Unusual Transformation of Polymer Coils in a Mixed Solvent Close to the Critical Point

We have discovered unusual behavior of polymer coils in a binary solvent ($\mathrm{nitroethane}+\mathrm{isooctane}$) near the critical temperature of demixing. The exceptionally close refractive indices of the solvent components make the critical opalescence relatively weak, thus enabling us to simultaneously observe the Brownian motion of the polymer coils and the diverging correlation length of the critical fluctuations. The polymer coils exhibit a collapse-reswelling-expansion-reshrinking transition upon approaching the critical temperature. While the first stage (collapse) can be explained by the theory of Brochard and de Gennes, the subsequent expansion-reshrinking transition is a new unexpected phenomenon that has not been observed so far. We believe that this effect is generic and attribute it to microphase separation of the solvent inside the polymer coil.

Figure 1

The dependence of the hydrodynamic radius $R_h$ of polymer coils on the temperature distance from the critical point. (a) PS-25 (0.05% and 0.01% mass); (b) PS-50 (0.025% and 0.05% mass); (c) PS-123 (0.01% mass); (d) PBMA-180 (0.04% mass). The behavior of the correlation length $\xi$ is shown by the corresponding dotted and dashed curves.

Figure 2

(a) Dependence of the critical temperature on polymer concentration; (b) universal scaled relationship between the shift of the demixing critical temperature in the PS solutions with respect to the value in the pure binary solvent reduced by the degree of polymerization ($N$) and polymer concentration. The uncertainty of $T-T_c$ measurements is within 0.01 K, which corresponds to the symbol size.

Figure 3

(a) Asymptotic divergence ($\xi ={\xi }_0{t}^{-0.63}$, shown by dotted curves) of the critical correlation length near the critical temperatures of different polymer solutions; (b) amplitudes of the correlation length for the same solutions. The average uncertainty of the amplitude values is about 10%.

Figure 4

(a) Scaled relationship between the hydrodynamic radius of polymer coils and the correlation length of the critical fluctuations for different polymer solutions ($R_h^0$ is hydrodynamic radius of a polymer coil for each solution outside the critical region); (b) qualitative interpretation of the collapse-reswelling-expansion-reshrinking transition by the relationship between the scaled hydrodynamic ratio ($R_h/R_h^0$, solid curve), the excess concentration inside the coil ($c_{\mathrm{in}}-c$, dashed curve), and the rescaled distance to the critical temperature inside the coil and bulk sample: $t^{*}=(T-T_c)/T_c({\xi }_0/R_h^0{)}^{\nu }$ and $t_{\mathrm{in}}^{*}=(T-T_c{)}_{\mathrm{in}}/T_c({\xi }_0/R_h^0{)}^{\nu }$ ($t_{\mathrm{in}}^{*}$, dotted curve).