A lightly cross-linked hydrogel has an average of lattice sites between cross-links…

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Rubber elasticity, swelling and gelation

Problem

A lightly cross-linked hydrogel has an average of

N_x = 250

lattice sites between cross-links and a Flory interaction parameter with water of

\chi = 0.40

(a good solvent,

\chi < 1/2

). Estimate the equilibrium volume swelling ratio

Q = V_{\rm swollen}/V_{\rm dry}

using the small-

\phi

scaling form of the Flory-Rehner condition,

Q \approx \left[N_x\left(\tfrac12 - \chi\right)\right]^{3/5}.