Configurational temperatures and interactions in charge-stabilized colloid

A system's temperature can be expressed in terms of its constituents' instantaneous positions rather than their momenta. Such configurational temperature definitions offer substantial benefits for experimental studies of soft condensed matter systems, most notably their applicability to overdamped systems whose instantaneous momenta may not be accessible. We demonstrate that the configurational temperature formalism can be derived from the classical hypervirial theorem, and introduce a hierarchy of hyperconfigurational temperature definitions, which are particularly well suited for experimental studies. We then use these analytical tools to probe the electrostatic interactions in monolayers of charge-stabilized colloidal spheres confined by parallel glass surfaces. The configurational and hyperconfigurational temperatures, together with a thermodynamic sum rule, provide previously lacking self-consistency tests for interaction measurements based on digital video microscopy, and thereby cast light on controversial reports of confinement-induced like-charge attractions. We further introduce a method to determine unknown parameters in a model potential by using consistency of the configurational and hyperconfigurational temperatures as a set of constraints. This approach, in principle, also should provide the basis for a model-free estimation of the pair potential.     

Configurational probabilities for symmetric dimers on a lattice: an analytical approximation with exact limits at low and high densities

A new approach is developed for lattice density functional theory of interacting symmetric dimers at high temperatures. Equations of equilibrium for two-dimensional square and three-dimensional cubic lattices are derived for the complete set of configurations in the first three shells around the central dimer, and rules of truncation for higher shells are based on exact results from the mathematical theory of domino tilings. This provides exact limits for both low and high densities. The new model predicts contributions of particular configurations which are in agreement with Monte Carlo simulations over the whole range of densities, including agreement with pocket Monte Carlo simulations at high densities.     

THE SPATIAL DISTRIBUTION AND MOMENTS OF CIRCULAR FREELY JOINTED CHAIN

The spatial distribution function and second moments of circular freely jointed chain are derived based on an analytical method. The circular Gauss chain, which is simple for long chains, is compared with the circular freely jointed chain, which is exact for short chains. It is shown that the Gauss chain model predicts a more compact configurational distribution than the exact freely jointed chain. The two chain models, however, become closer to each other when the chain length increases. It is found that the difference of the mean square radius of gyration calculated with these two chain models is a constant, independent of the chain length.     

Thermodynamics of symmetric dimers: lattice density functional theory predictions and simulations

A new lattice density functional theory (DFT) approach is proposed for symmetric dimers taking into account all possible configurations for molecules adjacent to a central dimer. Comparison with Monte Carlo simulations shows significant improvement of the proposed model compared to previously developed version of lattice DFT for dimers. It is shown that the new model gives accurate analytical solutions over a wide range of densities and temperatures. Phase transitions in dimers are analyzed and fundamental differences between dimers and monomers are discussed.     

A theoretical model for evaluation of configurational entropy of mixing with respect to shape and size of particles

A general method of evaluation of configurational entropy of a liquid mixture is presented. It is based on a generalized lattice model with no restrictions due to particle shape being introduced. A general formula for the entropy is derived. Achieved results open a way for a rigorous analysis of particle shape effect on mixing process. As an example, a new formula for the entropy of mixing of hard spheres in continuous space is derived which may respect a physical bound for packing ratio. A systematic approach to improve the model accuracy is proposed. The resultant alternative models are discussed in details. A comparison with literature data and the Mansoori-Carnahan-Starling formula is presented. Very good agreement is shown.     

Thermodynamic and orientational properties of two-dimensional multicomponent hard rectangle fluids

A molecular statistical model is developed for a two-dimensional multicomponent fluid composed of hard rectangles. The configurational partition function of such a system on a square lattice is evaluated by applying the orientation dependent version of the Flory-Huggins probability method. Unlike earlier treatments of similar problems, the final result for the configurational entropy is independent of the order of placement of the rectangular plate-like particles. The present approach has been extended to enable an analysis of both facewise and edgewise modes of adsorption of rectangular molecules on a planar surface. Further, the limit of infinitesimal lattice size has been considered as the generalized continuous version of the corresponding lattice model. The results obtained within the present continuous approach are compared with those of studies of related one-component hard body fluids.     

