Critical behavior of the banded-unbanded spherulite transition in a mixture of ethylene carbonate with polyacrylonitrile

We investigate the transition from unbanded to banded spherulitic growth in mixtures of ethylene carbonate with polyacrylonitrile. By carefully considering systematic errors, we show that the band spacing diverges with a power-law form showing scaling over nearly two decades. We also observe that the bands disorder as the transition point is approached. The critical exponent is nonclassical. One possible explanation is that the nonequilibrium transition is actually weakly first order (subcritical).

Figure 1

(Color online). Schematic diagram of sample holder, showing side and top views.

Figure 2

Front-velocity drifts in EC-PAN samples. Effects of sample inhomogeneities, aging, and sealing can be seen. Thick line: first run. Thin dotted lines: intermediate runs. Thick dotted line: 13th run.

Figure 3

Banded spherulitic growth in EC-PAN, $c=6.7\%$. Growth is to the right. (a) Typical image of bands. (b) FFT of image in (a), showing broad peak at the spatial frequency of the bands. (c) FFT with double 2D Gaussian fit superposed on it.

Figure 4

Front velocity and band spacing versus undercooling for $c=6.7\%$. Dashed lines are straight-line fits to segments of the front-velocity curve and a power-law fit to the band-spacing divergence.

Figure 5

(a) Band spacing vs undercooling for PAN concentrations of 2.80%, 2.95%, 3.57%, 4.04%, 6.08%, and 6.70%, with global fits shown as solid lines through each data set. (b) Corrected log-log plot of all six data sets. Solid line has a slope of 1.17. (c) Variation of critical undercooling (fits) with concentration.

Figure 6

(a) Scaled longitudinal correlation length vs concentration. (b) Largest observable band spacing vs. concentration.

Figure 7

Chemical structures of (a) ethylene carbonate and (b) polyacrylonitrile.

Figure 8

Liquidus curve for ethylene carbonate with added polyacrylonitrile $\left(102\mathrm{kD}\right)$.

Figure 9

Solid-liquid front velocity versus undercooling for different PAN concentrations, in the regime showing banding. ●, $2.80\mathrm{wt.}\%$; 엯, $2.95\mathrm{wt.}\%$; ◆, $3.57\mathrm{wt.}\%$; ▴, $4.04\mathrm{wt.}\%$; ▵, $6.08\mathrm{wt.}\%$; ∎, $6.70\mathrm{wt.}\%$.