  Responsive particles, such as biomacromolecules or hydrogels, display a broad
and polymodal distribution of conformations and have thus the ability to change
their properties (e.g, size, shape, charge density, etc.) substantially in
response to external fields or to their local environment (e.g., mediated by
cosolutes or pH). Here, we discuss the basic statistical mechanics for a model
of responsive colloids (RCs) by introducing an additional property degree of
freedom as a collective variable in a formal coarse-graining procedure. The
latter leads to an additional one-body term in the coarse-grained (CG) free
energy, defining a single-particle property distribution for an individual
polydisperse RC. We argue that in the equilibrium thermodynamic limit such a CG
system of RCs behaves like a conventional polydisperse system of non-responsive
particles. We then illustrate the action of external fields, which impose local
(position-dependent) property distributions leading to non-trivial effects on
the spatial one-body property and density profiles, even for an ideal
(non-interacting) gas of RCs. We finally apply density functional theory in the
local density approximation (LDA-DFT) to discuss the effects of particle
interactions for specific examples of i) a suspension of RCs in an external
field linear in both position and property, ii) a suspension of RCs with highly
localized properties (sizes) confined between two walls, and iii) a
two-component suspension where an inhomogeneously distributed (non-responsive)
cosolute component, as found, e.g., in the studies of osmolyte- or salt-induced
collapse/swelling transitions of thermosensitive polymers, modifies the local
properties and density of the RC liquid.
