Modeling of solute release from polymeric monoliths subject to linear structural relaxation

Abstract

A previously developed model of solute release from a swellable polymeric matrix induced by solvent uptake that obeys Fickian kinetics is here extended to cover the case of non‐Fickian solvent uptake caused by slow structural relaxation of the swelling polymer. For this purpose, we have adopted a model description of the absorption process (also previously developed in our laboratory), which has been shown to be capable of realistically simulating a wide range of non‐Fickian kinetics (including the well‐known two‐stage sorption and case II regimes). The aforementioned structural relaxation phenomena constitute important characteristics of glassy polymeric matrices. Accordingly, the predictions of the resulting combined model have been investigated in some detail in this series of articles. This particular article is concerned with the simplest version of the model, involving constant uptake kinetic parameters (diffusion coefficient and relaxation frequency) for both osmotically inactive and osmotically active solutes. Emphasis is put on possibilities of achieving and sustaining nearly constant release rates, and it is shown that such possibilities are considerably more numerous here than under conditions of Fickian solvent uptake kinetics. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1171–1188, 2002

Combined experimental and computer simulation study of the kinetics of solute release from a relaxing swellable polymer matrix. II. Release of an osmotically active solute

“…The transport of solvent (subscript W ) and solute (subscript N ), contained in a monolith in the form of a swellable thin film (of thickness 2 l ), preequilibrated with solvent at activity a W = a W 0 and exposed to bulk solvent ( a W = 1) at time t ≥ 0, is described by1, 3 with boundary conditions In eqs. (1) and (2), (2), (2), 0 ≤ x ≤ l represents distance across one‐half of the film (measured in units referred to the unswollen matrix), with x = 0 at the exposed surface; C,a,S , and D represent concentration (measured in mole or gram per unit volume or mass of unswollen polymer), activity, solubility coefficient, and (thermodynamic) diffusion coefficient, respectively, of the relevant species in the matrix.…”

“…The activity of solvent (water) a W , at given x, t , is defined to be equal to the relative vapor pressure (relative humidity) which would be at equilibrium with C W , at that x, t (with due vapor nonideality correction if desired), bearing in mind that the relevant a W value will also depend on (1) the value of C N , at the given x, t , if the solute is osmotically active,1, 3 and (2) the state of relaxation of the polymer 1, 2. These effects are taken into account by defining absorption isotherms for the fully relaxed and unrelaxed polymer matrix,1, 2 augmented1, 3 with a suitable dependence on C N . Thus, eqs.…”

“…(2), (2), (2), (2a), and (3) of Part I2 become, respectively, where f N ( C N ) may be any convenient function which can adequately represent the behavior of the particular system of interest, subject to the condition f N ( C N = 0) = 1. The linear expression was chosen for the theoretical investigations previously reported1, 3 as the simplest function fulfilling the aforementioned condition (while Polishchuk et al4 opted for an exponential dependence). For the same reasons, a unique K W 3 value was specified1 for eqs.…”

“…We then proceed to simulate on the computer the combined kinetic behavior of solvent and solute. This simulation is based on a previously developed modeling approach to solute release from relaxing glassy polymer matrices,1 complemented by (1) information gained from our preceding study of non‐Fickian liquid water uptake by CA films2 and (2) subsidiary solute sorption and diffusion measurements undertaken here, for the independent determination of model parameters.…”

“…The notation of refs. 1 and2 is maintained, except for the fact that it was found more convenient here to use a different mode of normalization of solute‐related parameters [see eq. (11) below].…”