Stratification in Drying Polymer–Polymer and Colloid–Polymer Mixtures

Abstract

Drying polymer-polymer and colloid-polymer mixtures were studied using Langevin dynamics computer simulations. Polymer-polymer mixtures vertically stratified into layers, with the shorter polymers enriched near the drying interface and the longer polymers pushed down toward the substrate. Colloid-polymer mixtures stratified into a polymer-on-top structure when the polymer radius of gyration was comparable to or smaller than the colloid diameter, and a colloid-on-top structure otherwise. We also developed a theoretical model for the drying mixtures based on dynamical density functional theory, which gave excellent quantitative agreement with the simulations for the polymer-polymer mixtures and qualitatively predicted the observed polymer-on-top or colloid-on-top structures for the colloid-polymer mixtures.

Influence of hydrodynamic interactions on stratification in drying mixtures

“…The implicit-solvent model predicted stratification in agreement with previous simulations and theoretical considerations. 17 However, no such stratification was found for the explicitsolvent model at the drying conditions considered. Despite good mapping of the equilibrium bulk properties (chemical potential, diffusion coefficient) between the explicit-and implicit-solvent models, hydrodynamic interactions out of equilibrium were shown to alter the polymer diffusion in a way that is consistent with the lack of stratification.…”

“…We used the average interface speed and the diffusion coefficients at infinite dilution to estimate film Péclet num- The qualitatively different behavior of the two models suggests a significant difference in the relative migration speeds of the polymer chains, which was previously shown to give rise to stratification for the implicit-solvent model. 12,15,17,22 At isothermal conditions, the relative migration speed ∆u predicted by the Howard et al model 15 is…”

“…17 The stratification was more pronounced for larger size ratios and faster drying speeds, although it was found to persist even at moderate drying rates. 13,15,17 Stratification has been modeled theoretically as a diffusion process 7,18 qualitatively predicted a maximum in the number of large colloids on top of the film when Pe 1 < 1 and Pe 2 > 1 (here 1 is the smaller colloid and 2 is the larger colloid). 20 For computational and theoretical convenience, many previous studies have employed a free-draining approximation for hydrodynamic interactions on the colloids or polymers, incorporating the Stokes drag on each particle but neglecting other interactions.…”

“…This approach gives the correct long-time dynamics, but distorts the internal relaxation modes of the polymers. 17 We measured diffusion constants of D 1 = 0.0342 σ 2 /τ for the M 1 = 10 polymers and D 2 = 0.0071 σ 2 /τ for the M 2 = 80 polymers from the polymer center-of-mass mean squared displacement in a cubic box with edge length L = 50 σ, giving 2.92 m/τ and 1.76 m/τ for the friction coefficients, respectively.…”

“…The liquid-vapor interface was modeled by the repulsive part of a harmonic potential. 15,17 (The complete form of the potential can be found in ref. 15.)…”