Origin of SAXS intensity in the low-$q$ region during the early stage of polymer crystallization from both the melt and glassy state

The isothermal crystallization from the melt and glassy state of poly(trimethylene terephthalate) has been studied with wide-angle x-ray diffraction, small-angle x-ray scattering (SAXS), and ultrasmall-angle x-ray scattering (USAXS). Large scattering intensity in the low-$q$ region has been observed with SAXS and USAXS during the early stage of melt and glass crystallizations. We have quantitatively analyzed the x-ray results using the scattering equations which can simultaneously deal with the hierarchical structures consisting of the crystallites and their aggregates. The results reveal the crystallization mechanism in which the crystalline nodules cover the entire sample with the aggregation regions. The conclusion quantitatively shows that the large SAXS intensity is not due to the density fluctuations of the liquid state but due to the correlations among the heterogeneous aggregation regions of the nodules.

Figure 1

(a) WAXD profiles and (c) crystallinity ${\varphi }_c^W$ as a function of $t_c$ for PTT crystallized at $60{}^{\circ }\mathrm{C}$ from the melt. (b) The WAXD profile of PTT crystallized at $60{}^{\circ }\mathrm{C}$ for 1000 sec from the melt state. The gray circles in (b) show the experimentally observed intensity. The thick solid black curve is the sum of the crystalline components (thin solid line) and the amorphous component (broken line). ${\varphi }_c^W$ in (c) is calculated from the WAXD profiles in (a).

Figure 2

SAXS and USAXS profiles $I_{\mathrm{sub}}\left(q\right)$ as a function of $t_c$ for PTT crystallized at $60{}^{\circ }\mathrm{C}$ from the melt state (a) until and (b) after 280 sec, (c) the USAXS profile of PTT crystallized for 275 sec, and (d) the USAXS profiles normalized by $q_{\mathrm{\Lambda }}$ and $I_{\mathrm{sub}}\left(q_{\mathrm{\Lambda }}\right)$ in (a) and (b). The solid curves in (c) are the fitting curve using $aexp(-b^2{q}^2)$ (chain curve) and $\mathrm{c}{q}^{-4}$ (dotted curve). The broken curve in (d) is a master curve. The right triangles in (c) and (d) indicate a slope of $-4$.

Figure 3

$t_c$-dependent (a) $Q_T$, $Q_H$, and $Q_L$, (b) $\chi$ and ${\varphi }_c$ obtained from SAXS and WAXD results, and (c) $1/q_{\mathrm{\Lambda }}$ and $q_{\mathrm{\Lambda }}^{3}I\left(q_{\mathrm{\Lambda }}\right)$. In (b) the values of ${\chi }^Q$ and ${\chi }^S$ were obtained from $Q_H$ (open circles) and from $q_{\mathrm{\Lambda }}^{3}I\left(q_{\mathrm{\Lambda }}\right)$ (open squares), respectively. The values of ${\varphi }_c$ were obtained from the $Q$ values (open triangles) and from the WAXD results (open diamonds) in Fig. 1, respectively.

Figure 4

(a) $I_L\left(q\right)$ for PTT crystallized at $T_c$ for $t_h$ from the melt state (filled symbols), and the glassy state (open ones), $T_c$-dependent (b) $t_h$ and (c) $1/q_{\mathrm{\Lambda },h}$, and (d) $I_L\left(q\right)$ normalized by $q_{\mathrm{\Lambda },h}$ and $I_L(q_{\mathrm{\Lambda },h},t_h)$ in (a).