Modeling of tensile moduli in polystyrene/ polybutadiene blends

Modeling of Tensile Moduli in Polystyrene/Polybutadiene Blends

SUSAN JOSEPH,1 SABU THOMAS2

1 Department of Chemistry, St. Stephen’s College, Pathanapuram, Kerala-689695, India

2 School of Chemical Sciences, Mahatma Gandhi University, Priyadarshini Hills P.O., Kottayam, Kerala-686560, India

Received 11 October 2001; revised 14 December 2001; accepted 25 January 2002Published online 00 Month 2002 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/polb.10139

ABSTRACT: The tensile moduli of polystyrene/polybutadiene blends were studied withreference to the effect of the blend ratio. A comparison between the experimentalresults and the theoretical predictions of the tensile properties was also made. Themodels selected were the parallel, series, Halpin–Tsai, Takayanagi, Kerner, andKunori models. Various theoretical models were applied to predict the location of thephase inversion region in these blends. Different equations were also applied for theprediction of the tensile modulus of cocontinuous structures for comparison. © 2002Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 755–764, 2002Keywords: tensile modulus; cocontinuous morphology; mechanical properties; theo-retical modeling

INTRODUCTION

Blending is one of the easiest and most cost-effec-tive ways of preparing multiphase polymeric ma-terials with desirable properties. However, mostof the polymer blends are found to be immiscible.1

The properties of a multiphase polymer systemcannot be deduced from the properties of the in-dividual phases. Instead, the properties dependon many factors, such as the spatial organizationof each phase and the nature of the interface.Most of the immiscible polymer blends are oftenproduced with melt-mixing technique, which gen-erates different types of morphologies. For thedesign and development of multiphase polymerblends, a thorough knowledge of the relationshipof the molecular characteristics, their rheologicaland interfacial properties, the melt processingconditions, and the flow-induced microstructureis highly essential. There are many reports on the

interrelationship of the processing conditions,morphology, and properties of these blends.2,3

Over the years, different techniques have beendeveloped to improve the compatibility of polymerblends. One solution to this problem is the selec-tion of a suitable blending technique to increasethe interfacial area by forming an interpenetrat-ing cocontinuous network structure. This type ofphase morphology results in direct load sharingwithout the need for stress transfer across thephases. The other method is physical compatibi-lization (in which an added copolymer interactswith corresponding phases) and reactive coupling(in which an interfacial chemical reaction takesplace between the phases). The types and scalesof the morphologies determine the blend proper-ties.4 Among the various parameters, mechanicalproperties are useful for deducing the morphologyor phase continuity in multiphase polymer blendsystems. In a droplet–matrix structure, mechan-ical properties depend on the modulus of the ma-trix phase. However, the modulus of the fibrousblend depends on the modulus of the dispersedphase.5 In cocontinuous blends, neither of theblend constituents contributes to the properties,

Correspondence to: S. Thomas (E-mail: [email protected])Journal of Polymer Science: Part B: Polymer Physics, Vol. 40, 755–764 (2002)© 2002 Wiley Periodicals, Inc.

755

but high isotropic values are expected because ofits interpenetrating structure.

An important aspect of phase morphology isthe microstructure, that is, the size, shape, anddistribution of dispersed particles or the coarse-ness and tortuosity of a continuous phase. Poly-blend morphology is understood mostly as thequalitative description of the spatial arrangementof blend component phases.6 Three basic mor-phologies are dispersed, stratified, and cocontinu-ous phases. During melt blending, the minorphase is broken up to form the dispersed phase.The interfacial tension, rheological properties,volume fraction of the components, melt viscosity,and complex strain field in the mixer (tempera-ture, time, intensity of mixing, nature of flow,etc.) control both the size and shape of the dis-persed phase. One of the key factors for achievingdesired properties is the control of the type anddimensions of the morphology. Droplet–matrixmorphologies improve the impact properties,7

fibrillar morphologies result in better tensileproperties,8,9 blends with lamellar structures en-hance barrier properties,10,11 and cocontinuousmorphologies show a combination of the charac-teristics of both polymer components. Willemse etal.12 reported an increase in modulus from 400 to750 MPa in a blend of 30% polystyrene (PS) inpolyethylene (PE) when the droplet–matrix struc-ture changed into a fully cocontinuous structure;this means that cocontinuous morphologies are aversatile means of obtaining new materials. Bothcontinuous and cocontinuous morphologies can begenerated for polymer blends, but the mechanismcontrolling these is still vague. For applicationsincluding barrier properties and polymer conduc-tivity, the mechanism controlling morphology13 ishighly essential.

