Nanoparticle Loading of Unentangled Polymers Induces Entanglement-Like Relaxation Modes and a Broad Sol–Gel Transition

Abstract

We combine molecular dynamics simulations, imaging and data analysis, and the Green–Kubo summation formula for the relaxation modulus G(t) to elicit the structure and rheology of unentangled polymer–nanoparticle composites distinguished by small NPs and strong NP–monomer attraction, εNPM ≫ k B T. A reptation-like plateau emerges in G(t) beyond a terminal relaxation time scale as the volume fraction, c NP, of NPs increases, coincident with a structure transition. A condensed phase of NP-aggregates forms, tightly interlaced with thin sheets of polymer chains, the remaining phase consisting of free chains void of NPs. Rouse mode analyses are applied to the two individual phases, revealing that long-wavelength Rouse modes in the aggregate phase are the source of reptation-like relaxation. Imaging reveals chain motion confined within the thin sheets between NPs and exhibits a 2D analogue of classical reptation. In the NP-free phase, Rouse modes relax indistinguishable from a neat polymer melt. The Fourier transform of G(t) reveals a sol–gel transition across a broad frequency spectrum, tuned by c NP and εNPM above critical thresholds, below which all structure and rheological transitions vanish.

Reduced Graphene-Oxide-Doped Elastic Biodegradable Polyurethane Fibers for Cardiomyocyte Maturation

“…86,87 The XD PU-10%rGO membrane exhibited high off-loaded stress, potentially due to rGO aggregation, which promotes fiber disentanglement and increased stress off-loading capacity. 88,89 This effect is further confirmed during XD creep analysis (Figure 4F). Nanoparticle aggregation within polymeric matrices reduces creep resistance.…”

“…The low rGO concentrations can enhance membrane mechanics, while higher concentrations may weaken ultimate tensile strength due to rGO aggregation. ,,, The initial modulus of the XD PU-10%rGO membrane was comparable with that of healthy myocardium, ranging from 0.02 to 0.5 MPa. , Native myocardium demonstrates adaptiveness to prolonged stress through collagen and elastin’s conformational changes, allowing it to unfurl and withstand stress. , Polymeric fibers have limited conformational changes, especially in the PD (Figure C), while the XD enables more fiber separation and reduced stress experience (Figure D). , The XD PU-10%rGO membrane exhibited high off-loaded stress, potentially due to rGO aggregation, which promotes fiber disentanglement and increased stress off-loading capacity. , This effect is further confirmed during XD creep analysis (Figure F). Nanoparticle aggregation within polymeric matrices reduces creep resistance. ,, Effective mechanical reinforcement with graphene derivatives relies on controlling particle aggregation within the polymeric matrix. ,,− Cyclic stretching of the fibrous membranes had overlapping stress–strain curves, indicating pseudoviscoelastic behavior (Figure G–I). Biaxial testing confirms the anisotropic mechanics of the aligned fibrous membranes, matching trends seen in the left ventricle wall (Figures J–L andS3).…”

Activity-Triggered Rheological Strengthening and Toughening of Nanoparticle-Doped Supramolecular Gels

“…The time-dependent averaged autocorrelation function is defined as ⟨ X p ( t )· X p (0)⟩/⟨ X p 2 ⟩, with the p th mode representing the length scale of NBSC subchains containing ( N – 1)/ p beads. The p th Rouse mode of a subchain containing ( N – 1)/ p beads is defined as − As shown in Figure a, NBSCs in the gel with passive NPs do not relax on length scales larger than l sub , confirming that the passive NPs cannot break the entangled structure of NBSCs. In contrast, the obtained autocorrelation functions for NBSCs in the gel with active NPs can, on all length scales, be fitted by the stretched exponential function used to describe the structural relaxation of unentangled chains where τ p and β p denote, respectively, the relaxation time and the stretching factor of subchains represented by the p th mode.…”

Rouse Mode Analysis of Relaxation in Polymer Blends

“…Note that for ideal chains, W eff and β p are constant without dependence on the mode p. The corresponding dependence of the stretching exponent β p and the effective monomeric relaxation rates W eff are shown in Figure 2. The stretching exponent β p has a minimum value when mode p represents polymer subchains of the same length scale as the kuhn length of the chains, l kh ≈ 2σ 0 for the adopted flexible chains, [26] caused by the asymmetrical mobilities of polymer subchains on this length scale along the directions perpendicular and parallel to the subchain contour length. The structural relaxation of subchains has no preferred direction on length scales significantly larger than the kuhn length, which leads to isotropic relaxation dynamics, that is, β p = 1 when N/p ≫ l kh .…”