Molecular conformations of dumbbell-shaped polymers in good solvent.

We study conformational properties of diluted dumbbell polymers composed of two rings attached to both ends of a linear spacer segment. Our investigation involves analytical methods of field theory and bead-spring coarse-grained molecular dynamics simulations. We focus on the influence of the relative length of the spacer segment to the length of side rings on the shape and the relative size of dumbbells as compared to linear polymers of equal mass. We find that dumbbells with short spacers exhibit a significantly more compact structure than linear polymers. Conversely, as the spacer length increases, the influence of the side rings on the size of the dumbbells becomes negligible. Consequently, dumbbell molecules with long spacers attain a size comparable to corresponding linear chains. Our analytical theory accurately predicts a quantitative conformational crossover between the behaviors of short-spacer and long-spacer dumbbells, which is further confirmed by our numerical simulations.

Shape analysis of random polymer networks.

We propose the model of a random polymer network, formed on the base on Erdös-Rényi random graph. In the language of mathematical graphs, the chemical bonds between monomers can be treated as vertices, and their chemical functionalities as degrees of these vertices. We consider graphs with fixed number of vertices N = 5 and variable parameter c (connectedness), defining the total number of links L = cN(N - 1)/2 between vertices. Each link in such graphs is treated as a Gaussian polymer chain. The universal rotationally invariant size and shape characteristics, such as averaged asphericity and size ratio of such structures are obtained both numerically by application of Wei's method and analytically within the continuous chain model. In particular, our results quantitatively indicate an increase of asymmetry of polymer network structure when its connectedness c decreases.

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 â†’ 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.