Phase Behavior of Melts of Diblock-Copolymers with One Charged Block

In this work we investigated the phase behavior of melts of block-copolymers with one charged block by means of dissipative particle dynamics with explicit electrostatic interactions. We assumed that all the Flory-Huggins \c{hi} parameters were equal to 0 and showed that the charge correlation attraction solely can cause microphase separation with long-range order; a phase diagram was constructed by varying the volume fraction of the uncharged block and the electrostatic interaction parameter {\lambda}. The obtained phase diagram was compared to the phase diagram of corresponding neutral diblock-copolymers. Surprisingly, the differences between these phase diagrams are rather subtle; the same phases are observed, and the positions of the ODT points are similar if the {\lambda}-parameter is considered as an "effective" \c{hi}-parameter. Next, we studied the position of the ODT for lamellar structure depending on the chain length N. It turned out that while for the uncharged diblock-copolymer the product \c{hi}crN was almost independent of N, for the diblock-copolymers with one charged block we observed a significant increase in {\lambda}crN upon increasing N. It can be attributed to the fact that the counterion entropy prevents the formation of ordered structures. This was supported by studying the ODT in diblock-copolymers with charged blocks and counterions cross-linked to the charged monomer units. The ODT for such systems was observed at significantly lower values of {\lambda} with the difference being more pronounced at longer chain lengths N. The diffusion of counterions in the obtained ordered structures was studied and compared to the case of a system with the same number of charged groups but homogeneous structure; the diffusion coefficient in a direction in the lamellar plane was found to be higher than in any direction in homogeneous structure

On scale-free and poly-scale behaviors of random hierarchical network

In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In particular, we compute numerically the spectral density of large random adjacency matrices defined by a hierarchy of the Bernoulli distributions $\{q_1,q_2,...\}$ on matrix elements, where $q_{\gamma}$ depends on hierarchy level $\gamma$ as $q_{\gamma}=p^{-\mu \gamma}$ ($\mu>0$). For the spectral density we clearly see the free--scale behavior. We show also that for the Gaussian distributions on matrix elements with zero mean and variances $\sigma_{\gamma}=p^{-\nu \gamma}$, the tail of the spectral density, $\rho_G(\lambda)$, behaves as $\rho_G(\lambda) \sim |\lambda|^{-(2-\nu)/(1-\nu)}$ for $|\lambda|\to\infty$ and $0<\nu<1$, while for $\nu\ge 1$ the power--law behavior is terminated. We also find that the vertex degree distribution of such hierarchical networks has a poly--scale fractal behavior extended to a very broad range of scales.Comment: 11 pages, 6 figures (paper is substantially revised

Phase Diagrams of Polymerization-Induced Self-Assembly Are Largely Determined by Polymer Recombination

In the current work, atom transfer radical polymerization-induced self-assembly (ATRP PISA) phase diagrams were obtained by the means of dissipative particle dynamics simulations. A fast algorithm for determining the equilibrium morphology of block copolymer aggregates was developed. Our goal was to assess how the chemical nature of ATRP affects the self-assembly of diblock copolymers in the course of PISA. We discovered that the chain growth termination via recombination played a key role in determining the ATRP PISA phase diagrams. In particular, ATRP with turned off recombination yielded a PISA phase diagram very similar to that obtained for a simple ideal living polymerization process. However, an increase in the recombination probability led to a significant change of the phase diagram: the transition between cylindrical micelles and vesicles was strongly shifted, and a dependence of the aggregate morphology on the concentration was observed. We speculate that this effect occurred due to the simultaneous action of two factors: the triblock copolymer architecture of the terminated chains and the dispersity of the solvophobic blocks. We showed that these two factors affected the phase diagram weakly if they acted separately; however, their combination, which naturally occurs during ATRP, affected the ATRP PISA phase diagram strongly. We suggest that the recombination reaction is a key factor leading to the complexity of experimental PISA phase diagrams

A simple model of a high temperature PEM fuel cell

We develop a simple analytical model of a high temperature hydrogen fuel cell with proton exchange membrane. The model is validated against experimental results obtained in our group. The model is pseudo two dimensional, steady-state and isothermal, it accounts for the crossover of reactant gases through the membrane and it can be solved analytically. The role of the crossover is considered in detail. (C) 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved