Marek Litniewski

Evaporation into vacuum: Mass flux from momentum flux and the Hertz–Knudsen relation revisited

We performed molecular dynamics simulations of liquid film evaporation into vacuum for two cases: free evaporation without external supply of energy and evaporation at constant average liquid temperature. In both cases we found that the pressure inside a liquid film was constant, while temperature decreased and density increased as a function of distance from the middle of the film. The momentum flux in the vapor far from the liquid was equal to the liquid pressure in the evaporating film. Moreover the pseudopressure (stagnation pressure) was found to be constant in the evaporating vapor and equal to the liquid pressure. The momentum flux and its relation to the pressure determined the number of evaporating molecules per unit time and as a consequence the mass evaporation flux. We found a simple formula for the evaporation flux, which much better describes simulation results than the commonly used Hertz-Knudsen relation.

The influence of the quencher concentration on the rate of simple bimolecular reaction: Molecular dynamics study

The paper presents the results of large-scale molecular dynamics simulations of the irreversible bimolecular reaction A+B --> C+B for the simple liquid composed of mechanically identical soft spheres. The systems with the total number of molecules corresponding to 10(7)-10(9) are considered. The influence of the concentration of a quencher (B) on the surviving probability of A and the reaction rate is analyzed for a wide range of the concentrations and for two significantly different reduced densities. It is shown that the quencher concentration dependence effect (QCDE) is, in fact, a composition of two QCDE effects: the short-time QCDE that increases the reaction rate and the long-time QCDE that decreases it. The paper also analyzes the influence of the concentration on the steady-state rate constant, k(ss), obtained by integrating the surviving probability. The excess in k(ss) due to finite quencher concentration changes the sign from negative to positive while going from low to high concentrations. Generally, the excess is extremely weak. It attains a 1% level only if the concentration is very high.

The influence of interactions between reagents on the excess in the rate of quenching reaction: Molecular dynamics study

The influence of the interactions between reagents on the excess in the rate coefficient, Deltak, for the instantaneous reaction A+B-->C+B have been investigated by performing large scale molecular dynamics simulations for simple soft spheres. The simulation method has enabled us to determine the contributions to Deltak coming from A-B as well as B-B interactions. The simulations have shown that positive values of Deltak that appear both for the liquid and for the Brownian system [M. Litniewski, J. Chem. Phys. 123, 124506 (2005); 124, 114501 (2006)] result from B-B interactions. If B-B interactions were absent, Deltak was always negative. The influence of B-B interactions was about three times higher for the Brownian system than for the liquid. A qualitative explanation for the effect has been proposed basing on a simple model and analyzing the influence of B-B interactions on fluctuations in concentrations of reagents. The influence of A-B interactions was completely negligible except for the liquid at short times, for which the cancellation of A-B interaction noticeably decreased Deltak.

Computer investigations on the mechanism of the influence of quencher concentration on the rate of simple bimolecular reaction

Molecular dynamics investigations on the influence of the concentration of B (quencher) on the rate coefficient, k(t), for the reaction A+B-->C+B are continued [M. Litniewski, J. Chem. Phys. 123, 124506 (2005); 124, 114501 (2006)]. The problem is investigated by analyzing the excess in the two-particle probability density function and in its radial moments. The simulations have been performed for the deterministic systems as gas and liquid as well as for the Brownian system. The influence of moderate changes of the reaction radius resulting in changes of the activation energy has been also considered. The most important result is that the excess in k(t) may be not only a direct consequence of fluctuations in concentrations. For the gas, the excess in the mean radial velocity of A towards B dominated over the excess in the value of the probability density function. As a result, the excess in k(t) was negative in spite of the excess in the relative spatial correlations between A and B was positive. The excess in the mean radial velocity was completely unimportant for dense liquids and the Brownian system.

Kinetics of fluorescence quenching for electron transfer and for energy transfer: Molecular dynamics tests for spherical molecules

The Smoluchowski approach to description of fluorescence quenching is tested by comparing the theory with computer simulations for the case of spherical molecules. The distance dependent sink terms describing the electron transfer mechanism and the Forster model for the energy transfer are considered. It is shown that the agreement between the rate coefficient from the model and from simulations depends on the strength of the solute-solvent interactions as well as on the speed of reaction itself. Comparing results of simulations for different quencher concentrations we estimate the strength of quencher concentration dependence effect and the range of times the effect may be significant. In the long time limit the increase in quencher concentration decreased the rate coefficient.

