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James F. Lutsko

Publications and source records attributed to James F. Lutsko.

At least 37 records · Page 2Linked to original sources
arXiv2014

Molecular theory of anomalous diffusion - Application to Fluorescence Correlation Spectroscopy

The nonlinear theory of anomalous diffusion is based on particle interactions giving an explicit microscopic description of diffusive processes leading to sub-, normal, or super-diffusion as a result competitive effects between attractive and repulsive interactions. We present the explicit analytical solution to the nonlinear diffusion equation which we then use to compute the correlation function which is experimentally measured by correlation spectroscopy. The theoretical results are applicable in particular to the analysis of fluorescence correlation spectroscopy of marked molecules in biological systems. More specifically we consider the case of fluorescently labeled lipids and we find that the nonlinear correlation spectrum reproduces very well the experimental data indicating sub-diffusive molecular motion of lipid molecules in the cell membrane.

cond-mat.stat-mech↗
arXiv2014

Extending classical nucleation theory to confined systems

Classical nucleation theory has been recently reformulated based on fluctuating hydrodynamics [J.F. Lutsko and M.A. Durán-Olivencia, J. Chem. Phys. 138, 244908 (2013)]. The present work extends this effort to the case of nucleation in confined systems such as small pores and vesicles. The finite available mass imposes a maximal supercritical cluster size and prohibits nucleation altogether if the system is too small. We quantity the effect of system size on the nuceation rate. We also discuss the effect of relaxing the capillary-model assumption of zero interfacial width resulting in significant changes in the nucleation barrier and nucleation rate.

cond-mat.soft↗
arXiv2014

A Two-parameter Extension of Classical Nucleation Theory

A two-variable stochastic model for diffusion-limited nucleation is developed using a formalism derived from fluctuating hydrodynamics. The model is a direct generalization of the standard Classical Nucleation Theory. The nucleation rate and pathway are calculated in the weak-noise approximation and are shown to be in good agreement with direct numerical simulations for the weak-solution/strong-solution transition in globular proteins. We find that Classical Nucleation Theory underestimates the time needed for the formation of a critical cluster by two orders of magnitude and that this discrepancy is due to the more complex dynamics of the two variable model and not, as often is assumed, a result of errors in the estimation of the free energy barrier.

physics.chem-ph↗
arXiv2014

New comments on "Possible divergences in Tsallis' thermostatistics''

In a recent letter ({\it{EPL}}, {\bf{104}} (2013) 60003; see also {\it {arXiv:1309.5645}}), Plastino and Rocca suggest that the divergences inherent to the formulation of nonextensive statistical mechanics can be eliminated {\it {via}} the use of $q$-Laplace transformation which is illustrated for the case of a kinetic Hamiltonian system, the harmonic oscillator. The suggested new formulation raises questions which are discussed in the present comment.

cond-mat.stat-mech↗
arXiv2013

Comment on "Possible divergences in Tsallis' thermostatistics"

The problematic divergence of the $q$-partition function of the harmonic oscillator recently considered in \cite{plastino} is a particular case of the non-normalizabilty of the distribution function of classical Hamiltonian systems in non-extensive thermostatistics as discussed previously in \cite{lutsko-boon}.

cond-mat.stat-mech↗
arXiv2013

Molecular theory of anomalous diffusion

We present a Master Equation formulation based on a Markovian random walk model that exhibits sub-diffusion, classical diffusion and super-diffusion as a function of a single parameter. The non-classical diffusive behavior is generated by allowing for interactions between a population of walkers. At the macroscopic level, this gives rise to a nonlinear Fokker-Planck equation. The diffusive behavior is reflected not only in the mean-squared displacement ($ \sim t^γ$ with $0 <γ\leq 1.5$) but also in the existence of self-similar scaling solutions of the Fokker-Planck equation. We give a physical interpretation of sub- and super-diffusion in terms of the attractive and repulsive interactions between the diffusing particles and we discuss analytically the limiting values of the exponent $γ$. Simulations based on the Master Equation are shown to be in agreement with the analytical solutions of the nonlinear Fokker-Planck equation in all three diffusion regimes.

cond-mat.stat-mech↗
arXiv2012

Classical nucleation theory from a dynamical approach to nucleation

It is shown that diffusion-limited classical nucleation theory (CNT) can be recovered as a simple limit of the recently proposed dynamical theory of nucleation based on fluctuating hydrodynamics (Lutsko, JCP 136, 034509 (2012)). The same framework is also used to construct a more realistic theory in which clusters have finite interfacial width. When applied to the dilute solution/dense solution transition in globular proteins, it is found that the extension gives corrections to the the nucleation rate even for the case of small supersaturations due to changes in the monomer distribution function and to the excess free energy. It is also found that the monomer attachement/detachment picture breaks down at high supersaturations corresponding to clusters smaller than about 100 molecules. The results also confirm the usual assumption that most important corrections to CNT can be acheived by means of improved estimates of the free energy barrier. The theory also illustrates two topics that have received considerable attention in the recent literature on nucleation: the importance sub-dominant corrections to the capillary model for the free energy and of the correct choice of the reaction coordinate.

