Semi‐classical formulation of time‐dependent discrete variable representation method

In this article, we apply a novel time‐dependent discrete variable representation (TDDVR) method proposed by Barkakaty and Adhikari to investigate tunneling through an Eckart barrier. This semi‐classical method is theoretically rigorous and straightforward to implement. Among the TDDVR formulations, this report presents the first derivation of a rigorous form of quantum force (QF) for the present perspective. The validity of this semi‐classical approach is demanded based on the excellent agreement of the tunneling probability with the corresponding quantum results. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Quantum analogue of the Kolmogorov–Arnold–Moser transition in different quantum anharmonic oscillators

The results of numerical computations are presented for the Bohmian trajectories of the family of different one‐ and two‐dimensional anharmonic oscillators, which exhibit regular or chaotic motion in both classical and quantum domains, depending on the values of the parameters appearing in the respective Hamiltonians. Quantum signatures of the Kolmogorov–Arnold–Moser (KAM) transition from the regular to chaotic classical dynamics of these oscillators are studied using a quantum theory of motion (QTM) as developed by de Broglie and Bohm. A phase space distance function between two initially close Bohmian trajectories, the associated Kolmogorov–Sinai–Lyapunov (KSL) entropy, the phase space volume, the autocorrelation function, the associated power spectrum, and the nearest‐neighbor spacing distribution, clearly differentiate the quantum analogues of the corresponding regular and chaotic motions in the classical domain. These quantum anharmonic oscillators are known to be useful in several diverse branches of science. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Predicting the effect of membrane spacers on mass transfer

Like many separation processes, ultrafiltration and reverse osmosis are often compromised by concentration polarization. Such polarization can be mitigated by static mixers and other flow barriers placed as spacers next to the membrane surface. These spacers can be shaped like ladders, herringbones, and helices. The effect of these spacers can be successfully predicted without adjustable parameters from extensions of the Lévêque equation. The predictions are in agreement with results of computational fluid mechanics and with electrochemical experiments. They supply a tool for optimizing spacer design.     

Statistical mechanics of hydrated electron recombination in liquid and supercritical water

The photochemical yield of hydrated electrons as a function of temperature in liquid and supercritical water is treated in terms of energy fluctuations of the medium. The geminate pair, consisting of a positive ion and a hydrated electron, is regarded as a H-like atom embedded in a completely relaxed dielectric continuum. If the local medium energy is larger than the ionization energy of this atom, the electron escapes its geminate partner. By making use of the classical theory of energy fluctuations, escape probability is described by a simple explicit function, the variable of which is a combination of temperature, relative permittivity, and specific heat. First our earlier calculations on the recombination of solvated electrons, produced by ionizing radiation in a number of polar liquids, are improved and then the theory is compared with the experimental results on temperature dependent electron survival by Kratz et al. [S. Kratz, J. Torres-Alcan, J. Urbanek, J. Lindner, and P. Vo?hringer, Phys. Chem. Chem. Phys. 12, 12169 (2010)]. Two adjustable parameters are needed to achieve reasonable quantitative agreement.     

Comprehensive theory for star-like polymer micelles; combining classical nucleation and polymer brush theory

A comprehensive theory is proposed that combines classical nucleation and polymer brush theory to describe star-like polymer micelles. With a minimum of adjustable parameters, the model predicts properties such as critical micelle concentrations and micellar size distributions. The validity of the present theory is evidenced in direct comparison to experiments; this revealed that the proportionality constant in the Daoud-Cotton model is of the order of unity and that the star-limit is valid down to relatively short corona chains. Furthermore, we show that the predicted saddle points in the free energy correspond to those solutions that are accessible with self-consistent field methods for self-assembly.     

Incorporation of nonlinear thermorheological complexity into the phenomenologies of structural relaxation

A distribution of activation energies is introduced into the nonlinear Adam-Gibbs ("Hodge-Scherer") phenomenology for structural relaxation. The resulting dependencies of the stretched exponential beta parameter on thermodynamic temperature and fictive temperature (nonlinear thermorheological complexity) are derived. No additional adjustable parameters are introduced, and contact is made with the predictions of the random first-order transition theory of aging of Lubchenko and Wolynes [J. Chem. Physics121, 2852 (2004)].     

