Threading-Induced Dynamical Transition in Tadpole-Shaped Polymers

Abstract

The relationship between polymer topology and bulk rheology remains a key question in soft matter physics. Architecture-specific constraints (or threadings) are thought to control the dynamics of ring polymers in ring–linear blends, which thus affects the viscosity to range between that of the pure rings and a value larger, but still comparable to, that of the pure linear melt. Here we consider qualitatively different systems of linear and ring polymers, fused together in “chimeric” architectures. The simplest example of this family is a “tadpole”-shaped polymer, a single ring fused to the end of a single linear chain. We show that polymers with this architecture display a threading-induced dynamical transition that substantially slows chain relaxation. Our findings shed light on how threadings control dynamics and may inform design principles for chimeric polymers with topologically tunable bulk rheological properties.

The influence of arm composition on the self-assembly of low-functionality telechelic star polymers in dilute solutions

“…Such responsive building blocks that can self-organize into higher-order structures may form soft patchy particles, which have directional interactions and varying softness. Furthermore, topological effects that arise in systems with complex architecture can alone lead to a range of interesting phenomena in and out of thermodynamic equilibrium for both low [9][10][11][12][13][14][15] and high system densities [16][17][18][19][20][21]. Functionalized biomolecules such as DNA-grafted colloidal particles represent a typical example where patchiness reflects the competition between inter-and intra-particle associations [22][23][24][25].…”

Non-Equilibrium Living Polymers

“…where P (L) = e −L/L0 /L 0 is the distribution of polymer lengths with mean L 0 and e −t/T d (L) is the longest contribution (p = 0 component) of the reptative relaxation for a polymer of length L. The solution to Eq. (2) can be found via a saddle-point approximation to be a stretched exponential with exponent 1/(β + 1), with β = 3 for reptation dynamics [2,11,12]. From the survival function µ(t), the stress relaxation can be found as G(t) = G 0 µ(t), with G 0 an instantaneous shear modulus.…”

“…dependence of relaxation time on the age of the sample, is peculiar of out-of-equilibrium systems. One way to monitor this ageing is to compute the age-dependent survival function η(t; T a ) = To+Ta Ta µ(t; T a )dt (12) where T a is the age of the sample and T o the observation time, assumed to be comparable that the relaxation time of the sample but shorter than the ageing time T a . The numerical implementation of this "breakage-only" case is straightforward and can be done as follows (source codes are available at a git repository, see acknowledgement section): starting from the algorithm for equilibrium living polymers (as explain in Fig.…”

Non-Equilibrium Living Polymers

“…For exponentially polydisperse polymers, the stress relaxation function is proportional to the following survival function where is the distribution of polymer lengths with mean and is the longest contribution ( component) of the reptative relaxation for a polymer of length L . The solution to Equation ( 2 ) can be found via a saddle-point approximation to be a stretched exponential with exponent , with for reptation dynamics [ 2 , 11 , 12 ].…”