Origin of translocation barriers for polyelectrolyte chains

For single-file translocations of a charged macromolecule through a narrow pore, the crucial step of arrival of an end at the pore suffers from free energy barriers, arising from changes in intrachain electrostatic interaction, distribution of ionic clouds and solvent molecules, and conformational entropy of the chain. All contributing factors to the barrier in the initial stage of translocation are evaluated by using the self-consistent field theory for the polyelectrolyte and the coupled Poisson-Boltzmann description for ions, without radial symmetry. The barrier is found to be essentially entropic, due to conformational changes. For moderate and high salt concentrations, the barriers for the polyelectrolyte chain are quantitatively equivalent to that of uncharged self-avoiding walks. Electrostatic effects are shown to increase the free energy barriers, but only slightly. The degree of ionization, electrostatic interaction strength, decreasing salt concentration and the solvent quality all result in increases in the barrier.Comment: J.Chem. Phys. 131, 21 (2009) - to be appeare

Dynamics of Diblock Copolymers in Dilute Solutions

We consider the dynamics of freely translating and rotating diblock (A-B), Gaussian copolymers, in dilute solutions. Using the multiple scattering technique, we have computed the diffusion and the friction coefficients D_AB and Zeta_AB, and the change Eta_AB in the viscosity of the solution as functions of x = N_A/N and t = l_B/l_A, where N_A, N are the number of segments of the A block and of the whole copolymer, respectively, and l_A, l_B are the Kuhn lengths of the A and B blocks. Specific regimes that maximize the efficiency of separation of copolymers with distinct "t" values, have been identified.Comment: 20 pages Revtex, 7 eps figures, needs epsf.tex and amssymb.sty, submitted to Macromolecule

Continuum Theory of Polymer Crystallization

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with $G \sim \exp(1/T \Delta T)$, where $G$ is the growth rate and $\Delta T$ is the super-cooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with $G \sim \Delta T$, for small $\Delta T$. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.Comment: 37 double-spaced pages including 8 figures, submitted to the Journal of Chemical Physic

Efficient Set Sharing Using ZBDDs

Set sharing is an abstract domain in which each concrete object is represented by the set of local variables from which it might be reachable. It is a useful abstraction to detect parallelism opportunities, since it contains definite information about which variables do not share in memory, i.e., about when the memory regions reachable from those variables are disjoint. Set sharing is a more precise alternative to pair sharing, in which each domain element is a set of all pairs of local variables from which a common object may be reachable. However, the exponential complexity of some set sharing operations has limited its wider application. This work introduces an efficient implementation of the set sharing domain using Zero-suppressed Binary Decision Diagrams (ZBDDs). Because ZBDDs were designed to represent sets of combinations (i.e., sets of sets), they naturally represent elements of the set sharing domain. We show how to synthesize the operations needed in the set sharing transfer functions from basic ZBDD operations. For some of the operations, we devise custom ZBDD algorithms that perform better in practice. We also compare our implementation of the abstract domain with an efficient, compact, bit set-based alternative, and show that the ZBDD version scales better in terms of both memory usage and running time

Simulation of structural and electronic properties of amorphous tungsten oxycarbides

Electron beam induced deposition with tungsten hexacarbonyl W(CO)6 as precursors leads to granular deposits with varying compositions of tungsten, carbon and oxygen. Depending on the deposition conditions, the deposits are insulating or metallic. We employ an evolutionary algorithm to predict the crystal structures starting from a series of chemical compositions that were determined experimentally. We show that this method leads to better structures than structural relaxation based on guessed initial structures. We approximate the expected amorphous structures by reasonably large unit cells that can accommodate local structural environments that resemble the true amorphous structure. Our predicted structures show an insulator to metal transition close to the experimental composition at which this transition is actually observed. Our predicted structures also allow comparison to experimental electron diffraction patterns.Comment: 17 Pages, 11 figure

Microphase separation in polyelectrolytic diblock copolymer melt : weak segregation limit

We present a generalized theory of microphase separation for charged-neutral diblock copolymer melt. Stability limit of the disordered phase for salt-free melt has been calculated using Random Phase Approximation (RPA) and self-consistent field theory (SCFT). Explicit analytical free energy expressions for different classical ordered microstructures (lamellar, cylinder and sphere) are presented. We demonstrate that chemical mismatch required for the onset of microphase separation ($\chi^{\star} N$) in charged-neutral diblock melt is higher and the period of ordered microstructures is lower than those for the corresponding neutral-neutral diblock system. Theoretical predictions on the period of ordered structures in terms of Coulomb electrostatic interaction strength, chain length, block length, and the chemical mismatch between blocks are presented. SCFT has been used to go beyond the stability limit, where electrostatic potential and charge distribution are calculated self-consistently. Stability limits calculated using RPA are in perfect agreement with the corresponding SCFT calculations. Limiting laws for stability limit and the period of ordered structures are presented and comparisons are made with an earlier theory. Also, transition boundaries between different morphologies have been investigated