physics.chem-ph↗
arXiv2012

Nucleation of colloids and macromolecules in a finite volume

A recently formulated description of homogeneous nucleation for Brownian particles in the over-damped limit based on fluctuating hydrodynamics is used to determine the nucleation pathway, characterized as the most likely path (MLP), for the nucleation of a dense-concentration droplet of globular protein from a dilute solution in a small, finite container. The calculations are performed by directly discretizing the equations for the MLP and it is found that they confirm previous results obtained for infinite systems: the process of homogeneous nucleation begins with a long-wavelength, spatially-extended concentration fluctuation that it condenses to form the pre-critical cluster. This is followed by a classical growth processes. The calculations show that the post-critical growth involves the formation of a depletion zone around the cluster whereas no such depletion is observed in the pre-critical cluster. The approach therefore captures dynamical effects not found in classical Density Functional Theory studies while consistently describing the formation of the pre-critical cluster.

cond-mat.soft↗
arXiv2012

Nucleation of colloids and macromolecules: does the nucleation pathway matter?

A recent description of diffusion-limited nucleation based on fluctuating hydrodynamics that extends classical nucleation theory predicts a very non-classical two-step scenario whereby nucleation is most likely to occur in spatially-extended, low-amplitude density fluctuations. In this paper, it is shown how the formalism can be used to determine the maximum probability of observing \emph{any} proposed nucleation pathway, thus allowing one to address the question as to their relative likelihood, including of the newly proposed pathway compared to classical scenarios. Calculations are presented for the nucleation of high-concentration bubbles in a low-concentration solution of globular proteins and it is found that the relative probabilities (new theory compared to classical result) for reaching a critical nucleus containing $N_c$ molecules scales as $e^{-N_c/3}$ thus indicating that for all but the smallest nuclei, the classical scenario is extremely unlikely.

cond-mat.soft↗
arXiv2011

A dynamical theory of nucleation for colloids and macromolecules

A general theory of nucleation for colloids and macromolecules in solution is formulated within the context of fluctuating hydrodynamics. A formalism for the determination of nucleation pathways is developed and stochastic differential equations for the evolution of order parameters are given. The conditions under which the elements of Classical Nucleation Theory are recovered are determined. The theory provides a justification and extension of more heuristic equilibrium approaches based solely on the free energy. It is illustrated by application to the low-concentration/high-concentration transition in globular proteins where a novel two-step mechanism is identified where the first step involves the formation of long-wavelength density fluctuations and the second step is the actual nucleation event occuring within the fluctuation.

cond-mat.soft↗
arXiv2011

A dynamical theory of homogeneous nucleation for colloids and macromolecules

Homogeneous nucleation is formulated within the context of fluctuating hydrodynamics. It is shown that for a colloidal or macromolecular system in the strong damping limit the most likely path for nucleation can be determined by gradient descent in density space governed by a nontrivial metric fixed by the dynamics. The theory provides a justification and extension of more heuristic equilibrium approaches based solely on the free energy. It is illustrated by application to liquid-vapor nucleation where it is shown that, in contrast to most free energy-based studies, the smallest clusters correspond to long wavelength, small amplitude perturbations.

cond-mat.soft↗
arXiv2011

A microscopic approach to nonlinear Reaction-Diffusion: the case of morphogen gradient formation

We develop a microscopic theory for reaction-difusion (R-D) processes based on a generalization of Einstein's master equation with a reactive term and we show how the mean field formulation leads to a generalized R-D equation with non-classical solutions. For the $n$-th order annihilation reaction $A+A+A+...+A\rightarrow 0$, we obtain a nonlinear reaction-diffusion equation for which we discuss scaling and non-scaling formulations. We find steady states with either solutions exhibiting long range power law behavior (for $n>α$) showing the relative dominance of sub-diffusion over reaction effects in constrained systems, or conversely solutions (for $n<α<n+1$) with finite support of the concentration distribution describing situations where diffusion is slow and extinction is fast. Theoretical results are compared with experimental data for morphogen gradient formation.

cond-mat.stat-mech↗
arXiv2011

On the role of metastable intermediate states in the homogeneous nucleation of solids from solution

