The confinement of an annealed branched polymer by a potential well

The Lifshitz equation for the confinement of a linear polymer in a spherical cavity of radius R has the form of the Schrödinger equation for a quantum particle trapped in a potential well with flat bottom and infinite walls at radius R. We show that the Lifshitz equation of a confined annealed branched polymer has the form of the Schrödinger equation for a quantum harmonic oscillator. The harmonic oscillator potential results from the repulsion of the many branches from the potential walls. Mathematically, it must be obtained from the solution of the equation of motion of a second, now classical, particle in a non-linear potential that depends self-consistently on the eigenvalue of the quantum oscillator. The resulting confinement energy has a 1/R⁴ dependence on the confinement radius R, in agreement with scaling arguments. We discuss the application of this result to the problem of the confinement of single-stranded RNA molecules inside spherical capsids

Collapse of a semiflexible polymer in poor solvent

We investigate the dynamics and the pathways of the collapse of a single, semiflexible polymer in a poor solvent via 3-D Brownian Dynamics simulations. Earlier work indicates that the condensation of semiflexible polymers generically proceeds via a cascade through metastable racquet-shaped, long-lived intermediates towards the stable torus state. We investigate the rate of decay of uncollapsed states, analyze the preferential pathways of condensation, and describe likelihood and lifespan of the different metastable states. The simulation are performed with a bead-stiff spring model with excluded volume interaction and exponentially decaying attractive potential. The semiflexible chain collapse is studied as functions of the three relevant length scales of the phenomenon, i.e., the total chain length $L$, the persistence length $L_p$ and the condensation length $L_0 = \sqrt{k_B T L_p/u_0}$, where $u_0$ is a measure of the attractive potential per unit length. Two dimensionless ratios, $L/L_p$ and $L_0/L_p$, suffice to describe the decay rate of uncollapsed states, which appears to scale as $(L/L_p)^{1/3} (L_0/L_p)$. The condensation sequence is described in terms of the time series of the well separated energy levels associated with each metastable collapsed state. The collapsed states are described quantitatively through the spatial correlation of tangent vectors along the chain. We also compare the results obtained with a locally inextensible bead-rod chain and with a phantom bead-spring model. Finally, we show preliminary results on the effects of steady shear flow on the kinetics of collapse.Comment: 9 pages, 8 figure

Dielectrophoresis of charged colloidal suspensions

We present a theoretical study of dielectrophoretic (DEP) crossover spectrum of two polarizable particles under the action of a nonuniform AC electric field. For two approaching particles, the mutual polarization interaction yields a change in their respective dipole moments, and hence, in the DEP crossover spectrum. The induced polarization effects are captured by the multiple image method. Using spectral representation theory, an analytic expression for the DEP force is derived. We find that the mutual polarization effects can change the crossover frequency at which the DEP force changes sign. The results are found to be in agreement with recent experimental observation and as they go beyond the standard theory, they help to clarify the important question of the underlying polarization mechanisms

Mean Field Fluid Behavior of the Gaussian Core Model

We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger (J. Chem. Phys. 65, 3968 (1976)), behaves like a weakly correlated ``mean field fluid'' over a surprisingly wide density and temperature range. In the bulk the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated HNC integral equation. The resulting pressure deviates very little from a simple, mean-field like, quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against de-mixing at high densities. Possible implications for semi-dilute polymer solutions are discussed.Comment: 13 pages, 2 columns, ReVTeX epsfig,multicol,amssym, 15 figures; submitted to Phys. Rev. E (change: important reference added

Knots in Charged Polymers

The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction localizes irreducible topological constraints into tight molecular knots, while composite constraints are factored and separated. Even when the forces are screened, tight knots may survive as local (or even global) equilibria, as long as the overall rigidity of the polymer is dominated by the Coulomb interactions. As entanglements involving tight knots are not easy to eliminate, their presence greatly influences the relaxation times of the system. In particular, we find that tight knots in open polymers are removed by diffusion along the chain, rather than by opening up. The knot diffusion coefficient actually decreases with its charge density, and for highly charged polymers the knot's position appears frozen.Comment: Revtex4, 9 pages, 9 eps figure

Kinetic Arrest in Polyion-Induced Inhomogeneously-Charged Colloidal Particle Aggregation

Polymer chains adsorbed onto oppositely charged spherical colloidal particles can significantly modify the particle-particle interactions. For sufficient amounts of added polymers, the original electrostatic repulsion can even turn into an effective attraction and relatively large kinetically stable aggregates can form which display several unexpected and interesting peculiarities and some intriguing biotechnological implications. The attractive interaction contribution between two oppositely particles arises from the correlated adsorption of polyions at the oppositely charged particle surfaces, resulting in a non-homogeneous surface charge distribution. Here, we investigate the aggregation kinetics of polyion-induced colloidal complexes through Monte Carlo simulation, in which the effect of charge anisotropy is taken into account by a DLVO-like intra-particle potential, as recentely proposed by Velegol and Thwar [D. Velegol and P.K. Thwar, Langmuir, 17, 2001]. The results reveal that in the presence of a charge heterogeneity the aggregation process slows down due to the progressive increase of the potential barrier height upon clustering. Within this framework, the experimentally observed cluster phases in polyelectrolyte-liposomes solutions should be considered as a kinetic arrested state.Comment: 9 pages. 11 figure

Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations

We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength ε and the globule size N [subscript G] is observed. We find two distinct dynamical regimes: a liquid-like regime (for ε ε[subscript s] with slow internal dynamics. The cohesion strength ε[subscript s] of this freezing transition depends on N G . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with ε and scales extensive in N [subscript G] . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.American Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi