Stochastic Theory of Discrete Binary Fragmentation—Kinetics and Thermodynamics

We formulate binary fragmentation as a discrete stochastic process in which an integer mass k splits into two integer fragments j, k−j, with rate proportional to the fragmentation kernel Fj,k−j. We construct the ensemble of all distributions that can form in fixed number of steps from initial mass M and obtain their probabilities in terms of the fragmentation kernel. We obtain its partition function, the mean distribution and its evolution in time, and determine its stability using standard thermodynamic tools. We show that shattering is a phase transition that takes place when the stability conditions of the partition function are violated. We further discuss the close analogy between shattering and gelation, and between fragmentation and aggregation in general.     

Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice

This is a general and exact study of multiple Hamiltonian walks (HAW) filling the two-dimensional (2D) Manhattan lattice. We generalize the original exact solution for a single HAW by Kasteleyn to a system ofmultiple closed walks, aimed at modeling a polymer melt. In 2D, two basic nonequivalent topological situations are distinguished. (1) the Hamiltonian loops are allrooted andcontractible to a point:adjacent one to another, and, on a torus,homotopic to zero. (2) the loops can encircle one another and, on a torus, canwind around it. Forcase 1, the grand canonical partition function and multiple correlation functions are calculated exactly as those of multiple rooted spanningtrees or of a massive 2Dfree field, critical at zero mass (zero fugacity). The conformally invariant continuum limit on a Manhattantorus is studied in detail. The melt entropy is calculated exactly. We also consider the relevant effect of free boundary conditions. The number of single HAWs on Manhattan lattices with other perimeter shapes (rectangular, Kagomé, triangular, and arbitrary) is studied and related to the spectral theory of the Dirichlet Laplacian. This allows the calculation of exact shape-dependent configuration exponents y. An exact surface critical exponent is obtained. Forcase 2, nested and winding Hamiltonian circuits are allowed. An exact equivalence to thecritical Q-state Potts model exists, whereQ ^1/2 is the walk fugacity. The Hamiltonian system is then always critical (forQ<-4). The exact critical exponents, in infinite numbers, are universal and identical to those of theO(n=Q ^1/2) model in its low-temperature phase, i.e. are those of dense polymers. The exact critical partition functions on the torus are given from conformai invariance theory. These models 1 and 2 yield the two first exactly solved models of polymer melts.     

Partition Lattice q-Analogs Related to q-Stirling Numbers

We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be constructed using an interpretation of Milne [9] for S[n, k] as sequences of lines in a vector space over the Galois field F _q. Another member is constructed so as to mirror the partial order in the subspace lattice.     

Path bundles on n-cubes

A path bundle is a set of 2^a paths in an n-cube, denoted Q_n, such that every path has the same length, the paths partition the vertices of Q_n, the endpoints of the paths induce two subcubes of Q_n, and the endpoints of each path are complements. This paper shows that a path bundle exists if and only if n>0 is odd and 0?a?n-⌈log₂(n+1)⌉.     

Salting-out gradients in centrifugal partition chromatography for the isolation of chlorogenic acids from green coffee beans

In addition to sample solubility constraints, the use of polarity gradients in normal-phase centrifugal partition chromatography (CPC) for the purification of complex mixtures is also limited by the instability of biphasic systems as a consequence of dramatic changes in the settling times along the gradient, leading in many cases to column bleeding when working under maximum efficiency conditions. In this paper an electrostriction approach is proposed as a strategy in reversed-phase CPC to fractionate intermediate polarity extracts in a single run by bringing its components into the “sweet spot” in a controlled fashion through a stepwise reduction of salt concentration in the aqueous mobile phase. The salting-out gradient method was successfully tested with the separation of the major chlorogenic acids (CGAs, hydroxycinnamoylquinic acids) present in green coffee beans (5-caffeoylquinic acid (5-CQA), 5-feruloylquinic acid (5-FQA) and 3,5-dicaffeoylquinic acid (3,5-diCQA)) using ethyl acetate-hexane as the stationary phase and an ionic gradient of LiCl (5.0, 2.5 and 0.1 M) as the mobile phase in one case and (NH₄)₂SO₄/KNO₃ (3.0 and 1.5 M/1.5 M) in another. Regioisomers of each chlorogenic acid obtained by base-catalyzed isomerisation were also separated by CPC using isocratic elution. The best resolution for both FQAs and diCQAs was achieved with a chloroform–n-butanol–0.01 M pH 2.5 phosphate buffer (84:16:100; v/v) system, while CQAs were best isolated using chloroform–n-butanol–0.01 M pH 2.5 phosphate buffer/5.0 M LiCl (82:18:100; v/v).     