The development of cocontinuous morphologyin polymer blends is one of the most interestingbut least understood phenomena because of thecomplexity and the lack of a characterizationmethod. In general, the blend component with thelowest viscosity and highest volume fractionforms the continuous phase, whereas the blendcomponent with the highest viscosity and lowestvolume fraction forms the dispersed phase. Thecontinuity of one phase within the other at lowvolume fractions depends on the size and shape ofthe dispersed phase. For spherical particles, thecontinuity of the minor phase is possible over 16vol % droplets (above the percolation thresholdvalue). The continuity of phases has a great im-pact on the resultant macroscopic properties ofblends. According to Veenstra et al.,14 cocontinu-

ous morphologies are not formed in a single vol-ume fraction but rather over a wide range ofvolume fractions; the range of the volume fractiondepends on processing conditions and the rheo-logical properties of the blend components. Perco-lation theory deals with the development of con-tinuity in polymer blends. According to this the-ory, at low concentrations, there is a dispersion ofparticles in the matrix. A gradual change in struc-ture, from dispersed to fully cocontinuous, takesplace in heterogeneous polymer blends with anincreasing volume fraction of the minor compo-nent.6 In dilute systems, droplet–matrix struc-tures prevail. At higher volume fractions, startingat the percolation threshold, interconnectedstructures of the minor component develop untilat still higher volume fractions the entire minorcomponent is incorporated into a single continu-ous phase network inside the matrix component,and a fully cocontinuous morphology is obtained.This continuous morphology can exist over arange of compositions, depending on the blendingconditions.14 Beyond this range, at still highervolume fractions, the phase network of the erst-while matrix component starts breaking downuntil finally this component becomes dispersed.This is because, as the concentration of the minorphase increases, particles become close enough tobehave as if they were connected. The furtheraddition of the minor phase extends the continu-ity network until it becomes continuous through-out the sample. It has been observed that a dis-persed morphology is formed when the blend com-position is highly asymmetric and a cocontinuousmorphology is formed when the minor componentwith higher melt viscosity forms the discretephase (the droplets) and the major componentwith higher melt viscosity forms the continuousphase. Knowledge of the dual-phase thresholdmay help in the design of blended materials. Thepercolation threshold is particularly important inthe design of conducting polymer composite ma-terials. The percolation of a continuous conduct-ing phase in an insulating matrix is required toachieve conductivity throughout the blend sam-ple.

Thermoplastic elastomers from blends of PSand polybutadiene (PB) combine the superior pro-cessability characteristics of PS and elastic prop-erties of PB. PB is characterized by good resil-ience, resistance to abrasion, and low heatbuildup but poor chemical resistance and process-ability. However, PS exhibits high modulus, gooddielectric properties, and superior processingcharacteristics, even though it is extremely brit-

756 JOSEPH AND THOMAS

tle. The temperature range of PB applications canbe increased through blending with PS. Despitethe positive aspects described for PS/PB blends,the performance of PS/PB blends is not up toexpectations. This is because these blends areimmiscible and incompatible and are character-ized by narrow interface, coarse morphology, highinterfacial tension, poor physical and chemicalinteractions across the phase boundaries, andpoor mechanical properties. However, the hardphase of PS acts as a pseudocrosslink at ambienttemperature, thereby preventing the flow of theelastomeric phase under stress. Similarly, theelastomeric phase of PB gives flexibility and elas-ticity to the blend material.

