Statistical Thermodynamic Theory Research Articles

Adsorbate-Induced Surface Stress of Chloride Monolayer on Au(111) Electrode

The statistical thermodynamic theory of adsorbate-induced surface stress of anion adsorption monolayer on Au(111) has been established by using the lattice gas model and considering various components of the adsorbate−adsorbate interaction energies in the adlayer, such as the substrate-mediated interaction, the electrostatic energies, Lennard-Jones potential, and so on. The adsorbate-induced surface stress, its components due to various intermolecule forces, and the area elasticity modulus in chloride adions at the Au(111) electrode surface have been calculated. The calculated surface stress of chloride adions on Au(111) approximates the experiment results and the difference between the surface stress and the surface tension is the same order of magnitude as that of the surface stress. Among various components of the adsorbate−adsorbate interaction energies in the adlayer, the substrate-mediated interaction is significant for the adsorbate-induced surface stress, which shows that the indirect contribution...

Structures of hard-sphere fluids from a modified fundamental-measure theory

We reformulate Rosenfeld’s fundamental-measure theory using the excess Helmholtz energy density from the Boublik–Mansoori–Carnahan–Starling–Leland equation of state instead of that from the scaled-particle theory. The new density functional theory yields improved density distributions, especially the contact densities, of inhomogeneous hard-sphere fluids as well as more accurate direct and pair correlation functions of homogeneous hard spheres including those of highly asymmetric mixtures. This new density functional theory will provide an accurate reference for the further development of a statistical-thermodynamic theory of complex fluids at uniform and at inhomogeneous conditions.

Molecular theory of hydrophobic effects: "She is too mean to have her name repeated.".

This paper reviews the molecular theory of hydrophobic effects relevant to biomolecular structure and assembly in aqueous solution. Recent progress has resulted in simple, validated molecular statistical thermodynamic theories and clarification of confusing theories of decades ago. Current work is resolving effects of wider variations of thermodynamic state, e.g., pressure denaturation of soluble proteins, and more exotic questions such as effects of surface chemistry in treating stability of macromolecular structures in aqueous solution.

In situ structural properties of N2-, O2-, and air-clathrates by neutron diffraction

The crystal structures of type II N2-,O2-, and air-clathrate hydrates have been studied under their thermodynamic conditions of stability by neutron powder diffraction. The isothermal compressibilities were deduced from the refined lattice constants and found to be significantly different for N2 and O2 clathrate hydrates. The water host lattice structure rearranges as a function of pressure with a resulting change of the volume ratio of small and large cages. The cage fillings were established on an absolute scale for the first time. The large cages were found to be partly occupied by two molecules. The results are compared with predictions based on the statistical thermodynamic theory of van der Waals and Platteeuw. While the filling follows the predicted trend significant differences exist in detail.

Self-Organization and Self-Similarity in Boiling Systems

AbstractBoiling system is a typical open dissipative structure. Focusing on the investigation of boundary adjacent to heating plate surface in boiling system, nonlinear non-equilibrium statistical thermodynamics theory of open systems was originally constructed. The competitive bubble formation was realized by non-equilibrium phase transition caused by the interactions among active sites or bubbles. The “natural selection” among all possible sites was mathematically outlined. It was by the means of “natural selection” that a kind of self-organized and self-similar structure was formed. The present studies theoretically explained the experimental observations from other researchers, and gave more reasonable guidance of enhancing boiling heat transfer, such as by way of installing artificial cavities. Beyond the scope of boiling systems, the present studies not only have far-reaching theoretical implications on explaining time, life, thermodynamic, self-similar, fluctuation, order and chaos etc., but also can find many promising applications from new perspectives, such as wider industrial optimization, the recognitions of pattern and reproduction pattern of by computer etc.

Theoretical investigation on reactivity of singlet radical phosphinidene: reaction mechanism of its reacting with polar hydrogen chloride molecule

We have obtained two initial complexes (linear HPHCl and HPClH), and studied the reaction mechanism of singlet radical phosphinidene with polar hydrogen chloride molecule by ab initio molecular orbital theory at HF/6-31G(d), MP2(fc)/6-311+G(d,p) and G2 levels. Moreover, we have also calculated the thermodynamic and kinetic functions from 100 to 1100K in steps of 200K making use of the statistical thermodynamics and Eyring transition state theory with Wigner correction. It is concluded that there are two parallel reaction paths: Reaction A, an addition reaction which has the transition state (TS) formed by three-membered ring, has thermodynamic favor but does not have kinetic favor at low temperatures. However, it has both thermodynamic favor and kinetic favor at high temperatures comparing with Reaction B, a dehydrogenation reaction which has the TS formed by four-membered ring.

