Phase behavior of binary and polydisperse suspensions of compressible microgels controlled by selective particle deswelling

We investigate the phase behavior of suspensions of poly($N$-isopropylacrylamide) (pNIPAM) microgels with either bimodal or polydisperse size distribution. We observe a shift of the fluid-crystal transition to higher concentrations depending on the polydispersity or the fraction of large particles in suspension. Crystallization is observed up to polydispersities as high as 18.5%, and up to a number fraction of large particles of 29% in bidisperse suspensions. The crystal structure is random hexagonal close-packed as in monodisperse pNIPAM microgel suspensions. We explain our experimental results by considering the effect of bound counterions. Above a critical particle concentration, these cause deswelling of the largest microgels, which are the softest, changing the size distribution of the suspension and enabling crystal formation in conditions where incompressible particles would not crystallize.

Figure 1

(a) Microgel particle and its counterion cloud that extends towards the outside (dark red shell) and the inside (light red shell) of the particle. The fixed charges and the counterions are represented by $\ominus$ and $\oplus$, respectively. (b) Dilute suspension where only a small fraction of the counterions ($●$) can leave the particle due to thermal fluctuations. (c) Concentrated suspension with percolated counterion clouds. The bound counterions freely explore the volume between the microgels.

Figure 2

Relative viscosity ${\eta }_{\text{r}}$ as a function of microgel concentration given by the polymer mass fraction $c$ for (a) s21, $R_h=(78.6\pm 0.6)$ nm, $m_{\text{p}}=(0.9\pm 0.1)\times {10}^{-19}$ kg; (b) s2, $R_h=(139\pm 1)$ nm, $m_{\text{p}}=(6.3\pm 0.6)\times {10}^{-19}$ kg; (c) s16, $R_h=(167\pm 2)$ nm, $m_{\text{p}}=(9.2\pm 0.7)\times {10}^{-19}$ kg; (d) s11, $R_h=(182\pm 2)$ nm, $m_{\text{p}}=(14\pm 2)\times {10}^{-19}$ kg. The experimental data ($●$) are fitted with Eq. (2) (curves).

Figure 3

Scattered intensity ($▹$) and structure factor ($◊$) of sample s2 in (a) the fluid state at $\zeta =0.51\pm 0.01$, (b) the crystalline state at $\zeta =0.64\pm 0.02$, and (c) the disordered solid state at $\zeta =0.82\pm 0.02$. The form factors measured using SANS ($○$) at $\zeta =0.08\pm 0.01$ and SAXS ($\square$) at $\zeta =0.06\pm 0.01$ are shown in each panel.

Figure 4

Concentration series of sample s3 showing, with increasing $\zeta$, the fluid, fluid-crystal coexistence, fully crystalline, and glassy state. In crystalline samples, the iridescence due to Bragg peaks is visible.

Figure 5

Freezing ($○$) and melting ($\square$) points observed in (a) s-samples with particle radii in the range from 110 nm to 200 nm, (b) b-samples with varying fraction of large particles, $n_{\text{l}}$, and (c) p-samples with polydispersities between 11% and 18.5%. The behavior of the freezing and melting points is highlighted by the dotted blue and dashed black lines, respectively. The magenta lines in (b) represent the freezing and melting lines for $n_{\text{l}}\lesssim 2.5\%$. All phase behavior data are taken at $T=(18.3\pm 0.5){}^{\circ }\mathrm{C}$.

Figure 6

Representation of the size distribution of (a) a b-sample with $n_{\text{l}}=10\%$ and (b) a p-sample with $p=15\%$ with all particles fully swollen (thin green curve) and with large particles deswollen (thick black curve). The blue dashed curve and red dash-dotted curve show the size distributions of the involved small and large s-samples, respectively. The light gray areas highlight the fraction of large particles that deswell, whereas the dark gray areas represent the fraction of large particles that cooperates with the small ones in the deswelling mechanism.

