was obtained for high cis BR andmedium cis BR

Acknowledgements

This work was supported by the Universidad de BuenosAires, Argentina (Research Project X808) and partially bythe Agencia Nacional de Promocion Cientıfica y Tecnologica(PICT 1650/06). The authors want to thank LanxessS.A.(Argentina) for the polymers and Fate SAICI (Argentina)for the preparation of the samples.

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