Recent developments in the kinetic theory of fracture of polymers

Summary The statistical and mechanical models underlying the kinetic theories of fracture of glasses, thermoplasts and rubbers are analyzed and specified for polymers in their glassy state. Special attention is given to results from recent electron resonance experiments, and to the elastic, anelastic and permanent deformation of a polymer before and during the experiment leading to failure. A model is constructed which is in accordance with the observed material behavior, and which consists of an elastic molecular network embedded in a viscoelastic continuum. On the basis of the specified conditions times-to-break are calculated as a function of applied load and degree of orientation of the polymer network. The calculated times-to-break are compared with experimental data.The extensibility of the theory to fracture of rubbers and to failure under multiaxial or time-dependent stress is discussed. A fracture criterion is proposed which may be called the kinetic version ofSt. Venant's criterion of maximum elastic strain, in which the critically of a state of stress is essentially determined by the components of normal stress and the ratio of two longitudinal elastic moduli, namely that of the molecular network and that of the sample as a whole.

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Zusammenfassung In der vorliegenden Arbeit werden die statistischen und mechanischen Modelle untersucht, die der kinetischen Theorie des Bruches von Gläsern, Thermoplasten und Gummi zu Grunde liegen. Dabei werden die für Hochpolymere im glasartigen Zustand zutreffenden Voraussetzungen angegeben. Die Ergebnisse jüngster ESR-Versuche und die elastische, anelastische und plastische Verformung des Polymeren werden besonders in Betracht gezogen. Ein mathematisches Modell des Festkörpers wird formuliert, das in Übereinstimmung mit den beobachteten Eigenschaften des Materials ist, und das aus einem elastischen Netzwerk besteht, eingebettet in eine viskoelastische Umgebung. Auf der Grundlage der angegebenen Bedingungen werden für einachsig belastete Proben Bruchzeiten als Funktion der Last und des Orientierungsgrades des polymeren Netzwerkes berechnet. Diese Bruchzeiten werden mit experimentell bestimmten Werten verglichen.Die Erweiterung des vorgelegten Modells auf den Bruch von Elastomeren und auf mehrachsige oder zeitabhängige Spannungszustände wird untersucht. Ein Bruchkriterium wird vorgeschlagen, das die Kinetische Version vonSt. Venant's Kriterium der größten elastischen Verformung genannt werden könnte. Darin wird die Bruchgefährlichkeit eines Spannungszustandes durch die größte Komponente der Normalspannung und das Verhältnis zweier elastischer Moduln bestimmt, nämlich das Verhältnis des Moduls eines Netzwerkfadens und des longitudinalen Moduls (in Orientierungsrichtung) der Probe insgesamt.

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With 4 figures in 5 details     

Mean-field kinetic nucleation theory

A new semiphenomenological model of homogeneous vapor-liquid nucleation is proposed in which the cluster kinetics follows the "kinetic approach to nucleation" and the thermodynamic part is based on the revised Fisher droplet model with the mean-field argument for the cluster configuration integral. The theory is nonperturbative in a cluster size and as such is valid for all clusters down to monomers. It contains two surface tensions: macroscopic (planar) and microscopic. The latter is a temperature dependent quantity related to the vapor compressibility factor at saturation. For Lennard-Jones fluids the microscopic surface tension possesses a universal behavior with the parameters found from the mean-field density functional calculations. The theory is verified against nucleation experiments for argon, nitrogen, water, and mercury, demonstrating very good agreement with experimental data. Classical nucleation theory fails to predict experimental results when a critical cluster becomes small.     

Recent developments in the theory of one- and two-electron molecules

Recent theoretical work dealing with one- and two-electron molecules is reviewed. Results obtained using both the variational method and the perturbation theory are discussed for the ground states as well as for excited states of the molecules. Emphasis is placed on those results which are sufficiently accurate to yield definite conclusions with regard to either the system or the method.     

Recent developments in non-enzymatic catalytic oxidative kinetic resolution of secondary alcohols

The goal of this review is to collect the recent developments in non-enzymatic catalytic oxidative kinetic resolutions of secondary alcohols reported since the beginning of 2011. It is divided into four sections, dealing successively with manganese-catalysed oxidative kinetic resolutions of secondary alcohols, palladium-catalysed oxidative kinetic resolutions of secondary alcohols, oxidative kinetic resolutions of secondary alcohols catalysed by other metals and organocatalysed oxidative kinetic resolutions of secondary alcohols.     