Hydration theory for molecular biophysics

Protein stabilization by the presence of water may in part be a manifestation of hydration water destabilizing the unfolded state. This chapter presents a molecular theory of hydration that highlights the role of water in protein stabilization. The focus is on potential distribution theorem whose physical basis and statistical thermodynamic framework with applications to protein solution thermodynamics and protein folding is discussed. The chapter also presents the derivation of an extension of the potential distribution theorem, the quasi-chemical theory, and proposes its implementation to the hydration of folded and unfolded proteins. The perspective and current optimism are justified by the understanding gained from successful applications of the potential distribution theorem to the hydration of simple solutes. The developments shown in the chapter illustrate a thoroughgoing reconstruction of molecular statistical thermodynamic theory of solutions. There are several motivations for this effort, but particularly, the conventional molecular theories are not compelling for biophysical applications and do not make strong connections to the molecular intuitions involved in consideration of simulation and experiment. Some of the discussion treats basic elements of statistical thermodynamics, known in specialized settings but weightier than is typical for this setting. The chapter includes examples to clarify and reinforce the basic concepts.

Relaxation Kinetics of Lipid Membranes and Its Relation to the Heat Capacity

We investigated the relaxation behavior of lipid membranes close to the chain-melting transition using pressure jump calorimetry with a temperature accuracy of ∼10 -3 K. We found relaxation times in the range from seconds up to about a minute, depending on vesicular state. The relaxation times are within error proportional to the heat capacity. We provide a statistical thermodynamics theory that rationalizes the close relation between heat capacity and relaxation times. It is based on our recent finding that enthalpy and volume changes close to the melting transition are proportional functions.

Thermodynamic and surface properties of liquid Mg–Zn alloys

A statistical thermodynamic theory, in conjunction with a complex formation model, was used to investigate the thermodynamic and surface properties of liquid Mg–Zn alloys. Our expressions reproduce the thermodynamic functions such as free energy of mixing and enthalpy of mixing. The study of concentration fluctuations in the long-wavelength limit ( S CC(0)) provides structural information about liquid Mg–Zn alloys. S CC(0) was further used to obtain the chemical short-range order parameter ( α 1) to quantify the degree of order. The study shows that Mg atoms cause a decrease of surface tension in Mg–Zn liquid alloys.

Reactivity of liquid crystals in the region of nematic — isotropic phase transition.

Abstract In the present paper a statistical-thermodynamic theory of nematic liquid crystals, developed by us on the basis of the fundamentals of statistical physics and chemical thermodynamics with the help of experimental data for the activation energy of the viscous flow of nematic and isotropic liquids is suggested. Using the theory and as an illustration a number of nematics from mesogenic molecules with chemically inactive groups in the terminal position, physical-chemical characteristics are obtained, which help to better revealing the mechanism of the viscous flow of liquid crystals in nematic and isotropic phases, their reactivity in such processes as a displacement of nematic-isotropic equilibrium taking place at phase transition, conformational changes of molecules establishing the composition of equilibrium subsystems and the time of their relaxation.

ChemInform Abstract: Rediscovering the Lattice-Fluid Theory for Phase Equilibria of Complex Mixtures

Various lattice statistical-thermodynamic theories after E. A. Guggenheim [Guggenheim, 1952] have been proposed with different assumptions on nonrandomness, the explicitness of the solution, and the model parameters. During the last decade, the present authors proposed a general approximation tool to the quasichemical solution of the nonrandom lattice-fluid combinatory and formulated a new rigorous EOS and the improved versions including the unified group contribution extensions and systems with strong association. In this study, developments of those EOSs are discussed with emphasis on the practical utility of each model.

Effect of three-body forces on the phase behavior of charged colloids

Statistical-thermodynamic theory for predicting the phase behavior of a colloidal solution requires the pair interaction potential between colloidal particles in solution. In practice, it is necessary to assume pairwise additivity for the potential of mean force between colloidal particles, but little is known concerning the validity of this assumption. This paper concerns interaction between small charged colloids, such as surfactant micelles or globular proteins, in electrolyte solutions and the multibody effect on phase behavior. Monte Carlo simulations for isolated colloidal triplets in equilateral configurations show that, while the three-body force is repulsive when the three particles are near contact, it becomes short-ranged attractive at further separations, contrary to a previous study where the triplet force is attractive at all separations. The three-body force arises mainly from hard-sphere collisions between colloids and small ions; it is most significant in solutions of monovalent salt at low concentration where charged colloids experience strong electrostatic interactions. To illustrate the effect of three-body forces on the phase behavior of charged colloids, we calculated the densities of coexisting phases using van der Waals-type theories for colloidal solutions and for crystals. For the conditions investigated in this work, even though the magnitude of the three-body force may be as large as 10% of the total force at small separations, three-body forces do not have a major effect on the densities of binary coexisting phases. However, coexisting densities calculated using Derjaguin–Landau–Verwey–Overbeek theory are much different from those calculated using our simulated potential of mean force.