Mechanical analysis for evaluating the me-chanical properties of thermoplastic elastomers iswidely accepted. This study is most useful whenwe correlate the experimental mechanical proper-ties with theoretical values. The tensile proper-ties have been evaluated as a function of blendmorphology. More emphasis has been given to theregion of cocontinuity. Some of the models showedgood agreement with the experimental values.These models clearly indicate that parameterssuch as the viscosity ratio between the dispersedphase and matrix, orientation, and morphologyinfluence the properties decisively. The limita-tions of these models are also considered.

EXPERIMENTAL

Materials

PS (Polystron 678 SF-1, crystal grade) suppliedby Polychem Ltd. (India) and cis-1,4-polybuta-diene supplied by Indian Petrochemical Co., Ltd.(Vadodara) under the trade name cisamer G.Pwere used in this work.

Blend Preparation, Compounding, and SpecimenPreparation

Polymer blending was conducted in a Haake rheo-cord with a rotor speed of 60 rpm at 180 °C for 8min of mixing time. One of the blend components,PS, was premixed for 2 min to turn it into a melt,and the second component, PB, was introducedinto the melt in bits. The mixing was recordedfrom the moment PB was added. After mixing,the molten material was sheeted out through alab mill at a nip setting of 2.5 mm. The sheetedblend was taken out and pressed in a mold underthe hot condition. It was then compression-

molded in an electrically heated hydraulic pressat 180 °C for 4 min in a specially designed mold sothat the mold with the specimen could be cooledimmediately after molding, with the specimenstill kept under compression. Samples for tensiletests were punched out from the molded sheets.The melt-mixed samples were denoted S00, S30,S50, S70, and S100, where S stands for PS and thesubscripts indicate the content of PS in the blend.

Tensile testing of the samples under static con-ditions was performed at 25 � 2 °C according tothe ASTM Standard D 638-81 test method withdumbbell-shaped test specimens at a crossheadspeed of 50 mm/min with a Zwick universal test-ing machine (model 1445). The dumbbell speci-mens tested had a large radius of curvature sothat a uniaxial state of stress was maintained,and they were free of pores and cracks. At leastfive specimens for each blend were used for themean value.

Phase Morphology Analysis

The melt-mixed samples were held in liquid ni-trogen for some time so that a brittle fracturecould be obtained, thereby avoiding large defor-mations in the surface to be examined by scan-ning electron microscopy. A Philips XL20 scan-ning electron microscope operating at 20 kV wasused to view the specimen. For facilitating theidentification of phases and for enhancing mor-phological features, the cryogenically brokensamples of the blends were etched with suitablesolvents. For S70, the minor phase of PB wasetched with n-heptane, and for S30 and S50, bu-tan-2-one was used as the etchant for dissolutionof the dispersed PS phase. The sample were thendried and coated with gold and examined under ascanning electron microscope.

RESULTS AND DISCUSSION

Modeling of Tensile Moduli

The very important role of mechanical propertiesin understanding the behavior of thermoplasticelastomers is well known. Mechanical propertiesare widely suited for the analysis of multicompo-nent composites through a comparison of experi-mental results and predictions based on variousmodels. The application of various compositemodels gives insight into the properties of indi-vidual components. It also helps to check the as-sumptions regarding the structure and mecha-

POLYSTYRENE/POLYBUTADIENE BLENDS 757

nism and the properties of the interface. Severaltheories have been proposed to predict the tensileproperties in terms of various parameters. Thesetheories can be classified into two categories: (1)based on composition and (2) based on morphol-ogy.15 Most of these theories assume perfect ad-hesion between the phases and a macroscopicallyhomogeneous and isotropic sample. Differentmodels examined to predict the mechanical be-haviors of the blends include the parallel, series,Halpin–Tsai, Takayanagi, Kerner, and Kunorimodels. The highest upper bound parallel model(Voight prediction) is given by the rule of mix-tures. The application of these models requiresknowledge of the experimental mechanical behav-ior of the pure component polymers PS and PB.The two simple models are the so-called paralleland series models, which should represent theupper and lower bounds of the tensile strengthpredictions. The highest upper bound parallelmodel is given by the rule of mixtures16 as fol-lows:

