Self- and mutual-diffusion coefficients in the dodecane/polystyrene system

The self-diffusion coefficient of dodecane in cross-linked polystyrene was measured using pulsed gradient spin echo nuclear magnetic resonance (PGSE–NMR) spectroscopy. The concentration and temperature dependence of the diffusion coefficient was analyzed by the Fujita and Vrentas–Duda models. Parameters describing the Fujita model were determined from fitting of diffusion data to the PVT behavior of the system. Parameters describing the Vrentas–Duda model were determined from the analysis of the viscosity of dodecane, the viscoelastic relaxation properties, and the glass transition temperature of polystyrene as well as from the diffusion coefficient of the system, measured from independent experiments. Both the Fujita and Vrentas–Duda models described well the concentration and temperature dependence of the diffusion coefficient. Mutual diffusion coefficients were determined from these results. © 1994 John Wiley & Sons, Inc.     

Numerical simulation of bubble growth in viscoelastic fluid with diffusion of dissolved foaming agent

Viscoelastic simulations of bubble growth in polypropylene (PP) physical foaming were performed. A multimode Phan‐Thien Tanner (PTT) model was used to analyze the dynamic growth behavior of spherically symmetric bubbles with the diffusion of a foaming agent (CO₂). Changes in the dissolved foaming agent concentration in the polymer and in the strain of the polymer melt surrounding the bubbles were simulated with the Lagrangian FEM method. The simulation technique was validated by comparison with the bubble growth data, which were experimentally obtained from visual observations of the PP/CO₂ batch foaming system. The simulation results demonstrated that the strain‐hardening characteristic of polymer does not strongly affect the bubble growth rate. The linear viscoelastic characteristic is more influential, and the relaxation mode around 0.01 s is the most important factor in determining the bubble growth rate during the early stage of foaming. A multivariate analysis for the simulation results was also carried out. This clarified that bubble nucleus population density, surrounding pressure, initial dissolved foaming agent concentration, and diffusion coefficient are more important factors than the viscoelastic characteristics. POLYM. ENG. SCI., 45:1277–1287, 2005. © 2005 Society of Plastics Engineers     

Diffusivity and solubility of organic vapors in modified polyethylene films. I. Technique and analysis of results

A new method of analyzing unsteady-state sorption data was developed to determine the diffusivity and solubility of vapors in polymer films. The equilibrium weight increase yields the solubility directly. Analysis of the unsteady-state data gives the diffusion coefficient and its concentration dependence. A complete method for the analysis of either absorption or desorption results is presented for any type of concentration dependence of the diffusion coefficient. In this paper the method is applied to the Fujita free volume theory. The apparatus and the experimental procedures are discussed in detail.     

Relation between dynamic mechanical properties and dye diffusion behavior in acrylic fibers from polymer blends

The extension of the relation between the dynamic viscoelastic parameters (“E” and tan δ) and diffusion coefficient (D) to modified acrylic blend fibers indicates that the dependence of dye diffusion on polymer chain mobility is a general phenomenon not limited to a single component system. The relationship of D to mechanical properties permits one to “tailor” fibers with good mechanical properties while maintaining adequate dye-diffusion behavior.     

A Model for the Diffusion of Moisture in Adhesive Joints. Part I: Equations Governing Diffusion

A methodology is proposed to relate the diffusion coefficient of small penetrant molecules in polymers to temperature, strain, and penetrant concentration. The approach used is based on well-known free volume theories. It is assumed that the transport kinetics is governed by the constant redistribution of the free volume, caused by the segmental motions of the polymeric chains. An expression for the diffusion coefficient is inferred from the temperature, strain, and penetrant concentration dependence of the free volume. The stress dependence of solubility is predicted from the Hildebrand theory. It is shown that the resulting constitutive equations exhibit many features desirable for joint durability studies. Finally, a non-Fickian driving force arising from differential swelling is included in the governing equations.     

Diffusion coefficient measurements by solvent absorption in concentrated polymer solution

Diffusion coefficient measurements for solvents in concentrated polymer solutions require consideration of both concentration dependence of the diffusion coefficient and surface resistance to mass transport. Solutions to the diffusion equation have been generated where these effects are explored. A method to account for both concentration dependence and surface (absorption) resistance in the experimental determination of diffusion coefficients is given and demonstrated with an example where a multiplying factor of over 300 is required to adjust the apparent diffusion coefficient to the value sought.     