Gas–liquid partition coefficients and Henry's law constants of methyl mercaptan in aqueous solutions of Fe(II)–CDTA chelate complex

Utilization of ferric chelate complex of trans-1,2-cyclohexanediaminetetraacetic acid (CDTA) for the oxidative scrubbing of H₂S and CH₃SH in Kraft mill streams can be beneficial from the standpoints of iron protection against precipitation and oxygen-mediated regenerative oxidation of the ferrous chelate CDTA. The physical solubility of methyl mercaptan in CDTA–Fe(III) complex cannot be measured directly because of oxidation of the sulfur-bearing gaseous species with the ferric chelate. Therefore, this investigation was carried out to determine the gas–liquid partition coefficients and Henry's law constants of methyl mercaptan in aqueous iron-free CDTA solutions and non-reacting ferrous chelate solutions (CDTA–Fe(II) complex), using the static headspace method with an estimated accuracy of about 2%. Experiments with aqueous solutions of chelate concentrations varying between 38 and 300 mol m⁻³ were carried out at temperatures between 298 and 333 K and atmospheric pressure. It was shown that the methyl mercaptan solubility decreases with increasing temperature for all systems but was not much influenced, in the studied conditions, by the chelate concentration especially at larger temperatures.     

非线性Af—Bg型自由基交替共聚反应的固化理论

利用高分子反应统计理论,给出了非线性Ａｆ－Ｂｇ型自由基交替共聚反应的溶胶－凝胶分配方程和反应体系的凝凝胶化条件,这些结果是进一步研究与凝胶网络性能相关的网络结构参数的基础。     

COSMO-RS: A novel view to physiological solvation and partition questions

Both, dielectric continuum solvation models as well as surface or group based methods using polarity and lipophilicity parameters have been proven to be useful tools for the analysis of solvation and partition questions. For the first time, COSMO-RS provides an integrated theory, which combines the aspects of continuum solvation and surface interactions, and which ends up with chemical potentials of molecules in almost arbitrary solvents and mixtures. Due to its sound theoretical basis, COSMO-RS does not only provide a new quantitative access to solvation and partition properties in well defined solvents, but it also opens a novel view and gives a better understanding of the general problem of solvation. Finally, this allows for a generalisation of COSMO-RS to sophisticatedphysiological partition problems involving as complex phases as blood, brain, or cell membranes. The use of COSMO-RS for drug discovery and design is demonstrated by applications to blood-brain partition coefficients, and water solubility.     

Partition coefficients of methylated DNA bases obtained from free energy calculations with molecular electron density derived atomic charges

Partition coefficients serve in various areas as pharmacology and environmental sciences to predict the hydrophobicity of different substances. Recently, they have also been used to address the accuracy of force fields for various organic compounds and specifically the methylated DNA bases. In this study, atomic charges were derived by different partitioning methods (Hirshfeld and Minimal Basis Iterative Stockholder) directly from the electron density obtained by electronic structure calculations in a vacuum, with an implicit solvation model or with explicit solvation taking the dynamics of the solute and the solvent into account. To test the ability of these charges to describe electrostatic interactions in force fields for condensed phases, the original atomic charges of the AMBER99 force field were replaced with the new atomic charges and combined with different solvent models to obtain the hydration and chloroform solvation free energies by molecular dynamics simulations. Chloroform–water partition coefficients derived from the obtained free energies were compared to experimental and previously reported values obtained with the GAFF or the AMBER‐99 force field. The results show that good agreement with experimental data is obtained when the polarization of the electron density by the solvent has been taken into account, and when the energy needed to polarize the electron density of the solute has been considered in the transfer free energy. These results were further confirmed by hydration free energies of polar and aromatic amino acid side chain analogs. Comparison of the two partitioning methods, Hirshfeld‐I and Minimal Basis Iterative Stockholder (MBIS), revealed some deficiencies in the Hirshfeld‐I method related to the unstable isolated anionic nitrogen pro‐atom used in the method. Hydration free energies and partitioning coefficients obtained with atomic charges from the MBIS partitioning method accounting for polarization by the implicit solvation model are in good agreement with the experimental values. © 2018 Wiley Periodicals, Inc.