title: Transient interfacial tension of partially miscible polymers.
abstract: The interfacial tension of three different binary polymer blends has been measured as function of time by means of a pendent drop apparatus, at temperatures ranging from 24 degrees C to 80 degrees C. Three grades of polybutene (PB), differing in average molecular weight and polydispersity, are used as dispersed phase, the continuous phase is kept polydimethylsiloxane (PDMS), ensuring different asymmetry in molecular weight across the interface. The interfacial tension changes with time and, therefore, this polymer blends can not be considered fully immiscible. Changes in interfacial tension are attributed to the migration of low-molecular weight components from the source phase into the interphase and, from there, into the receiving phase. In the early stages of the experiments, just after the contact between the two phases has been established, the formation of an interphase occurs and the interfacial tension decreases with time. As time proceeds, the migration process slows down given the decrease in driving force which is the concentration gradient and, at the same time, molecules accumulated in the interphase start to migrate into the "infinite" matrix phase. A quasi-stationary state is found before depletion of the low-molecular weight fraction in the drop occurs and causes the interfacial tension sigma(t) to increase. The time required to reach the final stationary value, sigma(stat), increases with molecular weight and is a function of temperature. Higher polydispersity leads to lower sigma(stat) and a weaker dependence of sigma(stat) on temperature is found. A model coupling the diffusion equation in the different regimes is applied in order to interpret the experimental results. Numerical solutions of the diffusion equation are proposed in the cases of a constant and a changing interphase thickness. In the latter case, the interphase is defined by tracking with time a fixed limiting concentration in the transient concentration profiles and the variations found in sigma(t) are attributed to the changes in the interphase thickness. A discrete version of this continuous model is proposed and scaling arguments are reported in order to compare the results obtained with the predictions of the continuous model. The kinetic model as proposed by Shi et al. [T. Shi, V.E. Ziegler, I.C. Welge, L. An, B.A. Wolf, Macromolecules 37 (2007) 1591-1599] appears as a special case of the discrete model, when depletion is not taken into account. Using the models, time scales for the diffusion process can be derived, which fit the experimental results quite well.
authors.affiliation: Eindhoven University of Technology, Department of Mechanical Engineering, Eindhoven, The Netherlands.
authors.forename: C
authors.initials: C
authors.lastname: Tufano
authors.forename: G W M
authors.initials: GW
authors.lastname: Peters
authors.forename: P D
authors.initials: PD
authors.lastname: Anderson
authors.forename: H E H
authors.initials: HE
authors.lastname: Meijer