Monte Carlo simulation of polymeric materials: Recent progress

Monte Carlo simulations are presented, dealing with phase diagrams of block copolymer melts and polymer blends, including the unmixing kinetics of the latter systems. The theoretical background is briefly reviewed: Ginzburg-type criteria reveal that in mixtures of long flexible polymers a “crossover” occurs from mean-field behavior (as described by Flory-Huggins theory) to nonclassical Ising-type behavior, and spinodal curves can be unusually sharp. This crossover is demonstrated by large scale simulations of the bond fluctuation model, and it is also shown that for symmetric mixtures the critical temperature scales with chain length as T_c α N. The prefactor in this relation is distinctly smaller than predicted by Flory-Huggins, but the Curro-Schweizer integral equation theory prediction T_c α √N is clearly ruled out. Tests of the Cahn theory on the initial stages of spinodal decomposition of polymer blends will also be reported. To conclude, the mesophase formation in block copolymers is discussed, and it is shown that the simulations agree very well with experiment. The pronounced chain stretching that already occurs in the disordered phase is compelling evidence against the validity of simple random phase approximation concepts for these systems. This shows how Monte Carlo simulations can assist in better understanding large classes of polymeric materials.     

含无规共聚物三元共混体系SMMA-PMMA-SAN相行为

含无规共聚物共混体系的相容性研究正在成为近年来的研究热点 ,因为相容的驱动力来自共聚物分子内不同单体链段间的排斥性相互作用 [1～ 3] .目前研究这类体系还主要采用过份简化的 F- H平均场理论 ,用旨在克服平均场理论缺陷的 Flory状态方程 ( EOS)理论仅局限于研究二元共聚物共混体系[4～ 8] .与三元共混体系相比 ,用 EOS理论预测含两个无规共聚物三元体系相行为尚需确定共聚物 -共聚物间的二元参数 sj/si,Xij和 Qij.若用 Ax B1- x和 Cy D1- y分别代表共聚物 1和 2 ,则 A,B,C,D代表相应共聚物中的单体单元 ,x,y分别是 1和 2的共…     

Miscibility and phase separation in polymer blends studied by laser light scattering

In this paper major emphasis has been placed on the phase behavior of miscible polymer blends, especially on blends containing random copolymers. Blends containing random copolymers generally tend to phase separation at elevated temperatures (LCST behavior). Experimental determination of miscibility areas as a function of temperature and copolymer composition by laser light scattering provides the interaction parameters necessary for theoretical explanations and predictions of various phase separation phenomena. Just above the LCST polymer blends exhibit regular highly interconnected two-phase morphologies. The rate of decay of these structures is estimated. The phase separation kinetics can be pursued by laser light scattering and is discussed in terms of CAHN's linearized theory. It can be shown that the linear theory adequately describes the early stage of phase decomposition. The linear theory is also applicable to the reverse phenomenon, the phase dissolution below LCST. unlike the case of phase separation the diffusion-controlled regime is that in the late stage of phase dissolution.     

The influence of polymer structure and component ratios on blend miscibility

The mean field, rigid lattice treatment as applied to polymer mixtures has been used to estimate segment-segment interaction parameters for a wide range of polymers. These parameters incorporate, without distinction, contributions from non-combinatorial entropy effects, dispersion forces and any specific interactions that operate in the polymer blend. Thus while these parameters can be used to predict successfully the nature of the phases in untested polymer blends, structural effects may also play a role in determining miscibility, and these may have to be assessed individually. Examples of structural effects are described using chlorine-containing polymers and blends of copolymers with an anhydride ring attached in two different ways to the polymer chain. The extension of binary interaction parameters to the prediction of phase behaviour in complex ternary copolymer blends and the effect on the phase behaviour of changing the component ratios in the blends, is also illustrated.     

