External field-driven property localization in liquids of responsive macromolecules

We explore theoretically the effects of external potentials on the spatial distribution of particle properties in a liquid of explicitly responsive macromolecules. In particular, we focus on the bistable particle size as a coarse-grained internal degree of freedom (DoF, or "property"), σ, that moves in a bimodal energy landscape, in order to model the response of a state-switching (big-to-small) macromolecular liquid to external stimuli. We employ a mean-field density functional theory (DFT) that provides the full inhomogeneous equilibrium distributions of a one-component model system of responsive colloids (RCs) interacting with a Gaussian pair potential. For systems confined between two parallel hard walls, we observe and rationalize a significant localization of the big particle state close to the walls, with pressures described by an exact RC wall theorem. Application of more complex external potentials, such as linear (gravitational), osmotic, and Hamaker potentials, promotes even stronger particle size segregation, in which macromolecules of different size are localized in different spatial regions. Importantly, we demonstrate how the degree of responsiveness of the particle size and its coupling to the external potential tune the position-dependent size distribution. The DFT predictions are corroborated by Brownian dynamics simulations. Our study highlights the fact that particle responsiveness can be used to localize liquid properties and therefore helps to control the property- and position-dependent function of macromolecules, e.g., in biomedical applications.