Andrey Milchev

Atomistic theory of electrolytic nucleation: I

Abstract The kinetics of electrolytic nucleation at high supersaturation are considered. According to the ideas developed by Walton, the critical nucleus is assumed to consist of a small number of atoms. Expressions describing the steady state nucleation rate are obtained considering two possible mechanisms of cluster formation: by direct attachment of ions from the volume of the electrolyte and by surface diffusion of adatoms. The nucleation on active centres is also considered.

Capillary rise in nanopores : Molecular dynamics evidence for the lucas-washburn equation

When a capillary is inserted into a liquid, the liquid will rapidly flow into it. This phenomenon, well studied and understood on the macroscale, is investigated by molecular dynamics simulations for coarse-grained models of nanotubes. Both a simple Lennard-Jones fluid and a model for a polymer melt are considered. In both cases after a transient period (of a few nanoseconds) the meniscus rises according to a (time)1/2 law. For the polymer melt, however, we find that the capillary flow exhibits a slip length delta, comparable in size with the nanotube radius R. We show that a consistent description of the imbibition process in nanotubes is only possible upon modification of the Lucas-Washburn law which takes explicitly into account the slip length delta. We also demonstrate that the velocity field of the rising fluid close to the interface is not a simple diffusive spreading.

Off‐lattice Monte Carlo simulation of dilute and concentrated polymer solutions under theta conditions

A recently introduced bead‐spring type model of polymer chains with purely repulsive interactions between the beads is modified to allow for attractive forces at intermediate distances. This new model is suitable for the study of thermal properties of three‐dimensional polymer solutions and melts and can be efficiently simulated with Link–Cell Monte Carlo methods. As a first step, the single chain lengths up to N=128 beads are studied and the theta temperature θ is located. It is shown that the data are compatible with the theoretically predicted crossover scaling behavior, and that the properties of collapsed chains can be studied for reasonably low temperatures T<θ. In addition to static properties (chain radii, polymer density inside the coil, internal energy, specific heat) also dynamic properties are obtained, namely various mean square displacements and relaxation times and the self diffusion constant. While for T=θ (and long enough chains), there is reasonable agreement with the Rouse model, a diff...

Single-polymer dynamics under constraints: scaling theory and computer experiment

The relaxation, diffusion and translocation dynamics of single linear polymer chains in confinement is briefly reviewed with emphasis on the comparison between theoretical scaling predictions and observations from experiment or, most frequently, from computer simulations. Besides cylindrical, spherical and slit-like constraints, related problems such as the chain dynamics in a random medium and the translocation dynamics through a nanopore are also considered. Another particular kind of confinement is imposed by polymer adsorption on attractive surfaces or selective interfaces--a short overview of single-chain dynamics is also contained in this survey. While both theory and numerical experiments consider predominantly coarse-grained models of self-avoiding linear chain molecules with typically Rouse dynamics, we also note some recent studies which examine the impact of hydrodynamic interactions on polymer dynamics in confinement. In all of the aforementioned cases we focus mainly on the consequences of imposed geometric restrictions on single-chain dynamics and try to check our degree of understanding by assessing the agreement between theoretical predictions and observations.

Driven polymer translocation through a nanopore: A manifestation of anomalous diffusion

We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic variable, the translocated number of segments s(t), displays an anomalous diffusive behavior even in the presence of an external force. The anomalous dynamics of the translocation process is governed by the same universal exponent α=2/(2ν+2−γ1), where ν is the Flory exponent and γ1 the surface exponent, which was established recently for the case of non-driven polymer chain threading through a nanopore. A closed analytic expression for the probability distribution function W(s, t), which follows from the relevant fractional Fokker-Planck equation, is derived in terms of the polymer chain length N and the applied drag force f. It is found that the average translocation time scales as . Also the corresponding time-dependent statistical moments, and reveal unambiguously the anomalous nature of the translocation dynamics and permit direct measurement of α in experiments. These findings are tested and found to be in perfect agreement with extensive Monte Carlo (MC) simulations.

Polymer translocation through a nanopore: A showcase of anomalous diffusion

The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one-dimensional anomalous diffusion process in terms of the reaction coordinate s (i.e., the translocated number of segments at time t ) and shown to be governed by a universal exponent alpha=2(2nu+2-gamma(1), where nu is the Flory exponent and gamma(1) is the surface exponent. Remarkably, it turns out that the value of alpha is nearly the same in two and three dimensions. The process is described by a fractional diffusion equation which is solved exactly in the interval 0<s<N with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments <s(t) and <s2(t)-<s(t)>2, which provide a full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.

A new off‐lattice Monte Carlo model for polymers: A comparison of static and dynamic properties with the bond‐fluctuation model and application to random media

A model for a multichain polymer system in three‐dimensional continuous space is studied by link cell Monte Carlo methods, using systems up to chain length N=64 and up to 16 384 monomers. The chains consist of beads with a hard core connected by rather stiff harmonic bonds, with a repulsive Lennard‐Jones‐type interaction between beads chosen such that chains cannot cross each other during their random motions. On RISC workstations the model performs only about a factor of 4 slower than the bond fluctuation lattice model, the qualitative behavior of the time‐dependent mean‐square displacements and relaxation functions being rather similar to the latter. For the model without obstacles, it is shown that the present continuum model can be approximately mapped on the lattice bond fluctuation model by a suitable rescaling of chain length and volume fraction. But the distinctive advantage of the present model is that it can be applied easily to random media (described by randomly placed rigid obstacles), withou...

Spherical polymer brushes under good solvent conditions: Molecular dynamics results compared to density functional theory

A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions by molecular dynamics methods and density functional theory. With increasing chain length, the monomer density profile exhibits a crossover to the star polymer limit. The distribution of polymer ends and the linear dimensions of individual polymer chains are obtained, while the inhomogeneous stretching of the chains is characterized by the local persistence lengths. The results on the structure factor of both single chain and full spherical brush as well as the range of applicability of the different theoretical tools are presented. Finally, a brief discussion of the experiment is given.

Polymer brushes under flow and in other out-of-equilibrium conditions

Polymer brushes are formed from flexible linear macromolecules tethered at one chain end to a solid substrate, forming a dense polymeric layer of polymer chains which are more or less stretched in the direction perpendicular to the substrate surface. These systems find interest also due to numerous applications (colloid stabilization, improvement of lubrication properties when the surfaces are exposed to shear, protection of the surface against adsorption of nanoparticles or proteins, etc.), for which often the dynamic non-equilibrium response of these brushes to external perturbation is important. The present review summarizes recent computer simulation studies pertinent to these questions. Polymer brushes exposed to shear due to flow of the solvent or a polymer melt the brush interacts with are discussed, and the friction between two brushes is discussed. Another topic that is emphasized is the interaction of polymer brushes with “nanoinclusions” (i.e., small colloidal particles or linear macromolecules down to oligomers), discussing the absorption or expulsion of these objects, and again the response to shear. The simulations are interpreted in terms of scaling concepts and other phenomenological theories wherever possible, and an outlook to related experiments is given.

Scaling exponents of forced polymer translocation through a nanopore

We investigate several properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulations in three dimensions (3D). Motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we estimate the exponents describing the scaling with chain length (Nof the average translocation time