# James F. LutskoUniversité Libre de Bruxelles | ULB · Department of Physics

James F. Lutsko

## About

162

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Introduction

My background is in nonequilibrium statistical mechanics and nowadays most of my time is spent on the study of crystallization and crystal growth. Previously, I have worked on non-classical diffusion, granular materials, symbolic learning, kinetic theory and the mechanical properties of solid interfaces. My work involves a combination of analytic theory, numerical analysis and computer simulation.

Additional affiliations

January 2002 - present

## Publications

Publications (162)

We present classical density functional theory calculations of the free-energy landscape for fluids below their triple point as a function of density and crystallinity. We find that, both for a model globular protein and for a simple atomic fluid modeled with a Lennard-Jones interaction, it is free-energetically easier to crystallize by passing thr...

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 nu...

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 num...

Nanoscale self-assembly is naturally subject to impediments at the nanoscale. The recently developed ability to follow processes at the molecular level forces us to resolve older, coarse-grained concepts in terms of their molecular mechanisms. In this Letter, we highlight one such example. We present evidence based on experimental and simulation da...

Recent advances in classical Density Functional Theory are combined with methods from stochastic process theory and rare event techniques to formulate a theoretical description of nucleation in general, including crystallization, that can predict non-classical nucleation pathways based on no input other than the interaction potential of the particl...

We report the investigation of various experimental conditions and their influence on polymorphism of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, commonly known as ROY. These conditions include an in-house-developed microfluidic chip with controlled mixing of parallel flows. We observed that different ROY concentrations and different...

Classical density functional theory for finite temperatures is usually formulated in the grand-canonical ensemble where arbitrary variations of the local density are possible. However, in many cases the systems of interest are closed with respect to mass, e.g., canonical systems with fixed temperature and particle number. Although the tools of stan...

Classical density functional theory for finite temperatures is usually formulated in the grand-canonical ensemble where arbitrary variations of the local density are possible. However, in many cases the systems of interest are closed with respect to mass, e.g. canonical systems with fixed temperature and particle number. Although the tools of stand...

The original derivation of power functional theory [M. Schmidt and J. M. Brader, J. Chem. Phys. 138, 214101 (2013)] is reworked in some detail with a view to clarifying and simplifying the logic and making explicit the various functional dependencies. We note various issues with the original development and suggest a modification that allows us to...

The original derivation of Power Functional Theory, Schmidt and Brader, JCP 138, 214101 (2013), is reworked with a view to simplifying the logic and making explicit the various functional dependencies. The result casts doubt on several aspects of PFT such as its ability to provide equations of motion for non-equilibrium systems. It is concluded tha...

We examine the effect of rough surfaces on crystal nucleation by means of kinetic Monte Carlo simulations. Our work makes use of three-dimensional kMC models, explicit representation of transport in solution and rough surfaces modeled as randomly varying height fluctuations (roughness) with exponentially decaying correlation length (topology). We u...

The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) is reexamined in the light of the recently introduced concept of global stability of the density functional based on its boundedness [Lutsko and Lam, Phys. Rev. E 98, 012604 (2018)]. It is shown th...

The standard model of classical density-functional theory (cDFT) for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated fundamental measure hard-sphere functionals suffer from potential numerical instabilities either due to possible ins...

The standard model of classical Density Functional Theory for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated Fundamental Measure hard-sphere functionals suffer from potential numerical instabilities either due to possible instabilit...

The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) are re-examined in the light of the recently introduced concept of global stability of the density functional based on its boundedness (Lutsko and Lam, Phys. Rev. E 98, 012604 (2018)). It is shown...

Recent theories of nucleation that go beyond classical nucleation theory predict that diffusion-limited nucleation of both liquid droplets and of crystals from a low-density vapor (or weak solution) begins with long-wavelength density fluctuations. This means that in the early stages of nucleation, “clusters” can have low density but large spatial...

Recent theories of nucleation that go beyond Classical Nucleation Theory predict that diffusion-limited nucleation of both liquid droplets and of crystals from a low-density vapor (or weak solution) begins with long-wavelength density fluctuations. This means that in the early stages of nucleation, 'clusters' can have low density but large spatial...

Standard Solid-On-Solid models of crystal growth represent the appearance and disappearance of molecules on the crystal surface as stochastic events. Here, in order to model more realistically the growth of crystals from solution, we introduce a dynamic model of the uid in contact with the crystal surface and in this way account explicitly for mass...

A novel microfluidic device that subjects a solution to a constant shear flow was developed. By taking advantage of the linear velocity profile in a lid driven flow configuration, small volumes (10⁻⁵ L) can be subjected to a constant shear profile with a shear rate between 0.1 and 100 s⁻¹ at accurately controlled temperatures between 20 °C and 50 °...

