Dynamic Heterogeneity in Fully Miscible Blends of Polystyrene with Oligostyrene

Binary blends of polystyrene with oligostyrene are perfectly miscible ($\chi =0$) yet dynamically heterogeneous. This is evidenced by independent probing of the dipole relaxation perpendicular to the backbone by dielectric spectroscopy and molecular dynamics. The self-concentration model with a single intramolecular length scale qualitatively describes the slower segmental dynamics. A quantitative comparison based on MD, however, requires a composition-dependent length scale. The pertinent dynamic length scale that best describes the slow segmental dynamics in miscible blends relates to both intra- and intermolecular contributions.

Figure 1

Dielectric loss plotted as a function of frequency for the ${\mathrm{PS}}_3$ oligomer (upper left, temperatures in the range from 237.15 to 283.15 K), the $75/25$ blend (upper right, temperatures in the range from 319.15 to 336.15 K), the $50/50$ blend (lower left, temperatures in the range from 281.15 to 303.15 K), and the $25/75$ blend (lower right, temperatures in the range from 265.15 to 291.15 K). Lines are the result of fits to a summation of two Havriliak-Negami functions.

Figure 2

Time correlation function $P_1(t)$ for the PS 3mer and PS 65mer (${\mathrm{PS}}_{68}$) studied here from MD. The lines are KWW fits ($T=463\mathrm{K}$).

Figure 3

Arrhenius relaxation map of the segmental dynamics in the homopolymer ${\mathrm{PS}}_{68}$ (open squares) and ${\mathrm{PS}}_3$ (open circles) and the ${\mathrm{PS}}_{68}/{\mathrm{PS}}_3$ blends (triangles) with composition: $75/25/$ (top), $50/50$ (middle), and $25/75$ (bottom) obtained from MD (higher frequencies) and DS (lower frequencies). The slow and fast segmental dynamics in the blends are shown with filled and open symbols, respectively. In the blends the solid and dashed lines are fits based solely on MD predictions for self- and effective compositions Eq. (4) of the slow and fast dynamics using ${\phi }_{\mathrm{self}}{,}_A=0.48$ and ${\phi }_{\mathrm{self}}{,}_B=0.74$. The dash-dotted black line is the comparison to the SCLM model Eq. (2) with ${\phi }_{\mathrm{self}}{,}_A=0.26$. Notice the Arrhenius $T$ dependence for the fast segmental dynamics in the $75/25$ blend (confinement effects).

Figure 4

(a) Self-concentration for all binary blends and (b)–(d) effective concentrations for the different blends within a sphere as a function of the sphere radius calculated through MD simulations Eq. (4), LM Eq. (1), and SCLM model for $p=0.51$ Eqs. (2, 3) (for length scale radius of 0.9 nm and 0.4 nm for $A$ and $B$, respectively; $A$ is the 65mer and $B$ the 3mer) at $T=463\mathrm{K}$.

Figure 5

Composition dependence of (i) the ${\mathrm{PS}}_{68}$ static correlations ($d$) corresponding to the intermolecular atom-to-atom correlations in the blends (squares), and (ii) of the sphere radius (circles) that provides the best description of the slower segmental dynamics in the blends ($r$). The corresponding Kuhn length scale ($l_K$) is also shown with the dash-dotted line. Notice that the dynamic length scale, has a composition dependence (${\phi }^{-0.26}$), intermediate to the purely intermolecular (${\phi }^{-0.6}$) and intramolecular (${\phi }^0$) length scales.