Computer generation of king and color polynomials of graphs and lattices and their applications to statistical mechanics

A computer program is developed in Pascal for the generation of king and color polynomials of graphs. The king polynomial was defined by Motoyama and Hosoya and was shown to be useful in dimer statistics, enumeration of Kekulé structures, etc. We show that the king polynomial of a lattice is the same as the color polynomial of the associated dualist graph, where the color polynomial is defined here as the number of ways of coloring the vertices of a graph with one type of color (say, green) such that two adjacent vertices are not colored with the same color. Applications of these polynomials to exact finite method of lattice statistics are outlined.     

Rheological Characterization of Computationally Synthesized Reactor Populations of Hyperbranched Macromolecules: Bivariate Seniority‐Priority Distribution of ldPE

Summary: Hyperbranched molecules like low‐density polyethylene (ldPE) adopt a huge variety of molecular architectures. Previous work has shown that it is possible to computationally synthesize these architectures and to characterize them according to radius of gyration. Here, a method is presented and applied on ldPE to characterize populations using rheological quantities in terms of comb‐shaped and Cayley tree structures. Interbranch segments are assigned seniority and priority values that quantify their behavior in relaxation and elastic deformation processes. New general‐purpose algorithms have been developed to derive the full bivariate seniority/priority distribution using a representation from the graph theory of branched architectures. This paper describes the computation of bivariate chain length/degree of branching distributions (CLD/DBD) using a Galerkin finite element method for two scission mechanisms: linear and topological scission. The DBD is calculated using pseudo‐distributions. Random scission is treated with fragment length and branch point redistribution functions as obtained from scission statistics of branched molecules, preferentially yielding short and long fragments. Reactor populations of ldPE architectures are then obtained using computational synthesis. The seniority and priority distributions calculated indeed prove to be an adequate characterization method. They show good comparison, although not a complete overlap, with size characterization using a variant of the radius of gyration. It was possible to calculate a full bivariate seniority/priority fraction distribution, but due to the limited sample size its surface was not smooth. Subsequent work has shown the consequences for the prediction of rheological properties.

Seniority/priority values for segments of molecules for one chain length/number of branch points combination.     

Surface Tension of the Vapor–Liquid Interface with Finite Curvature

Based on the division of particles into internal and surface particles, the expression is derived closing the system of equations of classical thermodynamics for curvature-dependent surface tension, equimolar radius, and radius of tension surface. A solution to this system allows one to find the surface tension of new phase nucleus of any size (including minimal) and any sign of surface curvature. The obtained results indicate the weak size dependence of thermodynamic parameters that are the functions of surface tension; it is shown that Tolman's length cannot be determined using experimental determination of these parameters. It is shown that the work of nucleus formation strongly depends on its size and is the function of effective rather than true surface tension. Numerical simulation of clusters by the molecular dynamics method indicates that the pressure inside a fairly small cluster is described by Laplace's formula with the coefficient of surface tension for the plane surface of a liquid that agrees with the proposed theory.     

Automated grain mapping using wide angle convergent beam electron diffraction in transmission electron microscope for nanomaterials

The grain size statistics, commonly derived from the grain map of a material sample, are important microstructure characteristics that greatly influence its properties. The grain map for nanomaterials is usually obtained manually by visual inspection of the transmission electron microscope (TEM) micrographs because automated methods do not perform satisfactorily. While the visual inspection method provides reliable results, it is a labor intensive process and is often prone to human errors. In this article, an automated grain mapping method is developed using TEM diffraction patterns. The presented method uses wide angle convergent beam diffraction in the TEM. The automated technique was applied on a platinum thin film sample to obtain the grain map and subsequently derive grain size statistics from it. The grain size statistics obtained with the automated method were found in good agreement with the visual inspection method.     

