Theory of dielectric relaxations due to the interfacial polarization for two-component suspensions of spheres

A theoretical formula of dielectric relaxation in a form of complex relative permittivity is derived for dilute suspensions of spherical particles of two kinds on the basis of the Maxwell-Wagner theory of interfacial polarization. Another theoretical formula is derived further for concentrated suspensions of spheres of two kinds on condition that the formula derived above holds for the infinitesimally increasing process in concentration of the dispersed spheres. Furthermore a theoretical formula is derived for concentrated suspensions of shelled spheres of two kinds as the extension of the formula for concentrated suspensions. By use of the theoretical formulas proposed, values of the permittivities and the conductivities of the two-component suspensions were calculated for some examples with different sets of phase parameters. Results of the numerical calculation demonstrates dielectric relaxation profiles full of variety and characteristic of the suspensions containing two kinds of spheres covered with or without shells.     

浓差极化的介电模型——复合膜/溶液体系的数值模拟

提出了具有电导率和介电常数线性分布的介质的介电模型, 并导出了其内部电的和结构性质的参数与宏观测量的电容和电导之间定量关系的理论表达式, 以模拟复合膜中的多孔层部分的介电弛豫行为. 大量的模拟计算描述并解释了多孔层介电谱随介电常数分布、厚度等性质而变化的规律. 进一步对具有层状构造的复合膜以及复合膜和溶液相组成的多层体系的弛豫行为进行了数值模拟, 比较了三个体系(多孔层、复合膜、复合膜/液相层状体系)的介电谱, 结果揭示了介电谱对各层性质的依赖关系. 所提出的电导率和介电常数线性分布的多孔层的介电模型, 也可用于具有其他电导率、介电常数分布规律的体系.     

Diffusion of water and ethanol in ion-exchange membranes: limits of the geometric approach

Diffusion coefficients of water as a solvent and ethanol as a tracer in sulphonated polyethylene (SPE) were measured by the pulsed-gradient spin-echo NMR method. Comparison with the data available for a number of ionic and non-ionic polymers and solvents shows that, except for Nafion, all the materials exhibit a fairly universal dependence of diffusivity on the volume fraction of the solvent. This result is explained on the basis of the geometric obstruction approach and general conditions are formulated for the observed universal dependence. Explanations are proposed for the peculiar behaviour of Nafion and for the low diffusivity of ethanol within the same framework.     

Investigation of dielectric relaxations associated with the glass transition of vinylidene fluoride and trifluoroethylene copolymers by thermally stimulated current

Thermostimulated current (TSC) spectroscopy was applied to the characterization of dielectric relaxations associated with the glass transition of a series of P(VDF/TrFE) copolymers. The maximum temperature of the β-mode increases slightly as the TrFE unit content is increased, in the same manner as the glass transition temperature. By using the technique of fractional polarizations to the resolution of this relaxation mode, we have isolated, for all the polymers investigated, a series of elementary relaxation times that obey a compensation law. This behavior is characteristic of the free amorphous phase of polymers. The mean activation energy of this mode increases as the TrFE unit content is increased, due to a stiffening of molecular chains. Annealing of the copolymers above their ferroelectric-to-paraelectric transition induces a strong crystallinity increase of the materials. As a matter of fact, the amorphous phase is squeezed in to dimensions lower than the characteristic length scale associated with the glass transition. © 1995 John Wiley & Sons, Inc.     

Circuit simulation for the dielectric responses of the composites of copper phthalocyanine oligomers and sulfonated polyurethanes by separating the structural elements

The copper phthalocyanine (CuPc) oligomer with high dielectric constant was synthesized by the solution method. The FT‐IR and X‐ray diffraction results revealed its chemical structure. The high dielectric constant of CuPc was proved to result from the free movement of charge carriers along the conjugated orbitals. The composites of CuPc and sulfonated polyurethane (PUI) were prepared and the contents of CuPc in the composites were varied from 10 to 50 wt %. The dielectric performance was greatly enhanced for the composite compared with that of average polymers. Different from the behaviors appeared in a common composite with conductive fillers, there is no percolation phenomenon observed in the CuPc/PUI composite, and the dielectric constants of CuPc/PUI composites decreased with the increase in the CuPc content, which is assumed to due to the strong electrostatic interactions between CuPc and PUI. Considering the many‐body interactions within the bulk sample and the contact effect between the bulk sample and the metallic electrode, an equivalent circuit was established to simulate the dielectric behaviors of the composites and computational curve fitting was done. The results were in good agreement, indicating that the dielectric responses of the composites come from both the extrinsic and the intrinsic contributions. The extrinsic was associated with the Maxwell‐Wagner relaxation at the interface between the electrode and the bulk sample, and the intrinsic was associated with the huge dipoles provided by the mobile charges within the CuPc grains and the interaction among them in the bulk composites. A circuit model concerning the universal dielectric response was proposed in describing the intrinsic contribution, which quantitatively verified the strong interaction among the dipoles with the relaxation time, representing the aggregated structure of CuPc when its content was high in the composites. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1146–1155, 2009     

Poly(vinyl chloride)‐based miscible blends: Changes induced in the structural characteristics and in dielectric α relaxation of pure poly(vinyl chloride)

