Aleksey Vishnyakov

Bridging scales from molecular simulations to classical thermodynamics: density functional theory of capillary condensation in nanopores

With the example of the capillary condensation of Lennard-Jones fluid in nanopores ranging from 1 to 10 nm, we show that the non-local density functional theory (NLDFT) with properly chosen parameters of intermolecular interactions bridges the scale gap from molecular simulations to macroscopic thermodynamics. On the one hand, NLDFT correctly approximates the results of Monte Carlo simulations (shift of vapour–liquid equilibrium, spinodals, density profiles, adsorption isotherms) for pores wider than about 2 nm. On the other hand, NLDFT smoothly merges (above 7–10 nm) with the Derjaguin–Broekhoff–de Boer equations which represent augmented Laplace–Kelvin equations of capillary condensation and desorption.

Cavitation in Metastable Liquid Nitrogen Confined to Nanoscale Pores

We studied cavitation in metastable fluids drawing on the example of liquid nitrogen confined to spheroidal pores of specially prepared well-characterized mesoporous silica materials with mean pore diameters ranging from approximately 6 to approximately 35 nm. Cavitation was monitored in the process of evaporation/desorption from fully saturated samples with gradually decreasing vapor pressure at the isothermal conditions. The onset of cavitation was displayed by a sharp step on the desorption isotherm. We found that the vapor pressure at the onset of cavitation depended on the pore size for the samples with pores smaller than approximately 11 nm and remained practically unchanged for the samples with larger pores. We suggest that the observed independence of the cavitation pressure on the size of confinement indicates that the conditions of bubble nucleation in pores larger than approximately 11 nm approach the nucleation conditions in the bulk metastable liquid. To test this hypothesis and to evaluate the nucleation barriers, we performed grand canonical and gauge cell Monte Carlo simulations of nitrogen adsorption and desorption in spherical silica pores ranging from 5.5 to 10 nm in diameter. Simulated and experimental adsorption isotherms were in good agreement. Exploiting the correlation between the experimental cavitation pressure and the simulated nucleation barrier, we found that the nucleation barrier increased almost linearly from approximately 40 to approximately 70 k(B)T in the range of pores from approximately 6 to approximately 11 nm, and varied in diapason of 70-75 k(B)T in larger pores, up to 35 nm. We constructed the dependence of the nucleation barrier on the vapor pressure, which asymptotically approaches the predictions of the classical nucleation theory for the metastable bulk liquid at larger relative pressures (>0.6). Our findings suggest that there is a limit to the influence of the confinement on the onset of cavitation, and thus, cavitation of nanoconfined fluids may be employed to explore cavitation in macroscopic systems.

Prediction of the Critical Micelle Concentration of Nonionic Surfactants by Dissipative Particle Dynamics Simulations

Micellization of surfactant solutions is a ubiquitous phenomenon in natural systems and technological processes, and its theoretical description represents one of the cornerstone problems in the physical chemistry of colloidal systems. However, successful attempts of quantitative modeling confirmed by experimental data remains limited. We show, for the first time, that the dissipative particle dynamics with rigorously defined soft repulsion interaction and rigidity parameters is capable of predicting micellar self-assembly of nonionic surfactants. This is achieved due to a novel approach suggested for defining the interaction parameters by fitting to the infinite dilution activity coefficients of binary solutions formed by reference compounds that represent coarse-grained fragments of surfactant molecules. Using this new parametrization scheme, we obtained quantitative agreement with the experimental critical micelle concentration and aggregation number for several typical surfactants of different chemical structures. The proposed approach can be extended to various colloidal and polymeric systems beyond nonionic surfactant solutions.

Nucleation of liquid bridges and bubbles in nanoscale capillaries

Nucleation of liquid bridges and bubbles during condensation and evaporation of Lennard-Jones fluid in cylindrical pores is explored by Monte Carlo simulation. The isotherm of constrained critical nuclei is constructed using the gauge cell method. We confirm the Everett–Haynes scenario of bridging through the formation of a bump/undulation on the adsorption film. The molecular structure of growing bridges and cavitating bubbles is revealed. A new simulation approach is introduced to calculate the nucleation energy barriers. The method is based on the introduction and subsequent removal of a virtual “ghost” potential field with a tunable magnitude. Two computation schemes for determining the free energy of nuclei are elaborated based on the thermodynamic integration along a trajectory of states generated in the tunable ghost field and on the umbrella sampling. The methods developed are applicable to study various nucleation phenomena.

Calculations of Critical Micelle Concentration by Dissipative Particle Dynamics Simulations: The Role of Chain Rigidity

Micelle formation in surfactant solutions is a self-assembly process governed by complex interplay of solvent-mediated interactions between hydrophilic and hydrophobic groups, which are commonly called heads and tails. However, the head-tail repulsion is not the only factor affecting the micelle formation. For the first time, we present a systematic study of the effect of chain rigidity on critical micelle concentration and micelle size, which is performed with the dissipative particle dynamics simulation method. Rigidity of the coarse-grained surfactant molecule was controlled by the harmonic bonds set between the second-neighbor beads. Compared to flexible molecules with the nearest-neighbor bonds being the only type of bonded interactions, rigid molecules exhibited a lower critical micelle concentration and formed larger and better-defined micelles. By varying the strength of head-tail repulsion and the chain rigidity, we constructed two-dimensional diagrams presenting how the critical micelle concentration and aggregation number depend on these parameters. We found that the solutions of flexible and rigid molecules that exhibited approximately the same critical micelle concentration could differ substantially in the micelle size and shape depending on the chain rigidity. With the increase of surfactant concentration, primary micelles of more rigid molecules were found less keen to agglomeration and formation of nonspherical aggregates characteristic of flexible molecules.

