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ORIGINAL PAPER

Modeling and analysis of the compatibility

of polystyrene/poly(methyl methacrylate) blends

with four inducing effects

Dan Mu &Jian-Quan Li &Yi-Han Zhou

Received: 8 February 2010 /Accepted: 1 April 2010 /Published online: 5 June 2010# Springer-Verlag 2010

Abstract The compatibility of polystyrene (PS) and poly

(methyl methacrylate) (PMMA) blends was studied over awide range of compositions at 383, 413 and 443 K,respectively, by atomistic and mesoscopic modeling. Allthe calculated FloryHuggins interaction parametersshowed positive values; furthermore, they were all abovethe critical FloryHuggins interaction parameter value,which means that the PS/PMMA blends were immiscible.Both the addition of a block copolymer and the introductionof a shear field influenced the phase morphologies of the

blends, while the degree of influence depended on thecompositions of the blends. The study of PS/PMMA blendsdoped with nanoparticles showed that the mesoscopic phase

was influenced by not only the properties of the nano-particles, such as their size, number and number density,but also the compositions of the blends. The effect of thesurface roughness of the planes on the phase separation ofthe blends was also studied.

Keywords PS/PMMA blend . Inducing effect. Phasemorphology .Nanoparticle

Introduction

Polymer blend systems play an important role in the plasticindustry because they can be tuned to have a bettercombination of physical properties than the correspondinghomopolymers. The process of physical blending is mucheasier to perform than chemical blending (e.g., grafting),and the former is also more economical. As a general rule,the aim of blending is to obtain a product with new or better

properties. Because of the different physical properties ofcandidate polymers, it is not always easy to obtaincompletely miscible polymer mixtures. When the compo-nents of polymers can form energetically favorable inter-

actions, such as hydrogen bonding, dipole interactions, etc.,it is possible to obtain a miscible blend. For immiscible

blends, adding interferents is a common method ofchanging the microscopic morphology. This improves the

blend miscibility and thus enhances its properties.Polystyrene (PS) and poly(methyl methacrylate)

(PMMA) are conventional model systems in polymerscience. PS/PMMA blends are a well-known immisciblecombination [1-8], and their bulk and surface phaseseparation has been observed [9, 10]. Immiscible blendsare known to have properties combining those of theircomponent polymers, and also to have segregated structures

with domains that are predominantly formed from theindividual homopolymers. It has been shown that changingthe relative homopolymer proportions in such blends canchange the domain structure, surface morphology, and eventhe phase morphology [11-13].

Some contradictory results can be found in the literatureregarding the miscibilities of certain polymers and the

possibility of predicting miscibility from surface tension orfrom parameters derived from it. These contradictions can

be attributed to several reasons. Firstly, the structures and

D. Mu (*)Department of Chemistry, Zaozhuang University,

Shandong 277160, Chinae-mail: mudanjlu1980@yahoo.com.cn

J.-Q. LiPhysics and Electronic Engineering Department,Zaozhuang University,Shandong 277160, China

Y.-H. ZhouNational Analytical Research Center of Electrochemistryand Spectroscopy, Changchun Institute of Applied Chemistry,Chinese Academy of Sciences,Changchun, China

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the properties of partially miscible polymer blends dependon the processing conditions used, which may influenceconclusions about polymer compatibility when they arededuced from macroscopic properties or from the structureof the blend. Secondly, methods that can be used to predictmiscibility are limited [14, 15]. For example, variousexperimental difficulties can be encountered during the

determination of the FloryHuggins interaction parameter,, which can be used to characterize the strength of theinteraction between the polymers. can be determined byvarious methods, such as inverse gas chromatography,solvent diffusion, or the dependence of composition onmechanical properties, but all of these methods have theirdrawbacks. Finally, when blend systems have two calori-metric Tg values, it does not necessarily indicate that theircomponents are immiscible [16]. Fortunately, computercalculations and simulations have become available asefficient methods of solving these experimental problems.

This paper is divided into two main parts. The first part

is about the calculation of typical thermodynamic param-eters, such as the solubility parameter, of the studiedsystems via a microscopic calculation method, and com-

paring those calculated parameters with experimental datain order to maintain a high level of accuracy in furthercalculations and simulations; the second part describesmesoscopic dynamics simulations of several kinds ofinducing effects that can change the phase morphologiesof PS/PMMA blends. Mesoscale structures are of theutmost importance during the production processes ofmany materials, such as polymer blends, block copolymersystems, surfactant aggregates in detergent materials, latex

particles, and drug delivery systems.Mesoscopic dynamics models have been receiving increas-

ing attention recently, as they form a bridge betweenmicroscale and macroscale properties [17-20]. Mesoscopicdynamics (MesoDyn) [21-23] and dissipative particle dy-namics (DPD) [24,25] methods both treat the polymer chainat a mesoscopic level by grouping atoms together and thencoarse-graining them to be persistent-length polymer chains.These two mesoscopic modeling methods increase the scaleof the simulation by several orders of magnitude comparedwith atomistic simulation methods. MesoDyn utilizes dy-namic mean-field density functional theory (DFT), in which

the dynamics of phase separation can be described byLangevin-type equations to investigate polymer diffusion.Thermodynamic forces are found via mean-field DFT, usingthe Gaussian chain as a model. The most importantmolecular parameter is the incompatibility parameter N,where is the FloryHuggins interaction parameter and Nisthe degree of polymerization.