Enhanced thermal response of the SAd1 layer thickness in highly fluorinated thermotropic liquid crystals

X-ray studies of a homologous series of rod-shaped liquid crystal molecules with one tail perfluorinated and the other protonated, reveal large decreases in the smectic A layer spacing with increasing temperature. These materials form unique dimer phases in which the smectic layer spacing is dependent on the length of the perfluorinated tail and independent of the length of the protonated tail. The chain statistics of the perfluorinated tail significantly influence the thermal expansion coefficient since the length of the fluorinated tail defines the smectic layer spacing. Thermal expansion coefficients for the layer spacing observed here are negative and nearly an order of magnitude greater than for typical protonated rod-shaped thermotropic liquid crystals in the SA phase.     

Finite-Temperature Dimer Method for Finding Saddle Points on Free Energy Surfaces

The dimer method and its variants have been shown to be efficient in finding saddle points on potential surfaces. In the dimer method, the most unstable direction is approximately obtained by minimizing the total potential energy of the dimer. Then, the force in this direction is reversed to move the dimer toward saddle points. When the finite-temperature effect is important for a high-dimensional system, one usually needs to describe the dynamics in a low-dimensional space of reaction coordinates. In this case, transition states are collected as saddle points on the free energy surface. The traditional dimer method cannot be directly employed to find saddle points on a free energy surface since the surface is not known a priori. Here, we develop a finite-temperature dimer method for searching saddle points on the free energy surface. In this method, a constrained rotation dynamics of the dimer system is used to sample dimer directions and an efficient average method is used to obtain a good approximation of the most unstable direction. This approximated direction is then used in reversing the force component and evolving the dimer toward saddle points. Our numerical results suggest that the new method is efficient in finding saddle points on free energy surfaces. © 2019 Wiley Periodicals, Inc.     

Spectra of Husimi cacti: exact results and applications

Starting from exact relations for finite Husimi cacti we determine their complete spectra to very high accuracy. The Husimi cacti are dual structures to the dendrimers but, distinct from these, contain loops. Our solution makes use of a judicious analysis of the normal modes. Although close to those of dendrimers, the spectra of Husimi cacti differ. From the wealth of applications for measurable quantities which depend only on the spectra, we display for Husimi cacti the behavior of the fluorescence depolarization under quasiresonant Forster energy transfer.     

Intermolecular potentials with flexible monomers

Most available intermolecular potentials assume rigid monomers. Such an assumption is a reflection of a trivial observation that if monomer degrees of freedom are considered, the dimensionality of an intermolecular potential increases dramatically even for few-atom monomers. This puts strict limits on the sizes of clusters with flexible monomers that can be treated by ab initio methods since the number of grid points needed to fit a potential surface quickly becomes enormous. Most of the literature flexible-monomer potentials were obtained from the so-called site-site rigid-monomer potentials by simply allowing the sites to move with atomic nuclei as the monomers are deformed. This simple atom-following approach has been investigated in the present work, using water dimer and Ar-HF as test systems, and shown to be not adequate. A method has been proposed which uses properties of isolated flexible monomers to improve upon the atom-following approach without performing any dimer calculations outside the rigid-monomer grid. The method is shown to give for Ar-HF a 3D representation of the dispersion energy that should be adequate for HF motion in the ground and first excited vibrational states.     

Ring connectivity: measuring network connectivity in network covalent solids

In atomistic models of amorphous materials, ring statistics provide a measure of medium-range order. However, while ring statistics tell us the number of rings present in the model, they do not give us any information about the arrangement of rings, e.g., whether the rings are clustered and how big the cluster is. In this work we present a method to calculate the ring connectivity, or clustering, of rings. We first calculate the rings present in the model using the shortest path criteria of Franzblau and then find the rings that are connected together and group them into clusters. We apply our method to a set of models of disordered carbons, obtained using a reverse Monte Carlo procedure developed in a recent work. We found that in these carbon models the five-, six-, and seven-membered rings are connected together, forming clusters. After isolating the clusters, we found that they resemble defective graphene segments twisted in a complex way. The clusters give further insight about the arrangement of carbon atoms in microporous carbons at a larger length scale. Moreover, the method can be applied to any network covalent solid that contains rings and thus gives information about the ring connectivity present in such materials.     