In this work we investigate by means of dielectric relaxation spectroscopy how segmental motions occurring in poly(vinyl chloride) (PVC) are modified by blending of PVC with small amounts of two different homopolymers: crystalline poly(ϵ‐caprolactone) (PCL) and glassy syndiotactic poly(methylmethacrylate) (sPMMA). The dynamics of the α relaxation of PVC is severely changed by blending it with PCL or sPMMA becoming faster or slower, respectively. Simultaneously, the shape of the relaxation function is being importantly altered. It shows a stronger non‐Debye character being broader and strongly temperature‐dependent. This fact leads us to calculate distributions of relaxation times for the blends that are wider in comparison to the one obtained for pure PVC. Complementary X‐ray diffraction measurements have been performed in order to assure the absence of crystallinity in the blends, and some small variations can be deduced at the level of interchain structural correlations of PVC. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 234–247, 2000     

Experimental design and modelling in the investigation of PECVD parameters effects on the structural and gas transport properties of plasma polysiloxane membranes

The experimental design method was used to investigate the PECVD parameters effects on the properties of plasma polysiloxane membranes synthesized using octamethylcyclotetrasiloxane or hexamethyldisiloxane as monomers. On a wide experimental range and with a minimum number of experiments, the use of such a statistical tool enabled us to set up complete and reliable correlations, in the form of polynomial models connecting the gas transport properties (H₂ permeability coefficient, H₂/N₂ ideal selectivity) and the structural properties (growth rate, density, organic/inorganic nature) of synthesized films with the two most influent synthesis parameters of the PECVD process: the input power (represented by the input voltage) and the monomer flux. The polynomial models enabled us not only to statistically confirm the effects of the PECVD parameters displayed by previous classical experimental studies, but also to model, in the mathematical sense, the evolution of each property of materials taking into account the first and second orders effects of both PECVD synthesis parameters. By the use of a performing statistical tool, we managed to improve the knowledge of relations between synthesis parameters/structure/properties relative to our process.     

Phase and structural transitions in vicinal water on protein surfaces by means of the DSC

This paper presents investigations of phase and structural transitions occurring in water adsorbed on the surface of bovine serum albumin (BSA) and on the so-called intelligentrs or smart silica gel surface covered with a chemically bonded BSA phase. Cyclic changes of heat flow (HF) were observed in the samples studied during cooling and heating of the measuring cell of the differential scanning calorimetry (DSC) apparatus. These cyclic changes reflect structural transitions occurring in the water adsorbed on the surface at subambient and elevated temperatures. This is connected with cyclic changes (decay and reproduction) of ice-like structures existing in the adsorbed water layers. On the basis of quantitative investigations it appears that, depending on the direction of the cooling or heating process of the samples studied, the number of ice-like water structures in the surface film increases or decreases. It has been stated that the observed fluctuations occur spontaneously and suddenly in the whole volume of adsorbed water in different and not regular temperature ranges, especially at the paradoxical effect temperatures.Support from the Research Council (Dr. R. K. Gilpin and Dr. M. Jaroniec) of Kent State University (Ohio, USA) is acknowledged. The author thanks Dr. V. Tittlebach for providing the samples of pure BSA and silica gel with chemically, bonded BSA phase.     

Variation of the pH of the background electrolyte due to electrode reactions in capillary electrophoresis: Theoretical approach and in situ measurement

Electrode reactions during the electrophoretic process may change the pH of the buffer and subsequently the migration behavior of solutes with resultant loss of reproducibility. A theoretical treatment of pH variations due to electrolytic processes is presented. The choice of buffer appears to have a dramatic influence on the pH variations observed, even if substantial buffer action is expected at the pH chosen. The experimental evaluation of the separation of 4-hydroxy-3-methoxycinnamic acid and 3-hydroxybenzoic acid reveals that the quality of the separation decreases continuously from a baseline separation observed in the first experiment to a comigration of the two solutes (resolution = 0) in the ninth experiment. A pH decrease of about 0.05 pH units accounts for the observed changes in mobility. A novel in situ pH measurement approach is presented, in which the mobility, peak area, and peak height of an indicator dye are related to the pH in the capillary. This enables the identification and quantification of pH variations during electrophoretic runs: the pH decreases at the anodic side already after the first experiment and pH variations as small as 0.02 pH units can be measured. The variations in peak height appear to be less suited. The calculated pH variations are in close agreement with the ones obtained experimentally.     

Comparison of ISO-GUM and Monte Carlo methods for the evaluation of measurement uncertainty: application to direct cadmium measurement in water by GFAAS

The propagation stage of uncertainty evaluation, known as the propagation of distributions, is in most cases approached by the GUM (Guide to the Expression of Uncertainty in Measurement) uncertainty framework which is based on the law of propagation of uncertainty assigned to various input quantities and the characterization of the measurand (output quantity) by a Gaussian or a t-distribution. Recently, a Supplement to the ISO-GUM was prepared by the JCGM (Joint Committee for Guides in Metrology). This Guide gives guidance on propagating probability distributions assigned to various input quantities through a numerical simulation (Monte Carlo Method) and determining a probability distribution for the measurand.In the present work the two approaches were used to estimate the uncertainty of the direct determination of cadmium in water by graphite furnace atomic absorption spectrometry (GFAAS). The expanded uncertainty results (at 95% confidence levels) obtained with the GUM Uncertainty Framework and the Monte Carlo Method at the concentration level of 3.01 μg/L were ±0.20 μg/L and ±0.18 μg/L, respectively. Thus, the GUM Uncertainty Framework slightly overestimates the overall uncertainty by 10%. Even after taking into account additional sources of uncertainty that the GUM Uncertainty Framework considers as negligible, the Monte Carlo gives again the same uncertainty result (±0.18 μg/L). The main source of this difference is the approximation used by the GUM Uncertainty Framework in estimating the standard uncertainty of the calibration curve produced by least squares regression. Although the GUM Uncertainty Framework proves to be adequate in this particular case, generally the Monte Carlo Method has features that avoid the assumptions and the limitations of the GUM Uncertainty Framework.