Star Polymers in Correlated Disorder

Abstract

We analyze the impact of a porous medium (structural disorder) on the scaling of the partition function of a star polymer immersed in a good solvent. We show that corresponding scaling exponents change if the disorder is long-rangecorrelated and calculate the exponents in the new universality class. A notable finding is that star and chain polymers react in qualitatively different manner on the presence of disorder: the corresponding scaling exponents increase for chains and decrease for stars. We discuss the physical consequences of this difference.

Universal features of polymer shapes in crowded environments

“…(2,4) R (0, 0; q 1 , −q 1 , q 2 , −q 2 ; u, w) with four insertions φ 2 (q 1 ), φ 2 (−q 1 ), φ 2 (q 2 ), φ 2 (−q 2 ). The resulting expansion is too cumbersome to be presented here and will be given elsewhere [16]. Performing the derivatives with respect to the components of the vectors q 1 , q 2 we find:…”

“…The next step in our analysis will be to obtain the higher order expansions for the quantities of interest and to perform computer simulations in order to confirm these theoretical results by numerical values. Further details of our calculations as well as a generalization of the presented results to the case of polymers with complex topology will be given elsewhere [16].…”

Scaling of complex polymers: New universality classes and beyond

“…The scaling exponents of copolymer stars also determine the scaling of corresponding copolymer networks [5,9,13] and play role in a number of other phenomena, given below. Treating the model of star copolymers in a porous medium by the RG approach, we have found different scenarios of scaling behaviour and corresponding values for scaling exponents [6]. To summarise some results for the exponents, let us first introduce some notations.…”

Star copolymers in porous environments: Scaling and its manifestations

“…Note, that expressions for β uii , β wii restore the corresponding RG functions for a single polymer chain in long-range correlated disorder [20,21]. Here, I i are the loop-integrals:…”

“…The influence of such long-range correlated defects on the universal properties of single polymer has been analyzed within the renormalization group approach in Refs. [20,21].…”