Blends of styrene/acrylic acid copolymers and acrylic polymers

The miscibility of a series of styrene/acrylic acid copolymers with various polyacrylate and polymethacrylate homopolymers, as well as a series of styrene/methyl methacrylate copolymers, has been investigated. According to the binary interaction model, the miscibility diagram for styrene/acrylic acid copolymers with styrene/methyl methacrylate copolymers indicates that acid and ester groups interact endothermically. The phase behavior of the homopolymers also implies this. The analysis ignores the association and self-association observed for the polymer blends and the low-molecular-weight analogs used to model them. The heat of mixing of low-molecular-weight analogs depended greatly on both composition and acid structure.     

The structure and phase transitions in polymer blends,diblock copolymers and liquid crystalline polymers: The Landau-Ginzburg approach

The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards Hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers. The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chains close to critical points, fluctuations induced shift of phase boundaries. In particular we shall discuss shrinking of the polymer chains close to the critical point in polymer blends, size of the Ginzburg region in polymer blends and shift of the critical temperature. In the rigid-flexible diblock copolymers we shall discuss the density nematic order parameter correlation function. The correlation functions in this system are found to oscillate with the characteristic period equal to the length of the rigid part of the diblock copolymer. The density and nematic order parameter measured along the given direction are anticorrelated. In the flexible diblock copolymer system we shall discuss various phases including the double diamond and gyroid structures. The single chain statistics in the disordered phase of a flexible diblock copolymer system is shown to deviate from the Gaussian statistics due to fluctuations. In the one loop approximation one shows that the diblock copolymer chain is stretched in the point where two incompatible blocks meet but also that each block shrinks close to the microphase separation transition. The stretching outweights shrinking and the net result is the increase of the radius of gyration above the Gaussian value. Certain properties of homopolymer/copolymer systems are discussed. Diblock copolymers solubilize two incompatible homopolymers by forming a monolayer interface between them. The interface has a positive saddle splay modulus which means that the interfaces in the disordered phase should be characterized by a negative Gaussian curvature. We also show that in such a mixture the Lifshitz tricritical point is encountered. The properties of this unusual point are presented. The Lifshitz, equimaxima and disorder lines are shown to provide a useful tool for studying local ordering in polymer mixtures. In the liquid crystalline mixtures the isotropic nematic phase transition is discussed. We concentrate on static, equilibrium properties of the polymer systems.     

Prediction of miscibility regions in ternary blends of poly(styrene-stat-acrylonitrile), poly(acrylonitrile-stat-methyl methacrylate), and poly(styrene-stat-methyl methacrylate)

The miscibilities of ternary copolymer blends prepared from poly(styrene-stat-acrylonitrile), poly(styrene-stat-methyl methacrylate), and poly(methyl methacrylate-stat-acrylonitrile) were predicted by calculating the interaction parameter, χ_blend, for various blend combinations, from the corresponding binary segmental interaction parameters estimated from previous work. Binodal and spinodal curves were calculated using the Flory-Huggins theory and it was observed that the most accurate estimate of the boundary between miscible and immiscible blends was given by the spinodal. It has also been demonstrated that in some of the ternary blends with fixed copolymer compositions the miscibility of the blend can be altered by changing the ratio of the three components in the mixture. Conditions for miscibility in this ternary system, and possibly a general feature of all such systems, are (a) that at least two of the binary interaction parameters χ_ij are less than the critical value χ_crit, while the third should not be too much larger, that is, one of the copolymers may act as a compatibilizer for the other two copolymers, (b) that the difference Δχ = /χ₁₂ ? χ₁₃/ is small. © 1992 John Wiley & Sons, Inc.     

Dissipative particle dynamics study on the interfaces in incompatible A/B homopolymer blends and with their block copolymers

Dissipative particle dynamics, a simulation technique appropriate at mesoscopic scales, has been applied to investigate the interfaces in immiscible binary A/B homopolymer blends and in the ternary systems with their block copolymers. For the binary blends, the interfacial tension increases and the interface thickness decreases with increasing Flory-Huggins interaction parameter chi while the homopolymer chain length is fixed. However, when the chi parameter and one of the homopolymer chain length is fixed, increasing another homopolymer chain length will induce only a small increase on interfacial tension and slight decrease on interface thickness. For the ternary blends, adding the A-b-B block copolymer will reduce the interfacial tension. When the mole number of the block copolymer is fixed, longer block chains have higher efficiency on reducing the interfacial tension than the shorter ones. But for the block copolymers with fixed volume fraction, shorter chains will be more efficient than the longer ones on reducing the interfacial tension. Increasing the block copolymer concentration reduces interfacial tension. This effect is more prominent for shorter block copolymer chains.     

