The description of the change in characteristic temperatures of thermomechanical and viscoelastic properties of polymers and elastomers with deformation frequency or of temperature dependence of polymer p
The description of the change in characteristic temperatures of thermomechanical and viscoelastic properties of polymers and elastomers with deformation frequency or of temperature dependence of polymer properties is widely achieved by two equations: (1) the Williams‐Landel‐Ferry (WLF) equation and (2) the Arrhenius equation. Mostly the WLF equation is used. Often the distinction between the two descriptions is based on the argument: if volume processes play the key role, then WLF equation is the right one, if thermally activated processes play the key role, then Arrhenius equation is the right one. Both equations are based on the activation of processes, and always the temperature is the variable, which activate the processes. Both descriptions are methods to parameterize the temperature dependence of properties or the change of characteristic temperatures, as glass‐rubber transition temperature, with deformation rate. Also, the so‐called ‘volume processes’ are controlled by temperature, but the thermal activation can be small in energy to initiate the change in spatial position from one site to another for a molecule. This means both descriptions should be congruent. In this article, the congruence is shown and the relation between WLF parameters and Arrhenius parameters will be established. For this, a slight modification of the usual Arrhenius equation is necessary. Also, other descriptions are discussed in short: Doolittle equation and Vogel‐Fulcher equation, they were or are used to describe the change of viscosity with temperature in melts or solutions.
摘要 :
This research investigates the relationships of the pressure-volume-temperature (PVT)and the zero-shear viscosity of polymer melts through their correlations with the fractional free volume.Polystyrene (PS)has been used as a case ...
展开
This research investigates the relationships of the pressure-volume-temperature (PVT)and the zero-shear viscosity of polymer melts through their correlations with the fractional free volume.Polystyrene (PS)has been used as a case example in this study.First,the fractional free volume is determined from the Simha-Somcynsky (SS)equation of state (EOS)or the Sanchez-Lacombe (SL)EOS using the PVT data of a polymer melt.Then the fractional free volume is also determined from the Doolittle equation (with respect to the occupied volume)using the zero-shear viscosity and PVT data.These two fractional free volumes are compared to check if the EOS and the Doolittle equation consistently describe the PVT behaviors and the zero-shear viscosity through the fractional free volume.Before comparison,the fractional free volume based on the Doolittle equation is recalculated with respect to the total volume to be consistent with other fractional free volumes defined with respect to the total volume.
收起
摘要 :
The viscosity values of triglyceride and alcohol solutions with newtonian rheological behaviour (triacetin + butanol, tributyrin + butanol, tricaprylin + butanol, tributyrin + ethanol and tributyrin + hexanol) and with molar fract...
展开
The viscosity values of triglyceride and alcohol solutions with newtonian rheological behaviour (triacetin + butanol, tributyrin + butanol, tricaprylin + butanol, tributyrin + ethanol and tributyrin + hexanol) and with molar fraction composition between 0 and 1 are compared with those obtained from application of the equations of Krone, Doolittle and Macedo-Litovitz, in the temperature range 278-313 K.
收起
摘要 :
The constitutive equations of chemically and physically ageing rubber in the audible frequency range are modelled as a function of ageing temperature, ageing time, actual temperature, time and frequency. The constitutive equations...
展开
The constitutive equations of chemically and physically ageing rubber in the audible frequency range are modelled as a function of ageing temperature, ageing time, actual temperature, time and frequency. The constitutive equations are derived by assuming nearly incompressible material with elastic spherical response and viscoelastic deviatoric response, using Mittag-Leffler relaxation function of fractional derivative type, the main advantage being the minimum material parameters needed to successfully fit experimental data over a broad frequency range. The material is furthermore assumed essentially entropic and thermo-mechanically simple while using a modified William-Landel-Ferry shift function to take into account temperature dependence and physical ageing, with fractional free volume evolution modelled by a nonlinear, fractional differential equation with relaxation time identical to that of the stress response and related to the fractional free volume by Doolittle equation. Physical ageing is a reversible ageing process, including trapping and freeing of polymer chain ends, polymer chain reorganizations and free volume changes. In contrast, chemical ageing is an irreversible process, mainly attributed to oxygen reaction with polymer network either damaging the network by scission or reformation of new polymer links. The chemical ageing is modelled by inner variables that are determined by inner fractional evolution equations. Finally, the model parameters are fitted to measurements results of natural rubber over a broad audible frequency range, and various parameter studies are performed including comparison with results obtained by ordinary, non-fractional ageing evolution differential equations.
