Prototype of an Engineering Equation of State for Heterosegmented Polymers

Abstract

The square-well fluid thermodynamics and liquid structure derived from Barker-Henderson's perturbation theory, including a truncation correction, are used within a SAFT framework to develop a prototype of an engineering equation of state for alkane chains, referred to as SAFT1. For small n-alkanes, not only the vapor pressure and liquid density, but also the second virial coefficient, heat of vaporization, and heat capacity, are found to be more accurate. SAFT1 parameters are well behaved and hence easy to estimate reliably for high-molecular-weight alkanes and polyolefins. These parameters are found to predict cloud points in mixtures of homo-and heterosegmented molecules, such as polyolefins, without fitting. IntroductionIn chemical and polymer technology, we need thermodynamic models that are more and more predictive and less and less dependent on fitting to experimental data. The mathematical simplicity and the ease of coding, therefore, become relatively less important virtues, but the ease of estimating the parameters quickly and reliably becomes a very important virtue. One of the popular approaches to developing such thermodynamic models is rooted in perturbation theory, for example, the statistical associating fluid theory (SAFT).The SAFT equations of state have the following terms: a segment term that accounts for the nonideality of the reference fluid of nonbonded chain segments (monomers), a chain term that accounts for covalent bonding, and an association term that accounts for hydrogen bonding that leads to association. There may also be an optional term that accounts for polarity. The main differences between different versions of SAFT stem from how the segment and chain terms are estimated.For example, an engineering version of SAFT was developed by Huang and Radosz 1,2 on the basis of an argon equation of state (the so-called BACK equation of state) for the segment term and a hard-sphere paircorrelation function for the chain term. That version of SAFT has become popular because it is user-friendly; its parameters are well behaved and hence relatively easy to estimate for new large molecules. Furthermore, it has been extended to heterosegmented chains by Banaszak et al. 3 That extension, referred to as copolymer SAFT, explicitly accounts for variable polyolefin microstructure due to the variability in comonomer incorporation. A generic SAFT approach for developing equations of state has been proposed by Chapman et al. 4

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

“…The main contribution of our present work is to consider an appropriate approximation to evaluate the integral in equation (18) (equation (35) in the case of chains) such that we can dispense with the parameter Φ typically used. We have performed a comparison between the numerical integration of equation (35) …”

Modeling mass transfer of CO2 in brine at high pressures by chemical potential gradient

“…For non-electrolytes, the ionic contribution is set equal to zero. The segment, chain, and ion terms have been described in detail elsewhere [26][27][28][29]. Any other thermodynamic properties can be calculated from this residual Helmholtz energy.…”

Critical temperatures and pressures for hydrocarbon mixtures from an equation of state with renormalization-group theory corrections

“…The critical point can be determined by computational techniques for solving these two equations simultaneously, as discussed previously for binary and ternary systems [31][32][33][34][35][36][37], and for multi component mixtures [38][39]. These techniques, however, have to evaluate a large number of determinants and are computationally expensive, especially for mixtures with many components.…”