Phase equilibria in ternary polymer blends

The phase states and rheological properties of blends of three polymers??polystyrene, poly(methyl methacrylate), and the styrene-acrylonitrile copolymer??in the common solvent chloroform are studied. The phase diagrams are constructed and the positions of spinodals are determined via the method of turbidity points. The effect of the third polymer on the compatibility of the binary blend obeys Prigogine??s rule; that is, it is determined by the solubility of the added polymer in the first two components. The extremum composition dependence of rheological properties of ternary polymer systems in the vicinity of the separation point (the metastable region) is found. Through the method of convex-shell construction, the phase diagrams are calculated.     

聚丙烯与聚酯-聚醚多嵌段共聚物共混的研究

聚丙烯和聚酯-聚醚多嵌段共聚物的熔融共混物是微多相分散体系,其力学性能和软链段的结构有关。DSC和偏光显微镜图分别表明共混物中聚丙烯结晶度以及球晶尺寸随聚酯-聚醚的混入量而变小。聚丙烯和少量聚酯-聚醚多嵌段共聚物共混,可改进聚丙烯的流变性,吸湿性和染色性。     

Dependence of flory-Huggins χ parameters on the copolymer composition for solutions of poly(methyl methacrylate-ran-n-butyl methacrylate) in cyclohexanone

Intermolecular interactions in random copolymer systems depend on the copolymer composition as being observed as a miscibility window in the random copolymer blends. The copolymer composition dependencies of the Flory-Huggins χ parameter and the heats of mixing ▵H_M(∞) at infinite dilution were studied for the solutions of poly(methyl methacrylate-ran-n-butyl methacrylate) (MMAnBMA) in cyclohexanone (CHN). The copolymer composition dependencies of χ obtained from osmotic pressures and of ▵H_M(∞) measured with a microcalorimeter were concave curves. This suggests that the random copolymers MMAnBMA interact with CHN more attractively than do the homopolymers PMMA and PnBMA. This is caused by the repulsion effect between the MMA and nBMA segments. The equation-of-state theory extended to the random copolymer systems by us reproduced fairly well these thermodynamic properties. The χ parameter for the PMMA/PnBMA blends was calculated using the equation-of-state theory with the MMA/nBMA intersegmental parameters employed for the above random copolymer solutions in CHN. The χ value calculated thus was in satisfactory agreement with that obtained from the random copolymer solutions using the Flory-Huggins theory extended to multicomponent systems. © 1996 John Wiley & Sons, Inc.     

Miscibility of poly(vinyl chloride) with poly(methyl-co-hexyl acrylate) and poly(methyl-co-2 ethyl hexyl acrylate)

The miscibility and phase behavior in blends of PVC with poly(methyl-co-hexyl acrylate)[MHA] and poly(methyl-co-2 ethyl hexyl acrylate)[MEH] were studied. It was found that PVC is miscible with MHA copolymers having a HA volume fraction from 0.30 to 0.92 and MEH copolymers having an EH volume fraction from 0.30 to 0.83 at 100°C. By applying the mean field theory to the phase diagrams of these blend systems, segmental interaction parameters which represent the binary interaction between different monomer units were estimated. The calculated values reflect the fact that the miscibility window observed for PVC/MHA and PVC/MEH blend systems was attributed to the effect of repulsion between different monomer units within the copolymer. To investigate the effect of specific interaction on the miscibility for these blend systems, an attempt was also made to describe the blend interaction parameter as a function of polar group concentration in the acrylate copolymer. The blend interaction parameter values exhibit a u-shaped curve as a function of the weight fraction of C?O group in the copolymer, and the lowest blend interaction parameter value appears at about 0.24 C?O weight fraction.     

