  Polymer association at liquid-liquid interfaces is a promising way to
spontaneously obtain soft self-healing membranes. In the case of reversible
bonding between two polymers, the macromolecules are mobile everywhere within
the membrane and they can be absorbed into it at both boundaries due to binding
to macromolecules of the other type. In this work, we develop the theoretical
model of membrane growth based on these assumptions. The asymptotic dependence
of membrane thickness on time as h ~ t^(1/2), as typically observed in
experiments in a stationary regime, reveals an interdiffusion-controlled
process, where the polymer fluxes sustain the polymer absorption at the
membrane boundaries. The membrane growth rate is mainly determined by the
difference in equilibrium compositions at the boundaries, the association
constant, the polymer lengths and mobilities. This model is further used to
describe the growth of hydrogel membranes formed via H-bonding of polymers at
the interface between a solution of poly(propylene oxide) (PPO) in isopropyl
myristate and an aqueous solution of poly(methacrylic acid) (PMAA). The film
thickness is measured by reflectometric methods. The dependence of thickness on
time can be approximated by the power law t^(beta), where beta= 1/2 for the
PMAA solution at pH=3 and decreases with increasing pH and, hence, ionization
degree. The growth rate slows down about 25 times for 500-nm-thick films at pH
= 5.1 compared to the case of pH = 3. The ionization degree of PMAA solutions
was studied by potentiometric methods. Even a small change in ionization was
found to influence the growth rate of the film. A slowdown of the film growth
for the ionized polymer can be explained by a drop in the composition gradient
in the membrane, as is predicted by the proposed model.
