Two-particle friction in a mesoscopic solvent

The effects of hydrodynamic interactions on the friction tensors for two particles in solution are studied. The particles have linear dimensions on nanometer scales and are either simple spherical particles interacting with the solvent through repulsive Lennard-Jones forces or are composite cluster particles whose atomic components interact with the solvent through repulsive Lennard-Jones forces. The solvent dynamics is modeled at a mesoscopic level through multiparticle collisions that conserve mass, momentum, and energy. The dependence of the two-particle relative friction tensors on the interparticle separation indicates the importance of hydrodynamic interactions for these nanoparticles.     

Dynamics of polymers in a particle-based mesoscopic solvent

We study the dynamics of flexible polymer chains in solution by combining multiparticle-collision dynamics (MPCD), a mesoscale simulation method, and molecular-dynamics simulations. Polymers with and without excluded-volume interactions are considered. With an appropriate choice of the collision time step for the MPCD solvent, hydrodynamic interactions build up properly. For the center-of-mass diffusion coefficient, scaling with respect to polymer length is found to hold already for rather short chains. The center-of-mass velocity autocorrelation function displays a long-time tail which decays algebraically as (Dt)(-3/2) as a function of time t, where D is the diffusion coefficient. The analysis of the intramolecular dynamics in terms of Rouse modes yields excellent agreement between simulation data and results of the Zimm model for the mode-number dependence of the mode-amplitude correlation functions.     

First passage times for a tracer particle in single file diffusion and fractional Brownian motion

We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavy-tailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBm-defined by the Hurst parameter, H ∈ (0, 1)] is studied, of interest here as fBm and SFD systems belong to the same universality class. Extensive stochastic (non-Markovian) SFD and fBm simulations are performed and compared to two analytical Markovian techniques: the method of images approximation (MIA) and the Willemski-Fixman approximation (WFA). We find that the MIA cannot approximate well any temporal scale of the SFD FPTD. Our exact inversion of the Willemski-Fixman integral equation captures the long-time power-law exponent, when H ≥ 1/3, as predicted by Molchan [Commun. Math. Phys. 205, 97 (1999)] for fBm. When H < 1/3, which includes homogeneous SFD (H = 1/4), and heterogeneous SFD (H < 1/4), the WFA fails to agree with any temporal scale of the simulations and Molchan's long-time result. SFD systems are compared to their fBm counter parts; and in the homogeneous system both scaled FPTDs agree on all temporal scales including also, the result by Molchan, thus affirming that SFD and fBm dynamics belong to the same universality class. In the heterogeneous case SFD and fBm results for heterogeneity-averaged FPTDs agree in the asymptotic time limit. The non-averaged heterogeneous SFD systems display a lack of self-averaging. An exponential with a power-law argument, multiplied by a power-law pre-factor is shown to describe well the FPTD for all times for homogeneous SFD and sub-diffusive fBm systems.     

Brownian motion of a polymer-bound colloidal particle

A simple model of Brownian motion of a colloidal particle attached to the flat surface by a polymer thread is presented. The model results are discussed in terms of the measurability of the elastic properties of a linear polymer chain in the dispersion medium by observation of the motion of a colloidal particle connected to a fixed point by the polymer. Received: 11 November 1998 Accepted: 9 December 1998     

Brownian diffusion close to a polymer brush

In an effort to control particle diffusion near surfaces, we have studied the dynamics of colloidal hard spheres and soft compliant star copolymers on surfaces coated with polymer brushes using evanescent wave dynamic light scattering. The same experiments provide information on the brush structure and confined particle motion. The penetration into dense polydisperse brushes is size- and solvent-dependent.     

Anisotropic Brownian diffusion near a nanostructured surface

The Brownian diffusion of sub-micrometer-sized particles (diameter 0.52 microm) in the vicinity of a nanostructured surface was experimentally characterized. The surface consisted of a repeating pattern of rectangular grooves with depth 35 nm and pitch 400 nm. It was found that the one-dimensional particle diffusivity parallel to the nanogrooves was significantly higher than the diffusivity perpendicular to the grooves (1.518+/-0.274 (S.E.) microm2/s compared to 0.704+/-0.090 microm2/s). No such anisotropy in the one-dimensional Brownian diffusivity was found for particles near a flat surface.     