Molecular dynamics tests of the Smoluchowski–Collins–Kimball model for fluorescence quenching of spherical molecules

We test the Smoluchowski–Collins–Kimball (SCK) model of fluorescence quenching reaction in liquids. Our attention is focused on the description of diffusion controlled processes and we use the simplest microscopic model of binary de-excitation which occurs instantaneously. Molecular dynamics simulations have been performed for a wide range of densities and for various potentials of interparticle interactions. The large number of particles used (typically N = 681 472) allowed us to obtain quantitative results. The simulations show that at very short times the SCK model completely fails, especially if the distribution function of the reagents is not included in the model. Even if the short time data are excluded the diffusion constant obtained by fitting the simulation data with the SCK model may still be burdened with a 25% error when the distribution function is not taken into account. The error can be reduced to 10% level if this function is included in the model.

Molecular dynamics investigations on Lennard–Jones systems near the gas–liquid critical point

Abstract NVT simulations on Lennard–Jones (L–J) systems near the gas–liquid critical point were performed by a direct approach. As a result, the two necessary conditions for simulating the systems in accordance with the thermodynamic limit were proposed: (i) L / ξ ≳20 ( L : the box-length, ξ : the correlation length), (ii) the total time of evolution, t E >500 L–J units, for ξ ≈3.5. The proposed conditions are probably very close to the sufficient ones. The influence of finite-size effects on pressure and density of small systems was qualitatively predicted. The prediction was confirmed by the simulations but only for L markedly lower than the length of typical critical wave, 2 πξ . For L markedly higher, the evolutions were dominated by an effect called here the instability effect. The effect became negligible just when the condition for L / ξ was fulfilled. The ξ 0 ′ constant for L–J fluid was estimated from direct measurements of ξ to be 0.27±0.02 (L–J units). The thermodynamic parameters of the critical point, obtained from extrapolation, were in agreement with the results of other authors. The β C exponent was estimated from minimization for a high range of temperatures to be 0.346. A comparison of the efficiency of NVT and NpT methods was also performed and no distinct differences were noted.

Molecular dynamics study on the influence of quencher concentration on the reaction rate for ionic systems

The influence of concentrations of reagents on the rate of reaction: A+B-->C+B for low density equimolar mixtures of spherically symmetric ions immersed in the Brownian medium has been investigated by performing large scale molecular dynamics simulations. The Coulomb potential of ion-ion interactions is truncated at the cutoff distance large enough to make the kinetics of the reaction independent of its value. The simulations have been performed at conditions close to that for quenching reactions for fluophores. One of the simulation results is that the excess in the rate coefficient Delta k is always positive and converges to a constant value which is two to three orders in magnitude higher than that for the soft spheres immersed in the Brownian medium [Litniewski, J. Chem. Phys. 124, 114502 (2006)]. Delta k is approximately proportional to c however, if the concentration is high, positive deviations [O(c(2))] are noticeable. The simulation results are compared with simple model that bases on the superposition approximation. The model predicts most of the properties of Delta k. The predicted values are about 30%-40% lower than that from the simulations.

On the applicability of the step function nonradiative lifetime model for diffusion controlled reactions

We derive an approximate expression for the time-dependent reaction rate coefficient, k(t), of the Smoluchowski equation for the step function nonradiative lifetime (SFNL) model in the case of structureless liquid (i.e., if there are no spatial correlations between molecules of reactants). The SFNL model assumes that a reaction occurs with equal probability for reactants at distances between r0 and r1. The accuracy of the obtained analytical formula for k(t) is absolutely sufficient for practical applications like the interpretation of experiments on fluorescence quenching. A molecular dynamics has shown that the SFNL model much better describes the simulation results than the Smoluchowski–Collins–Kimball model if the distance between r1 and r0 cannot be neglected.

Computer investigations on the asymptotic behavior of the rate coefficient for the annihilation reaction A + A → product and the trapping reaction in three dimensions

We have performed intensive computer simulations of the irreversible annihilation reaction: A + A → C + C and of the trapping reaction: A + B → C + B for a variety of three-dimensional fluids composed of identical spherical particles. We have found a significant difference in the asymptotic behavior of the rate coefficients for these reactions. Both the rate coefficients converge to the same value with time t going to infinity but the convergence rate is different: the O(t(-1/2)) term for the annihilation reaction is higher than the corresponding term for the trapping reaction. The simulation results suggest that ratio of the terms is a universal quantity with the value equal to 2 or slightly above. A model for the annihilation reaction based on the superposition approximation predicts the difference in the O(t(-1/2)) terms, but overestimates the value for the annihilation reaction by about 30%. We have also performed simulations for the dimerization process: A + A → E, where E stands for a dimer. The dimerization decreases the reaction rate due to the decrease in the diffusion constant for A. The effect is successfully predicted by a simple model.