Homogeneous Crystallization of Poly(Ethylene Oxide) Confined to Droplets: The Dependence of the Crystal Nucleation Rate on Length Scale and Temperature

We present a study of homogeneous nucleation in polymer crystallization. Crystal nucleation is observed within discrete droplets of poly(ethylene oxide) that are formed by the dewetting of a thin film. The samples provide an ensemble of impurity-free droplets, with length scales that can easily be measured. Droplet crystallization is found in two distinct temperature regimes corresponding to homogeneous and heterogeneous nucleation. Here we focus on homogeneous nucleation and show that the nucleation rate scales with the volume of the crystallizable domain, indicating that we are observing homogeneous nucleation in the bulk of the droplets. In addition, the dependence of the nucleation rate on temperature is consistent with classical nucleation theory.

Figure 1

Optical microscopy image of a small section of the sample ($1000\mu \mathrm{m}$ wide) obtained at $T_c=-2.6°\mathrm{C}$. Amorphous droplets appear dark and semicrystalline droplets appear white under nearly crossed polarizers. The plot shows the fraction of crystallized droplets as a function of temperature upon cooling ($0.4°\mathrm{C}/\min$) for homogeneous nucleation.

Figure 2

Plot of the logarithm of the uncrystallized fraction as a function of time for the isothermal homogeneous crystallization of droplets at $T=-5°\mathrm{C}$. The data have been binned according to the base area of the droplets. The center of the bin range for the data sets is indicated in the legend [bin range: (44, 50, 75, 100, 125, 150, 175, 225) $\mu {\mathrm{m}}^2$].

Figure 3

Logarithmic plot of the time constant for the crystal nucleation of droplets as a function of the length scale of the droplets. The dependence of the time constant follows a power law: $\tau \sim R^{-n}$, where $n=3.2\pm 0.3$.

Figure 4

Semilogarithmic plot of the volume-normalized time constant, $\tau V$, as a function of temperature. The data show a linear dependence when $\tau V$ is plotted as a function of $1/[T_c(T_m-T_c{)}^2]$ as is expected from classical nucleation theory (see the inset). A fit to the averaged dewetted droplet data (solid symbols) is in remarkable agreement with the data from 19 (open symbols).