Thermomechanical method for determining the molecular weights of amorphous linear polymers

A thermomechanical investigation of polyisobutylene specimens under various time and stress conditions enabled us to extend the applicability of this method of determining the molecular weight of an undissolved polymer. The previously proposed mechanical model of a polymer, which is the basis of the relationship between the molecular weight of the polymer and the difference between the yield and glass-transition temperatures, must be refined to make allowance for the supramolecular structure.Mekhanika Polimerov, Vol. 3, No. 4, pp. 586–590, 1967     

Effect of polymer molecular weight on its reaction with nonporous and porous fillers

The effect of polymer molecular weight (using polyethylene and polyisobutylene) on the formation of polymer contact with the surface of porous and nonporous fillers has been studied. It has been shown that the extent of coating of a nonporous surface by polymer does not depend on polymer molecular weight, but the extent of coating of a porous surface is larger, the lower the molecular weight of the polymer; this is explained by a selective adsorption of macromolecules of lower molecular weight on the porous filler from the polymer melt.     

A Bailey Tree for Integrals

We introduce the notion of integral Bailey pairs. Using the single-variable elliptic beta integral, we construct an infinite binary tree of identities for elliptic hypergeometric integrals. Two particular sequences of identities are described explicitly.     

Scale effect in polyethylene

The influence of the scale effect on the life of high-density polyethylene specimens with a surface notch has been investigated. In making the notches the condition of geometric similarity was observed. It was established that the life is affected only by sharp notches; as the cross section of the specimen decreases, the value of the Bailey integral increases exponentially.     

Effect of the molecular weight of polystyrene on the viscosity of concentrated solutions

The viscosity of solutions of polystyrene of various molecular weights (from 1.04 · 10² to 3.8 · 10⁵) in a poor solvent (decalin) and a good solvent (ethylbenzene) has been measured at temperatures from 15 to 70°C over a broad range of shear stresses from 10² to 10⁶ dyne/cm². The nature of the solvent has a considerable influence on the critical molecular weight and the absolute value of the viscosities of the solutions over the entire range of molecular weights and on the form of the flow curves of decalin solutions of polystyrene as a function of temperature. The heat of activation of viscous flow increases with increase in molecular weight and shear stress on the interval 20–80°C. The results obtained are explained in terms of the effect of the molecular weight of the polymer, the nature of the solvent, stress and temperature on structure formation in the solution and on the orientation of the macromolecules and structures in the flow process.Ural Gor'kii State University, Sverdlovsk. Translated from Mekhanika Polimerov, No. 5, pp. 920–926, September–October, 1970.     

Velocity and pressure distribution in the gap of a disk extruder

The axisymmetric two-dimensional flow of a polymer melt in the plane gap of a disk extruder produced by the normal stress effect is considered. The polymer is assumed to be a nonlinear viscoelastic medium, whose strain history is expressed by means of kinematic matrices. A rheological equation of state of the medium, in which all the invariants of the kinematic matrices are function of strain rate intensity, is established. The laws of distribution of the radial and tangential velocity components over the gap are found from the solution of the equations of motion, and expressions are obtained for the radial pressure distribution and the integral thrust.Volgograd Polytechnic Institute. Translated from Mekhanika Polimerov, No. 3, pp. 515–521, May–June, 1971.     

The role of diffusion of aggressive media in the fracture of rubber under stress

Formulas expressing the time to rupture of rubbers in aggressive media were derived in terms of the rate of diffusion of these media and the rate of displacement of the leading boundary of the cracking zone. The effect of increasing stress (due to a reduction in the load-carrying capacity of the specimen cross section) on the long-time strength (according to the Bailey principle) was taken into account in these calculations. The calculated and experimental data are in satisfactory agreement when there is a destructive action of working media in the absence of overstressing due to crack formation and swelling.Mekhanika Polimerov, Vol. 3, No. 4, pp. 708–712, 1967     

Multi-Level Monte Carlo Path Integral Molecular Dynamics for Thermal Average Calculation in the Nonadiabatic Regime

