Alexander V. Popov

Ontology of temperature in nonequilibrium systems

The laws of thermodynamics provide a clear concept of the temperature for an equilibrium system in the continuum limit. Meanwhile, the equipartition theorem allows one to make a connection between the ensemble average of the kinetic energy and the uniform temperature. When a system or its environment is far from equilibrium, however, such an association does not necessarily apply. In small systems, the regression hypothesis may not even apply. Herein, it is shown that in small nonequilibrium systems, the regression hypothesis still holds, though with a generalized definition of the temperature. The latter must now be defined for each such manifestation.

Diffusion-influenced excited-state reversible transfer reactions, A*+B⇌C*+D, with two different lifetimes: Theories and simulations

We report accurate Brownian simulation results for the kinetics of the pseudo-first-order diffusion-influenced excited-state reversible transfer reaction A(*) + Bright harpoon over left harpoonC(*) + D with two different lifetimes using two different propagation algorithms. The results are used to test approximate solutions for this many-particle problem. Available theories fail when one of the two reactions or (decay) rate constants is large. To remedy this situation, we develop two uniform approximations, which are based on introducing a generalized Smoluchowski term into the relaxation-time approximation. The best of these is the extended unified theory of reversible target reactions, which reduces correctly in all limits and exhibits superior agreement with simulations.

A spectroscopic and computational exploration of the cybotactic region of gas-expanded liquids: methanol and acetone.

Local compositions in supercritical and near-critial fluids may differ substantially from bulk compositions, and such differences have important effects on spectroscopic observations, phase equilibria, and chemical kinetics. Here, we compare such determinations around a solute probe dissolved in CO2-expanded methanol and acetone at 25 degrees C from solvatochromic experiments with molecular dynamics simulations. UV/vis and steady-state fluorescence measurements of the dye Coumarin 153 in the expanded liquid phase indicate preferential solvation in both the S0 and S1 states by the organic species. Simple dielectric continuum models are used to estimate local compositions from the spectroscopic data and are compared to molecular dynamics simulations of a single C153 molecule dissolved in the liquid phase at bubble point conditions. The simulations provide information about the local solvent structure around C153. They suggest the presence of large solvent clustering near the electron-withdrawing side of the probe. Preferential solvation exists in both the S0 and S1 states, but a large disagreement between simulation and experiment exists in the S1 state. Potential reasons for this disparity are discussed.

Molecular dynamics out of equilibrium: mechanics and measurables

Molecular dynamics is fundamentally the integration of the equations of motion over a representation of an atomic and molecular system. The most rigorous choice for performing molecular dynamics entails the use of quantum‐mechanical equations of motion and a representation of the molecular system through all of its electrons and atoms. For most molecular problems involving at least hundreds of atoms, but generally many more, this is simply computationally prohibitive. Thus the art of molecular dynamics lies in choosing the representation and the appropriate equations of motion capable of addressing the requisite measurables. When used adroitly, it can provide both equilibrium (averaged) and time‐dependent properties of a molecular system. Many computational packages now exist that perform molecular dynamics simulations. They generally include force fields to represent the interactions between atoms and molecules (smoothing out electrons through the Born‐Oppenheimer approximation) and integrate the remaining particles classically. Despite these simplifications, all‐atom molecular dynamics remains computationally inaccessible if one includes the number of atoms required to simulate mesoscopic solvents. Here we use analytical models to demonstrate how molecular dynamics can be used to limit the solvent size in systems experiencing either equilibrium or nonequilibrium conditions. It is equally important to address the measurables (such as reaction rates) that are to be obtained prior to the generation of the data‐intensive trajectories. WIREs Comput Mol Sci 2014, 4:541–561. doi: 10.1002/wcms.1190

Effects of Solute Structure on Local Solvation and Solvent Interactions : Results from UV/Vis Spectroscopy and Molecular Dynamics Simulations

Solvation of heterocyclic amines in CO(2)-expanded methanol (MeOH) has been explored with UV/vis spectroscopy and molecular dynamics (MD) simulations. A synergistic study of experiments and simulations allows exploration of solute and solvent effects on solvation and the molecular interactions that affect absorption. MeOH-nitrogen hydrogen bonds hinder the n-pi* transition; however, CO(2) addition causes a blue shift relative to MeOH because of Lewis acid/base interactions with nitrogen. Effects of solute structure are considered, and very different absorption spectra are obtained as nitrogen positions change. MD simulations provide detailed solvent clustering behavior around the solute molecules and show that the local solvent environment and ultimately the spectra are sensitive to the solute structure. This work demonstrates the importance of atomic-level information in determining the structure-property relationships between solute structure, local salvation, and solvatochromism.

