David Reguera

Kinetic equations for diffusion in the presence of entropic barriers

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

New method to analyze simulations of activated processes

We present a new method to analyze molecular and Brownian dynamics simulations of activated processes based on the concept of mean first-passage times. The new method provides a simple and efficient strategy to evaluate reaction rates and it facilitates the localization of the transition state directly from the kinetics of the system without the need of thermodynamical considerations. It also provides a more rigorous value of the steady-state transition rate and gives valuable information about many important characteristics of the process. We illustrate the power of this new technique by its application to the study of nucleation in rare gases.

Finite-size effects in simulations of nucleation.

We investigate the importance of finite-size effects in simulations of nucleation processes. Most molecular dynamics simulations of first order phase transitions, such as vapor-liquid nucleation, are performed in the canonical NVT ensemble where, owing to the fixed total number of molecules N, the growth of the new phase causes the depletion of the metastable phase. This effect may lead to significant errors in the simulation and even to the impossibility of observing nucleation in a small finite system. We present a theory to estimate the system size beyond which these finite-size effects are expected to be negligible. This optimization saves valuable calculation time and can extend the range of supersaturations and rates attainable by simulations by several orders of magnitude. Our results are applicable to diverse situations, such as crystallization, capillary condensation, or the melting of nanoclusters.

Mechanical Properties of Viral Capsids

Viruses are known to tolerate wide ranges of pH and salt conditions and to withstand internal pressures as high as 100 atmospheres . In this paper we investigate the mechanical properties of viral capsids, calling explicit attention to the inhomogeneity of the shells that is inherent to their discrete and polyhedral nature. We calculate the distribution of stress in these capsids and analyze their response to isotropic internal pressure (arising, for instance, from genome confinement and/or osmotic activity). We compare our results with appropriate generalizations of classical (i.e., continuum) elasticity theory. We also examine competing mechanisms for viral shell failure, e.g., in-plane crack formation vs radial bursting. The biological consequences of the special stabilities and stress distributions of viral capsids are also discussed.

Entropic splitter for particle separation.

We present a particle separation mechanism which induces the motion of particles of different sizes in opposite directions. The mechanism is based on the combined action of a driving force and an entropic rectification of the Brownian fluctuations caused by the asymmetric form of the channel along which particles proceed. The entropic splitting effect shown could be controlled upon variation of the geometrical parameters of the channel and could be implemented in narrow channels and microfluidic devices.

Evaluating nucleation rates in direct simulations

We compare different methods for obtaining nucleation rates from molecular dynamics simulations of nucleation, using the condensation of Lennard-Jones argon as an example. All methods yield the same nucleation rate at the conditions where they can be applied correctly, with discrepancies smaller than a factor of 2. We critically examine the different approaches and highlight their respective strengths and possible limitations.

Nucleation rate isotherms of argon from molecular dynamics simulations.

We report six nucleation rate isotherms of vapor-liquid nucleation of Lennard-Jones argon from molecular dynamics simulations. The isotherms span three orders of magnitude in nucleation rates, 10(23)<J/cm(-3) s(-1)<10(26), in a temperature range of 45-70 K below the triple point. The rates are very accurately determined using the concept of mean first-passage times, which also allows a determination of the critical cluster size directly from the kinetics. The results deviate from classical nucleation theory (CNT) by two to seven orders of magnitude, which nevertheless is much smaller than the more than 20 orders of magnitude encountered in recent experiments in a similar temperature range. The extended modified liquid drop-dynamical nucleation theory (EMLD-DNT) shows excellent agreement with the simulation results with deviations of less than one order of magnitude over the entire studied temperature range. Both simulation and experiment confirm the same incorrect temperature trend of CNT, which seems to be corrected in the EMLD-DNT model. However, the predictions of CNT for the critical cluster sizes agree well with the results obtained from the simulations using the nucleation theorem, supporting the notion that CNT successfully estimates the location of the transition state but severely fails to predict its height.

Influence of thermostats and carrier gas on simulations of nucleation

We investigate the influence of carrier gas and thermostat on molecular dynamics (MD) simulations of nucleation. The task of keeping the temperature constant in MD simulations is not trivial and an inefficient thermalization may have a strong influence on the results. Different thermostating mechanisms have been proposed and used in the past. In particular, we analyze the efficiency of velocity rescaling, Nose-Hoover, and a carrier gas (mimicking the experimental situation) by extensive MD simulations. Since nucleation is highly sensitive to temperature, one would expect that small variations in temperature might lead to differences in nucleation rates of up to several orders of magnitude. Surprisingly, the results indicate that the choice of the thermostating method in a simulation does not have--at least in the case of Lennard-Jones argon--a very significant influence on the nucleation rate. These findings are interpreted in the context of the classical theory of Feder et al. [Adv. Phys. 15, 111 (1966)] by analyzing the temperature distribution of the nucleating clusters. We find that the distribution of cluster temperatures is non-Gaussian and that subcritically sized clusters are colder while postcritically sized clusters are warmer than the bath temperature. However, the average temperature of all clusters is found to be always higher than the bath temperature.

What drives the translocation of stiff chains

We study the dynamics of the passage of a stiff chain through a pore into a cell containing particles that bind reversibly to it. Using Brownian molecular dynamics simulations we investigate the mean first-passage time as a function of the length of the chain inside for different concentrations of binding particles. As a consequence of the interactions with these particles, the chain experiences a net force along its length whose calculated value from the simulations accounts for the velocity at which it enters the cell. This force can in turn be obtained from the solution of a generalized diffusion equation incorporating an effective Langmuir adsorption free energy for the chain plus binding particles. These results suggest a role of binding particles in the translocation process that is in general quite different from that of a Brownian ratchet. Furthermore, nonequilibrium effects contribute significantly to the dynamics; e.g., the chain often enters the cell faster than particle binding can be saturated, resulting in a force several times smaller than the equilibrium value.

Entropic particle transport in periodic channels

The dynamics of Brownian motion has widespread applications extending from transport in designed micro-channels up to its prominent role for inducing transport in molecular motors and Brownian motors. Here, Brownian transport is studied in micro-sized, two-dimensional periodic channels, exhibiting periodically varying cross-sections. The particles in addition are subjected to an external force acting alongside the direction of the longitudinal channel axis. For a fixed channel geometry, the dynamics of the two-dimensional problem is characterized by a single dimensionless parameter which is proportional to the ratio of the applied force and the temperature of the particle environment. In such structures entropic effects may play a dominant role. Under certain conditions the two-dimensional dynamics can be approximated by an effective one-dimensional motion of the particle in the longitudinal direction. The Langevin equation describing this reduced, one-dimensional process is of the type of the Fick-Jacobs equation. It contains an entropic potential determined by the varying extension of the eliminated channel direction, and a correction to the diffusion constant that introduces a space dependent diffusion. Different forms of this correction term have been suggested before, which we here compare for a particular class of models. We analyze the regime of validity of the Fick-Jacobs equation, both by means of analytical estimates and the comparisons with numerical results for the full two-dimensional stochastic dynamics. For the nonlinear mobility we find a temperature dependence which is opposite to that known for particle transport in periodic potentials. The influence of entropic effects is discussed for both, the nonlinear mobility and the effective diffusion constant.