mesodyn modeling study of the phase morphologies of miktoarm poly(ethylene oxide)- b ...

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Research ArticleReceived: 16 November 2012 Revised: 13 May 2013 Accepted article published: 22 May 2013 Published online in Wiley Online Library: 1 July 2013

(wileyonlinelibrary.com) DOI 10.1002/pi.4564

MesoDyn modeling study of the phasemorphologies of miktoarm poly(ethyleneoxide)-b-poly(methyl methacrylate)copolymers doped with nanoparticlesDan Mu,a,b∗ Jian-Quan Lic and Sheng-Yu Fenga∗

Abstract

Earlier studies have shown that poly(ethylene oxide) (PEO) and poly(methyl methacrylate) (PMMA) blocks are compatibleat 270 and 298 K, and that their Flory–Huggins interaction parameters have the same blending ratio dependence at bothtemperatures. At a much higher temperature (400 K), the behavior of PEO/PMMA blends is strikingly different as bothcomponents become incompatible, while the Flory–Huggins parameters are low. Here we investigate the effect of doping withnanoparticles on the degree of incompatibility of twelve miktoarm PEO-b-PMMA copolymers at 400 K. Since PEO tends to besemicrystalline and long chains aggregate easily, PEO-rich and long-chain copolymer blends feature the highest degree ofincompatibility for all nanoparticle arrangements and present cubic phase morphologies. In addition, the largest nanoparticlescan reinforce the microscopic phase separation of all PEO-b-PMMA copolymers. This shows that the main factor affecting thephase morphology is the size of the nanoparticles. Also, only the asymmetric Da3-type PEO-rich copolymers show a hexagonalcylindrical phase morphology, which illustrates the effect induced by the nanoparticles on the microscopic phase separationchanges of the PEO-b-PMMA copolymers. These induced effects are also related to the composition and molecular architectureof the copolymers.c© 2013 Society of Chemical Industry

Keywords: PEO-b-PMMA copolymer; phase morphology; nanoparticles; microscopic phase separation

INTRODUCTIONBecause of the inherent beauty and potential technologicalapplications, the molecular self-assembly of block copolymersto form nanostructured materials is an active area of research.Thin films of self-organizing diblock copolymers may be suitablefor semiconductor applications since they enable patterningof ordered domains with dimensions below photolithographicresolution over wafer-scale areas.1 Block copolymers areknown to generate nanoscale microdomains by microphaseseparation, if they are annealed at a temperature lowerthan their order–disorder transition temperatures.2 Recently,thin films formed of block copolymers with well-definednanostructures have received great attention for their potential

in nanofabrication applications.3–11 In these applications,controlling the morphology of the block copolymer thin film byadjusting the influencing factors to gain ordered phase-separatedmicrodomains has significance and potential meaning.

Poly(ethylene oxide) (PEO) and poly(methyl methacrylate)(PMMA) are both important polymers for synthesis andapplications in a variety of engineering and biomedical

areas.12–14 The study of PEO/PMMA blends is of interest becauseof the semicrystalline nature of PEO, the weak interactions betweenthe two polymers and the large difference in their glass transitiontemperatures, which make such blends a complex system. In aprevious paper we clarified the conflicting conclusions drawn bydifferent laboratories using various techniques from a theoretical

viewpoint. We found that PEO/PMMA blends tend to undergomicrophase separation at higher temperatures such as 400 K,while the blends are miscible at lower temperatures such as 270and 298 K.15 The amphiphilic graft and block copolymers made ofPMMA and PEO blocks have received increasing attention for theirpotential applications in modification of keratoprostheses,16 drugcarriers17 and biomedical materials.18,19 The study of PEO-b-PMMAcopolymers is of interest because of their crystallization behavior,and Sun et al. reported that the crystallization rate and the degreeof crystallinity decrease with an increase of PMMA content,20 whichmeans the PEO blocks in PEO-b-PMMA copolymers are prone tocrystallize.

Polymer nanocomposites are a new family of compositematerials consisting of nanoparticles dispersed in various

∗ Correspondence to: Dan Mu and Sheng-Yu Feng, School of Chemistry andChemical Engineering, Shandong University, Jinan 250100, Shandong, China.E-mail: [email protected]; [email protected]

a School of Chemistry and Chemical Engineering, Shandong University, Jinan250100, Shandong, China

b College of Chemistry, Chemical Engineering and Materials Science, ZaozhuangUniversity, Shandong 277160, China

c Opto-Electronic Engineering College, Zaozhuang University, Shandong?>,277160, China

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Phase morphologies of nanoparticle-doped PEO-b-PMMA www.soci.org

polymers. In recent years, considerable scientific and industrialinterest has been directed at their multiscale structures andtheir structure–property relationships.21–24 Also, the inducingeffect of nanoparticles on polymers provides a means tocreate functional materials that integrate the desirable featuresof each component.25 The self-assembly of block copolymerswith various molecular architectures permits access to variousmicrostructures. Therefore, we studied the inducing effects ofneutral nanoparticles on the microscopic separation of miktoarmPEO-b-PMMA copolymers in the work reported in this paper.The results can provide some hints of improving the phasemorphology, which can be applied to nanofabrication withimproved functionality.