However, owing to the soft interaction potential of theDPD method, it is not suitable to apply the DPD method in ourwork, especially when dealing with the interactions between

blending materials and planes or doped nanoparticles.Furthermore, in the study of the compatibility of PEO/PMMA

blends in our former work, the MesoDyn simulation methodwas successfully applied to detect the phase morphologies ofPEO/PMMA blends. From a theoretical point of view, theseresults clarified several conflicting conclusions of differentexperiments [26]. Therefore, the MesoDyn method has been

shown to be reliable when dealing with PS/PMMA blends.The mesoscale simulation process used in this paper wascarried out with the MesoDyn module in the Material Studiocommercial software provided by Accelrys.

Simulation details, results and discussions

This paper consists of two parts: calculations performed via(1) molecular dynamic (MD) simulations and (2) mesoscopicsimulations. The intermediate parameter connecting themicroscale and the mesoscale is the FloryHuggins param-

eter, . MD simulation is used to accurately study bulkpolymer properties when this is difficult to do experimental-ly. Although MD simulation is widely used nowadays, it isdifficult to detect the phase separation of blends via amicroscopic method, such as MD simulation. Therefore, it isnecessary to combine it with a mesoscopic method, such asMesoDyn simulation, to perform a full study of polymer

blends from the microscale to the mesoscale.

Atomistic molecular simulation

Model and simulation

The selection of the representative chain length (Nmon) wasour primary task. This simulation process was carried out atroom temperature (298 K) on an SGI workstation byfollowing the MD procedure in the commercial Cerius2

package program provided by Accelrys.The simulation processes (including the construction of the

models) were the same for both PS and PMMA, so we will usean atomistic chain length Nof 10 for PS as an example hereto describe the simulation process in detail. Initially, the

proposed polymer chain structure was generated using therotational isomeric state (RIS) model of Flory [27], which

describes the conformations of the unperturbed chains. ThreePS polymer chains were then generated following the same

principle, each with ten repeating units; they were then putinto a simulation box with a density of 1.05, which is thedensity of bulk PS [28]. Minimization was then done usingthe conjugate gradient method (CGM) with a convergencelevel of 0.1 kcal mol1 1 until the energy reached aminimum. This minimized configuration was refined by MDsimulation for 30 ns under constant temperature and density(NVT ensemble). A time step of 1 fs was used to ensure the

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stability of simulation. The NosHoover [30] thermostat ina canonical ensemble was used to create the canonicalmolecular dynamics trajectories, and the COMPASS forcefield was chosen to deal with such a condensed state system[31-33]. The spline treatment of van der Waals (VDW)interactions was chosen, with a spline window of between 11and 12 . The Ewald summation [34], an accurate method of

calculating long-range interactions, was applied in order tocalculate long-range electrostatic interactions. Next, therefined polymer was annealed in the temperature range from383 K (above 373 K [28], the Tg of PS) to 443 K (below513 K [28], the melting temperature Tm of PS) in steps of10 K for 50 cycles. The simulation time for each annealingcycle was set to 2 ns, and the system was minimized at the

beginning of each annealing cycle. Because such oligomersalways have strong endend interactions, a system consistingof oligomers is different from a real polymeric system. Thus,an MD simulation was executed with the NPT (with constanttemperature and pressure) ensemble for 20 ns; furthermore,

MD simulations with a repeating ensemble cycle from NVTto NPT were carried out three times with a simulation time of20 ns for each cycle to reduce the endend interactionssufficiently. Finally, an MD simulation was executed withthe NVT ensemble for 30 ns at 298 K to collect data. Ingeneral, about 200 ns was needed in total for each simulatedcase. During the whole simulation process, the selection ofthe appropriate force field was a crucial task for obtainingaccurate information about the structures and dynamics ofthe blends. The COMPASS force field has been shown to bea suitable choice for calculating solubility parameters,especially for polymeric systems [35].