EU � E1�I � E2�2 (1)

This model is applicable to materials in which thecomponents are connected parallel to one anotherso that the applied stress lengthens each compo-nent to the same extent. In the lowest lowerbound series model, the blend components arearranged in series (Reuss prediction) perpendicu-lar to the direction of the applied force. The mod-ulus prediction is given by the inverse rule ofmixtures:

1/EL � �I/E1 � �2/E2 (2)

In these models, EU is any mechanical property ofthe blend in the upper bound parallel model, andEL is the modulus of the blend in the series model.E1 and E2 are the mechanical properties of com-ponents 1 and 2, respectively; �1 and �2 are theircorresponding volume fractions. For both thesemodels, no morphology is required, but strain orstress can be continuous across the interface, andPoisson’s ratio is the same for both phases.

According to the Halpin–Tsai equation,17,18

E1

E ��1 � AiBi�2�

�1 � Bi�2�(3)

where

Bi ��E1/E2� � 1�E1/E2� � Ai

(4)

In the Halpin–Tsai equation, subscripts 1 and 2refer to the continuous and dispersed phases, re-spectively. The constant Ai is defined by the mor-phology of the system. For elastomer domainsdispersed in a continuous hard matrix, Ai is 0.66.Instead, if the hard material forms the dispersedphase, Ai is 1.5. This model has also been success-fully applied by several researchers to systems ofpolymer composites.19,20 It was reported that thismodel was also useful in determining the proper-ties of polymer blends that contained both contin-uous and discontinuous phases.

Takayanagi proposed a series–parallel model21,22

in which the concept of percolation is introduced.It is a phenomenological model consisting of amixing rule between two simple models involvingconnection in series (Reuss prediction) or in par-allel (Voight prediction) of the components. Ac-cording to this model,

E � �1 � ��E1 � ��1 � ��/E1 � ��/E2��1 (5)

E1 is the property of the matrix phase, E2 is theproperty of the dispersed phase, and � is thevolume fraction of the dispersed phase and isrelated to the degree of series–parallel coupling.The degree of parallel coupling of the model canbe expressed by

% Parallel � ��1 � ��/�1 � �� 100 (6)

According to Nielsen23 and Kunori and Geil,24

tensile failure of a blend is the result of the adhe-sion falling between the blend components. Whenthere is no adhesive force between the blend com-ponents, the tensile strength of the blend (�b) maybe written as

�b � �m�1 � Ad� (7)

where �m is the tensile strength of the matrix andAd represents the area of the fraction occupied bythe dispersed phase in a transversal cross section.Kunori and Geil24 assumed that when strong ad-hesive force existed between the blend compo-nents, the dispersed phase would contribute tothe strength of the blend. Therefore, eq 7 may bemodified as follows:

�b � �m�1 � Ad� � �dAd (8)

If the fracture propagates mainly through theinterface, eq 8 may be written as


�b � �m�1 � �d�2/3 � �d�d

2/3 (9)

If the fracture propagates through the matrix,then the equation becomes

�b � �m�1 � �d� � �d�d (10)

This equation is the same as the parallel modelequation.

Another important model for perfect adhesionis the Kerner equation.25 Kerner derived a theoryfor a matrix with spherical inclusions when thesystem is isotropic and the adhesion between thetwo phases is perfect. The upper and lower

bounds of this two-phase polymer material aregiven by eq 11:

Eb � Em��dEd/��7 � 5�m�Em � �8 � 10�m�Ed�

� �m/15�1 � �m�

�dEm/��7 � 5�m�Em

� �8 � 10�m�Ed � �m/15�1 � �m�� (11)

where Eb is the blend property, � is Poisson’s ratioof the matrix, and � is the volume fraction. Thesubscripts m, d, and b stand for the matrix, dis-persed phase, and blend, respectively.