Ubiquitous processes in nature and the industry exploit crystallization from multicomponent environments1–5; however, laboratory efforts have focused on the crystallization of pure solutes6,7 and the effects of single growth modifiers8,9. Here we examine the molecular mechanisms employed by pairs of inhibitors in blocking the crystallization of hae...

Crystallization is of major interest for the purification of biopharmaceuticals. Yet, good quality crystals are more difficult to obtain for most proteins because of their large molecular complexity. The use of nanopores has recently been suggested to enable crystallization under those unfavorable conditions. With the emergence of experimental resu...

Solvent-mediated interactions emerge from complex mechanisms that depend on the solute structure, its wetting properties, and the nature of the liquid. While numerous studies have focused on the first two influences, here, we compare the results from water and Lennard-Jones liquid in order to reveal to what extent solvent-mediated interactions are...

The foundation for any discussion of first order phase transitions is classical nucleation theory (CNT). CNT, developed in the first half of the twentieth century, is based on a number of heuristically plausible assumptions and the majority of theoretical work on nucleation is devoted to refining or extending these ideas. Ideally, one would like to...

A great deal of experimental evidence suggests that a wide spectrum of phase transitions occur in a multistage manner via the appearance and subsequent transformation of intermediate metastable states. Such multistage mechanisms cannot be explained within the realm of the classical nucleation framework. Hence, there is a strong need to develop new...

While in principle, classical density functional theory (cDFT) should be a powerful tool for the study of crystallization, in practice this has not so far been the case. Progress has been hampered by technical problems which have plagued the study of the crystalline systems using the most sophisticated fundamental measure theory models. In this pap...

While in principle, finite temperature density functional theory (ftDFT) should be a powerful tool for the study of crystallization, in practice this has not so far been the case. Progress has been hampered by technical problems which have plagued the study of the crystalline systems using the most sophisticated Fundamental Measure Theory models. I...

The previously established (Lutsko, JCP 136:034509, 2012 ) connection between Classical Nucleation Theory and fluctuating hydrodynamics is generalized to systems without spherical symmetry thus allowing for the systematic extension of CNT to such systems. The results are illustrated by application to CNT with moving clusters and the constructrion o...

Targeting specific technological applications requires the control of nanoparticle properties, especially the crystalline polymorph. Freezing a nanodroplet deposited on a solid substrate leads to the formation of crystalline structures. We study the inherent mechanisms underlying this general phenomenon by means of molecular dynamics simulations. O...

More often than not, minerals formed in Nature are grown at low supersaturation and from sources that are impure with respect to the crystals' main building blocks. Quite paradoxically, these conditions are in conflict with the established crystal growth theories that focus on the interplay between the crystal interface and impurities that are pres...

The last 25 years have seen an explosion of interest in the subject of nucleation driven by new experimental techniques and computer simulation methods. The theoretical community has struggled to keep pace with this onslaught. One of the main reasons is an adherence to the paradigm of classical nucleation theory—a theory more than 80 years old and...

Nanoscopic pores are used in various systems to attract nanoparticles. In general the behaviour is a result of two types of interactions: the material specific affinity and the solvent-mediated influence also called the depletion force. The latter is more universal but also much more complex to understand since it requires modeling both the nanopar...

At the nanometric scale, polymorphic crystal structures that would be un-
stable otherwise can become preponderant because surface effects play an
increasing role. Nanocrystals can be obtained by freezing a nanodroplet deposited on a solid substrate. We study the inherent mechanisms underlying this general phenomenon by means of molecular dynamics...

The temporal Fokker–Planck equation (Boon et al. in J Stat Phys 3/4: 527, 2003) or propagation–dispersion equation was derived to describe diffusive processes with temporal dispersion rather than spatial dispersion as in classical diffusion. We present two generalizations of the temporal Fokker–Planck equation for the first passage distribution fun...

Dense protein clusters are known to play an important role in nucleation of protein crystals from dilute solutions. While these have generally been thought to be formed from a metastable phase, the observation of similar, if not identical, clusters above the critical point for the dilute-solution/strong-solution phase transition has thrown this int...

The temporal Fokker-Plank equation [{\it J. Stat. Phys.}, {\bf 3/4}, 527 (2003)] or propagation-dispersion equation was derived to describe diffusive processes with temporal dispersion rather than spatial dispersion as in classical diffusion. %\cite{boon-grosfils-lutsko}. We present two generalizations of the temporal Fokker-Plank equation for the...

Crystals grow by laying down new layers of material which can either correspond in size to the height of one unit cell (elementary steps) or multiple unit cells (macrosteps). Surprisingly, experiments have shown that macrosteps can grow under conditions of low supersaturation and high impurity density such that elementary step growth is completely...