With the path integral approach, the thermal average in multi-electronic-state quantum systems can be approximated by the ring polymer representation on an extended configuration space, where the additional degrees of freedom are associated with the surface index of each bead. The primary goal of this work is to propose a more efficient sampling algorithm for the calculation of such thermal averages. We reformulate the extended ring polymer approximation according to the configurations of the surface indexes, and by introducing a proper reference measure, the reformulation is recast as a ratio of two expectations of function expansions. By quantitatively estimating the sub-estimators, and minimizing the total variance of the sampled average, we propose a multi-level Monte Carlo path integral molecular dynamics method (MLMC-PIMD) to achieve an optimal balance of computational cost and accuracy.     

Numerical solution of a singular integral equation arising in a cruciform crack problem

A singular integral equation arising in a cruciform crack problem is investigated in the present paper. Based on the convex technique, the piecewise Taylor-series expansion method is extended by introducing a weight parameter. An approximate solution of the singular integral equation is constructed and its convergence and error estimate are made. The variations of the approximate solutions associating with stress intensity factors are analyzed by considering internal pressures of power and sine functions, respectively. By comparing with the known methods, the observations reveal that a good approximation can be achieved using less derivative times, less discretization points, and a suitable weight parameter. The obtained results show that the crack growth is dependent on applied mechanical loadings.     

变直径串联喷嘴内流特性研究

喷嘴在分层注入过程中起到调节聚合物分子量和压力损失的作用,而多级喷嘴的结构,由于分子链的逐级剪切作用,可在保证注入粘度的同时,更大的减小压力的损失.在此基础上提出变直径多级喷嘴的几何结构,利用Fluent数值模拟软件,对单级喷嘴、等直径多级喷嘴进行数值模拟,分析不同结构喷嘴对三元复合溶液速度、压力、湍动能以及平均应变速率的影响,结果表明随着流量的增大,三种结构喷嘴的压力损失和平均应变速率均增大,合理的变直径串联喷嘴可以达到与等直径串联喷嘴相同的注入效果,同时尺寸较小,方便工程应用.     

Effect of molecular weight on strength and deformation characteristics of oriented amorphous polymers

Tensile tests were carried out on uniaxially oriented films of several amorphous linear polymers (polymethyl methacrylate, polystyrene, and poly-2,2-octamethylene-5,5-dibenzimidazol) of various molecular weights. It was shown that molecular weight has no direct effect on polymer strength, which is determined by structure. However, when polymer fibers and films are formed and stretched, the molecular weight of a given material affects the orientation of macromolecules and so predetermines the structure of the products obtained and, consequently, their strength.Mekhanika Polimerov, Vol. 3, No. 4, pp. 579–585, 1967     

含有直线状裂纹正交异性板的平面问题的应力函数

本文的解析对象为含有一与主轴呈任意角度直线状裂纹的无限大正交异性板的平面问题.采用加权积分法导出了能够表现裂纹尖端附近有限应力集中特征的应力函数.这样的计算模型消除了裂纹尖端的奇异性,可以比较真实地反映非金属材料微裂区的力学行为.     

Generalized criterion of the long-term strength of viscoelastic materials

A long-term strength condition of the same type as the Il'yushin [2] or Moskvitin [1] nonlinear criterion is proposed. A method is suggested for determining the stress and time functions forming part of the proposed criterion from the long-term strength diagrams and from the data of pulsed or stepped loading tests. It is shown, on the basis of the experimental data, that the proposed criterion, which in a particular case is identical with the Moskovitin criterion, describes the experimental results better than the Bailey criterion.     