SIMULATION METHODMesoscale structures are of utmost importance during theproduction of many materials, such as polymer blends, blockcopolymers, surfactant aggregates in detergent materials, latexparticles and drug delivery systems. Mesoscopic dynamics modelsare receiving increasing attention, as they form a bridge between

microscale and macroscale properties.26–29 As a useful simulationtechnique for fluids, MesoDyn has been successfully applied tostudy the microphase separation of block copolymers in our

previous studies.15,30–33

All of the simulations were carried out at 400 K with the MesoDynpackage from Accelrys (version 5.5) installed on an SGI workstation.MesoDyn is a professional mesoscale simulation method thatcan be used to study the microphase separation of polymers. Itutilizes a dynamic variant of mean-field density functional theorywith Langevin-type equations to investigate polymer diffusion,providing a coarse-grained method for the study of complex fluids,their kinetics and their equilibrium structures at large length andtime scales. The thermodynamic forces are found by mean-fielddensity functional theory, using the Gaussian chain as a model.The coarse-grained Gaussian chain consists of beads with equallengths and equal volumes. With the passage of time, when thefree energy of the system results in no distinct changes, the phaseseparation is considered completed.

We used an atomistic simulation method to study PEO/PMMAblends of ten different ratios, and obtained their correspondingFlory–Huggins interaction parameter data, χ , in our previouswork,15,32 which were consistent with the experimental resultsof Fernandes and co-workers.34,35 In addition, to determine theminimum size that can represent the real polymer chain, solubilityparameters of PEO and PMMA at carefully chosen differentmolecular weights were calculated up to a point when increasingthe polymer molecular weight did not change the value of thesolubility parameter, which were Nmon(PEO)=50 and Nmon(PMMA)= 50. The whole calculation procedure was similar to that of

Aminabhavi and co-workers.36–42 These parameters are listed inTable 1. The χ data of ten different compositions can cover mostcompositions at 400 K, and these data can be applied as the inputparameters to deal with the interacting energies of the miktoarmPEO-b-PMMA copolymers in this work. The connection betweenthe microscale and the mesoscale is as follows:

v−1εij = χabRT

where the parameter χab is calculated by atomistic simulation foreach blend composition at different temperature. R is the molar gasconstant, 8.314 J mol−1 K−1, and T is the simulation temperature.

Table 1. Simulation data for PEO/PMMA blends of variouscompositions at 400 K

System

number

Blend ratio

in unit cell

(PEO/PMMA)

Composition

(wt% PMMA)

Density

(g cm−3) χ

1 1:6 93.16 1.1873 0.00266

2 1:4 90.09 1.1870 0.00217

3 1:3 87.20 1.1867 0.00243

4 1:2 81.96 1.1862 0.00197

5 1:1 69.43 1.1849 0.00184

6 2:1 53.18 1.1833 0.00636

7 3:1 43.09 1.1823 0.00217

8 4:1 36.22 1.1816 0.00878

9 6:1 27.46 1.1807 0.01094

10 8:1 22.11 1.1802 0.00217

Figure 1. Schematic of miktoarm PEO-b-PMMA copolymer models used inthis study. The black circles represent the PEO component denoted as A,while the white circles represent the PMMA component denoted as B.

To account for numerical stability, the time step for thesimulation was chosen in such a way that a dimensionless timestep, τ , used by the program was 0.5 (i.e. between 0 and 1) andthe bond length was 1.154 nm throughout. Thus, time steps of 50ms were used for all the mesoscopic modeling. A constant noiseparameter value of 75.002 is preserved for the entire simulation(because too high or too low a value would lead to systeminstability). The chosen grid dimensions are 32 × 32 × 32 nm3,and the size of the mesh over which density variations are to beplotted, in MesoDyn length units, using the grid spacing field is

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www.soci.org D Mu, J-Q Li, S-Y Feng