Figures 1 and 2 show comparisons of the vari-ations in the theoretical and experimental curves

Figure 1. Comparison of the experimental tensile strengths and theoretical predic-tions for PS/PB blends.


of the tensile strength and Young’s modulus ofPS/PB blends as functions of the weight percent-age of PS. The predictions of these theories weremade with E1 � 0. 432 and E2 � 33.04 for thetensile strength and E1 � 0.699 and E2 � 297 forYoung’s modulus, respectively. In the experimen-tal curve, there is only a marginal increase intensile strength with the addition of up to 40 wt %PS to PB. A very large increase in tensile strengthbeyond phase inversion around S50 to S80 can beobserved. In immiscible blends, the tensilestrength usually depends on the particle size ofthe dispersed phase. Smaller and more uniformlydistributed particles are more effective in initiat-ing crazes and terminating them before they de-velop into catastrophic sizes. The lower values forthe tensile strength in this blend system up to

40% PS may be due to poor interfacial adhesionbetween the dispersed PS phase and the contin-uous PB matrix. The poor interfacial adhesioncauses premature failure as a result of the usualcrack-opening mechanism. The experimental val-ues of the tensile moduli are not so close to any ofthe aforementioned models. The values are seenbetween the series and parallel models. The mod-erate values indicate the absence of any favorableinteraction between the PS and PB phases.

Complementary evidence for this observationcan be obtained from morphological studies of afew selected samples by scanning electron micros-copy. Figure 3 (a–c) presents scanning electronmicrographs of S30, S50, and S70 blends. The mor-phology of blend S30 shows that in this blend, theminor phase of PS is dispersed as spherical inclu-

Figure 2. Comparison of the experimental Young’s moduli and theoretical predic-tions for PS/PB blends.


sions in the continuous PB matrix, as seen inFigure 3(a). When PS is the dispersed phase, therate of coalescence is lower because of the highviscosity of the PB phase, and so PB becomes acontinuous matrix. An interpenetrating cocon-tinuous morphology is obtained for S50, as seen in

Figure 3(b). At this particular composition, bothimmiscible phases are completely continuous(100% continuous), and there is no possible dis-tinction between the matrix and the dispersedphase. This is followed by a phase inversion.Therefore, at S70, the minor phase of PB is dis-persed as droplets in the continuous PS matrix, asseen in Figure 3(c). Morphological observationsgive a satisfactory explanation for the lower val-ues for the tensile strength in this blend systemup to 40% PS. This is explained by poor interfacialadhesion between the dispersed PS phase and thecontinuous PB matrix.

Tensile Moduli of Cocontinuous Regions

The phase continuity and phase inversion in poly-mer blends can be studied by the relation of thetensile moduli to modulus–composition models.16

It is interesting to apply different equations sug-gested for tensile moduli of cocontinuous struc-tures for comparison. Coran and Patel26 proposedan equation intended to account for phase inver-sion at a certain composition of the blend. Themodulus is expressed as a function of the upperand lower bounds with a fit parameter, n, which issupposed to depend on wetting and compatibility.It gives the point of phase inversion as � � (n1� n)/n.

According to Coran and Patel’s26 equation,

E � �2n�n�1 � 1��EU � EL� � EL (12)

The experimental data are close to this model, forwhich n is 1.89. This value corresponds to VH� 0.47 as the hard phase volume fraction, whichcorresponds to a phase inversion of PB from adispersed phase to a continuous phase. This ob-servation is consistent with our experimental ob-servations from mechanical and morphologicalstudies.

According to Lees,4 the tensile modulus for arandomly oriented dispersion is

Erandom �2 �

0

/2

Ed (13a)

where E is the angular dependence of the tensilemodulus. This modulus is

E �EUEL

EU � �EUEL�cos4(13b)

Figure 3. Scanning electron micrographs of (a) 30/70,(b) 50/50, and (c) 70/30 PS/PB blends.


where EU and EL have the same meanings asbefore. Lees considered two examples of moduli ofrandom blends for different aspect ratios. Equa-tions 13a and 13b are applicable at concentra-tions of the dispersed phase up to the maximumpacking density of the dispersed particles. For thehexagonal packing of parallel rods, this maximumpacking density can be up to about 90 vol % forspheres. The maximum packing density of ran-domly oriented rods depends on their aspect ratio(length to diameter ratio (L/D)) and is given bythe following relation:27,28

1/�max � 1.38 � 0.0376�L/D�1.4 (14)

An increase in the aspect ratio of the dispersedphase leads to a decrease in the packing density

and, consequently, to a smaller range of validityfor eqs 13a and 13b.