End-evaporation dynamics revisited

We present analytical results on the so-called end-evaporation kinetics in equilibrium polymeric systems following a temperature jump (T jump). A T jump prepares the system with a nonequilibrium length distribution, after which it relaxes back to its equilibrium state. Starting from a master equation, we develop a mean-field analytical theory based on a generating function approach, which allows explicit approximate expressions for the monomer and dimer concentrations to be derived in a discrete setting; the concentrations of the other chains as well as the average chain length were shown to be entirely expressible in terms of the monomer and dimer concentrations. We find that the calculated monomer and dimer concentrations as well as the average chain length are in good agreement with numerical simulation results and do not suffer from some of the defects of earlier continuum theories. Furthermore, the relaxation was shown to take place in three different stages. The first stage comprises the very fast relaxation of the monomers to almost their equilibrium concentration; the other polymer chains have hardly relaxed. During the second stage, which is highly nonlinear, a redistribution of material at practically constant monomer density takes place. Only in the final stage of the relaxation process the chain concentrations approach their true equilibrium values. In this stage there are only very small shifts in the concentrations of chains, which are governed by extremely slow "indirect" monomer-mediated processes.     

Parallel isoelectric focusing II

A miniature electrophoretic device is developed on the basis of a new isoelectric focusing (IEF) method, namely parallel isoelectric focusing. We report here the theory and the results of operation of a new parallel isoelectric device (PID). The main advantages and limitations of the method are discussed for miniaturization purposes. It is shown that the method guarantees the fast and complete separation of any complex protein mixtures under acceptable conditions, such as voltage source, temperature, size of the device, and separation process duration. It is shown that the main problem of PID miniaturization is the buffer design, and the relation between Immobiline buffer capacity and solution buffer capacity. The main experimental limitation of PID resolution is protein sensitivity to pH changes.     

Selective chain reaction of acetone leading to the successive growth of mutually perpendicular molecular lines on the si(100)-(2 x 1)-H surface

The successive growth of mutually perpendicular molecular lines from one dangling-bond (DB) site on the Si(100)-(2 x 1)-H surface has been realized through a substrate-mediated chain reaction at 300 K. Among various molecules, acetone molecules undergo the most facile chain reaction with a DB site, which proceeds selectively on the Si(100)-(2 x 1)-H surface, resulting in only single molecular lines in the parallel-row (parallel to the dimer row) direction. The smaller size and higher reactivity of acetone molecules enable us to successively grow a parallel-row acetone line from the end of a cross-row (perpendicular to the dimer row) allylmercaptan line simply by changing the feed of gas molecules into the reaction chamber. Since the length of a molecular line is controlled by the number of gas molecules impinged, it is possible to turn a chain reaction from the cross-row direction to the parallel-row direction at any desired point on the surface. The reaction path of the adsorbing molecules is discussed. The present study provides a new means of fabricating mutually perpendicular molecular lines through a chain reaction initiating at a preselected DB site on the Si(100)-(2 x 1) surface.     

Circular dichroism and theoretical calculations of pinacyanol dimer inclusion in γ-cyclodextrin

Aggregation of pinacyanol chloride is strongly enhanced through inclusion into γ-cyclodextrin, which was studied using both UV/Visible, derivative and Circular Dichroism (CD) spectroscopy. The intensities at 546 and at 507 nm were increased with the growing ratio of γ-cyclodextrin to dye. Both aggregates were shown to be optically active. CD spectra with two and three oppositely signed excitonic bands were shown. The structures of the aggregates have been analysed and discussed in terms of qualitative H-type aggregation and quantitative based on OSCI program. Applying eight different parameter sets aggregates of pinacyanol chloride ranging in size from 2 to 20 dye molecules were considered. The calculated energy splitting was adjusted, via the transition dipole length, to the experimentally observed band shift. Rotational strengths associated with the CD absorptions were calculated and used to obtain an estimate of the inherent twist of the dimer aggregate inside the γ-cyclodextrin cavity.     