Rediscovering the lattice-fluid theory for phase equilibria of complex mixtures

Various lattice statistical-thermodynamic theories after E. A. Guggenheim [Guggenheim, 1952] have been proposed with different assumptions on nonrandomness, the explicitness of the solution, and the model parameters. During the last decade, the present authors proposed a general approximation tool to the quasichemical solution of the nonrandom lattice-fluid combinatory and formulated a new rigorous EOS and the improved versions including the unified group contribution extensions and systems with strong association. In this study, developments of those EOSs are discussed with emphasis on the practical utility of each model.

THERMODYNAMIC ANALYSIS OF THE INTRINSIC STABILITY OF SUPERHEATED LIQUID IN A MICROMECHANICAL ACTUATOR WITH ELASTIC WALLS

The rise in internal pressure and or the increase in volume that results from heating of a liquid in a closed chamber can be used as a thermally driven actuator mechanism in MEMS components. The conditions at which phase instability and subsequent homogeneous nucleation occur in such systems is often of central importance, either because bubble formation is undesirable or because bubble formation is a desired part of the design behavior. This article examines the thermophysics of the onset of nucleation in a superheated liquid in a chamber with an elastic wall. Classical limits of thermodynamic intrinsic stability, which are usually derived for a system held at constant pressure, are not directly applicable to a system of this type. A model analysis is developed from the results of statistical thermodynamics theory and a Redlich-Kwong equation of state that can be used to predict the onset of nucleation in a liquid chamber with an elastic wall. The model predicts that the elastic modulus of the wall material together with the thermodynamic properties of the fluid dictate whether the thermodynamic limit of superheat will be reached during heating of liquid in the actuator chamber.

Compressibility factor for double Yukawa fluid

The long range atomic correlations through double Yukawa potential are subjected to statistical thermodynamic theory to obtain an analytical expression for the equation of state which is found to be valid over a wide range of temperature and pressure. This equation of state, which includes the softening of the hard sphere reference system and a realistic form of the distribution function, is used to calculate the deviation of the compressibility factor from the ideal condition in terms of repulsive and attractive forces.

Binding of Peripheral Proteins to Mixed Lipid Membranes: Effect of Lipid Demixing upon Binding

Binding isotherms have been determined for the association of horse heart cytochrome c with dioleoyl phosphatidylglycerol (DOPG)/dioleoyl phosphatidylcholine (DOPC) bilayer membranes over a range of lipid compositions and ionic strengths. In the absence of protein, the DOPG and DOPC lipids mix nearly ideally. The binding isotherms have been analyzed using double layer theory to account for the electrostatics, either the Van der Waals or scaled particle theory equation of state to describe the protein surface distribution, and a statistical thermodynamic formulation consistent with the mass-action law to describe the lipid distribution. Basic parameters governing the electrostatics and intrinsic binding are established from the binding to membranes composed of anionic lipid (DOPG) alone. Both the Van der Waals and scaled particle equations of state can describe the effects of protein distribution on the DOPG binding isotherms equally well, but with different values of the maximum binding stoichiometry (13 lipids/protein for Van der Waals and 8 lipids/protein for scaled particle theory). With these parameters set, it is then possible to derive the association constant, K r, of DOPG relative to DOPC for surface association with bound cytochrome c by using the binding isotherms obtained with the mixed lipid membranes. A value of K r (DOPG:DOPC) = 3.3–4.8, depending on the lipid stoichiometry, is determined that consistently describes the binding at different lipid compositions and different ionic strengths. Using the value of K r obtained it is possible to derive the average in-plane lipid distribution and the enhancement in protein binding induced by lipid redistribution using the statistical thermodynamic theory.

Viscous behavior of linear and three-branch alkanes: Linking the equilibrium and transport theories

A new model for zero-shear viscosity, η, is proposed. The model combines the Simha-Somcynsky (SS) statistical thermodynamic theory of liquids with the Eyring Significant Structure (ESS) transport theory. Using the new model, a successful linearization of the experimental viscosity vs. hole fraction data was obtained. A comparison between the new model and Utracki's relation, In η = α 0 + α 1 /(h + α 2 ) was also made. The former was found to be more successful for both linear and nonlinear structures, provided that an appropriate choice of the degrees of freedom of normal and activated states was made. The proportionality constant of the activation energy and transmission coefficient were also calculated for each species.