COMPUTER SIMULATION OF MISCIBILITY AND SELF-ASSEMBLY STRUCTURE FOR POLYMER-CONTAINING SYSTEMS WITH SPECIAL INTERACTIONS

The miscibility and structure of A-B copolymer/C homopolymer blends with special interactions were studied by aMonte Carlo simulation in two dimensions. The interaction between segment A and segment C was repulsive, whereas it wasattractive between segment B and segment C. In order to study the effect of copolymer chain structure on the morphologyand structure of A-B copolymer/C homopolymer blends, the alternating, random and block A-B copolymers were introducedinto the blends, respectively. The simulation results indicated that the miscibility of A-B block copolymer/C homopolymerblends depended on the chain structure of the A-B copolymer. Compared with alternating or random copolymer, the blockcopolymer, especially the diblock copolymer, could lead to a poor miscibility of A-B copolymer/C homopolymer blends.Moreover, for diblock A-B copolymer/C homopolymer blends, obvious self-organized core-shell smicture was observed inthe segment B composition region from 20% to 60%. However if diblock copolymer composition in the blends is less than40%, obvious self-organized core-shell structure could be formed in the B-segment component region from 10 to 90%.Furthermore, computer statistical analysis for the simulation results showed that the core sizes tended to increasecontinuously and their distribution became wider with decreasing B-segment component.     

Miscibility of polysulfone blends with poly(1‐vinylpyrrolidone‐co‐styrene) copolymers and their interaction energies

The miscibility of polysulfone (PSf) with various hydrophilic copolymers was explored. Among these blends, PSf gave homogeneous mixtures with poly(1‐vinylpyrrolidone‐co‐styrene) [P(VP–S)] copolymers when these copolymers contained 68–88 wt % 1‐vinylpyrrolidone (VP). Miscible PSf blends with P(VP–S) copolymers underwent phase separation on heating caused by lower critical solution temperature (LCST)‐type phase behavior. The phase behavior depended on the copolymer composition. Changes in the VP content of P(VP–S) copolymers from 65 to 68 wt % shifted the phase behavior from immiscibility to miscibility and the LCST behavior. The phase‐separation temperatures of the miscible blends first increased gradually with the VP content, then went through a broad maximum centered at about 80 wt % VP, and finally decreased just before the limiting content of VP for miscibility with PSf. The interaction energies of binary pairs involved in PSf/P(VP–S) blends were evaluated from the phase‐separation temperatures of PSf/P(VP–S) blends with lattice‐fluid theory combined with a binary interaction model. The decrease in the contact angle between water and the membrane surface with increasing VP content in P(VP–S) copolymers indicated that the hydrophobic properties of PSf could be improved via blending with hydrophilic P(VP–S) copolymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1401–1411, 2003     

最有效的相容剂是两嵌段还是多嵌段聚合物?

Monte Carlo simulations were used to investigate the compatibilizing behaviors of multi-block copolymers with different architectures in A/B/(block copolymer) ternary blends. The volume fraction of homopolymer A, employed as the dispersed phase, was 19%. The simulations illustrate how a di- or multi-block copolymer aggregates at the interfaces and influences the phase behaviour of such incompatible polymer blends. The di-block copolymer chains tend to "stand" on the interface whereas the multi-block chains lie on the interface.In comparison with the dj-block copolymer, the block copolymers with 4, or 10 blocks can occupy more areas on the interface, and thus the multi-block copolymers have higher efficiency for the retardation of the phase separation.     