Quantum chemical semiempirical approach to the structural and thermodynamic characteristics of fluoroalkanols at the air/water interface

In the framework of quantum chemical PM3 approximation, the geometrical structure and thermodynamic functions characteristics of the formation of monomers (n = 1-14, 34), dimers (n = 1-14, 34), and trimers and tetramers (n = 1-8) of fluoroalkanols with the composition C(n)F(2)(n+1)CH(2)CH(2)OH are calculated. It is shown that, in contrast to the fatty alcohols, which have a flat zigzag structure, the fluoroalkanol monomers are helical with an average backbone torsion angle equal to 162 degrees. For the minimum-energy structure of dimers, the self-organization of the molecules in a dimer was observed; that leads to an opposite alternation of the torsion angles corresponding to the matching atoms in the two molecules that form the dimer. This results in the fact that the most stable conformation of the dimer is the double helix. The lead (39.5 A) and diameter (7.3 A) of the double helix are determined from the calculations of C(34)F(69)CH(2)CH(2)OH dimers. Enthalpy, entropy, and Gibbs energy of the clusterization are shown to be linearly dependent on the length of the fluorinated chain. From the analysis of these thermodynamic quantities, it is concluded that dimerization of fluoroalkanols at the air/water interface takes place if the hydrocarbon link number exceeds 6, whereas for ordinary alcohols this characteristic number is 11. These calculated values agree with experimental data. The additive scheme for the evaluation of the clusterization free energies for arbitrary clusters is developed and applied to obtain the estimate of the Gibbs clusterization energy for infinitely large clusters.     

基于格子链的缩聚反应的动态Monte Carlo模拟

采用描述自回避格子链的键长涨落模型, 以动态Monte Carlo方法对AB型单体的线型缩聚反应动力学过程进行了模拟. 通过该方法可以得到反应过程中链的瞬时构象, 还可以得到反应程度、聚合度、分子量分布及其随时间的演化. 模拟得到了合理的结果, 同时验证了无规线团尺寸与平均链长的标度关系, 表明该方法用于研究逐步聚合反应过程是可行的, 并且与一般的研究聚合反应的Monte Carlo方法相比, 还能够同时得到构象等空间信息. 还比较了不同大小的模拟体系所得到的分子量和多分散系数的异同, 讨论了有限元胞效应.     

光系统I（PSI）反应中心的激子耦合

运用点偶极、单极跃迁电荷和跃迁密度等经典库仑作用的方法,考察了叶绿素a分子间面心距和错位结构等因素对激子耦合的影响．结果表明,当分子间距大于分子尺寸时,上述三种方法得到的结果基本一致;但当分子间距小于分子尺寸时,点偶极方法将明显高估激子耦合,跃迁密度的方法更适合计算分子间的激子耦合．此外,还使用上述方法计算了光系统Ⅰ（PSI）反应中心叶绿素a分子间激子耦合．结果表明,用跃迁密度计算PSI晶体结构（1jb0．pdb）e700的激子耦合为75.3cm^-1,而QM．MM优化的结构P700（ecAl．ecBl）的激子耦合为23．8cm^-1,这与考虑Dexter交换项的全对角化方法的结果（20cm^-1）一致,进而说明PSI反应中心并不是传统的P700强激子耦合对,而是ecAl-ecB2和ecBl-ecA2对强耦合二聚体构成的二聚体对．     

On the performance of molecular polarization methods. II. Water and carbon tetrachloride close to a cation

