Computational and Theoretical Polymer Science最新文献

Structural change in the ferroelectric phase transition of vinylidene fluoride (VDF)–trifluoroethylene copolymers has been simulated by using molecular dynamics (MD) technique. The force field parameters used in this simulation were those determined in the previous paper [Tashiro et al., Ferroelectrics 1995;171:281] but with some modifications to reproduce the molecular and crystal structures and the infrared/Raman spectra of PVDF crystal forms I, II, and III to a higher degree. The MD calculation was made for the crystal structures of VDF 50 and 70 mol% copolymers, where the MD unit cells consisted of 16–36 chains of different monomer sequences under the three-dimensional periodic boundary condition. In the VDF 50% copolymer case, for example, the trans-to-gauche conformational change was found to occur at about 390 K. The transition temperature estimated for VDF 70% copolymer was about 470 K, higher than that of VDF 50% copolymer. This indicates that the copolymer with higher VDF content exhibits the transition at higher temperature, consistent with the observed results. The molecular conformation in the high-temperature phase was found to be a statistical combination of TG⁺, TG⁻, T₃G⁺ and T₃G⁻ sequences. The population of TG⁺ and TG⁻ was higher and that of T₃G⁺ and T₃G⁻ was lower for the copolymer with higher VDF content, which was also consistent with the experimental data. The trans–gauche conformational change was done with large thermal rotation of the chains, resulting in the extinction of the electric polarization of the whole unit cell in the high-temperature phase. The ratio of the a and b axes of the basic unit cell was 1.73, characteristic of the hexagonal-type structure of the high-temperature phase.

Isotactic polypropylene has various crystalline modifications (α, β, γ, smectic). Molecular conformations in these modifications are common 3/1 helix of (TG)₃ or (TG^∗)₃. However crystal structures of the modifications, that is the modes of chain packing, are quite different and are subjects of intensive investigations nowadays. We study here, the detailed modes of chain packing in the α and β forms by Monte Carlo simulation. We assume that the molecular conformation is a rigid 3/1 helix, and that the chain axes are placed either in a monoclinic lattice (α form) or in a hexagonal lattice (β form). Most stable modes of chain packing are investigated, with respect to chain chirality (right or left handedness), chain rotation and translation, and the methyl-group direction (up or down positioning). We find that an initial random state in the monoclinic lattice converges to the α₁ or to the α₂ form, both with alternating rows of right-handed and left-handed helices; we also investigate a molecular process of growth of the α₂ crystal in the matrix α₁ crystal. On the other hand, the arrangement of the molecular axes in the hexagonal lattice is found to give rise to the β form structure, in which the chains form chiral domains surrounded by boundaries parallel to the (110) and (100) planes. It is also shown that detailed chain rotations (setting angles) have a unique superstructure, which conforms to the incommensurate packing recently proposed by Lotz and Meille.

Using the self-consistent field treatment, we investigate the structures and the phase behavior of micelles formed in symmetric and asymmetric triblock copolymer solutions. We find that the asymmetry of the block copolymer lowers the critical micelle concentration due to the gain of the conformational entropy.

High-precision computer simulations of bond-fluctuation (BF) model (volume fraction φ=0.5) are performed in the transition region between the non-entanglement and the entanglement regime. Defects of the model called X-traps are newly found which result in serious errors in the long-time behavior of the system. For samples free from X-traps, diffusion coefficient D of the center of mass, relaxation times τ_α for Rouse coordinate R_α (α=1,2) and τ_L for the end-to-end vector L are determined for chains of length N=16–180 within few percent of statistical errors. Their N-dependence changes around N=100 at which entanglement coupling is supposed to begin. By comparing D obtained by the simulations with experimental data of polystyrene melts and solutions, the average chain length per entanglement N_e was estimated to be 89, which is much larger than 30–42 reported by Paul et al. (J Phys II 1991;1:37). To see the origin of the discrepancy, statistical errors and system size effects are studied in detail and it was found that, to determine D within few percent of error, the number of independent chain samples N_sample should be larger than 10 000 and the size of simulation cells ℓ_cell should be larger than 4R_g; these conditions are not satisfied in the previous simulations. Critical chain length N_c^η for entanglement of BF model is estimated to be N_c^η=170 using the empirical relationship N_c^η/N_e=1.92 for polystyrene melts. It is argued that N_c^η=170 is a universal parameter of entanglement but N_e=89 is a specific value for polystyrenes and it may change with the materials with which comparisons are made.

Molecular dynamics calculations of an amorphous interfacial system of poly(methyl methacrylate) (PMMA) and poly(tetrafluoroethylene) (PTFE) containing about 10,000 interaction sites were performed for 15 ns under constant pressure and constant temperature conditions. The time evolutions of the thickness, density and number of atomic pairs in the interfaces suggested that the interfaces reached their equilibrium states with an interfacial thickness of about 2 nm at 500 K. The molecular motion in the interface and bulk was compared using mean square displacement and torsional autocorrelation function. The separation at a PMMA/PTFE interface was mimicked using non-equilibrium molecular dynamics calculations by applying the potential energy to the MD cell in a direction perpendicular to the interface. Initially, the PTFE layer close to the interface was deformed, and before complete separation, some segments of the PTFE molecules extended from the bulk to the surface of the PMMA layer, which were attached by the intermolecular interaction. The remaining PTFE molecules were entangled in the bulk, which probably prevented the transfer of the PTFE molecules to the surfaces of the PMMA layers. On the other hand, the PMMA layer was only slightly deformed. This separation behavior can be explained by taking into account the intermolecular interaction, the barrier to the conformational changes of the backbones and the entanglement of the PTFE molecules in the bulk.

