Direct Observation of Dynamic Tube Dilation in Entangled Polymer Blends: A Combination of Neutron Scattering and Dielectric Techniques

We report a microscopic observation of the time-dependent dynamic tube dilation process on isofrictional bidisperse melts. By applying neutron spin echo (NSE) and dielectric techniques on blends of long polyisoprene (PI) chains with short PI additives with different topology, we access the dynamics of the tube dilation process on a molecular scale. The time-dependent tube dilation is directly revealed by NSE as an additional time dependence of the dynamic structure factor in the local reptation regime. We identify the characteristic time of tube dilation as the terminal time of the additive.

Figure 1

Dielectric results obtained on mixtures of long PI chains with short linear chains (empty squares) and stars (filled diamonds). Filled circles show the pure long chains bulk results for comparison. The magnitude represented is the natural-log frequency derivative of the real part of the dielectric permittivity (sign changed). Data have been normalized according to the values of the segmental relaxation peak at 230 K (see SM [21]). The vertical arrow marks the frequency corresponding to ${\tau }_d^S$ for star additives deduced from NSE properly translated to 290 K by the temperature dependence given in the SM [21]. Inset: temperature dependence of the ratio between the frequency of the maximum of the long-chain normal mode in each mixture and in the homopolymer (same symbol code; lines show the average values).

Figure 2

Chain dynamic structure factor measured by NSE for PI chains at 423 K and the three $Q$ values investigated (squares: $\text{0.05\hspace{0.17em}\hspace{0.17em}}{\AA }^{-1}$; circles: $0.09{\AA }^{-1}$; diamonds: $0.13{\AA }^{-1}$). Empty symbols correspond to the pure PI system and filled symbols to PI chains (matrix) in the presence of short linear (a) and 8-arm stars (b) additives. Solid lines are the description of the dynamic structure factor of pure PI based on pure reptation mechanism. Dashed lines correspond to the phenomenological model described in the text for the PI chains in the presence of the additives, for which the tube diameter increases according to the dotted lines.

Figure 3

Master curve combining data on the imaginary part of the viscosity measured at different temperatures on 50% mixtures of long PI chains with short linear chains (blue empty squares) and stars (red filled diamonds) (see SM [21] Sec. VII where details about the rheological experiments are presented). Circles, crosses and empty diamonds show the pure long chains, pure short chains, and pure stars bulk results, respectively, for comparison. The reference temperature is 293 K. The vertical arrow marks the frequency corresponding to ${\tau }_d^S$ for the blend with star additives deduced from NSE and properly translated to 293 K with the temperature dependence given in the SM [21].