Impact of Single-Particle Compressibility on the Fluid-Solid Phase Transition for Ionic Microgel Suspensions

We study ionic microgel suspensions composed of swollen particles for various single-particle stiffnesses. We measure the osmotic pressure $\pi$ of these suspensions and show that it is dominated by the contribution of free ions in solution. As this ionic osmotic pressure depends on the volume fraction of the suspension $\varphi$, we can determine $\varphi$ from $\pi$, even at volume fractions so high that the microgel particles are compressed. We find that the width of the fluid-solid phase coexistence, measured using $\varphi$, is larger than its hard-sphere value for the stiffer microgels that we study and progressively decreases for softer microgels. For sufficiently soft microgels, the suspensions are fluidlike, irrespective of volume fraction. By calculating the dependence on $\varphi$ of the mean volume of a microgel particle, we show that the behavior of the phase-coexistence width correlates with whether or not the microgel particles are compressed at the volume fractions corresponding to fluid-solid phase coexistence.

Figure 1

(a) Crystal fraction versus generalized packing fraction for microgels with $c_X=1.6\mathrm{wt}\%$. (b) Liquid samples at various values of $\zeta$ for microgels with $c_X=0.2\mathrm{wt}\%$.

Figure 2

(a) Osmotic pressure versus $\zeta$ for microgels with different $c_X$ (see Table 1 for the symbol code). (b) Dimensionless osmotic pressure versus $\zeta$ for microgels with $c_X=0.2\mathrm{wt}\%$. Hollow symbols: membrane osmometer; crosses: dialysis. The solid line is the best fit to the theoretical model (see text) for $\zeta <0.63$. (c) Ionic microgel and its Donnan potential. (d) $\mathrm{\Gamma }Q$ versus $\sqrt{d_s}$.

Figure 3

(a) Packing fraction jump at the fluid-solid phase transition for various microgel suspensions. The horizontal line shows the hard-sphere value. The dashed line reflects the approximate constancy of $\mathrm{\Delta }\varphi$ for the stiffer microgels. The empty symbols correspond to an estimate of $\mathrm{\Delta }\varphi$ with the model discussed in the text but using an iterative approach that takes into account the $v=v(\varphi )$ change of the particles and hence the $\mathrm{\Gamma }$ change with $\varphi$ above random close packing. (b)–(h) Relative volume changes as a function of $\varphi$ for microgels with various $c_X$ as indicated on the graphs. The symbols indicate the suspension phase: (inverted triangle) liquid, (square) coexisting phases, and (circle) crystal.