Solute excluded-volume effects on the stability of globular proteins: A statistical thermodynamic theory

A statistical thermodynamic theory is developed to investigate the effects of solute excluded volume on the stability of globular proteins. Proteins are modeled as two states in chemical equilibrium: the denatured state is modeled as a flexible chain of tangent hard spheres (pearl-necklace chain) while the native state is modeled as a single hard sphere. Study of model proteins bovine pancreatic trypsin inhibitor and lysozyme in a McMillan-Mayer model solution of hard spheres indicates that the excluded volume of solutes has three distinct types of effects on protein stability: (1) small-size solutes strongly denature proteins, (2) medium-size solutes stabilize proteins at low solute concentrations and destabilize them at high concentrations, and (3) large-size solutes stabilize native-state proteins across the whole liquid region. The study also finds that increasing the chain length of hard-chain polymer solutes has an effect on protein stability that is similar to increasing the diameter of spherical solutes. This work qualitatively explains why stabilizers tend to be large size molecules such as sugars, polymers, polynols, nonionic, and anionic surfactants while denaturants tend to be small size molecules such as alcohols, glycols, amides, formamides, ureas, and guanidium salts. Quantitative comparison between theoretical predictions and experimental results for folding free energy changes shows that the excluded-volume effect is at least as important as the binding and/or electrostatic effects on solute-assisted protein-denaturation processes. Our theory may also be able to explain the effect of excluded volume on the Φ condensation of DNA. © 1996 John Wiley & Sons, Inc.

A multilayer theory for interfacial properties of systems containing hydrogen bonding molecules

We propose a generalized, lattice-based statistical thermodynamic theory for understanding the interfacial phenomena in systems containing hydrogen bonding molecules (often termed as associating molecules), such as water, amphiphiles, block copolymers and associating solid surfaces. The basic assumption is that the configurational partition function (Q) can be factored into two parts: (i) one term [Q(phys)] arising from the presence of nonassociating, or the “physical,” interactions, for which we adopt the self-consistent-field theory [Scheutjens and Fleer, J. Phys. Chem. 84, 178 (1980)], (ii) the other term [Q(hbond)] arising from the presence of hydrogen bond interactions, for which we propose a new association theory. The focus of the proposed association theory is on the correct counting of the number of H bonds that are formed between various types of donor and acceptor sites that satisfy the proximity and orientational requirements for bond formation. The expression for Q(hbond) is evaluated by accounting for the entropic loss and energy released upon the formation of each hydrogen bond, and the transient nature of hydrogen bonds. The equilibrium criteria for H bonding is satisfied by minimizing the free energy of the system with respect to the number of H bonds formed between each type of donor site present in each layer z and each type of acceptor site present in each layer z′, where z′=z, or z±1. It turns out that the final expression for Q(hbond), at equilibrium, depends only on the fraction of unbonded association sites of all types that are located at various distances from the interface, which are themselves related to the equilibrium constant of formation of H bond between various donor-acceptor pairs, temperature of the fluid and the concentration profile in the interfacial region. For systems containing pure, spherical, associating molecules in the fluid phase, our expression for Q(hbond) is found to be identical to that of the density functional theory [Segura et al., Mol. Phys. 90, 759 (1997)], except for the inherent differences existing between continuum and lattice treatments. We present the results of the proposed theory in two parts. First, we verify the thermodynamic consistency of our approach with the Gibbs adsorption rule. Second, to clearly elucidate the role of hydrogen bonding on interfacial properties, we provide results for systems containing a binary fluid mixture, which comprises of an associating monomeric solvent and an amphiphilic, di-block, chain molecule, against an associating solid surface.

Nonequilibrium statistical thermodynamic theory for viscoelasticity of polymers

In this paper, we propose a new molecular relaxation mechanism for polymers by considering the change in the actual microscopic structure under macroscopic stress fields. The effects of both intramolecular and intermolecular forces on the inner rotation and the relative slippage of links are taken into account. A constraint potential function, along with a constraint tensor, is introduced to describe the constraint exerted by the surrounding medium. A unified three-dimensional constitutive framework for the viscoelasticity of polymers including thermal effects is established by making use of nonequilibrium statistical thermodynamics, which can be reduced to James and Guth's (1943) non-Gaussian polymer network theory for rubber elasticity. The model compares well with the experimental data for PMMA and plasticized PVC over a wide range of temperatures.