From Free Energies to Phase Diagrams of Compressible Microgels

Microgels are soft colloidal particles composed of crosslinked polymer networks that swell by absorbing solvent. Their responsiveness to temperature and concentration enables applications such as drug delivery and photonic crystals. In concentrated suspensions, their elasticity and compressibility allow microgels to deswell, facet, and interpenetrate, influencing phase behavior. We model microgels by coupling the Hertz elastic pair potential with the Flory–Rehner theory of polymer networks [1]. To quantify how particle softness affects thermodynamic stability, we compute the Helmholtz free energies of fluid and crystalline phases using Monte Carlo simulations combined with thermodynamic integration, employing the ideal gas and Einstein crystal as reference systems for the fluid and solid phases, respectively. By matching the chemical potentials and pressures of the coexisting fluid and solid phases, we determine the coexistence region and construct the phase diagram over a range of crosslink fractions. Compared with incompressible Hertzian spheres [2], compressible microgels crystallize at lower volume fractions, consistent with experiment [3].

[1] M. Urich and A. R. Denton, Soft Matter 12, 9086 (2016).

[2] J. C. Pàmies et al., J. Chem. Phys. 131, 044514 (2009).

[3] M. Pelaez-Fernandez et al., Phys. Rev. Lett. 114, 098303 (2015).