Transport properties of organic vapors in nanocomposites of isotactic polypropylene

Isotactic polypropylene nanocomposites were obtained by the melt blending of polypropylene‐graft‐maleic anhydride and organophilic layered silicate (OLS) consisting of synthetic fluorohectorite modified by cation exchange with protonated octadecylamine. The composition of the inorganic clay was varied between 2.5 and 10 wt %, and films of the composites were obtained via hot‐press molding. X‐ray analysis showed that nanocomposites in which silicate layers were either delaminated or ordered as in an intercalated structure were obtained. The elastic modulus of the samples was higher than that of the pure polymer over a wide temperature range and increased with increasing inorganic content. The transport properties, sorption and diffusion, were measured for two organic vapors, dichloromethane and n‐pentane. For both vapors, the sorption was not very different from that of the pure polymer, whereas the zero‐concentration diffusion parameter strongly decreased with increasing OLS content. Therefore, the permeability, that is, the product of sorption and diffusion, decreased for both vapors as a result of the decreased value of the diffusion parameter. The decrease was higher for the less interacting n‐pentane. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1798–1805, 2003     

关于Fejer算子的逼近度

用Ｋｎ记Ｆｅｊｅｒ算子的逼近度．本文证明是单调增加的，而且     

Unimodal and bimodal networks of poly(dimethyl-siloxane) in pure shear

Model networks of poly(dimethylsiloxane) (PDMS) were prepared by tetrafunctionally endlinking hydroxyl-terminated chains of various molecular weights. Some networks were prepared from mixtures of chains so as to yield a bimodal distribution of network chain lengths and, in some cases, these networks were prepared in solution. The stress–strain behavior of these unimodal and bimodal networks was studied in pure shear, which was imposed by stretching a sheet of the network having a large ratio of width to length in the direction perpendicular to the width. The pure-shear moduli of both types of networks generally were found to depend markedly on strain. Stress–strain isotherms for unimodal networks prepared from chains of one or the other of two molecular weights were well interpreted using the constrained-junction model of Flory and Erman. The bimodal networks showed large increases in the pure-shear modulus at high strains which were similar to those reported for uniaxial extension and compression. Endlinking in solution decreases the modulus in general and its upturn in particular, presumably because of diminished chain-junction entangling.     

Conductivity and the electric modulus in polymers

At relatively high temperatures and low frequencies the electrical properties of many polymers are dominated by ionic conductivity. In cases where the glass transition is obscured by conductivity, it can be revealed by treating the data in terms of the electric modulus. The magnitude of the activation energy for conductivity (24–67 kcal/mol) for Nylons 6, 66, and 6I, polybutylene terephthalate, and polycarbonate indicates that the transport of charged particles requires the motion of polymer segments.     

Bulk hydrosilylation reaction of poly(dimethylsiloxane) chains catalyzed by a platinum salt: Effect of the initial concentration of reactive groups on the final extent of reaction

Model silicone networks obtained by curing linear poly(dimethylsiloxane) (PDMS) chains with end‐vinyl groups, (B₂), with a polyfunctional silane‐terminated crosslinker of functionality f, (A_f), through a hydrosilylation reaction have been widely used. In these networks, the principal characteristics of their ultimate molecular structure are strongly affected by the final extent of reaction reached during the crosslinking reaction. This work analyzes the effect of the initial concentration of the reactive end groups on the maximum attainable extent of reaction under normal bulk crosslinking conditions. This was accomplished by examining the reaction between linear B₂ PDMS chains with difunctional and trifunctional silanes. The experimental results were fitted by an exponential equation to have an empirical equation able to predict the maximum extent of reaction to be obtained as a function of the initial concentration of reactive groups. Molecular parameters relevant to this study, such as the degree of polymerization, the weight‐average molecular weight for the A₂ + B₂ system, or the weight fraction of solubles for the A₃ + B₂ system, were calculated with a mean field theory (recursive approach). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1099–1106, 2003     

