Jan Wedekind

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.

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 is the best definition of a liquid cluster at the molecular scale

We investigate the ability of different cluster definitions to serve as a good reaction coordinate in molecular simulations of nucleation. In particular, the most commonly used Stillinger criterion [J. Chem. Phys. 38, 1486 (1963)] is compared with the cluster definition introduced by ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)]. The accuracy of these two different cluster definitions is tested by using molecular dynamics to study the vapor-liquid nucleation of Lennard-Jones argon as a model system. We are able to compare the size of the critical cluster identified by each cluster definition with a completely model-independent value provided by the nucleation theorem, aided by a recently introduced method that accurately extracts the location of the transition state directly from the kinetics. It is found that the Stillinger definition strongly overestimates the size of small molecular clusters by up to a factor of 2. A simple change of the Stillinger radius is unable to rectify this deficiency. On the contrary, the ten Wolde-Frenkel definition, while being only slightly more elaborate than a simple Stillinger criterion, is remarkably successful in identifying the correct molecular excess of the small clusters if the parameters are chosen adequately. The method described here can also be generalized to identify a proper reaction coordinate in other activated processes.

Crossover from nucleation to spinodal decomposition in a condensing vapor

The mechanism controlling the initial step of a phase transition has a tremendous influence on the emerging phase. We study the crossover from a purely nucleation-controlled transition toward spinodal decomposition in a condensing Lennard-Jones vapor using molecular dynamics simulations. We analyze both the kinetics and at the same time the thermodynamics by directly reconstructing the free energy of cluster formation. We estimate the location of the spinodal, which lies at much deeper supersaturations than expected. Moreover, the nucleation barriers we find differ only by a constant from the classical nucleation theory predictions and are in very good agreement with semiempirical scaling relations. In the regime from very small barriers to the spinodal, growth controls the rate of the transition but not its nature because the activation barrier has not yet vanished. Finally, we discuss in detail the influence of the chosen reaction coordinate on the interpretation of such simulation results.

Kinetic reconstruction of the free-energy landscape.

We present a new general method to trace back a lot of valuable information from direct simulations and experiments of activated processes. In particular, it allows the reconstruction of the free-energy landscape for an arbitrary reaction coordinate directly from the out-of-equilibrium dynamics of the process. We demonstrate the power of this concept by its application to a molecular dynamics simulation of nucleation of a Lennard-Jones vapor. The same method can be also applied to Brownian dynamics and stochastic simulations.

Unraveling the ''Pressure Effect'' in Nucleation

The influence of the pressure of a chemically inert carrier gas on the nucleation rate is one of the biggest puzzles in the research of gas-liquid nucleation. Experiments can show a positive effect, a negative effect, or no effect at all. The same experiment may show both trends for the same substance depending on temperature, or for different substances at the same temperature. We show how this ambiguous effect naturally arises from the competition of two contributions: nonisothermal effects and pressure-volume work. Our model clarifies seemingly contradictory experimental results and quantifies the variation of the nucleation ability of a substance in the presence of an ambient gas. Our findings are corroborated by molecular dynamics simulations and might have important implications since nucleation in experiments, technical applications, and nature practically always occurs in the presence of an ambient gas.

Homogeneous nucleation rates of 1-pentanol.

We have measured isothermal homogeneous nucleation rates J for 1-pentanol vapor in two different carrier-gases, argon, and helium, using a two-valve nucleation pulse chamber. The nucleation rates cover a range of 10(5)<J/cm(-3) s(-1)<10(9) at temperatures between 235<T/K<265. We observed no influence of the carrier gas on location and slope of the nucleation rate isotherms. These measurements are part of an international effort to examine 1-pentanol using various experimental techniques, which was initiated in Prague in 1995. In the present paper nucleation rate data obtained by several groups are compared to each other and to the classical nucleation theory. As expected, the classical theory is not able to quantitatively predict the experimental results. Nevertheless, relating the experimental data to the classical theory provides a suitable way to compare data of widely differing nucleation rates obtained by different experimental techniques. This comparison helps judging mutual support of the data and, at the same time, provides a rather interesting insight into the accuracy of the individual experimental techniques.