Pan, Vekilov and Lubchenko [J. Phys. Chem. B, 2010, 114, 7620] have proposed that dense stable protein clusters appearing in weak protein solutions above the solubility curve are composed of protein oligomers. The hypothesis is that a weak solution of oligomer species is unstable with respect to condensation causing the formation of dense, oligomer...

Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g. Zeldovich-Frenkel or Becker-D\"oring-Tunitskii equations. Starting from a pheno...

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 clu...

It is widely accepted that many phase transitions do not follow nucleation pathways as envisaged by the classical nucleation theory. Many substances can traverse intermediate states before arriving at the stable phase. The apparent ubiquity of multi-step nucleation has made the inverse question relevant: does multistep nucleation always dominate si...

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 whi...

The growth of crystals from solution is a fundamental process of relevance to such diverse areas as X-ray diffraction structural determination and the role of mineralization in living organisms. A key factor determining the dynamics of crystallization is the effect of impurities on step growth. For over 50 years, all discussions of impuritystep int...

Classical nucleation theory has been recently reformulated based on
fluctuating hydrodynamics [J.F. Lutsko and M.A. Dur\'{a}n-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 cl...

Note that the author(s) has the following rights: – immediately after publication, to use all or part of the article without revision or modification, including the EPLA-formatted version, for personal compilations and use only; – no sooner than 12 months from the date of first publication, to include the accepted manuscript (all or part), but not...

The growth of crystals from solution is a fundamental process of relevance to such diverse areas as X-ray-diffraction structural determination and the role of mineralization in living organisms. A key factor determining the dynamics of crystallization is the effect of impurities on step growth. For over fifty years, all discussions of impurity-step...

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}.

We present a master equation formulation based on a Markovian random walk model that exhibits subdiffusion, classical diffusion, and superdiffusion as a function of a single parameter. The nonclassical diffusive behavior is generated by allowing for interactions between a population of walkers. At the macroscopic level, this gives rise to a nonline...

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 [J. F. Lutsko, J. Chem. Phys. 136, 034509 (2012)]. The same framework is also used to construct a more realistic theory in which clusters have finite inter...

A dynamical theory of nucleation based on fluctuating hydrodynamics is described. It is developed in detail for the case of diffusion-limited nucleation appropriate to colloids and macro-molecules in solution. By incorporating fluctuations, realistic fluid-transport and realistic free energy
models the theory is able to give a unified treatment of...

In a recent publication[PRE 86, 04012 (2012)], Santos has presented a
self-consistency condition that can be used to limit the possible forms of
Fundamental Measure Theory. Here, the direct correlation function resulting
from the Santos functional is derived and it is found to diverge for all
densities.

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 con...

A microscopic theory for reaction-difusion (R-D) processes is developed from Einstein’s master equation including a reactive term. The mean field formulation leads to a generalized R-D equation for the n-th order annihilation reaction A + A + A + ... + A → 0, and the steady state solutions exhibit long range power law behavior showing the relative...

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 t...

We develop a microscopic theory for reaction-diffusion (RD) processes based on a generalization of Einstein's master equation [Ann. Phys. 17, 549 (1905)] with a reactive term and show how the mean-field formulation leads to a generalized RD equation with nonclassical solutions. For the nth-order annihilation reaction A+A+A+···+A→0, we obtain a nonl...

A fundamental issue in the modern study of phase transitions is the
description of the process of nucleation, i.e. the choices of nucleation
pathways. Proteins, in particular, are well-known to sometimes
crystallize by passing through a meta-stable amorphous state and
simulation and theory have shown that this is also true of many other
systems. Th...

Homogeneous nucleation is formulated within the context of fluctuating hydrodynamics. It is shown that for a colloidal 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. This is illustrated by application to low-density/high-density liquid tr...

We examine the non-extensive approach to the statistical mechanics of Hamiltonian systems with H = T +V, where T is the classical kinetic energy. Our analysis starts from the basics of the formalism by applying the standard variational method for maximizing the entropy subject to the average energy and normalization constraints. The analytical resu...

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...

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 pro...

A recurring question in nonequilibrium statistical mechanics is what deviation from standard statistical mechanics gives rise to non-Boltzmann behavior and to nonlinear response, which amounts to identifying the emergence of “statistics from dynamics” in systems out of equilibrium. Among several possible analytical developments which have been prop...

It is pointed out that some of the generic physical properties of a nanocrystalline material are similar to those of a grain-boundary superlattice. The structure and elastic properties of a superlattice of twist boundaries on the (110) plane of silicon are calculated as a function of modulation wavelength using a three-body potential. All elastic m...

