Effects of Copolymer Sequence Distribution on the Miscibility ofPoly(ethylene oxide)/Poly(styrene-co-acrylic acid) Blends: AMolecular Simulation Approach

Kyoungsei Choi and Won Ho Jo*

Department of Fiber and Polymer Science, Seoul National University, Seoul 151-742, Korea

Received September 21, 1995; Revised Manuscript Received September 10, 1996X

ABSTRACT: The effect of the copolymer sequence distribution on the miscibility of a poly(ethylene oxide)(PEO)/poly(styrene-co-acrylic acid) (SAA) blend has been investigated by molecular simulations. Themolecular simulation provides a method to calculate the interaction energy parameter and hydrogen-bond energy. It is observed that both the sequence distribution and the composition of the SAA copolymersignificantly affect the degree of miscibility. For a fixed composition, there exists an optimal range ofsequence distributions for which the blend system is miscible.

IntroductionIt is possible to obtain polymer blends of more

desirable properties by mixing miscible polymers, andthus it is very important to examine the factors affectingthe miscibility of polymer mixtures. The miscibility ofhomopolymer/copolymer blends has been successfullydescribed by the binary interaction model.1-4 Based onthe model, the effect of the composition of the copolymeron the miscibility of PEO/SAA blends was systematicallyinvestigated in our laboratory.5 It was suggested thatboth the specific interaction between ethylene oxide(EO) and acrylic acid (AA) segments and the intramo-lecular repulsive force in the SAA copolymer are re-sponsible for the miscibility.Progress in polymerization technology now allows

control of the microstructural features of polymers suchas tacticity. Experimental studies of the tacticity effecton polymer blend miscibility have been reported in somepublications.6-9 It is reported that the tacticity of apolymer can affect the conformation of the chain, theprobability of contact between interacting sites, and theinteraction parameter, all of which will inevitably havean influence on miscibility. A theoretical approach tothe tacticity effect has been initiated using an integralequation formalism,10 and the molecular origin of thetacticity effects on blend miscibility was examined.11The sequence distribution of the copolymer in ho-

mopolymer/copolymer blends will affect the chargedistribution and the probability of contact betweeninteraction sites, and consequently affect the miscibilityof the blend. However, the binary interaction model isinadequate to study the sequence effect due to theassumption of a random distribution. Thus, Balazs etal.12 developed a model describing the sequence effecton miscibility and showed that there is an optimal rangeof sequence distributions for which the homopolymer/copolymer system is miscible by using their own model.In this paper, we analyze the effect of the copolymer

sequence distribution in PEO/SAA blends by calculatingthe interaction energy parameters and the hydrogen-bond energy using molecular simulation methods.

Theoretical BackgroundFor simplicity, we denote the monomeric units of AA,

styrene, and EO as a, b, and c instead of using the full

names. The free energy of mixing for a binary mixtureof a homopolymer and a copolymer, cN1/(afb1-f)N2, is givenby1-3

where øtot is the parameter that represents the strengthof the polymer-polymer interaction. The homopolymercN1 has a volume fraction φ1 and degree of polymeriza-tion N1, and the copolymer (afb1-f)N2 has a volumefraction φ2 and degree of polymerization N2 with thecomposition of f and 1 - f. When the binary interactionmodel is invoked, the total interaction energy parameterøtot is given by

However, the simple binary interaction model is inad-equate to study the sequence effects owing to itsassumption of a random distribution. Assuming thatthe interaction energy parameters of all a-a and b-bpairs are equivalent and equal to zero and that all a-binteractions are equivalent to the average interactionparameter øjab, Balazs et al.12 expressed øtot as the sumof the contribution of the composition øcomp and thesequence distribution ødist as follows:

where fa and fb are the fractions of a and bmolecules inthe copolymer, faa, fab, and fbb are the pair probabilitiesof aa, ab, and bb pairs in a single chain, and thus fa )faa + fab, fb ) fbb + fba and fab ) fba. The øjac is the averageof the interactions between a occupying the central sitein the triads and c, i.e., øaaa:c, øaab:c, and øbab:c. The øjbcis similarly the average of øaba:c, øabb:c, and øbbb:c.Although there are nine possible a-b interactions, allinteractions will be assumed equivalent to the averageinteraction parameter øjab which is the intramolecularinteraction in the copolymer chain. Then, ∆øa and ∆øbare defined by eqs 6 and 7, respectively.