Self-Assembly in Nafion Membranes upon Hydration: Water Mobility and Adsorption Isotherms

By means of dissipative particle dynamics (DPD) and Monte Carlo (MC) simulations, we explored geometrical, transport, and sorption properties of hydrated Nafion-type polyelectrolyte membranes. Composed of a perfluorinated backbone with sulfonate side chains, Nafion self-assembles upon hydration and segregates into interpenetrating hydrophilic and hydrophobic subphases. This segregated morphology determines the transport properties of Nafion membranes that are widely used as compartment separators in fuel cells and other electrochemical devices, as well as permselective diffusion barriers in protective fabrics. We introduced a coarse-grained model of Nafion, which accounts explicitly for polymer rigidity and electrostatic interactions between anionic side chains and hydrated metal cations. In a series of DPD simulations with increasing content of water, a classical percolation transition from a system of isolated water clusters to a 3D network of hydrophilic channels was observed. The hydrophilic subphase connectivity and water diffusion were studied by constructing digitized replicas of self-assembled morphologies and performing random walk simulations. A non-monotonic dependence of the tracer diffusivity on the water content was found. This unexpected behavior was explained by the formation of large and mostly isolated water domains detected at high water content and high equivalent polymer weight. Using MC simulations, we calculated the chemical potential of water in the hydrated polymer and constructed the water sorption isotherms, which extended to the oversaturated conditions. We determined that the maximum diffusivity and the onset of formation of large water domains corresponded to the saturation conditions at 100% humidity. The oversaturated membrane morphologies generated in the canonical ensemble DPD simulations correspond to the metastable and unstable states of Nafion membrane that are not realized in the experiments.

DPD Simulation of Protein Conformations: From α‑Helices to β‑Structures

We suggest a coarse-grained model for DPD simulations of polypeptides in solutions. The model mimics hydrogen bonding that stabilizes α-helical and β-structures using dissociable Morse bonds between quasiparticles representing the peptide groups amenable to hydrogen bonding. We demonstrate the capabilities of the model by simulating transitions between coil-like, globular, α-helical, and β-hairpin configurations of model peptides, varying Morse potential parameters, the hydrophobicities of residue side chains, and pH, which determines the charges of residue side chains. We construct a model triblock polypeptide mimicking the sequence of residues α-synuclein at two different pHs. The conformations of this model polypeptide depend on pH similarly to the behavior observed experimentally. The suggested approach to accounting for hydrogen bond formation within the general DPD framework may make the DPD method a competitive alternative to CGMD for modeling equilibrium and dynamic properties of proteins and polypeptides, especially during their transport in confined environments.

A simulation method for the calculation of chemical potentials in small, inhomogeneous, and dense systems

We present a modification of the gauge cell Monte Carlo simulation method [A. V. Neimark and A. Vishnyakov, Phys. Rev. E 62, 4611 (2000)] designed for chemical potential calculations in small confined inhomogeneous systems. To measure the chemical potential, the system under study is set in chemical equilibrium with the gauge cell, which represents a finite volume reservoir of ideal particles. The system and the gauge cell are immersed into the thermal bath of a given temperature. The size of the gauge cell controls the level of density fluctuations in the system. The chemical potential is rigorously calculated from the equilibrium distribution of particles between the system cell and the gauge cell and does not depend on the gauge cell size. This scheme, which we call a mesoscopic canonical ensemble, bridges the gap between the canonical and the grand canonical ensembles, which are known to be inconsistent for small systems. The ideal gas gauge cell method is illustrated with Monte Carlo simulations of Lennard-Jones fluid confined to spherical pores of different sizes. Special attention is paid to the case of extreme confinement of several molecular diameters in cross section where the inconsistency between the canonical ensemble and the grand canonical ensemble is most pronounced. For sufficiently large systems, the chemical potential can be reliably determined from the mean density in the gauge cell as it was implied in the original gauge cell method. The method is applied to study the transition from supercritical adsorption to subcritical capillary condensation, which is observed in nanoporous materials as the pore size increases.

Monte Carlo simulation study of droplet nucleation

A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.

Specifics of freezing of Lennard-Jones fluid confined to molecularly thin layers

Freezing of a Lennard-Jones fluid between solid surfaces was studied using grand canonical Monte Carlo and molecular dynamics simulations. We explored the formation of frozen phases of hexagonal and orthorhombic symmetry in mono-, bi-, and tri-layer structures. The freezing transition, the type of lattice, and translational and orientational ordering were identified on the basis of orientational order parameters, in-plane two-body and three-body translational correlation functions, orientational correlation functions, and analysis of molecular mobilities. We have found that the freezing temperature is a nonmonotonous function of the pore width: orthorhombic bi-layer freezes at lower temperatures than hexagonal monolayer and hexagonal bi-layer. As the pore width increases, the transition from a hexagonal monolayer to an orthorhombic bi-layer occurred via disordered liquidlike and quasi-long-range four-fold ordered bi-layers. The latter, “quadratic” structure is characterized by an algebraically decaying fo...