Non-equilibrium interface equations: An application to thermo-capillary motion in binary systems

Interface equations are derived for both binary diffusive and binary fluid systems subjected to non-equilibrium conditions, starting from the coarse-grained (mesoscopic) models. The equations are used to describe thermo-capillary motion of a droplet in both purely diffusive and fluid cases, and the results are compared with numerical simulations. A mesoscopic chemical potential shift, owing to the temperature gradient, and associated mesoscopic corrections involved in droplet motion are elucidated.Comment: 12 pages; Latex, revtex, ap

Entropically Driven Formation of Hierarchically Ordered Nanocomposites

Using theoretical models, we undertake the first investigation into the rich behavior that emerges when binary particle mixtures are blended with microphase-separating copolymers. We isolate an example of coupled self-assembly in such materials, where the system undergoes a nanoscale ordering of the particles along with a phase transformation in the copolymer matrix. Furthermore, the self-assembly is driven by entropic effects involving all the different components. The results reveal that entropy can be exploited to create highly ordered nanocomposites with potentially unique electronic and photonic properties. © 2002 The American Physical Society

Binary hard sphere mixtures in block copolymer melts

We perform a self-consistent-field/density-functional-theory hybrid analysis for a system of diblock copolymers mixed with polydisperse, hard, spherical particles of various chemical species. We apply this theory to study the equilibrium morphologies of two different binary sphere/diblock melts. First, we examine the case where the particles have two different sizes, but both types are preferentially wetted by one of the copolymer blocks. We find that the single-particle distributions for the two species do not track one another and that the particles show a degree of entropically generated separation based on size, due to confinement within the diblock matrix. Second, we study the case where the particles are all the same size, but are of two different chemical species. We find that, as expected, the particle distributions reveal a degree of enthalpically driven separation, due to the spheres’ preferential affinities for different blocks of the copolymer. © 2002 The American Physical Society

Self-assembly of a binary mixture of particles and diblock copolymers

Using theoretical models, we undertake the first investigation into the synergy and rich phase behavior that emerges when binary particle mixtures are blended with microphase-separating copolymers. We isolate an example of spontaneous hierarchical self-assembly in such hybrid materials, where the system exhibits both nanoscopic ordering of the particles and macroscopic phase transformation in the copolymer matrix. Furthermore, the self-assembly is driven by entropic effects involving all the different components. The results reveal that entropy can be exploited to create highly ordered nanocomposites with potentially unique electronic and photonic properties. © 2003 The Royal Society of Chemistry

Dynamics of Phase Behavior of a Polymer Blend Under Shear Flow

We study the dynamics of the phase behavior of a polymer blend in the presence of shear flow. By adopting a two fluid picture and using a generalization of the concept of material derivative, we construct kinetic equations that describe the phase behavior of polymer blends in the presence of external flow. A phenomenological form for the shear modulus for the blend is proposed. The study indicates that a nonlinear dependence of the shear modulus of the blend on the volume fraction of one of the species is crucial for a shift in the stability line to be induced by shear flow.Comment: 16 pages, late

Simple biophysics underpins collective conformations of the intrinsically disordered proteins of the Nuclear Pore Complex

Nuclear Pore Complexes (NPCs) are key cellular transporter that control nucleocytoplasmic transport in eukaryotic cells, but its transport mechanism is still not understood. The centerpiece of NPC transport is the assembly of intrinsically disordered polypeptides, known as FG nucleoporins, lining its passageway. Their conformations and collective dynamics during transport are difficult to assess in vivo. In vitro investigations provide partially conflicting results, lending support to different models of transport, which invoke various conformational transitions of the FG nucleoporins induced by the cargo-carrying transport proteins. We show that the spatial organization of FG nucleoporin assemblies with the transport proteins can be understood within a first principles biophysical model with a minimal number of key physical variables, such as the average protein interaction strengths and spatial densities. These results address some of the outstanding controversies and suggest how molecularly divergent NPCs in different species can perform essentially the same function

Transition-Event Durations in One Dimensional Activated Processes

Despite their importance in activated processes, transition-event durations -- which are much shorter than first passage times -- have not received a complete theoretical treatment. We therefore study the distribution of durations of transition events over a barrier in a one-dimensional system undergoing over-damped Langevin dynamics.Comment: 39 pages, 11 figure

The effective potential, critical point scaling and the renormalization group

The desirability of evaluating the effective potential in field theories near a phase transition has been recognized in a number of different areas. We show that recent Monte Carlo simulations for the probability distribution for the order parameter in an equilibrium Ising system, when combined with low-order renormalization group results for an ordinary $\phi^4$ system, can be used to extract the effective potential. All scaling features are included in the process.Comment: REVTEX file, 22 pages, three figures, submitted to Phys. Rev.

A phase-field model of Hele-Shaw flows in the high viscosity contrast regime

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady state finger the width of which goes to one half of the channel width as the velocity increases

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study

We implement a phase-field simulation of the dynamics of two fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. We demonstrate the use of this technique in different situations including the linear regime, the stationary Saffman-Taylor fingers and the multifinger competition dynamics, for different viscosity contrasts. The method is quantitatively tested against analytical predictions and other numerical results. A detailed analysis of convergence to the sharp interface limit is performed for the linear dispersion results. We show that the method may be a useful alternative to more traditional methods.Comment: 13 pages in revtex, 5 PostScript figures. changes: 1 reference added, figs. 4 and 5 rearrange