Using lattice-fluid model, a continuous thermodynamic framework is presented for phase-equilibrium calculations for binary solutions with a polydisperse polymer solute. A two-step process is designed to form a real po...Using lattice-fluid model, a continuous thermodynamic framework is presented for phase-equilibrium calculations for binary solutions with a polydisperse polymer solute. A two-step process is designed to form a real polymer solution containing a solvent and a polydisperse polymer solute occupying a volume at fixed temperature and pressure. In the first step, close-packed pure components including solvent and polymers with different molar masses or different chain lengths are mixed to form a closed-packed polymer solution. In the second step, the close-packed mixture, considered to be a pseudo-pure substance is mixed with holes to form a real polymer solution with a volume dependent on temperature and pressure. Revised Freed's model developed previously is adopted for both steps. Besides pure-component parameters, a binary size parameter cr and a binary energy parameter e12 are used. They are all temperature dependent. The discrete-multicomponent approach is adopted to derive expressions for chemical potentials, spinodals and critical points. The continuous distribution function is then used in calculations of moments occurring in those expressions. Computation procedures are established for cloud-point-curve, shadow-curve, spinodal and critical-point calculations using standard distribution or arbitrary distribution on molar mass or on chain length. Illustrative examples are also presented.展开更多
using close-packed lattice models,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.An expressionfor the Helmholtz function of ...using close-packed lattice models,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.An expressionfor the Helmholtz function of mixing is based on the revised Freed model developed previously.Asize parameter c_r and an energy parameter ε are used;the former can be temperature dependent,while the latter can depend on both temperature and chain-length of the polymer.The discretemulticomponent approach is adopted to derive expressions for chemical potentials,spinodals and criti-cal points.The continuous distribution function is then used in calculations of moments occurring inthose expressions.Computation programs are established for cloud-point-curve,shadow-curve,spinodal and critical-point calculations for polymer solutions with standard distribution or arbitrarydistribution of polymer.In the latter case,the derivative method developed previously is applied.lllustrations for phase-equilibrium calculations are展开更多
文摘Using lattice-fluid model, a continuous thermodynamic framework is presented for phase-equilibrium calculations for binary solutions with a polydisperse polymer solute. A two-step process is designed to form a real polymer solution containing a solvent and a polydisperse polymer solute occupying a volume at fixed temperature and pressure. In the first step, close-packed pure components including solvent and polymers with different molar masses or different chain lengths are mixed to form a closed-packed polymer solution. In the second step, the close-packed mixture, considered to be a pseudo-pure substance is mixed with holes to form a real polymer solution with a volume dependent on temperature and pressure. Revised Freed's model developed previously is adopted for both steps. Besides pure-component parameters, a binary size parameter cr and a binary energy parameter e12 are used. They are all temperature dependent. The discrete-multicomponent approach is adopted to derive expressions for chemical potentials, spinodals and critical points. The continuous distribution function is then used in calculations of moments occurring in those expressions. Computation procedures are established for cloud-point-curve, shadow-curve, spinodal and critical-point calculations using standard distribution or arbitrary distribution on molar mass or on chain length. Illustrative examples are also presented.
文摘using close-packed lattice models,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.An expressionfor the Helmholtz function of mixing is based on the revised Freed model developed previously.Asize parameter c_r and an energy parameter ε are used;the former can be temperature dependent,while the latter can depend on both temperature and chain-length of the polymer.The discretemulticomponent approach is adopted to derive expressions for chemical potentials,spinodals and criti-cal points.The continuous distribution function is then used in calculations of moments occurring inthose expressions.Computation programs are established for cloud-point-curve,shadow-curve,spinodal and critical-point calculations for polymer solutions with standard distribution or arbitrarydistribution of polymer.In the latter case,the derivative method developed previously is applied.lllustrations for phase-equilibrium calculations are