Modeling of polyethylene and poly (L-lactide) polymer blends and diblock copolymer: chain length and volume fraction effects on structural arrangement

Dissipative particle dynamics (DPD), a mesoscopic simulation approach, has been used to investigate the chain length effect on the structural property of the immiscible polyethylene (PE)/poly(L-lactide) (PLLA) polymer in a polymer blend and in a system with their diblock copolymer. In this work, the interaction parameter in DPD simulation, related to the Flory-Huggins interaction parameter chi, is estimated by the calculation of mixing energy for each pair of components in molecular dynamics simulation. The immiscibility property of PE and PLLA polymers induces the phase separation and exhibits different architectures at different volume fractions. In order to observe the structural property, the radius of gyration is used to observe the detailed arrangement of the polymer chains. It shows that the structure arrangement of a polymer chain is dependent on the phase structure and has a significantly different structural arrangement character for the very short chains in the homopolymer and copolymers. The chain length effect on the degree of stretching or extension of polymers has also been observed. As the chain length increases, the chain exhibits more stretching behavior at lamellae, perforated lamellae, and cylindrical configurations, whereas the chain exhibits a similar degree of stretching or extension at the cluster configuration.     

Compatibility between polystyrene copolymers and polymers in solution via hydrogen bonding

It has been applied the concept of improving miscibility, by introducing and optimizing the extent of intermolecular hydrogen-bonding interactions between two polymers. We select a commodity polymer such as polystyrene, to study the compatibility in chloroform with poly(vinyl pyridine) and poly(vinyl pyrrolidone), both considered as proton acceptors. In order to enhance polymer-polymer miscibility, polystyrene is slightly modified by copolymerization with methacrylic acid, in the first case, and with vinyl-phenol comonomer, in the second one. In this way, two series of polystyrene-based copolymers are synthesized and characterized bearing ca. 8% (w/w) of -OH groups. The miscibility gaps through the binodal ternary phase diagrams, interpolymer interaction parameter from viscometry and the evaluation of the interassociation equilibrium constant, K, by FT-IR spectroscopy serve to analyze the effect of the spacing of interacting moieties along the polystyrene chain. Our results prove that polymer-polymer miscibility increases with an increase in the methacrylic-acid content in the copolymer chain; however, when the polar group is vinyl phenol, this continuous trend is disrupted.     

Structure formation in polymer blends as a result of phase separation and deformation processes

Polymeric blends, which are materials consisting of two or more polymers, are gaining in practical importance and scientific interest. The properties of these materials are greatly affected by their state of miscibility. This paper reviews selected thermodynamic and rheological considerations regarding the phase behavior and the morphological control of polymer blends. Major emphasis is placed on the phase behavior of poly-blends comprising random copolymers. - The majority of polymer blends are microheterogeneous systems. There is consequently, a great need for control of the phase morphology during processing of immiscible polymers to achieve the desired property combinations. The key to this are both the microrheology of the phases and the macrorheology of the dispersion itself. In a qualitative way, one can establish that the ratio of the viscosities and the difference in the elasticities of the components determine sizes and shapes, respectively, of the phases indicating that the variety of morphologies observed in polymer-polymer systems subjected to shearing has to be attributed to the viscoelasticity of each component. Furthermore, particular compositions are associated with changes in the morphology. This fact supports the particular compositions as an inherent feature of the melt rheology of polyblends.     

Miscibility behaviour of blends of a thermoplastic polyester polyurethane with vinyl polymers

A method based on the intrinsic viscosities of transfer has been used to predict miscibility of polymer blends. This method has been applied to study the change in the phase behaviour of a microphase separated polyester polyurethane (PSPU) on blending with polyvinyl chloride (PVC), polyvinyl acetate (PVAc) and a vinyl chloride-vinyl acetate copolymer (VCVAc). The PVC/PSPU blends are found to exhibit complete miscibility over the entire composition range. PVAc/PSPU blends show immiscibility while VCVAc/PSPU blends show partial miscibility. Thermal analysis and scanning electron microscopic studies of the blend films have confirmed the results evaluated on the basis of the viscosity method.     

共聚物混溶性热力学-分子内排斥作用与附加共聚焓

基于聚合物分子间物理相互作用和统计平均场理论,引入附加共聚焓定义,使聚合物分子间的作用得到量化,同时推导出二元共混体系相互作用参数和三元共混体系混合焓关系式.利用所导出的公式解释一些常见聚合物共混体系和增溶体系.导出的关系式很好地解释了聚合物的热力学混溶性,但不能解释聚合物共混增溶作用.