* To whom correspondence should be addressed.X Abstract published in Advance ACS Abstracts, February 1,

1997.

∆GRT

)φ1

N1ln φ1 +

φ2

N2ln φ2 + φ1φ2øtot (1)

øtot ) føac + (1 - f)øbc - f(1 - f)øab (2)

øtot ) øcomp + ødist (3)

øcomp ) faøjac + fbøjbc - fafbøjab (4)

ødist )faa

2

fa∆øa +

fbb2

fb∆øb (5)

1509Macromolecules 1997, 30, 1509-1514

S0024-9297(95)01421-5 CCC: $14.00 © 1997 American Chemical Society

A negative ∆øa implies that aaa-c interactions areenergetically more favorable than any other type of a-cinteractions, and a similar comment is applicable to ∆øb.The parameters θ and δ are introduced to specify thesequence distribution and the composition, respectively.

θ can range from 0 for a block copolymer to 1 for analternating copolymer, with the value 0.5 for a randomcopolymer. For symmetric copolymers, δ ) 0, and thecopolymer composition can be expressed by δ.

Model and SimulationThe Dreiding 2.21 force field13 was adopted for our

simulations, and the Cerius2 software from MolecularSimulations Inc. was used. The intramolecular interac-tions were described by force field terms including bond,bending, torsion, and inversion; the intermolecularinteractions by terms including van der Waals, electro-static, and hydrogen bonding.131. Validation of the Force Field. The Hildebrand

solubility parameters of several homopolymers werecalculated and compared to experimental data to ex-amine the validity of the force field. The procedures toprepare an equilibrated structure are as follows. Anatactic PS chain with 20 repeating units and a mesodiad content of 50% was produced and then packed intoa cubic simulation box with 3-D periodic boundaries.The size of the cubic box was chosen to correspond tothe experimental density 1.05 g/cm3.14 At the first stagefollowing generation of the initial structure in thesimulation box, the energy of the structure was roughlyminimized by the conjugate gradient method. Then, thestructure was relaxed by performing NVT-moleculardynamics at 1000 K for 20 000 steps (1 step correspondsto 1 fs), followed by NVT-molecular dynamics at 300 Kfor 20 000 steps. To save computation time duringrough equilibrations, the long-range nonbonded interac-tions were treated by cutting off the potential curve at8.0 Å. This cutoff introduces discontinuities in thepotentials and forces. Thus, a spline function15 wasused to connect the potentials and forces over 8.0-8.5Å to prevent the discontinuity. The structure wasfinally equilibrated by NVT-molecular dynamics at 300K for 10 000 steps followed by energy minimizationusing conjugate gradients, where the Ewald method16was used to calculate the nonbonded interactions.The Hildebrand solubility parameter is the square

root of the cohesive energy density, which is defined asthe energy difference when a polymer of unit volume isevaporated in vacuum. Solubility parameters wereobtained for five different equilibrated structures pro-duced from initial configurations with different tacticitysequences but containing the same meso-diad fractionsby following the standard method,17 where the energyof the bulk-state polymer was obtained using the Ewaldmethod. The same procedures were applied to calculatethe solubility parameters of PEO and poly(acrylic acid)(PAA), using densities of 1.128 and 1.045 g/cm3 for PEO

and PAA, respectively.14,21 The atactic PAA was mod-eled with a meso-diad fraction of 50%.2. Determination of Miscibility. The procedures

