A simplified equation of state for polymer melts from perturbed Yukawa hard-sphere chain

This paper addresses the modeling of the pressure?Cvolume?Ctemperature (PVT) properties of 14 polymer melts using simplified Yukawa hard-sphere-chain equation of sate (EOS) plus first-order perturbation theory. Three pure-component parameters appeared in the EOS have been determined via the volumetric data. These parameters reflect the segment number, non-bonded segment?Csegment interaction energy, and segment size. Likewise, this study considered chains that interact through a range-parameter of Yukawa potential with l.8. The reliability of the proposed model has been assessed by comparing the results with 1,315 experimental data points over a broad range of pressures and temperatures for which, their measured values were available in the literature. Our calculations on the specific volume of studied liquid polymers reproduce very accurately the experimental PVT data. The overall average absolute deviation of the calculated specific volumes from literature data was found to be 0.89?%.     

Heat capacity of polymer melts from the polymer chain-of-rotators equation of state

Recently, the chain-of-rotators equation of state derived from the rotational partition function was extended to polymers. Values of the three equation of state (EOS) parameters were obtained from fitting with experimental pressure–volume–temperature data and the parameters were correlated with the structure of the polymer repeat unit. In this article, the residual molar heat capacity derived from an EOS is added to the ideal gas heat capacity from Benson's group contribution method to obtain the polymer molar heat capacity at constant pressure, C_p. Predictions from the polymer chain-of-rotators (PCOR) using correlated parameters are compared with those obtained from PCOR, Sanchez–Lacombe, Flory–Orwoll–Vrij, and the perturbed-hard-sphere chain equations of state using parameters fitted from experimental data. Deviations of calculated C_p from the formula of van Krevelen for liquid polymers are likewise presented. With the correlations developed for its parameters, the PCOR offers the advantage of predicting the C_p for polymer melts from just the knowledge of the polymer's structure. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:841–848, 1998     

A new semiempirical equation of state for fluids—I: Derivation

A semiempirical equation of state has been developed for non-polar and weakly polar fluid substances from the square well model of the inter-molecular     

A new rheological constitutive equation for the network model of polymer melts

A new network model is suggested and a constitutive equation is developed on the basis of the assumed validity of Boltzmann's superposition principle for the shear stress. The predictions of the model concerning the relaxation behavior of polymer melts after steady shear or instantaneous deformation are compared to Lodge's theoretical results and to experimental data from the literature.     

Prediction of PVT behavior of polymer melts by the group-contribution lattice-fluid equation of state

The group-contribution lattice-fluid equation of state (GCLF-EOS), which is capable of predicting equilibrium behavior in polymer systems, was developed by establishing group contributions of the lattice-fluid EOS using the PVT properties of low molecular weight compounds only. This model was used to predict the PVT behavior of common polymers over a wide temperature range in the melt region and over a wide range of pressures up to about 2,000 bar. The GCLF-EOS predicted accurately the effect of pressure and temperature on the specific volumes of the polymer melts. Prediction results by the GCLF-EOS were compared with those by the group-contribution volume (GCVOL) method. The GCLF-EOS requires only the structure of the polymer repeat unit in terms of their functional groups as input information. No other polymer properties are needed. The GCLF-EOS is the only model that is capable of predicting the specific volumes of polymer melts as a function of temperature and pressure.     

Application of a constitutive equation to polymer melts

Yamamoto's integral constitutive equation in which the memory function is dependent on the second invariant of the rate of deformation tensor at past times has been found to be successful in predicting many of the nonlinear viscoelastic functions from the linear viscoelastic data for melts of linear polyethylenes, polypropylenes, and polystryene but not for those of branched polyethylenes with high level of long-chain branching. A specific functional form for the rate-dependent relaxation spectrum is used and is based on the physical meaning resulting from the molecular entanglement theory of Graessley on steady shearing flow. No arbitrary constant is involved in such an interconversion scheme. The data examined are dynamic storage modulus and loss modulus, steady flow viscosity, first normal stress difference, and parallel superimposed small oscillations on steady shear flow. The theory predicts that in such parallel superimposed experiments, storage modulus G′(ω,\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) divided by the square of frequency shows a maximum under finite shear and that G′(ω,\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) would itself become negative at a frequency whose value is about one third the superimposed rate of shear. The experiments are in line with such predictions. Possible reasons for the failure of the theory for branched polyethylenes are considered, and a possible approach is suggested so that the interconversion scheme may be successful for such resins.     

A new semiempirical equation of state for fluids—II: Application to pure substances

The semiempirical equation of state proposed in our previous paper is applied to the calculation of thermodynamic properties of pure fluid substances.     

Numerical evaluation of the thermodynamic equation for the state of polymer melts from pressure-volume-temperature (pVT) data

A refinement of the numerical calculation of reducing PVT parameters has been given by using the Marquardt-Levenberg nonlinear least-squares algorithm. Three different polymers were analyzed and evaluated by the proposed method. The precision of the PVT measurement makes sense for an improvement of the evaluation by applying the Marquardt algorithm.     

Application of equation of state and artificial neural network to prediction of volumetric properties of polymer melts

The modified ISM EOS and artificial neural network (ANN) methods were used to predict the PVT behavior of polymer melts containing polystyrene (PS), polycarbonate bisphenol-A (PC), polyvinylidene fluoride (PVDF), polypropyleneglycol (PPG), polyethylene glycol (PEG), polypropylene (PP), poly vinylchloride's properties (PVC), poly(1-butene) (PB1), polycaprolactone (PCL), polyethylene (PE) and polyvinyl methyl ether (PVME) over the entire range of available temperature and pressure. The obtained results show that the modified ISM EOS and ANN models have good agreement with the experimental data with mean average absolute deviation of 0.58% and 0.20%, respectively.     