Table 2. Molecular information of miktoarm PEO-b-PMMAcopolymers

Group

Molar ratio

of A5 to B6 Architecture Symbol

Group 1 1:4 A3[A(B6)2]2 a1

A8[A(B12)2]2 Da1

1:6 A3[A(B6)3]2 a2

A8[A(B12)3]2 Da2

Group 2 4:1 B4[B(A5)2]2 b1

B10[B(A10)2]2 Db1

6:1 B4[B(A5)3]2 b2

B10[B(A10)3]2 Db2

Group 3 5:1 (A5)3BB4B(A5)2 a3

(A10)3BB10B(A10)2 Da3

1:5 (B6)3AA3A(B6)2 b3

(B12)3AA8A(B12)2 Db3

1 nm. Bond length is 1.1543 A times the cell length to guaranteethe isotropy of all grid-restricted operators. We accept the orderparameter calculated for the last frame as the parameter to judgethe phase morphologies.

MODEL CONSTRUCTIONThe block copolymer chains are built of PEO (denoted ‘A’) andPMMA (denoted ‘B’) components as A3[A(B6)2]2, A3[A(B6)3]2,B4[B(A5)2]2, B4[B(A5)3]2, (A5)3BB4B(A5)2 and (B6)3AA3A(B6)2, de-noted as a1, a2, b1, b2, a3 and b3. These six models are shownschematically in Fig. 1. The a1, a2 and a3 models are the componentexchange between A and B from the corresponding b1, b2 andb3 models. When we increase the chain lengths of these sixmodels to be two times longer than before, we gain anothersix models, A8[A(B12)2]2, A8[A(B12)3]2, B10[B(A10)2]2, B10[B(A10)3]2,(A10)3BB10B(A10)2 and (B12)3AA8A(B12)2, denoted as Da1, Da2, Db1,Db2, Da3 and Db3, respectively. Table 2 lists the system number,molar ratio of each system, composition, density and χ values.The architectures of groups 1 and 2 are all symmetric, and theyhave the reverse component between these two groups. On thecontrary, the structures are asymmetric in group 3.

Table 3. Characteristics of doped nanoparticles

Number System Np rp (nm) hp (nm) NL Ntp

1 4-3-4-2 4 3 4 2 8

2 4-3-4-3 4 3 4 3 9

3 4-3-4-4 4 3 4 4 16

4 4-3-8-2 4 3 8 2 8

5 4-3-8-3 4 3 8 3 9

6 4-6-8-2 4 6 8 2 8

7 8-3-4-2 8 3 4 2 16

As experimental results show that the presence of nanoparticlescan reduce the degree of segregation of a polymer system, leadingto a well-ordered structure of the composite,43 so we created seventypes of column-shaped nanoparticle arrangements to cooperatewith the MesoDyn simulations. Table 3 lists the nanoparticlenumber of each layer (Np), the radius of each nanoparticle (rp), theheight of each nanoparticle (hp), the layer number (NL) and thetotal number of nanoparticles doped (Ntp). Among these cases,the 4-3-4-2 case (with 4 nanoparticles in each layer, radius of 3nm, height of 4 nm and layer number of 2) is used as the base.Other cases are derived from it and built in the following manner:adding only one more nanoparticle in the center forms case 4-3-4-3; increasing the layer number to 4, without change in othersettings forms case 4-3-4-4; doubling the nanoparticle densityof every layer forms case 8-3-4-2; doubling the nanoparticleheight forms case 4-3-8-2; adding one more nanoparticle intothe middle of the simulation box to increase the layer numberto 3 based on case 4-3-8-2 forms case 4-3-8-3; and doubling theradius of nanoparticles based on case 4-3-8-2 forms case 4-6-8-2.The interaction parameters between the nanoparticles and thepolymers are accepted as the default values as in MesoDyn, thatis, v− 1εij = 5.

SIMULATION RESULTS AND DISCUSSIONThe order parameter, P, is defined as the average volume of thedifference between local density squared and the overall density

Figure 2. P values of 12 miktoarm PEO-b-PMMA copolymers at 400 K. The iso-density surfaces of these copolymers at 400 K are displayed at the top: red,PEO component; green, PMMA component.

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squared, as given by

Pi = 1

V

∫

V

[η2

i (r) − η2i

]dr

where ηi is the dimensionless density (volume fraction) of speciesi. The larger the value of P, the greater is the phase separation. Adecrease in P indicates better compatibility or miscibility, and thepolymer phases mix more randomly.