Brownian motion of an asymmetrical particle in a potential field

It is well known that a free ellipsoidal Brownian particle exhibits anisotropic diffusion for short times which changes to isotropic at long times, and, that the long-time diffusion coefficient is an average of the translational diffusion coefficients along the different semiaxes of the particle. We show analytically that in the presence of external forces, the long-time diffusion coefficient is different from that of a free particle. The magnitude of the difference in the two diffusion coefficients is found to increase proportionately with the particle's asymmetry, being zero only for a perfectly spherical Brownian particle. It is also found that, for asymmetrical particles, the application of external forces can amplify the non-Gaussian character of the spatial probability distributions which consequently delays the transition to the classical behavior. We illustrate these phenomena by considering the quasi-two-dimensional Brownian motion of an ellipsoidal rigid particle in linear and harmonic potential fields. These two examples provide insight into the role played by particle asymmetry in electrophoresis and microconfinement due to a laser trap or due to intracellular macromolecular crowding.     

Transient response of a Brownian particle with general damping

We study the transient response of a Brownian particle with general damping in a system of metastable potential well. The escape rate is evaluated as a function of time after an infinite wall is removed from the potential barrier. It takes a relaxation time for the rate to reach its limit value and this rate relaxation time differs from the relaxation time of the majority of the probability around the bottom of the potential well. The rate relaxation time is found to depend on the temperature as well as the damping constant. It involves the diffusion time and the instanton time, in general agreement with recent studies of the overdamped case by Bier et al. [Phys. Rev. E 59, 6422 (1999)].     

Diffusion coefficient of Brownian particle in rough micro-channel

This study examines the feasibility of using of the lattice Boltzmann method to determine how the surface roughness of a quadrate channel affects the diffusion coefficient of Brownian particle(s). The surface was represented by a regular array of spheres. Surface roughness reduced the diffusion coefficient of the Brownian particle(s) because of a change in the velocity autocorrelation function decay and in pressure. Additionally, the neighboring particles increased the diffusion coefficient of Brownian particle.     

Simultaneous nonlinear diffusion of a solvent and organic penetrant in a polymer

We obtain the exact solution of a fairly large class of somewhat simplified problems involving the simultaneous nonlinear Fickian diffusion of a poor solvent and a dilute organic penetrant, such as a plasticizer, in a semi-infinite polymer slab immersed in the solvent bath. Such problems can also provide useful estimates during certain time regimes of release of drugs from implants, and pesticides and pheromones from certain slow or controlled-release polymeric devices, insofar as these are affected by an environmental solvent bath. We assess the effect of various simplifications made (e.g., neglect of the penetrant concentration dependence in the diffusion coefficient, cross diffusion of solvent and penetrant, and a variety of boundary conditions) by solving exactly some additional specialized cases.     

Nucleation theory in Langevin's approach and lifetime of a Brownian particle in potential wells

The multivariable theory of nucleation suggested by Alekseechkin [J. Chem. Phys. 124, 124512 (2006)] is further developed in the context of Langevin's approach. The use of this approach essentially enhances the capability of the nucleation theory, because it makes possible to consider the cases of small friction which are not taken into account by the classical Zel'dovich-Frenkel theory and its multivariable extensions. The procedure for the phenomenological determination of the nucleation parameters is described. Using the similarity of the Kramers model with that of nucleation, the lifetime of a Brownian particle in potential wells in various dimensionalities is calculated with the help of the expression for the steady state nucleation rate.     

Brownian dynamics simulation and experimental study of colloidal particle deposition in a microchannel flow

This paper reports an analysis of the irreversible deposition of colloidal particles from the pressure-driven flow in a microchannel within the framework of DLVO theory. A theoretical model is presented on the basis of the stochastic Langevin equation, incorporating the random Brownian motion of colloidal particles. Brownian dynamics simulation is used to compute the particle deposition in terms of the surface coverage. To validate the theoretical model, experiments are carried out using the parallel-plate flow cell technique, enabling direct videomicroscopic observation of the deposition kinetics of polystyrene latex particles in NaCl electrolytes. The theoretical predictions are compared with the experimental results, and good agreement is found.     

Wigner function approach to the quantum Brownian motion of a particle in a potential

Recent progress in our understanding of quantum effects on the Brownian motion in an external potential is reviewed. This problem is ubiquitous in physics and chemistry, particularly in the context of decay of metastable states, for example, the reversal of the magnetization of a single domain ferromagnetic particle, kinetics of a superconducting tunnelling junction, etc. Emphasis is laid on the establishment of master equations describing the diffusion process in phase space analogous to the classical Fokker-Planck equation. In particular, it is shown how Wigner's [E. P. Wigner, Phys. Rev., 1932, 40, 749] method of obtaining quantum corrections to the classical equilibrium Maxwell-Boltzmann distribution may be extended to the dissipative non-equilibrium dynamics governing the quantum Brownian motion in an external potential V(x), yielding a master equation for the Wigner distribution function W(x,p,t) in phase space (x,p). The explicit form of the master equation so obtained contains quantum correction terms up to o(h(4)) and in the classical limit, h --> 0, reduces to the classical Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation coinciding in all respects with that of Agarwal [G. S. Agarwal, Phys. Rev. A, 1971, 4, 739]. In the high dissipation limit, the master equation reduces to a semi-classical Smoluchowski equation describing non-inertial quantum diffusion in configuration space. The Wigner function formulation of quantum Brownian motion is further illustrated by finding quantum corrections to the Kramers escape rate, which, in appropriate limits, reduce to those yielded via quantum generalizations of reaction rate theory.     