Thermodynamic and orientational properties of two-dimensional multicomponent hard rectangle fluids

A molecular statistical model is developed for a two-dimensional multicomponent fluid composed of hard rectangles. The configurational partition function of such a system on a square lattice is evaluated by applying the orientation dependent version of the Flory-Huggins probability method. Unlike earlier treatments of similar problems, the final result for the configurational entropy is independent of the order of placement of the rectangular plate-like particles. The present approach has been extended to enable an analysis of both facewise and edgewise modes of adsorption of rectangular molecules on a planar surface. Further, the limit of infinitesimal lattice size has been considered as the generalized continuous version of the corresponding lattice model. The results obtained within the present continuous approach are compared with those of studies of related one-component hard body fluids.     

Exact solution for the quasi-classical model of vibrational population inversion in exothermal exchange reactions

An exact solution is found for the quasi-classical model of population inversion in exothermal exchange reactions. The model is formulated using natural reaction coordinates and is based on the following assumptions: (1) The chemical systems under study should have a small parameter, namely, the product of the curvature of the reaction path by the classical amplitude of the transversal vibrational motion. (2) Classical turning points are absent within the interaction region for the vibrational levels involved in nonadiabatic transitions. An analytical expression is derived for the vibrational transition probabilities P_mn under these restrictions. In particular, for the transitions from a zero level and probabilities P_on form a two-parameter binomial distribution, whereas a more simple model devised by Hofacker and Levine results in a one-parameter Poisson distribution.     

A mean field analysis of the static dielectric behavior of linear lower alcohols

The static dielectric responses of methanol, ethanol, and 1-propanol up to 1-hexanol are discussed in terms of a stiff-chain lattice model for the alcohol clusters. An analytical expression for the Kirkwood correlation factor gK is derived in terms of the canonical partition function associated to the configurational statistics of any of the dimers building up a chain. This allows for the estimate of the dipole moment mu0 of an alcohol molecule in the liquid phase from the temperature dependence of the dielectric constant. All alcohol species appear to be characterized by a dipole moment larger than in the vapor phase. The Kirkwood correlation factor is found to be an increasing function of the alkyl tail length.     

玻璃化液体中构型熵与展宽弛豫函数关系的研究

The relationship between the transport properties and thermodynamic properties in glass forming liquids was investigated. The configurational entropy of Adam-Gibbs theory on cooperatively rearranging regions and the theoretic function derived from extremal value model were used to propose a brief that non-exponential stretched exponent in KWW form relaxation function is equal to the relative configurational entropy of cooperatively rearranging region in liquids, and is inversely proportional to the critical number of molecules occurring configurational transformation in a cooperatively rearranging region. Therefore, the new physical significance on glassy configuration is imposed on the stretched exponent, and theoretical developments and empirical correlations between the structural relaxation and configurational entropy are established. Further, an improved expression of β(T) was proposed to eliminate the deviation of the fit by using Vogel-Fulcher-Tammann equation from viscosity data at higher temperatures, which conforms well over 200 K temperature range. The improvement on β(T) is correspondent to the improvement on the difference in thermal capacities between isobaric and isochoric processes.     

Extended Veytsman statistics for the solid–fluid transition in the framework of lattice fluid

Lattice fluid can describe a vapor–liquid transition but not a solid–fluid transition. In this work, we propose a simple and analytic term which yields a solid–fluid transition when coupled with a lattice based equation of state (EOS). The proposed term is derived based on the two assumptions that (1) solid can be considered as highly associated phase affected by strong attractive force and (2) this force is distinct from the conventional attractive forces yielding a vapor–liquid transition. To formulate these assumptions, we extend Veytsman statistics by modifying its density dependency. The derived term was combined with a quasi-chemical nonrandom lattice fluid theory (QLF) developed by the authors. The combined model was found to require only two parameters besides 3 QLF parameters for physical properties calculation of three phases. When tested against equilibrium properties of 8 components, the combined model was found to closely reproduce melting pressure, sublimation pressure, and vapor pressure, but underestimate solid density as well as heat of melting at the triple point temperature. It was found that the present approach can yield a solid–liquid transition at all temperatures.     

Influence of small rings on the thermodynamics of equilibrium self-assembly

The competition between the formation of linear chain clusters and ring structures in an equilibrium self-assembling system is reexamined by developing a new Flory-Huggins type theory that combines an estimate for the loss of configurational entropy ΔS(ring) upon ring formation with the standard treatment of the free energy of a polydisperse solution of linear chains. The excess entropy of ring formation ΔS(ring) is obtained from an analytical fit to exact enumeration data for self-avoiding chains and rings with 30 or fewer steps on a cubic lattice. Illustrative calculations of the spinodal curves and the extent and the average degree of self-assembly highlight the physical conditions for which the cyclic structures impact the thermodynamic characterization of equilibrium self-assembling systems.     

