{'fraction_non_alphanumeric': 0.023064250411861616, 'fraction_numerical': 0.0032948929159802307, 'mean_word_length': 5.136363636363637, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Translational dynamics of a particle with anchored chains in entangled polymers.

We investigate the dynamics of a spherical particle of an arbitrary size immersed in entangled linear polymers. In particular, we calculate analytically and numerically the velocity autocorrelation function (VAF) of the particle, using the microscopic boundary layer model developed by Sung [Physics of Complex Fluids and Biological Systems, edited by W. Sung et al. (Min Eum Sa Co, Seoul, 1993)]. The model incorporates the short-range dynamical effect of the interface chains attached to the particle and simultaneously entangled with background chains, as well as the longer-range viscoelastic response from the background, treated as a continuum. The VAF calculated therefrom manifests the interplay of elastic response at short times and viscous relaxation via chain reptation at long times. The VAF at long times decays very slowly with the long-time tails suppressed due to the entanglement constraint. On the other hand, the constraint gives rise to an elastic response at short times, leading to enhanced caging of the particle. We discuss the various modes of the particle dynamics that emerge as the particle size varies.