Large scale molecular dynamics simulation is conducted for a system of entangled polymers in shear flow. The polymer consists of 100, 200 and 400 beads, which is 3–10 times larger than the number of beads between the entanglement points. The simulation reproduces many characteristic features of the rheological properties of real polymeric liquids. The steady state viscosity $\text{η(}\text{γ}\text{̇}\text{)}$ plotted against the shear rate $\text{γ}\text{̇}$, approaches a power law curve $\text{η(}\text{γ}\text{̇}\text{)∼}\text{γ}\text{̇}{}^{\mathrm{-n}}$ which is independent of the molecular weight with the exponent n≃1. The second normal stress coefficient $\text{Ψ}{}_2\text{(}\text{γ}\text{̇}\text{)}$ is negative and its ratio to the first normal stress coefficient $\text{Ψ}{}_1\text{(}\text{γ}\text{̇}\text{), −Ψ}{}_2\text{/Ψ}{}_1$ approaches to zero with the increase of the shear rate. The bond orientation is measured as a function of the position of the bond along the chain, and the profile is consistent with the recent theory of Mead et al. for the convective constraint release.

We consider a system composed of planar zigzag chain molecules of ferroelectric polymer PVDF. Taking the Lennard–Jones potential and the dipole–dipole interaction into consideration and assuming restrictions on molecular degrees of freedom, we have performed a Monte Carlo simulation which enables us to discuss the polarization reversal of PVDF under constant external electric field. Our simulation shows that the phenomenon is accompanied by nucleation and expansion of reversed domains. It also indicates that the dipole–dipole interaction between molecules causes growth anisotropy of the reversed domains.

Molecular dynamics (MD) simulation of the local motion of a polystyrene (PS) chain with anthryl group at the chain end surrounded by benzene molecules was performed and the results were compared with those obtained experimentally by the fluorescence depolarization method. The molecular weight dependence of the relaxation time of the probe obtained by the MD simulation was qualitatively in agreement with the results obtained by the fluorescence depolarization method. We also estimated the molecular weight dependence of the relaxation time for the end-to-end vector. Below the degree of polymerization (DP)≤3, the mean relaxation time T_m for the end-to-end vector was similar to that for the vector corresponding to the transition moment of the probe. With the increase of DP, the T_m for the probe tended to reach an asymptotic value unlike that for the end-to-end vector, which monotonically increased with DP. This indicates that the entire motion of a polymer coil contributes to the local motion to a lesser extent as the molecular weight increases. The MD simulations using artificial restraints showed that the rotational relaxation of the probe at the chain end for a dynamically stiff PS chain is realized by the cooperative rotation of the main chain bonds. The internal modes which takes place below 5 monomer units mainly led to the rotational relaxation of the probe at the PS chain end. Finally, the change of T_m with the position along the PS main chain was examined.

On the basis of the Aniansson–Wall (A–W) theory, a calculation method for the time evolution of association-number distribution during micelle formation of diblock copolymer in solution is presented. The rate constant for the elemental process of a chain expulsion from a micelle is evaluated as a function of the association number by application of Halperin's treatment based on the Kramers rate theory. Numerical calculations are carried out for both cases of micellization from unimer state and micellar relaxation under a temperature jump from one micellar state to another. In the micelle relaxation, the micelle size changes stepwise with two steps, clearly showing the characteristic feature of the A–W mechanism, where there exist two processes, the fast process undergoing by consuming/releasing free unimers and the slow process accompanied with almost no change of unimer concentration. On the contrary, in the micellization from unimer state, the very fast process is observed, where the free chains get together quickly to form temporal micelles, and is followed by an ordinary micellar relaxation.

A novel index for comparing different simulation model polymers with respect to entanglement is proposed. It is the number of elements $\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}$ of ring polymers whose average number of entanglement per molecule is unity; $\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}$ can be calculated with a small-scale computer simulation. We also proposed a method to equilibrate the entangled ring polymers. As an example we calculated $\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}$ with a molecular dynamics simulation using a bead-spring (BS) model which is equivalent to the model proposed by Kremer and Grest [J Chem Phys 92 (1990) 5057], and with a Monte Carlo simulation using bond fluctuation (BF) model. We obtained $\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}\text{=82±1}$ for BS model with volume fraction φ=0.43 and $\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}\text{=59±1}$ for BF model with φ=0.5. By comparing with the recent result of our group, N_e=89 for BF model with φ=0.5, we can assume that $\text{N}{}_{\mathrm{<mtext>e</mtext>}}\text{≃1.5}\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}\text{.}$ If this assumption holds for BS model, its N_e is estimated to be 120, which is 3.4 times greater than the estimated value by Kremer and Grest. The origin of this difference is discussed.