Entropy-induced separation of star polymers in porous media

TL;DR

This paper investigates how long-range correlated porous media influence the entropy and scaling behavior of star polymers, revealing that disorder amplifies entropic effects and affects polymer separation.

Contribution

It provides a quantitative analysis of star polymer scaling in correlated porous media using field-theoretical renormalization group methods and calculations of scaling exponents.

Findings

Disorder alters the scaling behavior of star polymers beyond a certain correlation strength.

Star polymers exert higher osmotic pressure and are expelled more in correlated porous media.

Chains prefer more correlated media, while star polymers prefer less correlated environments.

Abstract

We present a quantitative picture of the separation of star polymers in a solution where part of the volume is influenced by a porous medium. To this end, we study the impact of long-range-correlated quenched disorder on the entropy and scaling properties of $f$-arm star polymers in a good solvent. We assume that the disorder is correlated on the polymer length scale with a power-law decay of the pair correlation function $g(r) \sim r^{-a}$. Applying the field-theoretical renormalization group approach we show in a double expansion in $\epsilon=4-d$ and $\delta=4-a$ that there is a range of correlation strengths $\delta$ for which the disorder changes the scaling behavior of star polymers. In a second approach we calculate for fixed space dimension $d=3$ and different values of the correlation parameter $a$ the corresponding scaling exponents $\gamma_f$ that govern entropic effects. We find that $\gamma_f-1$, the deviation of $\gamma_f$ from its mean field value is amplified by the disorder once we increase $\delta$ beyond a threshold. The consequences for a solution of diluted chain and star polymers of equal molecular weight inside a porous medium are: star polymers exert a higher osmotic pressure than chain polymers and in general higher branched star polymers are expelled more strongly from the correlated porous medium. Surprisingly, polymer chains will prefer a stronger correlated medium to a less or uncorrelated medium of the same density while the opposite is the case for star polymers.