Stochastic dynamics of penetrable rods in one dimension: Occupied volume and spatial order

The occupied volume of a penetrable hard rod (HR) system in one dimension is probed through the use of molecular dynamics simulations. In these dynamical simulations, collisions between penetrable rods are governed by a stochastic penetration algorithm (SPA), which allows for rods to either interpenetrate with a probability δ, or collide elastically otherwise. The limiting values of this parameter, δ = 0 and δ = 1, correspond to the HR and the ideal limits, respectively. At intermediate values, 0 < δ < 1, mixing of mutually exclusive and independent events is observed, making prediction of the occupied volume nontrivial. At high hard core volume fractions φ0, the occupied volume expression derived by Rikvold and Stell [J. Chem. Phys. 82, 1014 (1985)] for permeable systems does not accurately predict the occupied volume measured from the SPA simulations. Multi-body effects contribute significantly to the pair correlation function g2(r) and the simplification by Rikvold and Stell that g2(r) = δ in the penetrative region is observed to be inaccurate for the SPA model. We find that an integral over the penetrative region of g2(r) is the principal quantity that describes the particle overlap ratios corresponding to the observed penetration probabilities. Analytic formulas are developed to predict the occupied volume of mixed systems and agreement is observed between these theoretical predictions and the results measured from simulation.

Molecular Dynamics Simulations of Solvation and Solvent Reorganization Dynamics in CO2-Expanded Methanol and Acetone.

Composition-dependent solvation dynamics around the probe coumarin 153 (C153) have been explored in CO2-expanded methanol and acetone with molecular dynamics (MD) simulations. Solvent response functions are biexponential with two distinct decay time scales: a rapid initial decay (∼0.1 ps) and a long relaxation process. Solvation times in both expanded solvent classes are nearly constant at partition compositions up to 80% CO2. The extent of solvation beyond this composition has the greatest tunability and sensitivity to bulk solvent composition. Solvent rotational correlation functions (RCFs) have also been used to explore rotational relaxation. Rotations have a larger range of time scales and are dependent on a number of factors including bulk composition, solvent-solvent interactions, particularly hydrogen bonding, and proximity to C153. The establishment of the solvation structure around a solute in a GXL is clearly a complex process. With respect to the local solvent domain around C153, it was seen to be primarily affected by a nonlinear combination of the rotational and diffusive transport dynamics.

Nonequilibrium heat flows through a nanorod sliding across a surface

The temperature-ramped irreversible Langevin equation [A. V. Popov and R. Hernandez, J. Chem. Phys. 134, 244506 (2007)] has been seen to describe the nonequilibrium atomic oscillations of a nanorod dragged across a surface. The nanorod and surface consist of hydroxylated α-Al(2)O(3) layers as was studied earlier by Hase and co-workers [J. Chem. Phys. 122, 094713 (2005)]. The present approach corresponds to the reduced Frenkel-Kontorova-Tomlinson model in which only one element of the vibrational chain representing a surface layer is considered explicitly. The key new concept centers on a separation of the environment into two effective reduced-dimensional baths: an equilibrium bath arising from the thermostated vibrations of the crystal lattice and a nonequilibrium bath arising from driven oscillations at the contact between the nanorod and the surface. The temperature of the latter is defined by the mean energy of a representative atomic oscillator for a given layer. The temporal temperature fluctuations and the dependence of the static part of the temperature on the sliding velocity are close to those found in the MD simulations of Hase and co-workers.

Kinetics of intra- and intermolecular excited-state proton transfer of ω -(2-hydroxynaphthyl-1)-decanoic acid in homogeneous and micellar solutions

The bifunctional photoacid ω-(2-hydroxynaphthyl-1)-decanoic acid (1S2N) takes part both in intramolecular excited-state proton transfer (ESPT) to the anion of a fatty acid and in intermolecular ESPT in the presence of a water solvent. Excited-state intraand intermolecular proton transfer of 1S2N was investigated in homogeneous ethanol/water solution and in micellar solutions of various surfactants. The interfacial potential of micelles was changed by using cationic (CTAB), non-ionic (Brij-35) and anionic (SDS) surfactants. With the decrease of the interfacial potential, the protolytic photodissociation of naphthol and the diffusion-controlled intramolecular ESPT to carboxylic anion were suppressed. PAPER Author to whom any correspondence should be addressed. REcEivEd

Effective surface coverage of coarse-grained soft matter.

The surface coverage of coarse-grained macromolecules bound to a solid substrate is not simply proportional to the two-dimensional number density because macromolecules can overlap. As a function of the overlap probability δ, we have developed analytical formulas and computational models capable of characterizing this nonlinear relationship. For simplicity, we ignore site-site interactions that would be induced by length-scale mismatches between binding sites and the radius of gyration of the incident coarse-grained macromolecular species. The interactions between macromolecules are modeled with a finite bounded potential that allows multiple macromolecules to occupy the same binding site. The softness of the bounded potential is thereby reduced to the single parameter δ. Through variation of this parameter, completely hard (δ = 0) and completely soft (δ = 1) behavior can be bridged. For soft macromolecular interactions (δ > 0), multiple occupancy reduces the fraction of sites ϕ occupied on the substrate. We derive the exact transition probability between sequential configurations and use this probability to predict ϕ and the distribution of occupied sites. Due to the complexity of the exact ϕ expressions and their analytical intractability at the thermodynamic limit, we apply a simplified mean-field (MF) expression for ϕ. The MF model is found to be in excellent agreement with the exact result. Both the exact and MF models are applied to an example dynamical system with multibody interactions governed by a stochastic bounded potential. Both models show agreement with results measured from simulation.