We define a new parameter to describe the inducing effectof surfaces. The order parameter value of every miktoarm PEO-b-PMMA copolymer without inducing surface effects (‘plain’) isa; in addition, the order parameter value of the correspondingcopolymer with inducing effect is b. The value of b/a is definedas the variable rate of order parameter (VROP). By comparingthe VROP values, we can determine the most effective inducing

surfaces on changing the phase morphology of the miktoarmPEO-b-PMMA copolymers. When the VROP value is greater than1, the doping can be considered to have a reinforcing effect;otherwise, the doping can be considered to have a weakeningeffect. The larger the value of VROP, the greater is the inducinginfluence.

Modeling plain miktoarm PEO-b-PMMA copolymersFigure 2 shows the P values of the 12 plain miktoarm PEO-b-PMMAcopolymers at 400 K. There are several features in this figure thatare worth noting:

(1) The P values of long-chain copolymers are higher than thoseof short-chain ones with the same architecture, that is, PDa1 >

Pa1, PDa2 > Pa2, PDb1 > Pb1, PDb2 > Pb2, PDa3 > Pa3 and PDb3

> Pb3. Longer chains have more opportunities to ‘meet with’the same component, to form aggregating areas and even

Figure 3. P and VROP values of 12 miktoarm PEO-b-PMMA copolymers doped with nanoparticles at 400 K. The insert iso-surface images in (a1) are of thea2-type PEO-b-PMMA copolymer doped with seven kinds of nanoparticle arrangements, (a2) are of the b2-type, (a3) are of the b3-type, (b1) are of theDa2-type, (b2) are of the Db2-type and (b3) are of the Db3-type.


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to produce phase separation. The longer the chain, the moreordered is the phase morphology.

(2) For the long-chain copolymers, the P values of PEO-richcopolymers are higher than those of PMMA-rich ones. Thisresults from the nature of the PEO block tending to crystallize,20

which, combined with the iso-density images at the top of Fig.2, suggests that PEO-rich copolymers could form microscopicseparation. The order of P values of PEO-rich copolymers isPDb1 > PDa3 > PDb2, which all have one B6 segment, but withfour, five and six A5 segments, respectively; accordingly, theorder of P values of PMMA-rich copolymers is PDa1 > PDb3 >

PDa2, which all have one A5 segment, but with four, five andsix B6 segments, respectively. Therefore, decreasing the PEOcomponent in PEO-rich copolymers or the PMMA componentin PMMA-rich copolymers both can increase the degree oforder of phase morphology.

Modeling miktoarm PEO-b-PMMA copolymers doped withnanoparticlesFigures 3(a1), (a2) and (a3) show the P values for the12 miktoarm PEO-b-PMMA copolymers in three groups with

the seven kinds of nanoparticle arrangements at 400 K.Figures 3(b1), (b2) and (b3) show the corresponding VROPvalues. A reference line is drawn through VROP = 1 in Figs3(b1), (b2) and (b3). We can detect which architecture ofcopolymer could undergo the inducing effect on changing thephase morphology. The following features of the plots arenoteworthy:

(1) The order of P values in Fig. 3(a1) is PDa1 > Pa1 > Pa2 ≈ PDa2, it isPDb1 > PDb2 > Pb1 ≈ Pb2 in Fig. 3(a2) and it is PDa3 > Pa3 > Pb3

≈ PDb3 in Fig. 3(a3). This reveals that the architecture is moreimportant than the chain length, especially for the PEO-richcopolymers.

(2) The order of VROP values in Fig. 3(b1) is VROPa2 ≈ VROPDa2

> VROPa1 > VROPDa1, except for the case of the Da1-type copolymer being induced by the 4-3-4-2 nanoparticlearrangement; it is VROPb2 > VROPb1 > VROPDb1 ≈ VROPDb2

in Fig. 3(b2); and it is VROPb3 > VROPDb3 > VROPa3 >

VROPDa3 in Fig. 3(b3). In addition, the VROP values of theDa3-type copolymer being induced by all seven nanoparticlearrangements are all below the reference line, which means the

Figure 4. P and VROP values of 12 miktoarm PEO-b-PMMA copolymers doped with nanoparticles at 400 K. The insert iso-surface images in (a1), (a2) and(a3) are of the PEO-b-PMMA copolymers in groups 1, 2 and 3 doped with 4-3-4-2 nanoparticles, respectively. The insert iso-surface images in (b1), (b2)and (b3) are of the PEO-b-PMMA copolymers in groups 1, 2 and 3 doped with 4-3-4-3 nanoparticles, respectively.


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Figure 5. Iso-density surfaces of Da1-type PEO-b-PMMA copolymerdoped with nanoparticles at 400 K: red, PEO component; green, PMMAcomponent.