Time,temperature, and strain effects on viscoelastic Poisson's ratio of epoxy resins

Poisson's ratio of polymeric materials, although generally assumed as a constant, is known to display a viscoelastic dependence on time, temperature, and strain. This article investigates the phenomenology of this dependence on two crosslinked epoxy systems with different glass transition temperatures. Poisson's ratio measurements are performed by contact extensometers simultaneously measuring the axial and transverse deformations under two different tensile testing conditions: (i) constant deformation rate, in which the effects of strain, strain rate, and temperature are highlighted; (ii) stress relaxation (or constant deformation), where the dependence of Poisson's ratio on time is studied at various strain levels. The viscoelastic Poisson's ratio increases as strain, temperature, and time increases, with trends markedly depending on the materials glass transition. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

Test of ‘scaling laws’ describing the concentration dependence of osmotic pressure,diffusion and sedimentation in semidilute macromolecular solutions

Data of osmotic pressure, diffusion and sedimentation in semidilute macromolecular solutions are systematized with regard to scaling laws. The observed main features are: (a) the concentration dependence of the osmotic pressure both at good and theta solvent conditions is in excellent agreement with that predicted by the scaling laws. (b) The concentration dependence of the mutual diffusion coefficient D_m could not uniquely be described by a simple scaling law. A difference in concentration dependence between D_m and the cooperative diffusion coefficient was observed for polystyrene under good solvent conditions. (c) The concentration dependence of the permeability coefficient (related to sedimentation) and the sedimentation coefficient were for most of the systems in close agreement with that predicted by the scaling laws.     

Effects of viscosity-dependent diffusion in the analysis of rotating disk electrode data

This paper demonstrates the application of a modified Levich equation for chemical systems with varying viscosity. A commonly used technique to analyze rotating disc electrode (RDE) experiments is to fit the data to the Levich equation assuming a constant effective diffusion coefficient which may be valid for conditions where the viscosity does not vary significantly (less than an order of magnitude). However, most diffusion coefficient models (e.g. Stokes–Einstein) show an inverse relationship with viscosity which consequently indicates that a constant effective diffusion coefficient may result in poorer model-to-data agreement. Here, data are presented for a series of RDE experiments for the electrodissolution of Cu in phosphoric acid, water and glycerin based baths. Viscosity changes of greater than one order of magnitude allow for testing the assumption of a constant effective diffusion coefficient. The collected data, as well as data published elsewhere, can be explained by a modified Levich equation which takes into account the viscosity dependence of the diffusion coefficient.     

Generic relaxation spectra of solid polymers. I. Development of spectral distribution model and its application to stress relaxation of polypropylene

An important aspect of designing polymeric articles for engineering applications and predicting their properties over their lifetime is the computation of their time-dependent viscoelastic behavior. A simplified numerical computational technique based on a Gaussian spectral distribution model was developed to describe this behavior over a wide range of time and temperature. The model was used to describe the stress-relaxation behavior of isotactic polypropylene (iPP) over a wide range of strain, time, and temperature. It appears that a spectrum with two components (one distribution for the amorphous zone and the other for the crystalline zone) is sufficient to describe the viscoelastic behavior of iPP. The parameters specifying the distributions (mean relaxation time, standard deviation, and relaxation strength) may be obtained by nonlinear regression analysis and the temperature dependence of the distributions may be evaluated experimentally. An excellent fit between experimental data and the mathematical model is observed. The method may be applied generally for any linear viscoelastic property (e.g., static and dynamic relaxation and creep in tensile or shear) and for any polymer. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1101–1115, 1997     

Mechanical and optical characterization of a photoviscoplastic material

The mechanical and optical properties of a polyester blend over a wide range of strain rates has been investigated for loading and unloading. The mechanical behavior, while being complex, was modeled adequately with a generalization of the four-parameter viscoelastic model. The optical behavior has at least a three-phenomenological coefficient dependence on the mechanical variables. Further, the stress birefringence is of opposite sign to that of the deformation.     

Diffusion Characteristics in Ethyl Alcohol and Glucose Solutions Using Kedem-Katchalsky Equations

Formulas for calculating the viscosity and diffusion coefficients for two-component aqueous non-electrolyte solutions as a function of the solution concentration under isothermal conditions were derived. The dependence of diffusion coefficient, filtration coefficient, and dynamic viscosity coefficient for these solutions on the solution concentration was estimated and evaluated. Based on the obtained formulas, the results of diffusion coefficient, membrane filtration coefficient, and dynamic viscosity calculations for aqueous solutions of ethanol and glucose are presented and compared with literature data.     

A multi-phase model for VOC emission from single-layer dry building materials

A multi-phase model for the emission of VOC from dry building materials is developed. Dry building materials are viewed as porous media. A general adsorption isotherm is used to construct the concentration equation in the porous media. The boundary conditions at the material-air interface are presented for both CFD model and one compartment model. With the use of Henry’s law for the adsorption isotherm, an analytical solution is obtained and further is validated with the comparison of the experiment performed by Yang et al. [1], yielding a relatively good agreement. The effects of the model parameters on the emission are investigated in detail. Increasing the effective diffusion coefficient and the partition coefficient tends to promote the emission and increase the peak value of the concentration in the air. The effect of the porosity depends on the degree of the dependence of the effective diffusion coefficient on the porosity. When a weak dependence exists, the increase of the porosity tends to suppress the emission and decrease the peak value of the concentration in the air. However, when a strong dependence exists, the increase of the porosity tends to promote the emission and increase the peak value of the concentration in the air.     

