Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

Abstract

The Langevin dynamics of a self -interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one -loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, (∆/b d )N 2−νd ≥ 1, where ∆ is a disorder strength, b is a Kuhnian segment length, N is a chain length and ν is the Flory exponent. We have derived the general equation for the non -ergodicity function f (p) which characterizes the amplitude of frozen Rouse modes with an index p = 2πj/N . The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same critical disorder strength ∆c ∼ N −γ where the exponent γ ≈ 0.25 and does not depend from the solvent quality.

Constitutive equations for weakly entangled linear polymers

“…One can note that dynamics of a polymer chain in random fields was studied extensively [18,19], as a possible mode of motion of a macromolecule in entangled system. One can also note that this equation (at m = 0) is identical to the Langevin equation, which was formulated [20] to study the behaviour of polymer chain in a random static field. However, the force ϕį in Eq.…”

Polymer Chain Dynamics in a Random Environment: Heterogeneous Mobilities

“…With this we were able to quantitatively describe both the local as well as the dynamics at the chain level with a common set of parameters. The apparent strong disagreement of the dynamics at the chain level with that from macroscopic diffusion is not clear but might be related to the broad distribution of mobilities, to mesoscopic structure formation [15], or to entropic trapping [9], or to all of them.…”

“…In such a situation, the low-T g component moves in the random environment created by the frozen high-T g component -a qualitatively different scenario compared to that where both components move on similar time scales [8]. Beyond its interest for blend dynamics including plasticizing effects, this situation may create an experimental test bed facilitating investigations of polymer chains in random environments, which presently was mainly studied theoretically (see, e.g., [9,10] and references therein).…”

Surface functionalization of porous chitosan microsphere with silver nanoparticle and carbon dot

“…The resulting bluish white emulsion was freezed at −20°C for 2 h. At this low temperature, the dispersed water droplets containing dissolved chitosan were converted into ice particles. Thus, the polymeric chains of chitosan were quenched [20]. At room temperature when the ice starting melting, ethanol was added to make the melting process faster than the rate of relaxation of quenched polymeric chains of chitosan.…”