Role of Distributions of Intramolecular Concentrations on the Dynamics of Miscible Polymer Blends Probed by Molecular Dynamics Simulation

Using molecular dynamics simulations we show that a given monomer in a miscible polymer blend experiences broad distributions of both connectivity driven self-concentrations and thermodynamically controlled intermolecular concentration fluctuations. While these distributions should play a significant role in determining the constituent’s dynamics across the whole concentration range, the distribution of self-concentrations is particularly important in the dilute limit, where intermolecular concentration fluctuations should be absent. These conclusions allow us to rationalize the recent literature results that report the apparent self-concentration determined in the dilute limit surprisingly depended on the blend partner.

Figure 1

Distributions of intramolecular compositions coming from monomers on the same chain as the central monomer, in various spherical volumes surrounding monomers of a given type. MD simulation data are shown as symbols, and fits of Eq. (4) to the simulation data are shown as lines, for $R_c=1.5\sigma$ (black circles), $2.0\sigma$ (red triangles), $2.5\sigma$ (blue squares), and $3.5\sigma$ (green diamonds). Inset: NMR determinations of self-concentration for dilute polyisoprene (PI) ($T_g$ shown as vertical dashed line) [11] in blends with three higher-$T_g$ partners [polyvinylethylene PVE, polystyrene PS2 ($M_n=1860$), and PS11 ($M_n=11000$)] plotted as a function of the $T_g$ of the blend partner. Filled symbols were determined from the ratio of measured relaxation times to those of pure PI, and open symbols were determined by fitting the measured relaxation times to the Vogel equation, as described in 11. The horizontal dashed line is the LM expected ${\varphi }_{\mathrm{self}}=0.45$ for PI. The solid line is the predicted trend using the results for $R_c=1.5\sigma$ (see text).

Figure 2

Probability distribution function $P(\varphi )$ for spherical volumes surrounding a central monomer for $R_c=1.5\sigma$ with different bulk blend compositions: Red open circles have ${\varphi }_{\mathrm{bulk}}=0.04$; blue triangles ${\varphi }_{\mathrm{bulk}}=0.20$; black squares ${\varphi }_{\mathrm{bulk}}=0.40$; pink diamonds ${\varphi }_{\mathrm{bulk}}=0.60$; cyan stars ${\varphi }_{\mathrm{bulk}}=0.80$. The $P_C({\varphi }_{\mathrm{intra}})$ distribution is also shown as filled green circles. MD simulation data are shown as symbols, and predictions for each data set using the model described in the text are shown by lines. Arrows denote the LM predicted values of ${\varphi }_{\mathrm{eff}}$.

Figure 3

Effective composition within a sphere of radius $R_c$ as functions of bulk blend composition, for three different choices of $R_c$: Red triangles $R_c=1.5\sigma$; blue stars $R_c=2.5\sigma$; black circles $R_c=3.5\sigma$. The lower dashed line is ${\varphi }_{\mathrm{eff}}={\varphi }_{\mathrm{bulk}}$ and the three solid lines are Eq. (5), displaced from the dashed line by ${\varphi }_{\mathrm{self}}/2$. The upper dashed line is the LM prediction [10] ${\varphi }_{\mathrm{eff}}={\varphi }_{\mathrm{self}}+{\varphi }_{\mathrm{bulk}}$ ($1-{\varphi }_{\mathrm{self}}$) with the average ${\varphi }_{\mathrm{self}}=0.358$ for $R_c=1.5\sigma$.