THE EFFECT OF DRUG DISSOLUTION ON DRUG RELEASE FROM SWELLING POLYMERIC MATRICES: MATHEMATICAL MODELING

A mathematical model of simultaneous dissolution and diffusion controlled drug release from swellable, non-erodible viscoelastic polymer matrices is developed. The model assumes that the drug is loaded into the dry matrix as a solid phase. Two unsteady-state mass balances are required for both the drug and the incoming external penetrant. The Camera-Roda and Sarti equation is considered for the determination of the penetrant uptake, while Ficlc's equation accounting for the density gradient developing in the matrix is considered for the drug diffusion. Assuming that upon dissolution a drug phase transition may occur which affects the drug solubility without altering the diffusion coefficient. This analysis revealed that the features of the drug release kinetics are sensibly affected by the viscoelastic properties of the swollen matrices and by the drug dissolution and phase transition rates.     

Effects of pressure on the non-linear viscoelastic behaviour of polymers: 1. Polypropylene

A comprehensive study of the pressure and strain rate dependence of the room temperature shear stress strain behaviour of isotropic polypropylene is described. The maximum (yield) stress is observed to increase smoothly with increasing pressure and strain rate in the pressure regime where the 1% shear modulus is passing through the main β relaxation. This indicates the differing roles of the crystalline and amorphous regions of the material at large and small strains. A modified Ree—Eyring model is shown to describe well the pressure and strain rate dependence of the maximum stress data but is inadequate to describe corresponding features of the small strain results. A semiquantitative viscoelastic analysis is used to delineate several types of non-linear behaviour at different strain and pressure levels indicating the complexity of the mechanical response of a semicrystalline polymer.     

Significance of deformation rate softening of memory in viscoelastic fluid mechanics and polymer processing

It is pointed out that in viscoelastic fluid constitutive equations, non-linear response to deformation rate and strain beyond the second order is usually interpreted in terms of the deformation rate or strain dependence of the memory function. These non-linearities act to decrease the extent of the memory. The dependence may be characterized by one or more dimensionless material parameters. A new dimensionless group based on the primary material parameters describing the intensity of the deformation rate dependence of the memory function is introduced and its significance is discussed. This is called the Yamamoto number. The solutions of viscoelastic fluid mechanics problems are considered to depend upon both the Weissenberg and Yamamoto numbers. Such problems include topics of interest in polymer melt processing such as uniaxial elouigatioiial flow, fiber spinning and vortex development in extrusion through a die entry.     

Effects of rheological properties and processing parameters on ABS thermoforming

Understanding effects of material and processing parameters on the thermoforming process is critical to the optimization of processing conditions and the development of better materials for high quality products. In this study we investigated the influence of both rheological properties and processing parameters on the part thickness distribution of a vacuum snap‐back forming process. Rheological properties included uniaxial and biaxial elongational viscosity and strain hardening and/or softening while processing parameters included friction coefficient, heat transfer coefficient, and sheet and mold temperatures. The Wagner two parameter nonlinear viscoelastic constitutive model was used to describe rheological behavior and was fit to shear and elongational experimental data. The linear viscoelastic properties along with the Wagner model were utilized for numerical simulation of the thermoforming operation. Simulations of pre‐stretched vacuum thermoforming with a relatively complex mold for a commercial refrigerator liner were conducted. The effects of nonlinear rheological behavior were determined by arbitrarily changing model parameters. This allows determination of which rheological features (i.e., elongational mode, viscosity, and strain hardening and/or softening) are most critical to the vacuum snap‐back thermoforming operation. We found that rheological and friction properties showed a predominant role over other processing parameters for uniform thickness distribution.     

Nonlinear viscoelastic behavior of wool fibers in a single step relaxation test

Experimental data and their analysis are presented on the nonlinear viscoelastic behavior of wool fibers in extensional stress–relaxation up to strains of 18.5%. The analysis, assuming a two-phase structure for the fiber, consists of superimposing the experimental curves onto the master curve for the nonaging material by multiplicative scaling and shifting on the logtime scale. The scaling and shift factors reflect the strain induced phase changes of the morphological components. Though different in their physical nature, these transitions show the same strain dependence.     

Diffusion-thermal stability of gas filtration combustion waves in an inert porous medium

A mathematical model for the filtration gas combustion taking into account thermal conductivity, diffusion, and intense interfacial heat transfer is presented. The temperature dependence of the chemical reaction rate is approximated by a δ-function and the thermal-expansion coefficient of gases behind the combustion front is taken into account. Unsteady combustion regimes are analyzed using the method of small perturbations. The boundaries of the longitudinal and spatial stability for steady regimes of the filtration combustion wave are obtained. The dependence of the Lewis number on the thermal-expansion coefficient of the gas mixture along the boundary of stability is derived, along with other relations.