Polymers in media with long-range-correlated quenched disorder

Universal size properties of a star-ring polymer structure in disordered environments

We consider the complex polymer system, consisting of a ring polymer connected to the f_{1}-branched starlike structure, in a good solvent in the presence of structural inhomogeneities. In particular cases f_{1}=1 and f_{1}=2, such a system restores the synthesized tadpole-shaped polystyrenes [Doi et al., Macromolecules 46, 1075 (2013)MAMOBX0024-929710.1021/ma302511j]. We assume that structural defects are correlated at large distances x according to a power law x^{-a}. Applying the direct polymer renormalization approach, we evaluate the universal size characteristics such as the ratio of the radii of gyration of star-ring and star topologies, and compare the effective sizes of single arms in complex structures and isolated polymers of the same total molecular weight. The nontrivial impact of disorder on these quantities is analyzed.

Loop statistics in polymers in crowded environment

We analyze the probability to find a single loop in a long flexible polymer chain in disordered environment in d dimensions. The structural defects are considered to be correlated on large distances r according to a power law ∼r(-a). Working within the frames of continuous chain model and applying the direct polymer renormalization scheme, we obtain the values of critical exponents governing the scaling of probabilities to find the loops of various positions along the chain as function of loops' length. Our results quantitatively reveal that the presence of structural defects in environment decreases the probability of loop formation in polymer macromolecules.

Ring polymers in crowded environment: conformational properties

We analyze the universal size characteristics of flexible ring polymers in solutions in presence of structural obstacles (impurities) in d dimensions. One encounters such situations when considering polymers in gels, colloidal solutions, intra- and extracellular environments. A special case of extended impurities correlated on large distances r according to a power law ~r(-a) is considered. Applying the direct polymer renormalization scheme, we evaluate the estimates for averaged gyration radius ⟨R(g ring)⟩ and spanning radius ⟨R(1/2 ring)⟩ of typical ring polymer conformation up to the first order of double ɛ = 4 - d, δ = 4 - a expansion. Our results quantitatively reveal an extent of the effective size and anisotropy of closed ring macromolecules in disordered environment. In particular, the size ratio of ring and open (linear) polymers of the same molecular weight grows when increasing the strength of disorder according to ⟨R(g ring)(2)⟩/⟨R(g chain)(2)⟩=½(1+(13/48)δ).

Equivalence of quenched and annealed averaging in models of disordered polymers

The equivalence of the influence of quenched and annealed disorder on the scaling properties of long flexible polymer chains is proved by analyzing the O(m)-symmetric field theory in the polymer (de Gennes) limit m → 0. Additional symmetry properties of the model in this limit are discussed.

Star copolymers in porous environments: scaling and its manifestations

We consider star polymers, consisting of two different polymer species, in a solvent subject to quenched correlated structural obstacles. We assume that the disorder is correlated with a power-law decay of the pair-correlation function g(x)~x(-a). Applying the field-theoretical renormalization group approach in d dimensions, we analyze different scenarios of scaling behavior working to first order of a double ɛ=4-d, δ=4-a expansion. We discuss the influence of the correlated disorder on the resulting scaling laws and possible manifestations such as diffusion-controlled reactions in the vicinity of absorbing traps placed on polymers as well as the effective short-distance interaction between star copolymers.

Entropy-induced separation of star polymers in porous media

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 adsorption of polymers in a medium with long-range correlated quenched disorder

The process of adsorption on a planar wall of long flexible polymer chains in a medium with quenched long-range correlated disorder is investigated. We focus on the case of correlations between defects or impurities that decay according to the power law x(-a) for large distances x , where x= (r,z) . A field theoretical approach in d=4-epsilon and directly in d=3 dimensions up to one-loop order for the semi-infinite |phi|(4) m-vector model (in the limit m-->0 ) with a planar boundary is used. The whole set of surface critical exponents at the adsorption threshold T= T(a) , which separates the nonadsorbed region from the adsorbed one, is obtained. Moreover, we calculate the crossover critical exponent Phi and the set of exponents associated with it. We perform calculations in a double epsilon=4-d and delta=4-a expansion and also for a fixed dimension d=3 , up to one-loop order for different values of the correlation parameter 2< a < or =3 . The obtained results indicate that for systems with long-range correlated quenched disorder a different set of surface critical exponents arises. All the surface critical exponents depend on a . Hence, the presence of long-range correlated disorder influences the process of adsorption of long flexible polymer chains on a wall in a significant way.

Polymers in long-range-correlated disorder

We study the scaling properties of polymers in a d-dimensional medium with quenched defects that have power law correlations approximately r(-a) for large separations r. This type of disorder is known to be relevant for magnetic phase transitions. We find strong evidence that this is true also for the polymer case. Applying the field-theoretical renormalization group approach we perform calculations both in a double expansion in epsilon=4-d and delta=4-a up to the one-loop order and second in a fixed dimension (d=3) approach up to the two-loop approximation for different fixed values of the correlation parameter, 2<or=a<or=3. In the latter case the numerical results need appropriate resummation. We find that the asymptotic behavior of self-avoiding walks in three dimensions and long-range-correlated disorder is governed by a set of separate exponents. In particular, we give estimates for the nu and gamma exponents as well as for the correction-to-scaling exponent omega. The latter exponent is also calculated for the general m-vector model with m=1,2,3.