A new semiempirical equation of state for fluids—III Application to phase equilibria in binary mixtures

The equation of state derived in a previous publication [1] is used to correlate vapour-liquid, liquid-liquid, and gas-gas equilibria in binary mixtures. Special mixing rules for the parameters of the equation of state are derived from a quasichemical lattice model. It is possible to describe phase equilibria at very high pressures (beyond 1000 bar) with reasonable accuracy. The unlike interaction potential parameters, which are used as adjustable data to obtain a good fit, have physically reasonable values.     

A mechanism for extrusion instabilities in polymer melts

A mechanism for explaining some of the instabilities observed during the extrusion of polymer melts is further explored. This is based on the combination of non-monotonic slip and elasticity, which permits the existence of periodic solutions in viscometric flows. The time-dependent, incompressible, one-dimensional plane Poiseuille flow of an Oldroyd-B fluid with slip along the wall is studied using a non-monotonic slip equation relating the shear stress to the velocity at the wall. The stability of the steady-state solutions to one-dimensional perturbations at fixed volumetric flow rateis analyzed by means of a linear stability analysis and finite element calculations. Self-sustained periodic oscillations of the pressure gradient are obtained when an unstable steady-state is perturbed, in direct analogy with experimental observations.     

Bead-spring polymer melts

This analysis of polymer rheology uses conditional probability distributions to describe the phase space dynamics of all macromolecules in a polymer melt. The result is a viscoplastic constitutive equation for the polymer stress. Using conditional probability distributions makes the use of a large number of bead-spring chains in the modeling system possible, but precludes evaluating the intermolecular contribution to the total stress. Both the kinetic and intramolecular contributions are evaluated for a system composed of an arbitrary number of bead-spring chains that interact with one another using molecular dispersion forces. The analysis predicts that the kinetic contribution is isotropic and the intramolecular contribution is viscoplastic. The intermolecular contribution is assumed negligible in comparison to the intramolecular contribution because it results from physical bonds among chains, while the intramolecular contribution results from chemical bonds within a chain. © 1993 John Wiley & Sons, Inc.     

A single-mode rheological model for steady flows of polymer melts

The steady shear viscosity (η_s), the steady first normal stress coefficient (Ψ₁), the steady second normal stress coefficient (Ψ₂), and extensional viscosity (η_e) are four important parameters for polymer melts during polymer processing. In this article, we propose a stress and rate-dependent function to describe creation and destruction of polymer junctions. Moreover, we also introduce a movement expression to describe nonaffine movement of network junctions. Based on network theory, a nonaffine single-mode rheological model is presented for the steady flow of polymeric melts, and the equations of η_s, Ψ₁, Ψ₂, and η_e are derived from the model accordingly. Furthermore the dependences of η_s and η_e on model parameters are discussed for the model. Without a complex statistical simulation, the single-mode model with four parameters yields good quantitative predictions of the steady shear and extensional flows for two low density polyethylene melts reported from previous literature in very wide range of deformation rates. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

PVT scaling parameters for polymer melts

Scaling parameters for two PVT equations of state are evaluated for 11 polymer melt systems using a nonlinear least square fitting algorithm that analyzes all of the experimental data simultaneously. Two different criteria are considered in this evaluation. In the first method, the fitting criterion is the difference between the calculated and experimental volume. In the second method, the criterion is the difference between the calculated and experimental pressure. In both cases, the differences between the scaling parameters obtained using the simultaneous fit procedure and those obtained using the earlier consecutive fit procedure are a few percent, which can have a significant effect in some calculations. In addition to being a more consistent method of evaluating scaling parameters, the simultaneous fit procedure leads to much better agreement between calculated and experimental values, in some cases by a factor of 2.     

A simple,versatile and inexpensive rheometer for polymer melts

A simple, versatile biconical rehemoter has been developed. This device provides shear creep and creep recovery data for polymer melts over a temperature range of 200–500°F. and a range of applied shear stresses from 2 × 10³ to 9 × 10⁵ dynes/cm². Extensive reheological data have been obtained for two samples each of polyisobutylene and high-density polyethylene. These illustrate the value of the device in obtaining data useful for predicting and understanding the processing properties of polymer melts.     

Transitions in polymer melts

It is shown that the liquid-liquid transition T_ll in polymer melts need not be a true polymer transition but can be an artifact of the torsional braid analysis technique. The shift in T_ll with molecular weight then is due to the variation of viscosity with molecular weight.     

A semi-empirical equation of state for fluids

An eight parameter equation of state for calculating the volumetric behaviour of fluids has been derived on the basis of three main assumptions:—The thermodynamic equation of state P +(?E|?V)_T = T(?S|?V)_T as a general theoretical frame.—The Maxwell relation (?P|?T)_V = (?S|?V)_T as a thermodynamic link between the empirical parameters of the equation.—A Van der Waals-type potential for attractive forces.The new equation has been applied to ten fluids, five polar and five apolar, in an experimental range up to three times the critical density and up to five times the critical temperature.The new equation compares favorably in accuracy with the BWR equation.     

A generalized equation of state for polymers

A simple, generalized equation of state has been developed that describes the pressure–volume–temperature behavior of both addition and condensation polymers. Use of the equation requires only that the polymer's glass temperature and density at 25°C. and one atmosphere be known. The equation applies to both amorphous and crystalline polymers for pressures up to 10,000 atm. It also appears to hold for copolymers. Polymer glass temperatures can also be estimated with the equation.