On predicting self-diffusion coefficients in fluids

A modification of an existing correlative equation for self-diffusion coefficients is presented. A free-volume theory for liquids has been corrected to reproduce diffusivities of hard-sphere and Lennard–Jones fluids from low-density limit to melting points, and has been applied to correlate a wide database of non-polar, polar, quantic and hydrogen-bonding substances, although it is unable to fit helium, water and hydrogen fluoride. The adjustable parameters are generalized with available fluid properties, and the three resulting predictive formulas present lower deviations than other correlative equations used in a predictive way for non-quantic and non-associated fluids.     

Improving description of hydrogen bonds at the semiempirical level: water–water interactions as test case

Hydrogen bonding is not well described by available semiempirical theories. This is an important restriction because hydrogen bonds represent a key feature in many chemical and biochemical processes, besides being responsible for the singular properties of water. In this study, we describe a possible solution to this problem. The basic idea is to replace the nonphysical gaussian correction functions (GCF) appearing in the core–core repulsion terms of most MNDO‐based semiempirical methods by a simple function exhibiting the correct physical behavior in the whole range of intermolecular separation distances. The parameterized interaction function (PIF) is the sum of atom‐pair contributions, each one having five adjustable parameters. In this work, the approach is used to study water–water interactions. The parameters are optimized to reproduce a reference ab initio intermolecular energy surface for the water–water dimer obtained at the MP2/aug‐cc‐pVQZ level. OO, OH, and HH parameters are reported for the PM3 method. The results of PM3‐PIF calculations remarkably improve qualitatively and quantitatively those obtained at the standard PM3 level, both for water–dimer properties and for water clusters up to the hexamer. For example, the root‐mean‐square deviation of the PM3‐PIF interaction energies, with respect to ab initio values obtained using 700 points of the water dimer surface, is only 0.47 kcal/mol. This value is much smaller than that obtained using the standard PM3 method (4.2 kcal/mol). The PM3‐PIF water dimer energy minimum (−5.0 kcal/mol) is also much closer to ab initio data (−5.0±0.01 kcal/mol) than PM3 (−3.50 kcal/mol). The method is therefore promising for the development of new semiempirical approaches as well as for application of combined quantum mechanics and molecular mechanics techniques to investigate chemical processes in water. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 572–581, 2000     

Mesoscale simulation of morphology in hydrated perfluorosulfonic acid membranes

Current fuel cell proton exchange membranes rely on a random network of conducting hydrophilic domains to transport protons across the membrane. Despite extensive investigation, details of the structure of the hydrophilic domains in these membranes remain unresolved. In this study a dynamic self-consistent mean field theory has been applied to obtain the morphologies of hydrated perfluorosulfonic acid membranes (equivalent weight of 1100) as a model system for Nafion at several water contents. A coarse-grained mesoscale model was developed by dividing the system into three components: backbone, side chain, and water. The interaction parameters for this model were generated using classical molecular dynamics. The simulated morphology shows phase separated micelles filled with water, surrounded by side chains containing sulfonic groups, and embedded in the fluorocarbon matrix. The size distribution and connectivity of the hydrophilic domains were analyzed and the small angle neutron scattering (SANS) pattern was calculated. At low water content (lambda<6, where lambda is the number of water molecules per sulfonic group) the isolated domains obtained from simulation are nearly spherical with a domain size smaller than that fitted to experimental SANS data. At higher water content (lambda>8), the domains deform into elliptical and barbell shapes as they merge. The simulated morphology, hydrophilic domain size and shape are generally consistent with some experimental observations.     

Hofmeister effects: interplay of hydration, nonelectrostatic potentials, and ion size

The classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloids, and corresponding theories of electrolytes, are unable to explain ion specific forces between colloidal particles quantitatively. The same is true generally, for surfactant aggregates, lipids, proteins, for zeta and membrane potentials and in adsorption phenomena. Even with fitting parameters the theory is not predictive. The classical theories of interactions begin with continuum solvent electrostatic (double layer) forces. Extensions to include surface hydration are taken care of with concepts like inner and outer Helmholtz planes, and "dressed" ion sizes. The opposing quantum mechanical attractive forces (variously termed van der Waals, Hamaker, Lifshitz, dispersion, nonelectrostatic forces) are treated separately from electrostatic forces. The ansatz that separates electrostatic and quantum forces can be shown to be thermodynamically inconsistent. Hofmeister or specific ion effects usually show up above ≈10(-2) molar salt. Parameters to accommodate these in terms of hydration and ion size had to be invoked, specific to each case. Ionic dispersion forces, between ions and solvent, for ion-ion and ion-surface interactions are not explicit in classical theories that use "effective" potentials. It can be shown that the missing ionic quantum fluctuation forces have a large role to play in specific ion effects, and in hydration. In a consistent predictive theory they have to be included at the same level as the nonlinear electrostatic forces that form the skeletal framework of standard theory. This poses a challenge. The challenges go further than academic theory and have implications for the interpretation and meaning of concepts like pH, buffers and membrane potentials, and for their experimental interpretation. In this article we overview recent quantitative developments in our evolving understanding of the theoretical origins of specific ion, or Hofmeister effects. These are demonstrated through an analysis that incorporates nonelectrostatic ion-surface and ion-ion dispersion interactions. This is based on ab initio ionic polarisabilities, and finite ion sizes quantified through recent ab initio work. We underline the central role of ionic polarisabilities and of ion size in the nonelectrostatic interactions that involve ions, solvent molecules and interfaces. Examples of mechanisms through which they operate are discussed in detail. An ab initio hydration model that accounts for polarisabilities of the tightly held hydration shell of "cosmotropic" ions is introduced. It is shown how Hofmeister effects depend on an interplay between specific surface chemistry, surface charge density, pH, buffer, and counterion with polarisabilities and ion size. We also discuss how the most recent theories on surface hydration combined with hydrated nonelectrostatic potentials may predict experimental zeta potentials and hydration forces.     

Quantum effects in liquid water and ice: model dependence

This paper explores the influence of choice of potential model on the quantum effects observed in liquid water and ice. This study utilizes standard rigid models and a more formal context for the rigid-body centroid molecular dynamics methodology used to perform the quantum simulations is provided. Quantum and classical molecular dynamics simulations are carried out for liquid water and ice Ih at 298 and 220 K, respectively, with the simple point charge/extended and TIP4P-Ew water models. The results obtained for equilibrium and dynamical properties are compared with those recently reported on TIP4P [L. Hernandez de la Pena and P. G. Kusalik, J. Chem. Phys. 121, 5992 (2004); L. Hernandez de la Pena et al., J. Chem. Phys 123, 144506 (2005)]. For the liquid, an energy shift of about 8% and an average molecular uncertainty of about 11 degrees were found independently of the water model. The self-diffusion coefficient consistently increases by more than 50% when going from the classical to the quantum system and quantum dynamics are found to reproduce the experimental isotopic shifts with the models examined. The ice results compare remarkably well with those previously reported for the TIP4P water model; they confirm that quantum effects are considerable and that the quantum mechanical uncertainty and the energy shifts due to quantization are smaller in ice than in liquid water. The relevance of these findings in the context of the construction of water models is briefly discussed.     

Modeling of phase equilibria with CPA using the homomorph approach

For association models, like CPA and SAFT, a classical approach is often used for estimating pure-compound and mixture parameters. According to this approach, the pure-compound parameters are estimated from vapor pressure and liquid density data. Then, the binary interaction parameters, k_ij, are estimated from binary systems; one binary interaction parameter per system. No additional mixing rules are needed for cross-associating systems, but combining rules are required, e.g. the Elliott rule or the so-called CR-1 rule. There is a very large class of mixtures, e.g. water or glycols with aromatic hydrocarbons, chloroform-acetone, esters-water, CO₂-water, etc., which are classified as “solvating” or “induced associating”. The classical approach cannot be used and the cross-association interactions are difficult to be estimated a priori since usually no appropriate experimental data exist, while the aforementioned combining rules cannot capture the physical meaning of such interactions (as at least one of the compounds is non-self-associating). Consequently, very often one or more of the interaction parameters are optimized to experimental mixture data. For example, in the case of the CPA EoS, two interaction parameters are often used for solvating systems; one for the physical part (k_ij) and one for the association part (β^cross). This limits the predictive capabilities and possibilities of generalization of the model. In this work we present an approach to reduce the number of adjustable parameters in CPA for solvating systems. The so-called homomorph approach will be used, according to which the k_ij parameter can be obtained from a corresponding system (homomorph) which has similar physical interactions as the solvating system studied. This leaves only one adjustable parameter for solvating mixtures, the cross-association volume (β^cross). It is shown that the homomorph approach can be used with success for mixtures of water and glycols with aromatic hydrocarbons as well as for mixtures of acid gases (CO₂, H₂S) with alcohols and water. The homomorph approach is less satisfactory for mixtures with fluorocarbons as well as for aqueous mixtures with ethers and esters. In these cases, CPA can correlate liquid-liquid equilibria for solvating systems using two adjustable parameters. The capabilities and limitations of the homomorph approach are discussed.     

