Edith M Sevick

Monte Carlo calculations of cluster statistics in continuum models of composite morphology

We describe a simple and efficient algorithm for sampling physical cluster statistics in Monte Carlo simulations of continuum morphology models. The algorithm produces a variety of information including the pair connectedness function, cluster size distribution, and mean cluster size. The approach can be applied to any system, given a definition of a physical cluster for that system. Results are presented for two types of models commonly used in studies of percolation phenomena; randomly centered spheres and the concentric shell (extended sphere) model. The simulation results are used to assess the accuracy of the predictions of the Percus–Yevick closure of the Ornstein–Zernike equation for the pair connectedness function.

A chain of states method for investigating infrequent event processes occurring in multistate, multidimensional systems

This paper describes novel numerical methods for constructing reaction paths and evaluating transition state theory (TST) rate constants for multidimensional, multistate systems. The reaction path is represented as a tethered, freely jointed chain of states with configuration specified by minimization of a function that is derived from the differential description of the path. The method is general and applicable to systems of arbitrary dimension and does not require a priori knowledge of the first‐order saddle point, or the topology of the states. Also presented is a novel procedure for numerical determination of the TST rate constant. The procedure is based on Monte Carlo importance sampling using a tethered chain with links modeled as harmonic springs. The beads of the chain and the points at which links pierce the dividing surface separating states serve as biased sampling points for Monte Carlo numerical integration. The methods presented here are tested using the Muller potential surface. The applic...

The Kawasaki identity and the Fluctuation Theorem

In this paper we show that the Fluctuation Theorem of Evans and Searles [D. J. Evans, D. J. Searles, Phys. Rev. E 50, 1645 (1994)] implies that the Kawasaki function exp(-Omega(t)) is unity for all time t. We confirm this relationship using experimental data obtained using optical tweezers, and show that the Kawasaki function is a valuable diagnostic tool.

Piston-Rotaxanes as Molecular Shock Absorbers

We describe the thermomechanical response of a new molecular system that behaves as a shock absorber. The system consists of a rodlike rotaxane connected to a piston and tethered to a surface. The response of this system is dominated by the translational entropy of the rotaxane rings and can be calculated exactly. The force laws are contrasted with those for a rigid rod and a polymer. In some cases, the rotaxanes undergo a sudden transition to a tilted state when compressed. These piston-rotaxanes provide a potential motif for the design of a new class of materials with a novel thermomechanical response.

An optical trap experiment to demonstrate fluctuation theorems in viscoelastic media

Conventional 19th century thermodynamics has limited our understanding of statistical physics to systems in the thermodynamic limit, at or near equilibrium. However, in the last decade two new theorems, collectively referred to as fluctuation theorems or FTs, were introduced that quantify the energy distributions of small systems that are driven out of equilibrium, possibly far from equilibrium, by an external field. As such the FTs represent a much needed extension of non-equilibrium thermodynamics that can potentially address systems of interest in the 21st century, including nano/micro-machines and single biomolecular function. Optical trapping has served as an ideal experimental technique for demonstrating these theorems. Measurement of picoNewton scale forces over nanometre-sized displacements of a trapped micron-sized particle allows us to measure the energies to a fraction of thermal energy along the particles trajectory—precisely what is needed to demonstrate the predictions of the FTs. Here we review the fluctuation theorems, as cast by Evans and Searles (1994 Phys. Rev. E 50 1645; 2002 Adv. Phys. 51 1529; 2004 Aust. J. Chem. 57 1119) and Crooks (1999 Phys. Rev. E 60 2721), and provide a discussion of their importance and a comparison of their arguments. We further demonstrate an optical trap experiment that confirms the FTs. We have chosen to review an optical trapping experiment that is identical to a previously published experiment (Carberry et al 2004 Phys. Rev. Lett. 92 140601), but where the solvent is viscoelastic rather than purely viscous. This represents the first experimental demonstration where dynamics of the colloidal particle are complex and not known a priori.

Demonstration of the steady-state fluctuation theorem from a single trajectory

The fluctuation theorem (FT) quantifies the probability of Second Law of Thermodynamics violations in small systems over short timescales. While this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state, there are a number of studies suggesting that th et heorem applies asymptotically in the long time limit to systems in a nonequilibrium steady state. The asymptotic application of the FT to such nonequilibrium steady-states has been referred to in the literature as the steady-state fluctuation theorem (or SSFT). In 2005 Wang et aldemonstrated experimentally an integrated form of the SSFT using a colloidal bead that was weakly held in ac ircularly translating optical trap. Moreover, they showed that the integrated form of the FT may, for certain systems, hold under non-equilibrium steady states for all time, and not just in the long time limit, as suggested by the SSFT. While demonstration of the integrated forms of these theorems is compact and illustrative, a proper demonstration shows the theorem directly ,r ather than in its integrated form. In this paper, we present experimental results that demonstrate the SSFT directly ,a nd show thatthe FT can hold for all time under nonequilibrium steady states.

Dilute heteroaggregation: A description of critical gelation using a cluster—cluster aggregation model

Abstract We investigate the critical behavior of binary heteroaggregation for dilute systems using a generalized cluster-cluster aggregation model which spans the conventional models of DLA (Diffusion Limited Aggregation) and RLA (Reaction Limited Aggregation). A new algorithm, based upon the time reversal technique, is used to investigate the reaction surface, namely its size and the extent to which it is kinetically screened, i.e., not equally accessible under diffusion, over a range of compositions, including compositions very close to (and at) critical gelation where conventional algorithms are limited by “kinetic slowing down.” We show that the reaction surface and its associated properties exhibit distinctive behavior in the gelling region where stoichiometry and kinetics permit formation of a network structure, as well as in the nongelling region where stoichiometry limits clusters to forming inert oligomers.

Micro-rheology near fluid interfaces

Using optical trapping, we have measured anisotropic and distance-dependent mobility of a colloidal particle near high surface tension fluid–fluid interfaces. These experimental results show that the parallel mobility is enhanced near a high surface tension liquid–gas surface, which is consistent with hydrodynamic predictions for a surface that does not support a stress, and that the parallel mobility is suppressed near a high surface tension liquid–liquid surface, consistent with a no-slip solid boundary. We demonstrate the potential for this optical technique to be applied to soft interfaces by predicting the normalized PSD using recent hydrodynamic predictions on particle mobility near soft surfaces.

Cluster integrals for square well particles : application to percolation

We present a calculation of the cluster integrals which appear in the density expansion of the inverse mean cluster size for an assembly of spherical particles with a square well potential where the range of connectedness is equivalent to the interparticle interaction range. This percolation series is constructed to third order in density, corresponding to four‐point graphs in the virial expansion, using a method first put forth by Katsura. We show, by virtue of this particular evaluation method, that the large number of integrals in the percolation problem reduces to the class of integrals already contained in the virial coefficient evaluation. Moreover, it can be shown that different particle systems, as for example square well particles and binary collection of hard particles, share the same class of integrals in percolation or virial solutions. In this paper, the method is developed and applied to the simplest percolation case, one where the attractive and connectedness ranges are equivalent. The resu...

Threading a Ring or Tube onto a Rod: An Entropically Rare Event

We calculate the entropy lost when a circular ring or a circular cylinder or tube is threaded onto a long rod in terms of the geometrical parameters, namely rod length and radius, the threaded ring radius, or the radius and length of a threaded tube. These formulas, constructed from a partition function, allow calculation of the fraction of rings/tubes threaded spontaneously onto rods. In all cases of practical interest, this fraction is very small and can be well represented by simple power laws depending strongly upon the geometrical parameters.