James F. Lutsko

Publications (128) View all

• Article: Molecular theory of anomalous diffusion

  James F. Lutsko, Jean Pierre Boon
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  ABSTRACT: 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 ($<r^2(t)>\sim t^{\gamma}$ with $0 <\gamma \leq 1.5$) 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 $\gamma$. 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.
  02/2013;
• Article: Direct correlation function from the consistent fundamental-measure free energies for hard-sphere mixtures

  James F. Lutsko
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  ABSTRACT: 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.
  Physical Review E 11/2012; 87(1-1). · 2.26 Impact Factor
• Article: Nucleation of colloids and macromolecules in a finite volume.

  James F Lutsko
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  ABSTRACT: 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 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.
  The Journal of chemical physics 10/2012; 137(15):154903. · 3.09 Impact Factor
• Article: Classical nucleation theory from a dynamical approach to nucleation

  James F. Lutsko, Miguel A. Durán-Olivencia
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  ABSTRACT: 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.
  08/2012;
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  Article: Nucleation of colloids and macromolecules: does the nucleation pathway matter?

  James F Lutsko
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  ABSTRACT: 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 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 droplets 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.
  The Journal of chemical physics 04/2012; 136(13):134502. · 3.09 Impact Factor