For cocontinuous polymer blends, differentequations for the tensile modulus as a function ofthe composition have been proposed. The relationgiven by Davies,29 which assumes the blend to bemacroscopically homogeneous and isotropic,takes the shape

E1/5 � E11/5�1 � E2

1/5�2 (15)

It is supposed to be applicable for cocontinuousstructures without any details being specified. Anumber of researchers found the Davies equationto describe their experimental data best.30,31

Figure 4. Comparison of the experimental results and theoretical predictions oftensile strength in cocontinuous morphologies.


Lyngaae-Jorgensen et al.32 gave a relation forthe moduli of blends above the percolation thresh-old (T) of the minor component:

E � E1 � �E2 � E1��2 � �c

1 � �c�T

(16)

where T is 1.7–1.9 and �c is 0.16; for fibers, �c ismuch lower. Kolarik33 introduced the cross or-thogon skeleton (COS) model for the mechanicalproperties of cocontinuous morphology. The mod-ulus of the COS model is

E � E1�1 � f�2 � E2f2 �2f�1 � f�

�1 � f�/E1 � f/E2(17)

where f is related to the volume fraction33 as �1

� (1 � f)2(1 � 2f). Figures 4 and 5 give compari-sons between experimental results and predictiontheory for tensile strength and Young’s modulus,respectively, obtained with the aforementionedequations of cocontinuity. Willemse et al.12 andVeenstra et al.14 gave clear descriptions of theevolution of cocontinuous morphologies. From thepicture given previously, the aforementionedequations cannot give a proper evaluation of themoduli of the blends over a broad compositionrange. Lyngaae-Jorgensen et al.32 took account ofthe onset of percolation but did not consider theonset of full cocontinuity. The COS model ac-counts for the cocontinuous morphologies, but itspredictions hardly differ from the values obtained

Figure 5. Comparison of the experimental results and theoretical predictions ofYoung’s modulus in cocontinuous morphologies.


by eqs 12–17. Applying these equations to ourblend system leads us to the conclusion that ex-perimental values are close to those of the Daviesmodel. At a lower weight percentage of PS, thevalues are also close to those of the Lyngaae-Jorgensen model. Cocontinuity is observed in thecomposition range 40–60% PS. The modulusvalue at this composition does not show any signof synergism on account of interfacial incompati-bility. Unlike other blend systems, no remarkablesynergism is found in PS/PB blends.

CONCLUSIONS

A comparison between experimental results andprediction theory for the tensile strengths andYoung’s moduli of PS/PB blends as functions ofcomposition and morphology was made. The mod-els selected were the series, parallel, Halpin–Tsai, Takayanagi, Kerner, and Kunori models.Tensile strength is correlated as a function of theblend ratio. The experimental values do not agreewell with any of the models and are between theseries and parallel models. The moderate valuesindicate the absence of any favorable interactionbetween PS and PB phases. Different equationshave been applied for tensile moduli of cocontinu-ous structures for comparison. The experimentalvalues are very close to those of the Davies equa-tion both for tensile strength and Young’s modu-lus. At a lower weight percentage of PS, the val-ues are also close to those of Lyngaae-Jorgensenmodel. Cocontinuity is observed in the composi-tion range 40–60% PS. Unlike other polymerblends, the cocontinuous region in PS/PB blendsshows only a marginal increase in tensile modulibecause of the incompatibility between thephases. The limitations of the different modelshave also been discussed.

This research was supported by the University GrantsCommission (New Delhi, India).

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Modeling of tensile moduli in polystyrene/ polybutadiene blends