Quantum approaches for the insertion dynamics of the H+ + D2 and D+ + H2 reactive collisions

The H(+)+D(2) and D(+)+H(2) reactive collisions are studied using a recently proposed adiabatic potential energy surface of spectroscopic accuracy. The dynamics is studied using an exact wave packet method on the adiabatic surface at energies below the curve crossing occurring at approximately 1.5 eV above the threshold. It is found that the reaction is very well described by a statistical quantum method for a zero total angular momentum (J) as compared with the exact ones, while for higher J some discrepancies are found. For J >0 different centrifugal sudden approximations are proposed and compared with the exact and statistical quantum treatments. The usual centrifugal sudden approach fails by considering too high reaction barriers and too low reaction probabilities. A new statistically modified centrifugal sudden approach is considered which corrects these two failures to a rather good extent. It is also found that an adiabatic approximation for the helicities provides results in very good agreement with the statistical method, placing the reaction barrier properly. However, both statistical and adiabatic centrifugal treatments overestimate the reaction probabilities. The reaction cross sections thus obtained with the new approaches are in rather good agreement with the exact results. In spite of these deficiencies, the quantum statistical method is well adapted for describing the insertion dynamics, and it is then used to evaluate the differential cross sections.     

The role of memory effects in scholastics approach to collinear diatom—diatom collisions

The role of memory effects in the stochastic approach to vibrational—vibrational transitions in collinear diatom—diatom collisions is studied. It is shown that with the help of a new recurrence relation for Clebsch—Gordan coefficients we were able to solve exactly a non-markovian master equation for a model hamiltonian. The derived solution for probabilities of V—V transitions is compared with markovian as well as exact semiclassical results over a wide range of velocities of the colliding molecules. We have found a substantial improvement of markovian results, both qualitative and quantitative, when the non-markovian effects have been included in the stochastic theory. This is in contrast with a recent study by King and Schatz who got for a restricted V—T model more accurate probabilities from the markovian approach than from the non-markovian one. The reasons for this are also discussed.     

端基附壁模型聚合物环形链的构象统计理论

环形链定义为两个端基均附壁的线形聚合物链所得的环 .采用精确计数和蒙特卡罗模拟方法 ,研究了自回避行走 (SAW)模型表示的环形链的构象 ,求得构象数和均方回转半径随链长的变化 .对于二维和三维SAW环形链 ,精确计数的最大链长分别为N =2 9和 1 9.用标度理论处理了数值结果 ,所得的标度指数和其他参数与理论预示值进行了比较 .模拟结果表明 ,SAW环形链限制壁平行方向的尺寸大于垂直方向的尺寸 ,与SAW尾形链尺寸的变化正好相反 .     

Lattice Monte Carlo simulations of three-dimensional charged polymer chains. II. Added salt

The configurational properties of strongly charged polyelectrolytes accompanied by counterions and salt ions in dilute solutions are simulated using the cooperative motion algorithm on the face-centered-cubic lattice. The calculations indicate that both positive and negative ions condense on the chains at sufficiently low temperatures and their amount depends on the concentration of added salt. As the temperature decreases from high to low, the chains undergo conformational changes from neutral-like, self-avoiding polymers by more outstretched forms to compact globules. The observed extension of the chains at intermediate temperatures is also affected by the amount of salt. Furthermore, configurations with the lowest energies recorded at the lowest temperatures are aggregates of single or more entangled chains and ions of both types.     

A quantum-classical treatment of non-adiabatic transitions

We have carried out molecular dynamics simulations of non-adiabatic processes with the help of a newly formulated potentially exact quantum-classical approach derived from a method proposed earlier [J. Chem. Phys. 118 (2003) 5302]. In this method, time-dependent Schroedinger equation is solved by representing Ψ on a moving Gauss–Hermite DVR grid, the motion of grid-centre being handled classically, but self consistently with the quantum evolution of the wavefunction. Electronic transitions are allowed anywhere in the configuration space among any number of coupled states. We have tested the method on three model problems proposed by J.C. Tully [J. Chem. Phys. 93 (1990) 1061]. These models are relevant to a wide range of gas-phase and condensed-phase phenomena occurring even at low energies. Excellent agreement of computed transition probabilities with corresponding quantum mechanical (DVR/FFT) results even in the deep quantum regime and its cost-efficiency (computational) are encouraging.