Size and Diffusivity of Polymer Rings in Linear Polymer Matrices: The Key Role of Threading Events

Long molecular dynamics simulations are performed for dilute solutions of ring poly­(ethylene oxide) (PEO) molecules in matrices of linear PEO chains where we systematically vary the molecular length of the ring and host chains. Our focus is on the effect of linear chain size on microscopic structure, conformation, and dynamics of the guest ring molecules, and how these properties vary with the corresponding ones in the pure ring melts. Ring molecules are found to be significantly swollen in all ring–linear blends simulated. Ring swelling is more pronounced in matrices of very short linear chains (molecular weights less than about 1.5 kg/mol) due to excess, chain-end free-volume effects. In these very short linear hosts, all PEO rings simulated (molecular weights between 2 and 10 kg/mol) diffuse faster than in their own melts. However, as the size of the host linear chains increases above the entanglement molecular weight, the diffusivity of rings decreases considerably. Interestingly enough, for the shorter PEO rings simulated (molecular weight equal to 2 kg/mol), the diffusion coefficient in long, entangled matrices approaches a constant value independent of the molecular weight of the matrix, whereas that of longer rings (molecular weight equal to 5k and 10k g/mol) decreases continuously (at least for the linear matrix molecular weights examined here). Our simulation predictions for the diffusion coefficient of PEO rings in the linear PEO matrices compare remarkably well with the recent pulse-field gradient NMR measurements of Kruteva et al. [Macromolecules 2017, 50, 9482–9493]. A detailed topological analysis reveals that long ring molecules are heavily threaded by the host linear chains. Their segmental and diffusive dynamics is therefore governed by the rate with which threadings are created and released. Threadings, which are quantified in detail in our analysis, are also seen to cause strong fluctuations in the instantaneous conformation of the host linear chains, thus influencing their average dimensions. Our work provides strong evidence that ring–linear threadings is the key mechanism governing the size, the conformation, and the dynamic behavior of ring–linear polymer blends.