Our initial study on the performance of molecular polarization methods close to a positive point charge [M. Masia, M. Probst, and R. Rey, J. Chem. Phys. 121, 7362 (2004)] is extended to the case in which a molecule interacts with a real cation. Two different methods (point dipoles and shell model) are applied to both the ion and the molecule. The results are tested against high-level ab initio calculations for a molecule (water or carbon tetrachloride) close to Li+, Na+, Mg2+, and Ca2+. The monitored observable is in all cases the dimer electric dipole as a function of the ion-molecule distance for selected molecular orientations. The moderate disagreement previously obtained for point charges at intermediate distances, and attributed to the linearity of current polarization methods (as opposed to the nonlinear effects evident in ab initio calculations), is confirmed for real cations as well. More importantly, it is found that at short separations the phenomenological polarization methods studied here substantially overestimate the dipole moment induced if the ion is described quantum chemically as well, in contrast to the dipole moment induced by a point-charge ion, for which they show a better degree of accord with ab initio results. Such behavior can be understood in terms of a decrease of atomic polarizabilities due to the repulsion between electronic charge distributions at contact separations. It is shown that a reparametrization of the Thole method for damping of the electric field, used in conjunction with any polarization scheme, allows to satisfactorily reproduce the dimer dipole at short distances. In contrast with the original approach (developed for intramolecular interactions), the present reparametrization is ion and method dependent, and corresponding parameters are given for each case.     

Development of many-body polarizable force fields for Li-battery components: 1. Ether, alkane, and carbonate-based solvents

Classical many-body polarizable force fields were developed for n-alkanes, perflouroalkanes, polyethers, ketones, and linear and cyclic carbonates on the basis of quantum chemistry dimer energies of model compounds and empirical thermodynamic liquid-state properties. The dependence of the electron correlation contribution to the dimer binding energy on basis-set size and level of theory was investigated as a function of molecular separation for a number of alkane, ether, and ketone dimers. Molecular dynamics (MD) simulations of the force fields accurately predicted structural, dynamic, and transport properties of liquids and unentangled polymer melts. On average, gas-phase dimer binding energies predicted with the force field were between those from MP2/aug-cc-pvDz and MP2/aug-cc-pvTz quantum chemistry calculations.     

On the inner structure and topology of clusters in two-component lipid bilayers. Comparison of monomer and dimer Ising models

It has been shown on model and biological systems that membrane clusters can affect in-plane membrane reactions and can control biochemical reaction cascades. Clusters of two-component phospholipid bilayers have been simulated by two Ising-type lattice models: the monomer and the dimer model. In each model the plane of one layer of the bilayer is represented by a triangular lattice, each site of which is occupied by an acyl chain of either a component 1 or a component 2 lipid molecule. The dimer model assumes that pairs of acyl chains (lipid molecules) are permanently connected, forming dimers on the lattice, while in the case of the monomer model this covalent connection between acyl chains is ignored. Phase diagrams of two-component phospholipid bilayers were successfully calculated by both models. In this work, we use Monte Carlo techniques to calculate thermodynamic averages of global and local characteristics of the largest component 2 cluster (such as outer/inner perimeter, percolation, minimal linear size, and local density) and compare the results obtained by the two models. A new method is developed to characterize the inner structure of the clusters. Each point of a cluster is classified based on its shortest distance (or depth) from the cluster's outer perimeter. Then local cluster properties, such as density, are calculated as a function of the depth. The depth analysis reveals that toward the cluster interior the average density usually decreases in midsize clusters and remains constant in very large clusters. On the basis of the simulations the following typical cluster topologies are identified at different cluster sizes and cooperativity parameter values: (i) branch-like, (ii) circular, (iii) band-like, and (iv) planar.We did not find qualitative differences between the cluster structures in the dimer and monomer model. However, at the same cluster size and cooperativity parameter value the cluster of the dimer model is more compact. The cluster properties of the dimer model are different from that of the monomer model because of the lower mixing entropy and higher formation energy of an elementary inner island.