used in this study consist of two simulation methods.One is a so-called docking method18 combined withBalazs et al.’s theory,12 and the other is moleculardynamics. The former is preferable to the latter,because the docking method requires much less com-putation time than the molecular dynamics does. Thus,our results mainly relied on the docking method todetermine the miscibility of the blends, and moleculardynamics was only employed for obtaining additionalsubsidiary information on the contact probability be-tween AA and EO.Docking Methods. Docking methods can provide

segmental interaction energy parameters.18,19 The in-teraction parameter øi:j can be calculated from a knowl-edge of pairwise interactions, wkl’s (k, l ∈ {i, j}), andcoordination numbers, zkl’s by using eq 10.

where wkl is an averaged pairwise interaction energywhen a segment l is in contact with the center segmentk. A similar explanation can be given for zkl .In order to simulate four wkl’s and zkl’s and to obtain

øi:j, the model segments i and j with proper chargedistributions must be prepared. Nine model segmentswere prepared in this system: aaa, aab, bab, aba, abb,bbb, and c for the calculation of øjac and øjbc; -a- and-b- for the calculation of øjab. For the triads, the partialcharges were calculated utilizing the charge equilibra-tion method,20 which is also available in the Cerius2software, after constructing and optimizing the triadstructure, and then the monomeric units on both sideswere removed. Thus, a monomer structure, which hasthe charge distribution of a monomer in the center ofthe triad, was prepared. For example, the structure ofa triad aba was produced, the partial charges werecalculated, and then a’s on both sides were removed,which produced a b segment with the charge distribu-tion of the b monomer in the triad aba. The b segmentwill be denoted as aba in order to distinguish from otherb segments which come from triads abb and bbb. Theother model segments aaa, aab, bab, abb, and bbb weregenerated by following similar procedures. These seg-ments of a and b were used for calculating øjac and øjbc.Additionally, the model segments -a-, -b-, and cweremade to have the total charge of zero, where the modelsegments -a- and -b- were prepared for calculatingøjab. As mentioned above, all the a-b interactions inthe copolymer chains were assumed to be equivalent tothe average interaction parameter øjab to reduce thenumber of interaction energy terms, and thus the modelsegments -a- and -b- were produced separately fromthe other model segments.No segments are allowed to make contact in the chain

direction due to the chain connectivity. Thus, allsegments were made inaccessible on both sides in thechain direction by introducing two dummy atoms at thehead and tail positions of the segments, which preventedcontacts with other atoms.A particular configuration of segments i and j was

produced with them touching each other, and thepairwise interaction energy for the configuration wascalculated. The same procedure was repeated 100 000times, and the Metropolis criterion was used to deter-mine whether to accept these configurations at a certain

∆øa ) øaaa:c - øjac (6)

∆øb ) øbbb:c - øjbc (7)

θ )fab2fafb

(8)

fa ) 12(1 + δ), fb ) 1

2(1 - δ), -1 e δ e 1 (9)

øi:j ) 1RT(12(zijwij + zjiwji) - 1

2(ziiwii + zjjwjj)) (10)

1510 Choi and Jo Macromolecules, Vol. 30, No. 5, 1997

temperature. The interaction energy wkl(T) was deter-mined by averaging the energies of all accepted con-figurations at a given temperature. The coordinationnumbers zkl’s were obtained by calculating and averag-ing the possible numbers of nearest neighbors (l) incontact with the center segment (k) over 500 trials. Moredetailed explanations can be found elsewhere.18

