John M. Prausnitz

Equation of state for fluids containing chainlike molecules

An equation of state for chain fluids has been derived through the r‐particle cavity‐correlation function (CCF) for chains obtained from sticky spheres; here r is the chain length. The r‐particle CCF is approximated by a product of effective two‐particle CCFs, accounting for nearest‐neighbor correlations and next‐to‐nearest‐neighbor correlations. For hard‐sphere chain fluids (HSCF), the density dependence for nearest‐neighbor effective two‐particle CCFs is determined by the equation of Tildesley–Streett for hard‐sphere dumbbells and that for next‐to‐nearest‐neighbor effective two‐particle CCFs by computer‐simulation results for hard‐sphere trimers. The final equation of state has a simple form which gives compressibility factors and second virial coefficients for homonuclear HSCFs covering a wide range of chain length (up to r=201) in excellent agreement with computer simulations. Satisfactory comparisons are also obtained between predicted and computer‐simulation results for homonuclear HSCF mixtures, HS...

Thermodynamics of phase equilibrium for systems containing gels

A gel is a three-dimensional cross-linked elastic polymer. When a gel is immersed into a liquid, it can swell, similar to a sponge. If the surrounding liquid is a solute-containing solution, a solute partitions between the gel and the surrounding liquid. This work derives the fundamental equations of phase equilibrium for such systems. These equations take into account the elastic properties of the gel. Criteria are given for the distribution of solutes between a gel and a coexisting liquid phase. Criteria are also presented for calculating three-phase equilibria where a swollen gel and a collapsed gel coexist with the surrounding liquid. Attention is given to a slightly ionized gel (polyelectrolyte) surrounded by a dilute aqueous electrolyte solution. The equations of equilibrium show that, when Donnan equilibria are taken into account, the pH inside the gel is not equal to that of the surrounding aqueous solution. The discussion presented here may be useful for design of gels used in medicine, pharmacy and biotechnology.

A molecular-thermodynamic model for polyelectrolyte solutions

Polyelectrolyte solutions are modeled as freely tangent-jointed, charged hard-sphere chains and corresponding counterions in a continuum medium with permitivity e. By adopting the sticky-point model, the Helmholtz function for polyelectrolyte solutions is derived through the r-particle cavity-correlation function (CCF) for chains of sticky, charged hard spheres. The r-CCF is approximated by a product of effective nearest-neighbor two-particle CCFs; these are determined from the hypernetted-chain and mean-spherical closures (HNC/MSA) inside and outside the hard core, respectively, for the integral equation theory for electrolytes. The colligative properties are given as explicit functions of a scaling parameter Γ that can be estimated by a simple iteration procedure. Osmotic pressures, osmotic coefficients, and activity coefficients are calculated for model solutions with various chain lengths. They are in good agreement with molecular simulation and experimental results.

Molecular thermodynamics of fluid mixtures containing molecules differing in size and potential energy

Abstract Recent computer-simulation work by Shing and Gubbins (1983) for binary mixtures has shown that common semiempirical models (van der Waals n -fluid models) are in error when the molecules of the two components differ appreciably in size; the error is most severe in the dilute region. While perturbation theories are much better, they (like computer simulations) are not as yet useful for engineering work because of prohibitive computer requirements. This work proposes an algebraic expression for the Helmholtz energy of a mixture which gives results in very good agreement with those reported by Shing and Gubbins. This expression, using the local-composition concept, is based on a simplified but realistic picture of a fluid mixture: short-range order and long-range disorder. The proposed expression uses the Mansoori-Carnahan-Starling-Leland equation for the contribution of repulsive forces. For the contribution of attractive forces, it uses a new expression based on not one but several radii for the first-neighbor shell, one radius for each component. With reasonable simplifications, the resulting equation for the Helmholtz energy indicates that the van der Waals “constant” a is a strict quadratic function of mole fraction only at very low densities; at advanced densities, there are small deviations from the quadratic mixing rule. For practical calculations, the computer requirements are nearly the same as those for conventional engineering models.

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

LBNL·44487 Preprint ERNEST ORLANDO LAWRENCE BEfRJ<.ELEY NAT~DNAL L-=ABDRATDRY Critical Temperatures and Pressures for Hydrocarbon Mixtures from an Equation of State with Renormalization-Group-Theory Corrections J. Jiang andJ.M. Prausnitz Chemical Sciences Division November 1999 Submitted to Fluid Phase Equilibria .:E: m !lJ ..J_ .g A CD oUlrn m rn rn OJ m _.J Szt5 !lJ c+ rn m ri- :z c-~ OJ OJ lO m iJ CL----- o :JtSl !lJ U1 -l_ ,D !lJ , t)QJ o , !lJ C i- o -s I· r OJ z r I m -t) o t- .r:. .r:. .r:. OJ --.J

Molecular thermodynamics of gas solubility

A molecular-thermodynamic model has been established for the solubilities of gases in non-polar and polar solvents and in aqueous solutions of electrolytes. To obtain an expression for the Helmholtz energy of the mixture, the pure components are first mixed isothermally to form an ideal gas mixture. Then each particle in the mixture is inflated into a hard sphere. Finally, all particles are charged with an appropriate potential to form a real liquid mixture; this charging step is based on an orderd first coordination shell and a random mixture beyond that first shell. This model agrees well with computer-simulation data. Calculated and observed Henrys constants are in good agreement over a wide range of temperature for various gases in benzene, cyclohexane, n-hexane, hexadecane and water, and in aqueous solutions of NaCl and KOH.