圆内平面弹性问题的边界积分公式

根据双解析函数可以得到单位圆内平面弹性问题应力函数的边界积分公式,但式中包含强奇异积分,不能用于直接计算．将边界上的应力函数展开为Fourier级数,再利用广义函数论中的几个公式进行卷积计算,可以得到不含强奇异积分核的边界积分公式,通过边界的应力函数值和法向导数的积分,直接得到圆内应力函数值,并给出几个算例,表明该结果用于求解单位圆内平面弹性问题十分方便．     

An infrared spectroscopic study of the breakdown of polymers under load

It has been found that when a uniaxial tension is applied to highly oriented polymer films of polypropylene, polyvinyl alcohol, or polyethylene, an increase in the intensity of the absorption bands corresponding to the vibrations of the C=O carbonyl groups is observed. These groups are produced by the oxidation of the free radicals formed on the rupture of the chemical bonds under the influence of mechanical stress. The composition of the products has been studied, and their concentration has been estimated. Curves giving the accumulation of C=O groups with time at constant load and with increase in stress for a fixed period of time under load have been studied. It is suggested that the rate of accumulation of C=O groups in both cases is determined chiefly by the rate of rupture of the molecular chains under load.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 433–436, May–June 1970.     

Macromolecular mechanics

The fundamentals of "macromolecular" mechanics are outlined and approximate quantitative relations are established between the parameters of the mechanical properties of elastically stretched macromolecules and the characteristics of the mechanical properties of polymers determined at significant uniaxial deformations. This new scientific approach is based on the assumption of "framework connectivity." The conditions of internally compensated mechanical equilibrium at the molecular level are investigated. Several variants of simple geometric models of the "framework" reinforcing the stretched polymer are proposed. A system of quantities characterizing the mechanical properties of the polymer and the "framework" is developed. According to the theory, the stress in the "framework" macromolecules, considered as a molecular elastic continuum, substantially exceeds the stress in the stretched polymer. The nature of the internal stresses and elastic aftereffect in glassy crystalline polymers subjected to significant deformation is reinterpreted.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 221–231, March–April, 1971.     

The effect of ultraviolet radiation on the stress relaxation rate of polymers

The effect of UV radiation on the stress relaxation rate for four different polymers was investigated. A reversible increase in the stress relaxation rate was noted: the rate increased during irradiation and declined after its termination. It is assumed that this effect involves the rupture of stressed polymer macromolecules by the action of UV rays.Mekhanika Polimerov, Vol. 3, No. 4, pp. 615–618, 1967     

Control of biopolymer poly-β-hydroxybutyrate characteristics by γ-irradiation

The influence of γ-irradiation on the structure and some mechanical properties of poly-β-hydroxybutyrate was studied. Specimens of PHB were γ-irradiated with various doses (1–20 Mrad) in air and vacuum. The molecular weight, structural characteristics of the crystalline and amorphous phases, characteristics of thermal degradation, and deformation of the polymer were determined. The crystallinity was found to increase with increase in the radiation dose and with the corresponding reduction in molecular weight. The increase of crystallinity was the greater the smaller the length of macromolecules (higher radiation dose). The melting temperature T _m , which characterizes the crystalline order, decreased with decrease in the molecular weight. The results of calorimetric studies suggest that radiation-caused degradation, which occurs at a temperature at which “cold” crystallization (60°C) is possible, might also affect the crystalline part of the polymer.     

Shifted versions of the Bailey and Well-Poised Bailey lemmas

The Bailey lemma is a famous tool to prove Rogers–Ramanujan type identities. We use shifted versions of the Bailey lemma to derive m-versions of multisum Rogers–Ramanujan type identities. We also apply this method to the Well-Poised Bailey lemma and obtain a new extension of the Rogers–Ramanujan identities.     

Experimental study of the effect of laser beams on transparent dielectrics

The destruction of transparent polymer blocks by laser action is investigated. It is established that microscopic breakdown regions, whose size remains constant in time, are formed in the zone of action of the laser pulse. The intensity of the radiation from these microregions varies with time and corresponds to a temperature of (2–4) · 10³°K. The microregions are located near, but not at the centers of the cracks. The previously irradiated region of the polymer is shown to be in a state of stress. The possibility of thermal explosion with subsequent crack formation is evaluated. The continued development of the cracks as a result of repeated irradiation is studied. The temperature of the gas in the large cracks has been measured and found to exceed room temperature by 15°. The molecular weight has been measured before and after irradiation and found to decrease. The effect of laser beams of various wavelengths is considered. The rate of growth of the disk-shaped cracks has been measured.Institute of Problems of Mechanics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 827–835, September–October, 1969.