收起
摘要 :
This study compares the film thickness, lubricant temperature, and traction curves of two groups of commonly used constitutive models for lubricants in thermo-elastohydrodynamic lubrication (TEHL) modelling. The first group consis...
展开
This study compares the film thickness, lubricant temperature, and traction curves of two groups of commonly used constitutive models for lubricants in thermo-elastohydrodynamic lubrication (TEHL) modelling. The first group consists of the Tait equation of state, the Doolittle Newtonian viscosity model, and the Carreau shear thinning model. The second group includes the Dowson equation of state, the Roelands-Houpert Newtonian viscosity model, and the Eyring shear thinning model. The simulations were conducted using a Computational Fluid Dynamic and Fluid-Structure Interaction (CFD-FSI) approach, which employs a homogeneous equilibrium model for the flow simulation along with a linear elastic solver to describe the deformation of the solid materials. The simulations were conducted under a load range of 100 kN/m to 200 kN/m and a slide-to-roll-ratio (SRR) range between 0 and 2 using Squalane lubricant. The results show up to a 10% deviation in central film thickness, a 31% deviation in coefficient of friction (CoF), and a 38% deviation in maximum lubricant temperature when using the different constitutive models. This study highlights the sensitivity of TEHL simulation results to the choice of constitutive models for lubricants and the importance of carefully selecting the appropriate models for specific applications.
收起
摘要 :
The concentration dependency of the diffusivity of a solvent in a polymer solution is derived on the basis of a free volume theory. Applying a molecular kinetics approach, the Fujita-Doolittle equation is modified. The result of n...
展开
The concentration dependency of the diffusivity of a solvent in a polymer solution is derived on the basis of a free volume theory. Applying a molecular kinetics approach, the Fujita-Doolittle equation is modified. The result of numerical simulation reveals that the diffusivity of solvent in a polymer solution depends largely on both the polymer chain structure and its concentration. The applicability of the analytical expression derived is justified by fitting the experimental data for n-alkyl acetate-(poly-methyl acrylate) polymer solutions ill the literature. (c) 2004 Elsevier Ltd. All rights reserved.
收起
摘要 :
Since many real-world engineering systems are too complex to be defined in precise terms, imprecision is often involved in any engineering design process. Fuzzy systems have an essential role in this fuzzy modelling, which can for...
展开
Since many real-world engineering systems are too complex to be defined in precise terms, imprecision is often involved in any engineering design process. Fuzzy systems have an essential role in this fuzzy modelling, which can formulate uncertainty in actual environment. In addition, this is an important sub-process in determining inverse, eigenvalue and some other useful matrix computations, too. One of the most practicable subjects in recent studies is based on LR fuzzy numbers, which are defined and used by Dubois and Prade with some useful and easy approximation arithmetic operators on them. Recently Dehghan et al. [M. Dehghan, M. Ghatee, B. Hashemi, Some computations on fuzzy matrices, submitted for publication.] extended some matrix computations on fuzzy matrices, where a fuzzy matrix appears as a rectangular array of fuzzy numbers. In continuation to our previous work, we focus on fuzzy systems in this paper. It is proved that finding all of the real solutions which satisfy in a system with interval coefficients is NP-hard. The same result can similarly be derived for fuzzy systems. So we employ some heuristics based methods on Dubois and Prade's approach, finding some positive fuzzy vector (x) over tilde which satisfies (Ax) over tilde = (b) over tilde where (A) over tilde and (b) over tilde are a fuzzy matrix and a fuzzy vector respectively. We propose some new methods to solve this system that are comparable to the well known methods such as the Cramer's rule, Gaussian elimination, LU decomposition method (Doolittle algorithm) and its simplification. Finally we extend a new method employing Linear Programming (LP) for solving square and non-square (over-determined) fuzzy systems. Some numerical examples clarify the ability of our heuristics. (c) 2005 Elsevier Inc. All rights reserved.
收起
原文获取