Molecular Dynamics. Another approach, moleculardynamics combined with molecular mechanics, can inprinciple provide more exact information on the pairwiseenergy. However, this method requires very longcomputing times and also yields interaction energiesthat depend strongly upon the initial configuration ofpolymers. Furthermore, strong specific interactionssuch as hydrogen bonding can prevent chains fromrelaxing, making it difficult to generate equilibriumstructures. Therefore, many samples and error analysisare essential to obtain meaningful results. Hydrogen-bond energies were calculated for PEO/SAA blends, inwhich the SAA chain is either a random or a blockcopolymer, to estimate the effect of local chain confor-mations on the interaction energy parameters. Theprimary box contains an SAA chain of 100-mers andfour PEO chains of 25-mers. Instead of one long PEOchain, four short PEO chains were employed to yield ahigher probability of interchain contact. Eight to twelvesamples were prepared with initially random torsionalangles and then relaxed by molecular mechanics. Thestructures were annealed at high temperature byNVT-molecular dynamics without turning on the strongspecific interactions such as electrostatic and hydrogen-bond energies, to prevent early fixation of the structuresand to ensure easy relaxation of the chains. Then, thestructures were relaxed again at room temperature byNVT-molecular dynamics. After equilibration, molec-ular dynamics was performed using the microcanonicalensemble, and the hydrogen-bond energies were calcu-lated. The density was fixed at 1.0 g/cm3 for all thesystems.

Results and Discussion

The simulated solubility parameters of homopolymersare listed in Table 1. The simulated results agree wellwith the experimental values, although the values havesome scattering which may arise from both smallnumber of samples and relatively short chain. Thissuggests that the Dreiding 2.21 force field is adequatefor PS, PEO, and PAA.Total charge values for the segments aaa, aab, and

bab produced by the charge equilibration method are-0.009, -0.111, and -0.204, respectively. It is recalledthat the total charge values of the segments aaa, aab,and bab correspond to those of the center monomer (a)only in each triad. The electron density in a increaseswith the substitution of b which donates electrons morereadily than a. Total charge values of the segments aba,abb, and bbb are 0.181, 0.028, and 0.032. This meansthat a monomer b connected to the electron-withdraw-ing monomer a as its neighbor has a more positive net

charge than when next to a b. Total charge values ofthe other model segments, -a-, -b-, and c are zero.The interaction energy parameters were calculated

for the model segments which have proper chargedistributions by the docking method. Figure 1a showsthat the interaction between a and c is favorable,especially when a is activated by b which donateselectrons to its covalent-bonded neighbors. It is note-worthy that the interaction between the sequence aaaand c is relatively unfavorable, which results in apositive ∆øa. This means that blockiness of amay leadto a negative contribution to miscibility. The experi-mental results showed that there exist both a specificinteraction between a and c and an intramolecularrepulsion between a and b.5 The experimental trendsare seen in Figure 1b, where øjab is seen to be stronglypositive whereas øjac has a strongly negative value.Balazs et al.12 assumed that øjac ) øaab:c ) øbaa:c ) øbab:c* øaaa:c and øjbc ) øabb:c ) øbba:c ) øaba:c * øbbb:c to reducethe number of interaction terms. However, in thepresent study, all the interaction terms such as øaab:c()øbaa:c), øbab:c, øaaa:c, øabb:c ()øbba:c), øaba:c, and øbbb:c werecalculated, and øjac and øjbc were taken as average valuesof corresponding triads, because it is unreasonable toassume øaab:c ) øbab:c and øabb:c ) øaba:c as one sees from

Table 1. Hildebrand Solubility Parameters in (MPa)1/2

solubility parameters

polymer density sample 1 sample 2 sample 3 sample 4 sample 5 average exptla

PS (at.) 1.050a 16.5 17.4 17.7 17.3 16.8 17.1 ( 0.4 17.52PEO 1.128a 20.4 23.7 18.1 23.8 22.5 21.7 ( 2.2 20.2 ( 2PAA (at.) 1.045b 18.1 17.3 19.3 19.7 19.8 18.8 ( 1.0 18.0a From ref 14 b From ref 21.

Figure 1. (a) Interaction energy parameters as a function oftemperature obtained by molecular simulations. (b) Theinteraction energy parameters which are calculated from thosein (a). The meaning of the notations in the inset is explainedin the text.