Using nucleation rates to determine the interfacial line tension of symmetric and asymmetric lipid bilayer domains

This work presents a novel method for experimentally quantifying interfacial line tension, which can be readily applied to study a wide variety of different lipid mixtures exhibiting phase coexistence. The method combines AFM imaging of lipid domain nucleation with classical nucleation theories. The results, using symmetric and asymmetric domains, permit the prediction of key physical parameters (critical nuclei size and nucleation rate) in multicomponent bilayer systems with implications toward understanding the dynamic nature of submicrometer domains (i.e., lipid rafts) in cell membranes.     

Theory of electrode polarization: application to parallel plate cell dielectric spectroscopy experiments

An extension of the model for electrode polarization of Cirkel et al. [Physica A 235 (1997) 269] is given. The problem is solved using both classical boundary conditions and the new boundary conditions using excess densities presented in a previous paper [J. Phys. Chem. B 105 (2001) 11743]. In the present paper, the electrodes are supposed to be ideal, meaning that charge transfer or adsorption are not considered. The advantage of the new boundary conditions lies in the possibility to extend to more complicated situations including for instance specific ion adsorption. We prove that the new boundary conditions and classical ones give the same results. A comparison of the model predictions, involving no adjustable parameters, experimental dielectric spectroscopy data is performed and fairly good agreement is found.     

Thermodynamic properties and phase transtions in the H2O/CO2/CH4 system

The availability of free energy densities as functions of temperature, pressure and the composition of all components is required for the development of a three-component phase field theory for hydrate phase transitions. We have broadened the extended adsorption theory due to Kvamme and Tanaka (J. Phys. Chem., 1995, 99, 7114) through derivation of the free energy density surface in case of CO(2) and CH(4) hydrates. A combined free energy surface for the liquid phases has been obtained from a SRK equation of state and solubility measurements outside hydrate stability. The full thermodynamic model is shown to predict water-hydrate equilibrium properties in agreement with experiments. Molecular dynamics simulations of hydrates in contact with water at 200 bar and various temperatures allowed us to estimate hard-to-establish properties needed as input parameters for the practical applications of proposed theories. The 5-95 confidence interval for the interface thickness for the methane hydrate/liquid water is estimated to 8.54 A. With the additional information on the interface free energy, the phase field theory will contain no adjustable parameters. We provide a demonstration of how this theory can be applied to model the kinetics of hydrate phase transitions. The growth of hydrate from aqueous solution was found to be rate limited by mass transport, with the concentration of solute close to the hydrate approaching the value characterizing the equilibrium between the hydrate and the aqueous solution. The depth of the interface was estimated by means of the phase field analysis; its value is close to the interface thickness yielded by molecular simulations. The variation range of the concentration field was estimated to approximately 1/3 of the range of the phase field.     

Rotational excitation of water by hydrogen molecules: comparison of results from classical and quantum mechanics

Quasiclassical trajectory calculations are carried out for rotational excitation of water by hydrogen molecules. State-to-state rate coefficients are determined at 100 K and are compared to available quantum results. A good agreement between classical and quantum rates is observed for downward transitions, with an average accuracy of classical results better than a factor of 2. It is thus found that the ambiguities described by Faure and Wiesenfeld [J. Chem. Phys. 121, 6771 (2004)] can be solved in the particular case of waterlike asymmetric-top molecules.     