Diffusion of single elements and steric limitations in kinetic theory of nucleation and crystallization

Translational and rotational diffusion equation of single elements in solution in the external orienting potential forces has been formulated. The equation should govern long-range diffusion effects in the kinetics of nucleation and crystal growth. Boundary conditions, adequate to the reversible reaction of cluster growth typical for kinetic model of nucleation and accounting for steric limitations, has been proposed. Uniaxial single elements in uniaxial orienting force field are considered.Depression of the concentration of single elements at the cluster boundary as controlled by kinetic factors, is predicted i. e., chemical rate constants, finite translational and rotational diffusion, supercolling, and steric limitations. Effective rate constants, controlled by long-range diffusion of single elements at steric limitations present, have been used. Two dimensionless kinetic factors (i. e., reduced addition-reaction rate constant and reduced rotational diffusion constant), supercooling, and steric tolerance anlge range, control process kinetics and distribution of single elements in the cluster's surroundings. Rate reduction factor responsible for the effects of long-range diffusion at steric limitations present is defined and applied for kinetic models of nucleation and crystal growth in unoriented and oriented systems.Computation examples are performed for a wide range of the model variables, and rate reduction effects of several orders of magnitude are predicted. The dominating role ranges of particular model variables, i. e., kinetic, thermodynamic, or steric variables, are discussed.     

A kinetic approach to the theory of heterogeneous nucleation on soluble particles during the deliquescence stage

Deliquescence is the dissolution of a solid nucleus in a liquid film formed on the nucleus due to vapor condensation. Previously, the kinetics of deliquescence was examined in the framework of the capillarity approximation which involves the thermodynamic interfacial tensions for a thin film and the approximation of uniform density therein. In the present paper we propose a kinetic approach to the theory of deliquescence which avoids the use of the above macroscopic quantities for thin films. The rates of emission of molecules from the liquid film into the vapor and from the solid core into the liquid film are determined through a first passage time analysis whereas the respective rates of absorption are calculated through the gas kinetic theory. The first passage time is obtained by solving the single-molecule master equation for the probability distribution of a "surface" molecule moving in a potential field created by the cluster. Furthermore, the time evolution of the liquid film around the solid core is described by means of two mass balance equations which involve the rates of absorption and emission of molecules by the film at its two interfaces. When the deliquescence of an ensemble of solid particles occurs by means of large fluctuations, the time evolution of the distribution of composite droplets (liquid film+solid core) with respect to the independent variables of state is governed by a Fokker-Planck kinetic equation. When both the vapor and the solid soluble particles are single component, this equation has the form of the kinetic equation of binary nucleation. A steady-state solution for this equation is obtained by the method of separation of variables. The theory is illustrated with numerical calculation regarding the deliquescence of spherical particles in a water vapor with intermolecular interactions of the Lennard-Jones kind. The new approach allows one to qualitatively explain an important feature of experimental data on deliquescence, namely the occurrence of nonsharp deliquescence, a feature that the previous deliquescence theory based on classical thermodynamics could not account for.     

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.     

Recent developments in radioimmunoassay

Recent developments in the radioimmunoassay of steroid and peptide hormones are discussed. The modern requirement for the rigorous demonstration and maintainance of accuracy is emphasized. The future of immunoassay in clinical chemistry is discussed with special reference to quality control and automation.     

Recent developments in isotachophoresis

This paper is summarizing the contributions to the analytical capillary isotachophoresis published during the period 1981-1984. It characterizes the present state of the method and covers theory, fundamental analytical aspects, instrumentation and applications. Special attention was payed to the fundamental analytical aspects, and a detailed discussion is given of the selection of electrolyte systems, stability of zones and separability of substances. The present commercial instrumentation is also briefly described.     

Recent developments in the chemistry of azaferrocenes

The simplest heteroferrocene, azaferrocene, was first described in 1964, and until recently, the chemistry of these compounds has remained largely unexplored. This review will focus on recent advances in the chemistry of azaferrocenes including methods of azaferrocene synthesis and functionalization. The electrochemical behavior of azaferrocenes and their applications in catalysis and biology will also be emphasized here.     

Recent developments in the characterisation of microemulsions

Microemulsions are becoming increasingly complex systems by containing more sophisticated surfactants, polymers, biomolecules, inorganic nanoparticles, etc. The detailed understanding of such more complex systems requires increasingly more refined and comprehensive characterisation. This is typically done by the combination of complementary techniques and is aided by the fact that several experimental methods have been improved (such as electron microscopy) in recent times, new ones have become available (such as fluorescence correlation spectroscopy), and the theoretical understanding of structural data is advancing.     

动力学拆分法的研究进展

综述了光活性化合物动力学拆分法的研究进展及其在不对称合成中的应用。