The role of metastable liquid phases in vapor-crystal nucleation is studied using Density Functional Theory(DFT). The model gives a semi-quantitatively accurate description of both the vapor-liquid-solid phase diagram for both simple fluids (Lennard-Jones interactions) and of the low-density/high-density/crystal phase diagram for model globular proteins (ten Wolde-Frenkel interaction). The density profile is characterized by two local order parameters, the average density and the crystallinity. The bulk free energy model is supplemented by squared-derivative terms in these order parameters to account for inhomogeneities thus producing a model similar in spirit to phase-field theory. It is shown that for both interaction models, the vapor-crystal part of the phase-diagram can be separated into regions for which metastable liquid phases are more or less stable than the vapor, but always less stable than the solid. The former case allows for the possibility of \emph{double nucleation} whereby liquid droplets nucleate from the vapor followed by a separate nucleation of the solid phase within the liquid droplets. Whether or not this actually occurs depends on the relative free energy barriers for vapor-solid and vapor-liquid nucleation and it is shown that for simple fluids, double nucleation is indeed favored at sufficiently large supersaturation. Finally, by studying the minimum free energy path from the vapor to the solid, the separate possibility of \emph{transient nucleation}, where the vapor-solid transition involves a single nucleation event but the sub-critical clusters tend to be liquid-like while small, is shown to also be possible when the metastable liquid exists, but the supersaturation is too small for double nucleation.

cond-mat.soft↗
arXiv2011

Density Functional Theory of Inhomogeneous Liquids IV. Squared-gradient approximation and Classical Nucleation Theory

The Squared-Gradient approximation to the Modified-Core Van der Waals density functional theory model is developed. A simple, explicit expression for the SGA coefficient involving only the bulk equation of state and the interaction potential is given. The model is solved for planar interfaces and spherical clusters and is shown to be quantitatively accurate in comparisons to computer simulations. An approximate technique for solving the SGA based on piecewise-linear density profiles is introduced and is shown to give reasonable zeroth-order approximations to the numerical solution of the model. The piecewise-linear models of spherical clusters are shown to be a natural extension of Classical Nucleation Theory and serve to clarify some of the non-classical effects previously observed in liquid-vapor nucleation. Nucleation pathways are investigated using both constrained energy-minimization and steepest-descent techniques.

cond-mat.soft↗
arXiv2010

The low-density/high-density liquid phase transition for model globular proteins

The effect of molecule size (excluded volume) and the range of interaction on the surface tension, phase diagram and nucleation properties of a model globular protein is investigated using a combinations of Monte Carlo simulations and finite temperature classical Density Functional Theory calculations. We use a parametrized potential that can vary smoothly from the standard Lennard-Jones interaction characteristic of simple fluids, to the ten Wolde-Frenkel model for the effective interaction of globular proteins in solution. We find that the large excluded volume characteristic of large macromolecules such as proteins is the dominant effect in determining the liquid-vapor surface tension and nucleation properties. The variation of the range of the potential only appears important in the case of small excluded volumes such as for simple fluids. The DFT calculations are then used to study homogeneous nucleation of the high-density phase from the low-density phase including the nucleation barriers, nucleation pathways and the rate. It is found that the nucleation barriers are typically only a few $k_{B}T$ and that the nucleation rates substantially higher than would be predicted by Classical Nucleation Theory.

cond-mat.stat-mech↗
arXiv2010

Kinetics of intermediate-mediated self-assembly in nano-sized materials: a generic model

We propose in this paper a generic model of a non-standard aggregation mechanism for self-assembly processes of a class of materials involving the mediation of intermediates consisting of a polydisperse population of nano-sized particles. The model accounts for a long induction period in the process. The proposed mechanism also gives insight on future experiments aiming at a more comprehensive picture of the role of self-organization in self-assembly processes.

cond-mat.mes-hall↗
arXiv2010

Kinetic roughening-like transition with finite nucleation barrier

Recent observations of the growth of protein crystals have identified two different growth regimes. At low supersaturation, the surface of the crystal is smooth and increasing in size due to the nucleation of steps at defects and the subsequent growth of the steps. At high supersaturation, nucleation occurs at many places simultaneously, the crystal surface becomes rough and the growth velocity increases more rapidly with increasing supersaturation than in the smooth regime. Kinetic roughening transitions are typically assumed to be due to the vanishing of the barrier for two-dimension nucleation on the surface of the crystal. We show here, by means of both analytic mean field models and kinetic Monte Carlo simulations that a transition between different growth modes reminiscent of kinetic roughening can also arise as a kinetic effect occurring at finite nucleation barriers.

cond-mat.soft↗