Complete thermodynamically consistent kinetic model of particle nucleation and growth: numerical study of the applicability of the classical theory of homogeneous nucleation

A complete thermodynamically consistent elementary reaction kinetic model of particle nucleation and growth from supersaturated vapor was developed and numerically evaluated to determine the conditions for the steady-state regime. The model treats all processes recognized in the aerosol science (such as nucleation, condensation, evaporation, agglomerationcoagulation, etc.) as reversible elementary reactions. It includes all possible forward reactions (i.e., of monomers, dimers, trimers, etc.) together with the thermodynamically consistent reverse processes. The model is built based on the Kelvin approximation, and has two dimensionless parameters: S0-the initial supersaturation and Theta-the dimensionless surface tension. The time evolution of the size distribution function was obtained over the ranges of parameters S0 and Theta. At low initial supersaturations, S0, the steady state is established after a delay, and the steady-state distribution function corresponds to the predictions of the classical nucleation theory. At high initial supersaturations, the depletion of monomers due to condensation on large clusters starts before the establishing of the steady state. The steady state is never reached, and the classical nucleation theory is not applicable. The boundary that separates these two regimes in the two dimensionless parameter space, S0 and Theta, was determined. The model was applied to several experiments on water nucleation in an expansion chamber [J. Wolk and R. Strey, J. Phys. Chem. B 105, 11683 (2001)] and in Laval nozzle [Y. J. Kim et al., J. Phys. Chem. A 108, 4365 (2004)]. The conditions of the experiments performed using Laval nozzle (S0=40-120) were found to be close to the boundary of the non-steady-state regime. Additional calculations have shown that in the non-steady-state regime the nucleation rate is sensitive to the rate constants of the initial steps of the nucleation process, such as the monomer-monomer, monomer-dimer, etc., reactions. This conclusion is particularly important for nucleation from supersaturated water vapor, since these processes for water molecules at and below the atmospheric pressure are in the low pressure limit, and the rate constants can be several orders of magnitude lower than the gas kinetic. In addition, the impact of the thermodynamic inconsistency of the previously developed partially reversible kinetic numerical models was assessed. At typical experimental conditions for water nucleation, S0=10 and Theta=10 (T=250 K), the error in the particle nucleation rate introduced by the thermodynamic inconsistency exceeds one order of magnitude.     

Relation between stress and segmental orientation during mechanical cycling of a natural rubber‐based compound

X‐ray diffraction technique is used to evaluate the evolution of the segmental orientation in a natural rubber sample during mechanical uniaxial stretching and in the Gaussian regime condition. The method proves to be sensitive enough for testing the validity of the stress‐optical law. Measurements are performed at different temperatures and show that the dependence of the orientation parameter upon elongation is very close to the prediction of classical phantom theories. On the contrary, a significant Mooney–Rivlin correction is needed to account for the stress–strain relation. Consequently, systematic deviations from the stress‐optical law are observed, in particular for elongations below 2. These deviations are adverse from predictions of both the constrained and the diffuse junction theories. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 943–950     

牛血清蛋白在NaCl水溶液中渗透压的研究

将NaCl水溶液中带电蛋白质分子间的静电排斥作用用Yukawa位能函数描述,蛋白质分子间的色散作用用Lennard-Jones位能函数描述,代替了经典DLVO理论。基于McMillan-Mayer渗透压统计理论,将Duh和Mier-Y-Teran的Yukawa状态方程与Cotterman等的Lennard-Jones微扰公式相结合,建立了一个新的状态方程,并采用该状态方程研究了含有NaCl的牛血清蛋白(简称BSA)水溶液的渗透压,依据BSA在0.15mol/LNaCl水溶液中的回归参数可预测其在1～5mol/LNaCl水溶液中的渗透压。该状态方程采用了两个回归参数(硬球直径和LJ参数),具有一定的关联和预测效果,并与己有的其它理论模型进行了比较。     

Is cluster evaporation statistical? A comparison of simulation results for Ar13 with exact classical phase space theory

We have simulated the dissociation reactionA _n →A _n?1+A for small clusters (L-J argon) with well defined internal energy and total angular momentum. Reaction rates and kinetic energy release distributions are compared to the predictions of several statistical theories, including RRK, the “Engelking” model, and phase space theory (PST). We have applied classical phase space theory in an essentially exact formulation using accurate anharmonic vibrational densities of states (and no adjustable parameters). We present a critical evaluation of the different theories and sensitivity of the results to the underlying assumptions.