Results and discussion

The cohesive energy density (CED) of each pure compo-nent was used to calculate the solubility parameter, ,according to the equation below:

dffiffiffiffiffiffiffiffiffiffi

CEDp

ffiffiffiffiffiffiffiffiffiEcoh

V

r ;

To determine the minimum representative polymer chainlength of the blend components, Nmon, cases with different

chain lengths, N=10, 20, 30, 40, 50, 60, 70 and 80 for bothPS and PMMA, were selected in order to calculate the value of each component. Figure1displays the dependenceofof PS on the number of repeating units of PS. It can beseen that a nearly constant value is approached when thenumber of repeating units reaches 30, and the values are8.32% smaller than the experimental data. This may resultfrom the presence of a bulky C6H5 group in PS, whichrestricts free rotation around the CC bond of its backbone.Figure 2 shows the calculated values for different

numbers of repeating units of PMMA. These become

constant from N=60 onwards, and they are 6.40% smallerthan the experimental results. This may result from the

presence of a bulky CH3 group in PMMA, which alsorestricts free rotation around the CC bond of its backbone.

The fact that the calculated relaxation times wereshorter than the experimental results presented a ratherdifficult obstacle to overcome in the simulations. How-ever, taking N=60 to represent the whole polymer chainfor PMMA appeared a reasonable approach. Hence, theminimum representative polymer chain lengths of PS andPMMA, Nmon(PS) and Nmon(PMMA), were chosen to be30 and 60, respectively. Figure 3 shows a flowchart that

illustrates the process described above.The blend systems were binary, with PS (density =

1.05 gcm3) and PMMA (density = 1.188 g cm3) as thecomponents. The glass transition temperature of PS is

Fig. 1 The solubility parameter for different PS chain lengths

Fig. 2 The solubility parameter for different PMMA chain lengths

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373 K, so PS is prone to crystallize at a low temperature.PMMA starts to soften at the glass transition temperature(Tg=378 K), and does not substantially depolymerize until453 K [36]. Therefore, the blending simulation temper-

atures adopted were 383, 413 and 443 K.PS/PMMA blends with different weight percentages of

PS were put in a three-dimensional (3D) periodic boundarysimulation box with the corresponding density. Table 1describes the blending models in detail, including the molarratios of PS to PMMA, the chain number per unit cell, thecompositions by weight, and the densities. The blend

properties calculated in subsequent studies depend on howwell the components are blended. Therefore, when the

blending model was generated, if the PS and the PMMA

chains were randomly distributed in the simulation box, themodel was assumed to be a well-mixed model and acceptedfor further simulations; otherwise, it was discarded, and anew blending model was built until the component chainscontacted each other sufficiently. Figure4shows a typical1/1 blend. Because of the endend interactions of short

polymer chains, the initial amorphous structure of the blend

must first be minimized. The subsequent simulation processwas the same as that used to calculatevalues for the purecomponents, and the simulation temperatures were also383, 413 and 443 K.

The tendency for binary polymer chains to mix depends onthe cohesive energies of the blends and their pure components.Both are applied to calculate the parameters of blends withdifferent compositions. The parameter is defined as

EmixRT

Vmon;

where Vmonis the unit volume of one monomer. Here, Vmonequals 165.54 cm3 mol1 for blends of PS/PMMA.Emixfora binary mixture is defined as

Emix f1 EcohV

pure1

f2 EcohV

pure2

EcohV

mix

;

where f is the volume fraction, and the subscripts pureand mixdenote the cohesive energy densities of the purecomponents and the binary mixture, respectively. is shownas a function of the PS volume fraction in Fig. 5. Severalfeatures of these data are impressive. Firstly, the three curves vary in almost the same way at different temperatures,

which means that temperature was not an efficient factor forchanging the degree of phase separation. This is a totallydifferent conclusion from that obtained for PEO/PMMA

blends, which are miscible [26]. Secondly, thevalue showsa decreasing trend as the volume fraction of PS increases,except for the 1/4 blend case, where it shows a small risingtrend. Then the 4/1, 6/1 and 8/1 blend cases also show anotherdecreasing trend in . These two decreasing trends are termedT1 and T2, respectively. Considering the absolute data onslope variation for T1 and T2, where T1 < T2, it is supposedthat the degree of phase separation would intensify withincreasing PS content when the blends have a higher content

of PS. In addition, the 1/4 and 4/1 blend cases producedoutstandingly highvalues for both the T1 and the T2 lines,which means that it is possible that extremely distinct phaseseparation was present in these two blend cases.

A positive value alone cannot prove that the blends areimmiscible; it is necessary to calculate the critical value of via the equation below:

AB critical1

2

1ffiffiffiffiffiffiffimA

p 1ffiffiffiffiffiffimB

p 2

;

Fig. 3 The procedure used to selectNmonfor PS

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where mAand mBrepresent the actual number of repeatingunits of PS and PMMA, respectively. When the calculatedand the critical values of are based on the same referencevolume, AB)criticalcan be used to estimate the compatibil-ity of the blends. The blends are miscible if (AB)calculated