Figure 7

Freezing-point ($●$) and the corresponding value of ${\zeta }_{\text{s}}^{\text{eff}}$ ($█$) for (a) b-samples vs the number-fraction of large particles, $n_{\text{l}}$, and (b) p-samples vs the polydispersity ${\sigma }_{\text{p}}$. The horizontal solid lines represent the mean value of ${\zeta }_{\text{s}}^{\text{eff}}$. In (b) the dashed horizontal line highlights the increase of ${\zeta }_{\text{f}}$ at ${\sigma }_{\text{p}}\approx 14\%$, and the vertical line shows the limiting polydispersity for crystallization in hard spheres.

Figure 8

(a) $d_{\text{nn}}$ versus ${\zeta }_{\text{tot}}$ for suspensions with small ($○$) and large ($◇$) s-samples as well as the bidisperse b-samples ($\square$) with $n_{\text{l}}=(4.7\pm 0.5)\%$. Solid symbols represent crystalline samples while open symbols represent disordered samples, both fluid and glassy. (b) $S\left(q\right)$ of ($\square$) bidisperse suspension with $n_{\text{l}}=(18\pm 2)\%$ and $\zeta =0.65\pm 0.02$, ($○$) crystal of s-sample with small particles at $\zeta =0.62\pm 0.01$, and ($◇$) crystal of s-sample with large particles at $\zeta =0.64\pm 0.02$. The detector image of the bidisperse sample is shown in the inset. (c–e) $d_{\text{nn}}$ versus ${\zeta }_{\text{tot}}$ with symbols as in (a) and with (c) $n_{\text{l}}=(29\pm 3)\%$, (d) $n_{\text{l}}=(38\pm 4)\%$, (e) $n_{\text{l}}=(79\pm 8)$%. In panels (a and c–e), the effective volume fraction of the small particles, ${\zeta }_{\text{s}}^{\text{eff}}$, is given in the upper $x$ axis. The violet vertical lines correspond to ${\zeta }_{\text{s}}^{\text{eff}}=1$. The dashed, dotted, and dash-dotted curves show fits to the data with the function $a{\zeta }^{-1/3}$ for suspensions with small particles only, large particles only, and bidisperse samples, respectively. (f) $S\left(q\right)$ of glassy samples: ($\square$) bidisperse suspension with $n_{\text{l}}=(79\pm 8)\%$ and $\zeta =0.60\pm 0.02$, ($○$) small s-sample at $\zeta =0.60\pm 0.01$, and ($◇$) large s-sample at $\zeta =0.60\pm 0.01$. The temperature is fixed to $T=(18.0\pm 0.5){}^{\circ }\mathrm{C}$ in all measurements.

Figure 9

(a–d) $d_{\text{nn}}$ versus ${\zeta }_{\text{tot}}$ for suspensions with ($○$) small and ($◇$) large s-samples as well as the ($\square$) polydisperse p-samples with (a) ${\sigma }_{\text{p}}=(14.0\pm 0.8)\%$, (b) ${\sigma }_{\text{p}}=(14.9\pm 0.1)$%, (c) $(14.7\pm 0.8)$%, and (d) $(13.5\pm 0.8)$%. (e) $S\left(q\right)$ of ($\square$) p-sample with ${\sigma }_{\text{p}}=(14.9\pm 0.1)\%$ and $\zeta =0.64\pm 0.01$, ($○$) crystal of only small monodisperse particles at $\zeta =0.67\pm 0.02$, and ($◇$) crystal of only large monodisperse particles at $\zeta =0.64\pm 0.02$. In the inset of (e), we show the detector image of the polydisperse sample. (f) $d_{\text{nn}}$ versus ${\zeta }_{\text{tot}}$ for ${\sigma }_{\text{p}}=(17\pm 1)\%$ and with symbols as in (a–d). $△$ symbols represent the third s-sample involved in the p-sample. (a–d and f) Solid symbols represent crystalline samples, while open symbols represent disordered samples, both fluid and glassy. The vertical violet lines correspond to ${\zeta }_{\text{s}}^{\text{eff}}=1$. The dashed, dotted, and dash-dotted curves show fits to the data with the function $a{\zeta }^{-1/3}$, for suspensions comprised of small and large particles, and polydisperse suspensions, respectively. The temperature is fixed to $T=(18.0\pm 0.5){}^{\circ }\mathrm{C}$ in all measurements.