Entropy-induced separation of star polymers in porous media

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) approximately 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 gammaf that govern entropic effects. We find that gammaf-1, the deviation of gammaf 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 that 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.

Critical dynamics and effective exponents of magnets with extended impurities

“…However this increase (of the order of 8 % if one compares z-exponents for point and line defects) is not dramatic to make MC simulations impossible due to enhanced critical slowing down. On the other hand, the same order of difference in critical exponents values holds also for the static exponents [20,21]. Therefore, we expect that the predicted change in the critical behavior of three dimensional magnets with extended impurities is within current experimental accuracy.…”

“…In our previous papers [20,21] we have also touched the question of existence of an upper marginal value for the defect dimensionality ε d . In our analysis, we observe the disappearance of a stable reachable FP for ε d slightly above 1.…”

“…Therefore, magnets with quenched extended defects of parallel orientation constitute a large class of systems with a bulk of unusual phenomena worth to be analyzed. Their asymptotic critical behavior was a subject of the field-theoretical renormalization group (RG) analyses [15,16,17,20,21]. In particular, a double expansion in both ε = 4 − d, ε d was suggested and RG functions were calculated [15] to order ε, ε d ; qualitatively, the crossover to a new universality class in the presence of extended defects was supported.…”

“…However, these divergent RG expansion did not give a reliable numerical estimate for the critical exponents -the goal highly desirable both for experimental and simulational purposes. Numerical estimates for the exponents describing static critical behavior of d = 3 magnets with parallel extended impurities were obtained only recently [20,21] by applying special resummation technique to the two-loop RG functions of Refs. [16,18].…”

Enhancement of the critical slowing down influenced by extended defects

“…Reliable estimates for the exponents describing static critical behaviour of such a model were obtained only recently [6] exploiting results of Refs. [5,7].…”