Freeze fracturing of hydrogels

At moderate temperatures below the freezing temperature of water, the pore water inside a hydrogel cannot freeze because the surface energy of an ice–water phase boundary mitigates against the nucleation of ice crystals inside the nanoscale pores. This is a well-known consequence of the Gibbs-Thomson effect. However, if ice forms adjacent to a hydrogel or within a large pore then it can continue to grow by drawing water out of the hydrogel by cryosuction. Equilibrium between hydrogel and adjacent ice occurs at a liquidus temperature related to the osmotic pressure of the gel and therefore to its polymer concentration. We first study the fundamental interplay between temperature gradients and osmotic pressure gradients leading to fluid flow through the gel towards a solidification front in one dimension when a saturated gel is brought into contact with an isothermal cold boundary. We then study the growth of an ice wedge in two dimensions when a slab of hydrogel is subject to a temperature gradient imposed along the slab. Ice growth proceeds by drawing water predominantly transverse to the slab but the resulting longitudinal gradient of osmotic pressure draws water additionally along the slab. Ice growth also compresses the hydrogel, inducing a deviatoric elastic strain field that is characteristic of either mode I or mode II crack opening, depending on the conditions imposed on the displacement field at the boundaries of the slab. These studies are relevant to the cryopreservation of biological tissue, for example.