Self‐diffusion of small molecules into rubbery polymers: A lattice free‐volume theory

Abstract

In the framework of the free-volume (FV) theory, a new equation was derived for the evaluation of self-diffusion coefficients of small molecules in polymers above the mixture glass transition temperature. The derivation of the equation turned out to be straightforward once the equivalence between the free volume and the unoccupied volume given by thermodynamic lattice theories is assumed. A parameter evaluation scheme is proposed, which is substantially simpler compared with the conventional Vrentas-Duda approach, even without losing generality. The key assumption is discussed, and its consistency is verified from a numerical viewpoint. A comparison with experimental solvent self-diffusion coefficients for several solvent/polymer binary systems con-firmed that the proposed theory presents good correlative ability over wide temperature and composition ranges. Moreover, the introduced thermodynamic foundation allows one to easily include the pressure effect too. In the frame of the proposed lattice free volume theory, the sizes of the polymer jumping units decrease with temperature and increase with pressure. Such behavior converges with theoretical expectations and opens the way for a predictive FV theory. V C 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: [529][530][531][532][533][534][535][536][537][538][539][540] 2010

Copolymerization of VDF and HFP in Supercritical Carbon Dioxide: A Robust Approach for Modeling Precipitation and Dispersion Kinetics

“…Experimental values of monomer diffusion coefficients at different T , P , and compositions are not available. Therefore, we used typical values of pre‐exponential coefficient and overlap factor: D 0,VDF = D 0,HFP = 10 −6 dm 2 · s −1 and γ = 0.2 48. Note that, for low‐molecular‐weight components (monomers and CO 2 ), MW c * = MW c .…”

“…Such theory involves a very large number of adjustable parameters, whose evaluation becomes very difficult, if not impossible, for copolymers, where the composition dependencies must be considered. This problem was circumvented by using the recently proposed lattice free‐volume (LFV) theory 48. In the frame of the LFV theory, the self‐diffusion coefficient of the monomer A in a multicomponent polymeric system is expressed as: where D 0,A is a prexponential coefficient, γ the overlap factor, and $\omega _{c}^{i} $ are the weight fractions of the different species in phase i ( i = sc or pa).…”

“…Instead of approximating the size of the repeating unit averaging the Lennard‐Jones diameter of the two monomers,54 a different evaluation approach was followed taking advantage of LFV theory. In fact, Costa and Storti48 have shown that the specific closed‐packed volume obtained by the SL theory provides a reasonable estimation of the molecular volume. Therefore, assuming spherical geometry, the size of a low‐MW component A is given by: …”

Simulation analysis of drying of ternary polymeric solution coatings

“…In high molecular weight polymer and high concentrations of polymer, the friction factor between the polymer and solvents ( 13 and 23 ) are much greater than friction factor between solvent pair ( 12 , 21 ) and themselves ( 11 , 22 ). Model equations are given in Table 1.…”

“…Costa and Storti [23] obtained a new formalism through which self-diffusion coefficients can be evaluated from pure solvent diffusivity data and easily accessible thermodynamic data using only one adjustable parameter by using a lattice theory: the Sanchez-Lacombe thermodynamic theory. They have developed following equation to calculate the self diffusion coefficient of solvent…”