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)∼r−a. Applying
the field-theoretical renormalization group approach we show in a double
expansion in ϵ=4−d and δ=4−a that there is a range of
correlation strengths δ 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 γf that govern entropic effects. We
find that γf−1, the deviation of γf from its mean field value
is amplified by the disorder once we increase δ 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.Comment: 14 pages, 7 figure