A new atomistic-simulation method for calculating the full local elastic-constant tensor in terms of local stress and local strain for inhomogeneous systems is described. Results of simulations of an isolated high-angle twist grain boundary are presented. A dramatic reduction in resistance to shear parallel to the grain boundary is observed, and it...

Lattice statics and lattice dyanamics computer simulation methods are applied to investigate the elastic properties of grain boundaries in fcc metals. The elastic constants in the GB reigon are found to differ significantly from their bulk ideal-crystal values. Due to the broken symmetry in the GB region a pronounced anisotropy of the elastic prope...

We propose in this paper a generic model of a nonstandard aggregation mechanism for self-assembly processes of a class of materials involving the mediation of intermediates consisting of a polydisperse population of nanosized particles. The model accounts for a long induction period in the process. The proposed mechanism also gives insight on futur...

The homogeneous entropy for continuous systems in nonextensive statistics reads $S^{H}_{q}=k_B\,{(1 - (K \int d\Gamma \rho^{1/q}(\Gamma))^{q})}/({1-q})$, where $\Gamma$ is the phase space variable. Optimization of $S^{H}_{q}$ combined with normalization and energy constraints gives an implicit expression of the distribution function $\rho (\Gamma)$...

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 combination of Monte Carlo simulations and finite temperature classical density functional theory calculations. We use a parametrized potential that can vary...

The Density Functional approach to equilibrium statistical mechanics is reviewed. Topics covered include the basic theory behind Density Functional Theory, exact density functionals in low dimension, and theories based on effective liquid approximations. Particular attention is given to more recent developments such as Fundamental Measure Theory fo...

The equilibrium density distribution and thermodynamic properties of a Lennard-Jones fluid confined to nanosized spherical cavities at a constant chemical potential was determined using Monte Carlo simulations. The results describe both a single cavity with semi-permeable walls as well as a collection of closed cavities formed at the constant chemi...

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 crysta...

Many recent papers have questioned Irving and Kirkwood's atomistic expression for stress. In Irving and Kirkwood's approach both interatomic forces and atomic velocities contribute to stress. It is the velocity-dependent part that has been disputed. To help clarify this situation we investigate (i) a fluid in a gravitational field and (ii) a steadi...

The validity of the principle of corresponding states is investigated for the case of a potential with more than one intrinsic length scale. The planar surface tension of coexisting liquid and vapor phases of a fluid of Lennard-Jones atoms is studied as a function of the range of the potential using both Monte Carlo simulations and density function...

The question of whether the Tsallis entropy is Lesche-stable is revisited. It is argued that when physical averages are computed with the escort probabilities, the correct application of the concept of Lesche-stability requires use of the escort probabilities. As a consequence, as shown here, the Tsallis entropy is unstable but the thermodynamic av...

There is increasing evidence that large classes of colloid materials crystallize via a non-standard nucleation mechanism involving
intermediate metastable phases. In this paper recent work on the microscopic derivation of the phase diagram and free energy
barriers in the nucleation of protein crystals, and on the kinetics of growth of solid particl...

The process of nucleation of vapor bubbles from a superheated liquid and of liquid droplets from a supersaturated vapor is investigated using the modified-core van der Waals model density functional theory [J. F. Lutsko, J. Chem. Phys. 128, 184711 (2008)]. A novel approach is developed whereby nucleation is viewed as a transition from a metastable...

The nucleation of vapor bubbles within a superheated fluid is studied using density functional theory. The nudged elastic band technique is used to find the minimum energy pathway from the metastable uniform liquid to the stable uniform gas thus emphasizing the analogy between the the nucleation problem and that of chemical reactions. The result is...

Previously, it has been shown that the direct correlation function for a Lennard-Jones fluid could be modeled by a sum of that for hard-spheres, a mean-field tail, and a simple linear correction in the core region constructed so as to reproduce the (known) bulk equation of state of the fluid [Lutsko, J. Chem. Phys. 127, 054701 (2007)]. Here, this m...

The Fokker-Planck equation for the probability f(r,t) to find a random walker at position r at time t is derived for the case that the probability to make jumps depends nonlinearly on f(r,t) . The result is a generalized form of the classical Fokker-Planck equation where the effects of drift, due to a violation of detailed balance, and of external...

We show that from a generalization of Einstein's master equation for the random walk one obtains a generalized equation for diffusion processes. The master equation is generalized by making the particle jump probability Pj(r) a functional of the particle distribution function f(r,t). If one demands that the resulting generalized diffusion equation...

We generalize Einstein's master equation for random walk processes by considering that the probability for a particle at position $r$ to make a jump of length $j$ lattice sites, $P_j(r)$ is a functional of the particle distribution function $f(r,t)$. By multiscale expansion, we obtain a generalized advection-diffusion equation. We show that the pow...