Anisotropic diffusion of elongated and aligned polymer chains in a nematic solvent

The translational diffusion constant, D, of a polymer solute in a single-domain, nematic liquid crystal solvent (5CB) is measured in directions parallel and perpendicular to the nematic director using a fluorescence two-beam, cross-correlation technique. The solute under investigation is the stiff, conjugated polymer, MEH-PPV. The ratio D parallel/D perpendicular) of diffusion constants (parallel and perpendicular to the director) is observed to be 1.9 +/- 0.3. This is surprisingly small considering that MEH-PPV is known to be both elongated and highly aligned along the liquid crystal director of 5CB. We therefore argue that the structural order parameter of the solvent governs the anisotropy of the diffusion of the solute.     

The diffusion coefficient of a swollen microgel particle

The drag on a permeable particle traversing through a Newtonian liquid is calculated. This is in terms of a single dimensionless group, Da, the Darcy number, which relates the particle permeability to the radius. For small values of the Darcy number the solution reverts to the well-known Stokes drag for smooth hard particles. For larger values of the Darcy number the drag is reduced. This drag allows calculation of the diffusion coefficient of such particles, again as a function of the Darcy number. The results are discussed in relation to microgel particles, which display swelling under certain conditions. The size of such particles is typically measured with dynamic light scattering, which measures the diffusion coefficient of particles and as such the analysis presented here shows the conditions under which dynamic light scattering is accurate. The Darcy number for microgel particles is estimated to be on the order of 10(-7).     

Trotter derivation of algorithms for Brownian and dissipative particle dynamics

This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, which we found equivalent to the proposal of Ermak and Buckholtz [J. Comput. Phys. 35, 169 (1980)] and not simply to the stochastic version of the velocity-Verlet algorithm. However, we checked on numerical simulations that both algorithms give similar results, and share the same "weak order two" accuracy. We then apply the same strategy to derive and test two numerical schemes for the dissipative particle dynamics. The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms.     

Micellization behavior of star-block copolymers in a selective solvent: A Brownian dynamics simulation approach

Micellization behavior of (AB)n type star-block copolymer in a selective solvent for its outer block is investigated by using a Brownian dynamics simulation. Micellar properties are compared in terms of the arm number (n) of star-block copolymer. It is observed that the critical micelle concentration (cmc) shows a minimum when the cmc is plotted against the arm number. The star-block copolymer with longer soluble block shows the cmc minimum at smaller arm number than that with shorter soluble block. Although the star-block copolymer with multiple arms forms more compact core as compared to diblock copolymer, the average aggregation number is inversely proportional to the arm number (approximately 1/n), which implies that the micelle size is invariant with the arm number. Theoretical predictions based on a simple mean field theory agree qualitatively well with the simulation results.     

Brownian force profile reconstruction of interfacial 1-nonanol solvent structure

Using Brownian force profile reconstruction (BFPR), we measured the solvent structure force profile of interfacial 1-nonanol between graphite and methyl terminated alkane thiol SAM surfaces. BFPR harnesses the thermal motion of the cantilever to accurately and precisely reconstruct force profiles that may be stiffer than the intrinsic cantilever stiffness. Novel methods to compensate instrument noise and seamlessly stitch together subsections of the force profile significantly improve upon previous reconstruction techniques using thermal noise. The increased accuracy and precision of BFPR could enable the measurement of stiff or rough energy landscapes such as solvent structure or ligand-protein binding. The force profile for interfacial 1-nonanol solvent structure was well fit by an exponentially decaying sinusoid function with a period of 4.5 A for distances greater than four molecular layers, revealing liquid behavior. Distances shorter than four molecular layers displayed solid behavior with interlayer transitions being 3.9 A and possible crystal orientation rearrangements causing submolecular steps upon subsequent confinement.     

Spectrum of position fluctuations of a Brownian particle bound in a harmonic trap near a plane wall

The spectrum of position fluctuations of a Brownian particle bound in a harmonic trap near a plane wall is calculated from an approximate result for the Fourier transform of the velocity autocorrelation function. Both a no-slip and a perfect slip boundary condition at the wall are considered. In both cases at low frequency the calculated spectrum differs markedly from recent experimental data. It is suggested that a partial slip boundary condition with a frequency-dependent slip coefficient may explain the experimental results.