Macromolecules, Vol. 30, No. 5, 1997 Miscibility of PEO/SAA Blends 1511

Figure 1a. Cantow et al.22 also criticized Balazs et al.’sassumption. They asserted that the assumption causessome inconsistency. They redefined ∆øa and ∆øb as ∆øa) øaaa:c - øaab:c ) øaab:c - øbab:c and ∆øb ) øbbb:c - øbba:c) øbba:c - øaba:c. Figure 1 shows øaab:c ≈ øjac and øaaa:c -øaab:c ≈ øaab:c - øbab:c at above room temperature, andthus our ∆øa has almost the same value as the ∆øaobtained using the definition of Cantow et al. In thecase of ∆øb, the situation is not the same as ∆øa, butthe ∆øb has too small a value compared with ∆øa toaffect ødist. Consequently, our simulation results for ødistare well consistent with those obtained from the defini-tion of Cantow et al.The total interaction energy parameter øtot, the com-

position dependent component øcomp, and the sequencedistribution dependent component ødist were obtainedby incorporating the simulated interaction parametersinto eqs 3-5. The monomer fractions (fa and fb) anddiad fraction (fab) were determined by varying θ and δin eqs 8 and 9. An increase of AA content in SAAproduces more AA-EO interactions, which is favorablefor miscibility and thus leads to a negative øcomp (Figure2a). In the limit that the composition of AA approaches

1.0, ødist becomes equal to ∆øa. In the other limit thatthe composition of AA approaches 0.0, ødist becomesequal to ∆øb. Because ∆øa is larger than ∆øb, ødistincreases with the AA content (Figure 2b). The blocki-ness of the sequence represented by lower θ has anegative effect on the miscibility, which seems to arisefrom the strong tendency of øaaa:c > øaab:c > øbab:c asshown in Figure 1a. As a result, the PEO is moremiscible with the SAA copolymer having an alternatingsequence (Figure 2c). The maximum value of θ islimited by the composition:

In the case of a symmetric copolymer (i.e. δ ) 0), θmaxequals unity such that the copolymer can have sequencedistributions ranging from block to alternating.The temperature dependence of the total interaction

parameter shows that there exists an optimum condi-tion for the composition at a given temperature (Figure3). Binary blends of PEO/PS and PEO/PAA are im-miscible and miscible, respectively, at room tempera-ture. The shape of curves implies that the homopolymer/homopolymer blends will exhibit UCST (upper criticalsolution temperature) behaviors.A drastic effect of the sequence distribution on the

miscibility can be found in Figure 4. As the AA contentin SAA increases from 5 mol % (Figure 4a) to 7 mol %(Figure 4b) to 10 mol % (Figure 4c), the blend becomesmore miscible. The blend with random copolymersbecomes miscible at a composition between 5 and 7 mol%, which agrees well with the experimental results.5 At7 mol %, the blend with block copolymers shows positiveøtot, while the blend with random copolymers hasnegative øtot. This is very interesting because themiscibility could be controlled only by the change ofcopolymer sequence distributions.The difference in the spatial distribution of interaction

sites may also affect the effective interaction. Thetheory adopted here, however, does not accommodatethe physical aspects of chain conformations, and thusthe probability of contacts between segments only basedon the mean field approximation is considered. In oursimulation, the information on the probability of con-tacts could be obtained by calculating hydrogen-bondenergy, because the number of contacts is proportionalto the hydrogen-bond energy. The intermolecular hy-drogen-bond energy between AA and EO (Figure 5d)

Figure 2. Interaction energy parameters at room tempera-ture obtained by combining molecular simulations and thetheory of Balazs et al.: (a) the composition dependent interac-tion energy parameter øcomp; (b) the sequence distributiondependent interaction energy parameter ødist; (c) the totalinteraction energy parameter øtot.

Figure 3. Total interaction energy parameters as a functionof temperature for θ ) 0.5.