Da3-type copolymer is little affected by the inducing effects.On the contrary, other cases are all above the reference line,revealing that doping with nanoparticles is a good method toimprove the degree of order of phase morphology.

Derived from the P and VROP values in Fig. 4, we can clarifywhich kind of nanoparticle arrangement has the most effectiveinfluence on changing the phase morphology. It also follows thesame relation that the P values of long-chain copolymers arehigher than those of short-chain ones induced by nanoparticles.Also, the P values of groups 2 and 3 are both higher than thoseof group 1. Combined with the iso-density images displayedat the top of Fig. 4, this suggests that no matter what kindof doping nanoparticle arrangement, phase separation wouldoccur in Db1-, Db2- and Da3-type copolymers, whose P valuesare all above 0.1. The 4-6-8-2 nanoparticle arrangement is themost efficient in changing the phase morphology, nearly allof whose VROP values are higher than those of the otherarrangements and higher than 1 in Figs 4(b1), (b2) and(b3).

Two representative phase morphologies and one more modelOwing to the markedly high P data for Da1- and Db1-typecopolymers induced by nanoparticles, it is necessary to exploresuch special miktoarm PEO-b-PMMA copolymers in more depth.We can observe particulars of the architecture and property ofDa1-type copolymer. Firstly, the ratio of PEO to PMMA blocksis 1:4, which is the lowest PEO component percentage amongthese copolymers. Secondly, each joint has two PEO segmentsand four PEO segments in total, which could mean this copolymer

Figure 6. Iso-density surfaces of Db1-type PEO-b-PMMA copolymerdoped with nanoparticles at 400 K: red, PEO component; green, PMMAcomponent.

Figure 7. Schematic of another type of miktoarm PEO-b-PMMA copolymermodel. The black circles represent the PEO component denoted as A, whilethe white circles represent the PMMA component denoted as B.

has much more opportunity to ‘meet with’ the same PEO blocks,further from PEO-rich regions, even phase separation occurring.Thirdly, the long-chained PEO block is flexible and lying outside,which can increase the ‘meeting opportunity’ during adjustmentof its placement and orientation. Fourthly, the semicrystallinenature of PEO could make it congregate easily, especially athigher temperatures such as 400 K. On the other hand, thearchitecture of the Db1-type copolymer is something like thatof the Da1-type copolymer, but with the A10 and B12 segmentsreversed.

Figures 5 and 6 display the iso-density images of Da1-and Db1-type copolymers, respectively, induced by the seven


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Figure 8. Iso-density surfaces of another type of miktoarm PEO-b-PMMAcopolymer doped with nanoparticles at 400 K: red, PEO component; green,PMMA component.

nanoparticle arrangements at 400 K. We can see clearly thelamellae and cubic phase morphologies. The cases presentlocal phase separation because of the inducing effect of beingdoped by nanoparticles, no matter what kind of arrangement.Figure 7 shows schematically one more miktoarm PEO-b-PMMAcopolymer designed, whose ratio of A10 to B12 is 6:1 and whichhas a symmetric architecture. Figure 8 presents cubic phasemorphologies induced by the seven nanoparticle arrangements,but the distance between two uniform areas is the smallestcompared with the other block copolymers, due to the highestPEO percentage and evenly distributed architecture of PEOsegments.

CONCLUSIONSWe have investigated the phase morphologies of plain andnanoparticle-doped miktoarm PEO-b-PMMA copolymers bymeans of MesoDyn simulations. The results show that P valuesof long-chain copolymers are higher than those of short-chainones in the same group. The composition and architecture ofcopolymers are both important factors in determining the Pvalues. The simulation results show that introducing nanoparticlesis a good way of improving the degree of order of the microscopicphase morphologies and has a reinforcing effect, especially for the4-6-8-2 nanoparticle arrangement, which has the most markedinfluence on changing the phase morphologies of the miktoarmPEO-b-PMMA copolymers. From the iso-surface images we can see

the PEO-rich and long-chain copolymers doped with nanoparticlesno matter what the nanoparticle arrangement, and they all presentspecial cubic phase morphologies at 400 K, including the plaincopolymer. It is worth mentioning that the asymmetric architectureof a PEO-rich copolymer such as the Da3-type copolymer showshexagonal cylindrical phase morphology.

ACKNOWLEDGEMENTSThis work was supported by the National Natural ScienceFoundation of China (21203164), China Postdoctoral ScienceFoundation funded project (2013M531586), Science-TechnologyFoundation for Middle-Aged and Young Scientists of ShandongProvince (BS2010CL048), and subsidized by the Foundation ofState Key Laboratory of Theoretical and Computational Chemistry.

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