硅橡胶基磁敏弹性体制备及其压缩力学性能实验研究

为了探究影响磁敏弹性体压缩力学性能的因素,制备了4种不同磁敏颗粒含量以及磁敏颗粒随机分布、磁敏颗粒成链分布的磁弹体,在材料试验机的基础上附加磁学模块开发了一套力磁耦合测试系统,对磁弹体进行准静态压缩实验研究.实验结果表明:在磁场强度一定的情况下,磁敏颗粒含量越高的磁弹体压缩模量越大;磁敏颗粒含量相同的磁弹体的压缩模量随着实验磁场强度的增加而增加;磁敏颗粒成链分布的磁弹体的压缩模量随磁场强度增长的幅度大于磁敏颗粒随机分布的磁弹体的增长幅度.     

New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations

Some new sixth-order compact finite difference schemes for Poisson/Helmholtz equations on rectangular domains in both two- and three-dimensions are developed and analyzed. Different from a few sixth-order compact finite difference schemes in the literature, the finite difference and weight coefficients of the new methods have analytic simple expressions. One of the new ideas is to use a weighted combination of the source term at staggered grid points which is important for grid points near the boundary and avoids partial derivatives of the source term. Furthermore, the new compact schemes are exact for 2D and 3D Poisson equations if the solution is a polynomial less than or equal to 6. The coefficient matrices of the new schemes are $M$-matrices for Helmholtz equations with wave number $K≤0,$ which guarantee the discrete maximum principle and lead to the convergence of the new sixth-order compact schemes. Numerical examples in both 2D and 3D are presented to verify the effectiveness of the proposed schemes.     

Experiment investigation on effects of elastic modulus on cavitation erosion of silicone rubber

Research into cavitation phenomena in various fields shows that the elastic modulus of a boundary has a potential impact on cavitation erosion. To obtain the direct relationship between the elastic modulus of the boundary and cavitiation erosion, single-layer samples with different chemical composition and moduli, and double-layer samples with different elastic moduli and the same surface layer material, were prepared with silicone rubber. The results of cavitation experiments on single-layer samples, show that the coating chemical composition and mechanical properties together affect the cavitation morphology of the coating, and dominant factors vary with erosion stage. Through the cavitation test of double-layer samples, it was found that there is a positive correlation between the elastic modulus of the coating and the degree of cavitation. This study helps us to understand the relationship between coating elastic modulus and cavitation more directly, and provides theoretical and technical guidance for the application of anti-cavitation for elastic coating in engineering.     

Ill-posed problems in rheology

Experimental data are always noisy and often incomplete. This leads to ambiguities if one wants to infer from the data some functions, which are related to the measured quantity through an integral equation of the first kind. In rheology many of such so-called ill-posed problems appear. Two techniques to treat such problems, the regularization method and the maximum entropy method, are applied to the determination of the relaxation spectrum from data of small oscillatory shear flow. With simulated data from a reference spectrum it is discussed how the inferred spectrum depends on the region, in which data are available. It turns out that information about the asymptotic behavior of the measured quantity can be of great help in determining the full spectrum also from incomplete data.Dedicated to Prof. Dr. J. Meissner on the occasion of his 60th birthday.     

On the damping function of shear relaxation modulus for entangled polymers

Published data of the damping function of the shear relaxation modulus, h(), are reviewed. This is the ratio of the relaxation modulus measured at a finite magnitude of shear, , to that at the limit of = 0. Majority of the data are in accord with the universal function of the Doi-Edwards tube model theory, in which the damping or the decrease of h() is attributed to the contraction along the tube of extended polymer chains. The weaker damping seems to be attributed to 1) comb-branching such as in LDPE; 2) lack of entanglement in too short chains; 3) bimodal molecular weight distribution. However, a star-branching does not cause a deviation from the tube model theory and a broadness of molecular weight distribution is not a major origin of a weaker damping. A star-branched polystyrene with 15 arms exhibits no strain dependence: h() = 1. For highly entangled systems with more than 50 entanglement points per molecule, the strain dependence is stronger than that of the Doi-Edwards theory. This could be due to a slip or an instability of deformation in the material.