Continuous thermodynamics for polydisperse polymer solutions

Abstract Continuous thermodynamics is a framework which combines continuum modeling for the compositions of complex and multicomponent mixtures with molecular thermodynamic models and efficient numerical methods. In this work, a generalized molecular-thermodynamic model for polydisperse polymer solutions is developed; it is formally similar to the classical Flory-Huggins theory but with a polymer-size dependent and polymer-concentration dependent Flory parameter. Most existing lattice models and equation-of-state models such as the Guggenheim, Orifino-Flory, Koningsveld-Kleintjens, Sanchez-Lacombe and Revised Freed models can be cast into this generalized model but with different polymer-size and polymer-concentration dependence for the Flory parameter. A generalized continuous-thermodynamics framework based on this generalized model is also presented; expressions for chemical potentials, spinodals and critical points are derived using both the discrete multicomponent method and the continuous functional procedure. Internally consistent results are obtained. Criteria for multiple critical points are also derived. Computer programs are established for polydisperse-polymer solutions with either a standard or an arbitrary distribution for the polymers molecular weight; in the latter case, the derivative method is applied, based on a previously developed spline fit. To illustrate the framework developed here, calculated liquid-liquid-equilibrium phase diagrams are shown, including UCST, LCST and hour-glass-shaped cloud-point curves, shadow curves, spinodals, critical points and their dependence on molecular parameters, on pressure and on molecular-weight distribution properties. used in those equations derived from ΔmixG. A binary energy parameter and a binary size parameter are used to fit experimental critical coordinates. Cloud-point curves, shadow curves, spinodals and critical points have been calculated under various conditions which cover different types of liquid-liquid-equilibrium phase equilibria including UCST, LCST and hour-glass shaped phase diagrams. If we have experimental critical points, spinodals, cloud-point curves and shadow curves, we can obtain the binary energy parameter and the binary size parameter as well as their temperature dependence if the experimental data cover a significant temperature range. Considering the difficulty of obtaining monodisperse polymer samples, we can now use a polydisperse polymer sample with a known molecular-weight distribution for experimental work (e.g. cloud points) and then use the parameters obtained experimentally to calculate phase-equilibrium properties for the same system but with a different molecular-weight distribution. Two different procedures, i.e., the discrete multicomponent method and the continuous functional method, have been used for deriving equations. Consistent results have been obtained by both methods. The discrete method is rigorous because polymer components are discrete. A continuous distribution function is only used to calculate various moments in those expressions. The functional method has the merit of mathematical integrity such that the continuous distribution function is built inside the whole framework. While the composition is, in fact, discrete, the continuous distribution provides a good approximation. The present work is only for solutions containing one solvent and one polydisperse polymer. Work in progress extends the methods discussed here to systems containing mixed solvents or mixed polymers and polymer blends with polydisperse polymers.

On the relationship between the equilibrium constants of consecutive association reactions

Anderko A. and Prausnitz J.M., 1994. On the relationship between the equilibrium constants of consecutive association reactions. Fluid Phase Equilibria, 95: 59-71. n nGeneralized association models for fluids require a large number of adjustable parameters (equilibrium constants) unless some effort is made to interrelate the different association constants. An association model has been developed by considering the probability of consecutive association reactions and the effect of that probability on the entropy of association. The relationship between the equilibrium constants of these reactions has been expressed by a function related to the Poisson distribution. When combined with an equation of state, the model accurately represents the properties of hydrogen fluoride and its mixtures with halogenated hydrocarbons. The Poisson distribution model is compared with the classical continuous linear association model. While the Poisson distribution model is superior for molecules that preferentially form associates of moderate size, the continuous linear model is more appropriate for molecules that can form polymers with a high degree of polymerization.

Equations of state from van der Waals theory: the legacy of Otto Redlich

Abstract Redlich showed that with carefully chosen modifications, the concepts of van der Waals can be effectively used for realistic respresentation of fluid-mixture properties. He placed emphasis on algebraic simplicity and on adherence to boundary conditions at low and at high densities. The spirit of Redlich has motivated recent and current work in equation-of-state development. A few examples are given here.

Monte Carlo simulations of hydrophobic polyelectrolytes. Evidence for a structural transition in response to increasing chain ionization

Monte Carlo simulation has been used to study the configurational properties of a lattice‐model isolated polyelectrolyte with attractive segment–segment interaction potentials. This model provides a simple representation of a hydrophobic polyelectrolyte. Configurational properties were investigated as a function of chain ionization, Debye screening length, and segment–segment potential. For chains with highly attractive segment–segment potentials (i.e., hydrophobic chains), large, global changes in polymer dimensions were observed with increasing ionization. The transformation from a collapsed chain at low ionization to an expanded chain at high ionization becomes increasingly sharp (i.e., occurs over a smaller range of ionization) with increasing chain hydrophobicity. The ionization‐induced structural transitions for this model hydrophobic polyelectrolyte are analogous to pH‐induced transitions seen in real polyelectrolytes and gels. These studies suggest a simple explanation for such transitions based o...