Nanoparticle Effect on the Dynamics of Polymer Chains and Their Entanglement Network

We explore the dynamics of entangled polymer chains embedded into nanocomposites. From primitive path analysis, highly entangled polymer chains are found to be significantly disentangled during increment of the volume fraction of spherical nonattractive nanoparticles (NPs) from 0 to 42%. A critical volume fraction, ${\varphi }_c=31\%$, is found to control the crossover from polymer chain entanglements to “NP entanglements.” While below ${\varphi }_c$, the polymer chain relaxation accelerates upon filling, above ${\varphi }_c$, the situation reverses: polymer dynamics becomes geometrically constrained upon adding NPs. Our findings provide a microscopic understanding of the dynamics of entangled polymer chains inside their composites, and offer an explanation for the unusual rheological properties of polymer composites.

Figure 1

(a)–(c) Snapshots of simulated systems at three different volume NP concentrations. Each chain has a randomly selected color, including black. NP effects on the distribution of (d) PP length $L_{\mathrm{pp}}$ and (e) tube diameter $a_{\mathrm{pp}}$. The solid lines in (d) and (e) are fitted Gaussian and beta functions, respectively.

Figure 2

(a) Normal mode analysis (see Supplemental Material [7], section IV) results for (top) reduced relaxation times ${\tau }_p^{*}{p}^2/N^2$ and (bottom) stretching parameters ${\beta }_p$, corresponding to the first 20 modes of FENE chains with different NP volume fractions $\varphi$. (b) Reduced disentanglement time ${\tau }_d$ vs reduced number of entanglements per chain $⟨Z_{\mathrm{kink}}⟩$ for PNCs with different $\varphi$. Below ${\varphi }_c=31\%$, the ${\tau }_d$ is found to be linearly proportional to $⟨Z_{\mathrm{kink}}⟩$, which indicates the “polymer entanglement”-dominated regime [9]. Beyond ${\varphi }_c=31\%$, the $⟨Z_{\mathrm{kink}}⟩$ continues diminishing while ${\tau }_d$ increases with $\varphi$, characterizing the NP entanglement-dominated regime. (c) Characteristic confinement length of FENE chains vs $\varphi$, compared with experimental results for PEP polymers (inset, from Ref. 5). $d_{\mathrm{app}}$ is the phenomenological or apparent tube diameter from $S(q,t)$/NSE measurements, $d_{\mathrm{geo}}$ is the calculated geometrical confinement length, and $d_{\mathrm{tube}}$ is the topological tube confinement, or the tube diameter $⟨a_{\mathrm{pp}}⟩$ obtained from PP analysis. The solid lines serve as guide.