θmax ) 11 + δ

(11)

1512 Choi and Jo Macromolecules, Vol. 30, No. 5, 1997

was obtained by subtracting the intramolecular hydro-gen-bond energies (Figure 5b and 5c) from the totalhydrogen-bond energy (Figure 5a). When the AA con-tent is small, AA segments in random copolymers whichhave more sparse distribution will have fewer chancesto meet EO segments because AA’s are buried in styrenesegments and thus the intermolecular interactions areprevented. When the AA content is large, the self-association of intramolecular AA’s in the block copoly-mer rapidly increases, which prevents the formation ofthe intermolecular hydrogen bond. Consequently, thereexists a competition between self-associations of AA’sand intermolecular hydrogen bonds of EO-AA pairs,and the competition is a function of the composition andthe sequence distribution. However, the hydrogen-bondenergies which reflect the local spatial distribution ofinteraction sites do not vary as much as the totalinteraction with the sequence distribution as shown inFigure 5. The total interaction between AA and EO canbe calculated from eq 12:

The results show the difference of about 600-1000%in the total interaction energies for block and random

copolymers, whereas the differences of hydrogen bondenergies are of about 20-40%. Therefore, the contribu-tion of the local spatial distribution of the interactionsites to the interaction energy is relatively small com-pared to the segmental interaction itself. One canconclude that it is not necessary to incorporate thecontribution of the local spatial distribution into thedetermination of miscibility for PEO/SAA blends. Inother words, the interaction energy parameters need notbe scaled by the ratios of contact probabilities arisingfrom the local spatial distribution, which means Balazset al.’s original theory is sufficient to estimate themiscibility of PEO/SAA blends. This is why moreextensive molecular dynamics with more refined densi-ties for the calculation of hydrogen bond has not beenconducted.As a virtual experiment performed on computers,

molecular simulation methods can provide helpful in-formation to understand the physical nature in aqualitative sense and may often give quantitativepredictions, although it is not always possible to com-pare all the simulated results with the real experimen-tal ones at this time. It is noteworthy that the effect ofsequence distribution on phase behaviors can be ap-proached in different ways. Recently, extensive re-search efforts have been devoted to models where theeffect of the sequence distribution manifests itself onlyin the number of different segment-segment inter-actions.23-25 However, their models have not beenexamined in this study.

Conclusions

Molecular simulations were carried out to study theeffect of sequence distribution of copolymer on themiscibility of PEO/SAA blends by calculating the inter-action energy parameters and hydrogen-bond energy.It is observed that both the composition and thesequence distribution significantly affect the degree ofmiscibility. For a fixed composition, there exists anoptimal range of sequence distribution for which theblend system is miscible. The sequence distribution

Figure 4. Total interaction energy parameter between PEOand SAA for (a) 5, (b) 7, and (c) 10 mol % of AA in SAA.

øtotal,ac )fab

2

faøbab:c + 2

fbafaafa

øbaa:c +faa

2

faøaaa:c (12)

Figure 5. Hydrogen-bond energy calculated by moleculardynamics and molecular mechanics: (a) total; (b) self-associa-tion between AA segments; (c) self-association between EOsegments; (d) interchain hydrogen bond between AA and EOsegments. Filled and open circles represent block and randomcopolymer, respectively.

Macromolecules, Vol. 30, No. 5, 1997 Miscibility of PEO/SAA Blends 1513

does not only affect the charge distribution of segmentswhich in turn affects the contact energy, but also affectsthe probability of contacts between interaction sites. Itis also observed that the segmental interaction energyitself is more important than the local spatial distribu-tion of the segments, to determine the effect of thecopolymer sequence distribution on the miscibility.There exists a competition between self-associations ofAA’s and intermolecular hydrogen bonds of EO-AApairs, and the competition is a function of the composi-tion and the sequence distribution.

Acknowledgment. The authors thank Cheil Indus-tries Inc. for their financial support.

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1514 Choi and Jo Macromolecules, Vol. 30, No. 5, 1997