Universal size ratios of Gaussian polymers with complex architecture: radius of gyration vs hydrodynamic radius

We study the impact of arm architecture of polymers with a single branch point on their structure in solvents. Many physical properties of polymer liquids strongly dependent on the size and shape measures of individual macromolecules, which in turn are determined by their topology. Here, we use combination of analytical theory, based on path integration method, and molecular dynamics simulations to study structural properties of complex Gaussian polymers containing fc linear branches and fr closed loops grafted to the central core. We determine size measures such as the gyration radius Rg and the hydrodynamic radii RH, and obtain the estimates for the size ratio Rg/RH with its dependence on the functionality f=fc+fr of grafted polymers. In particular, we obtain the quantitative estimate of the degree of compactification of these polymers with increasing number of closed loops fr as compared to linear or star-shape molecules of the same total molecular weight. Numerical simulations corroborate theoretical prediction that Rg/RH decreases towards unity with increasing f. These findings provide qualitative description of polymers with complex architecture in θ solvents

Structural properties of cyclic polyelectrolytes in dilute good solvent

Cyclic polymers display unique physical behaviors in comparison to their linear counterparts. Theoretical, computational and experimental studies have revealed that some of their distinctive properties are also observed in charged variants of cyclic polymers, known as cyclic polyelectrolytes (PEs), especially in terms of their structural responses to variations in the strength of electrostatic interactions. In this study, we investigate the impact of cyclic topology on the conformations of PE chains in dilute good solvent using scaling analysis and coarse-grained bead-spring molecular dynamics simulations. Our observations indicate that, in contrast to linear PE chains, cyclic topology results in more compact conformations at low and intermediate Bjerrum lengths. Moreover, two structural metrics, asphericity and prolateness, which quantify deviations from spherical and flat molecular shapes, exhibit non-monotonic behaviors for cyclic PEs. This stands in contrast to linear PEs, where these shape characteristics exhibit a monotonic trend with increasing Bjerrum length. A feasible analytical theory, developed to account for ionic distributions around cyclic PE chains, suggests that the fundamental difference between linear and cyclic chain conformations may be attributed to topological effects influencing long-range electrostatic interactions

Spatial segregation of mixed-sized counterions in dendritic polyelectrolytes

Langevin dynamics simulations are utilized to study the structure of a dendritic polyelectrolyte embedded in two component mixtures comprised of conventional (small) and bulky counterions. We vary two parameters that trigger conformational properties of the dendrimer: the reduced Bjerrum length, λ∗B, which controls the strength of electrostatic interactions and the number fraction of the bulky counterions, fb, which impacts on their steric repulsion. We find that the interplay between the electrostatic and the counterion excluded volume interactions affects the swelling behavior of the molecule. As compared to its neutral counterpart, for weak electrostatic couplings the charged dendrimer exists in swollen conformations whose size remains unaffected by fb. For intermediate couplings, the absorption of counterions into the pervaded volume of the dendrimer starts to influence its conformation. Here, the swelling factor exhibits a maximum which can be shifted by increasing fb. For strong electrostatic couplings the dendrimer deswells correspondingly to fb. In this regime a spatial separation of the counterions into core–shell microstructures is observed. The core of the dendrimer cage is preferentially occupied by the conventional ions, whereas its periphery contains the bulky counterions

Molecular structure of bottlebrush polymers in melts

Bottlebrushes are fascinating macromolecules that display an intriguing combination of molecular and particulate features having vital implications in both living and synthetic systems, such as cartilage and ultrasoft elastomers. However, the progress in practical applications is impeded by the lack of knowledge about the hierarchic organization of both individual bottlebrushes and their assemblies. We delineate fundamental correlations between molecular architecture, mesoscopic conformation, and macroscopic properties of polymer melts. Numerical simulations corroborate theoretical predictions for the effect of grafting density and side-chain length on the dimensions and rigidity of bottlebrushes, which effectively behave as a melt of flexible filaments. These findings provide quantitative guidelines for the design of novel materials that allow architectural tuning of their properties in a broad range without changing chemical composition

Molecular structure of bottlebrush polymers in melts

Bottlebrushes are fascinating macromolecules that display an intriguing combination of molecular and particulate features having vital implications in both living and synthetic systems, such as cartilage and ultrasoft elastomers. However, the progress in practical applications is impeded by the lack of knowledge about the hierarchic organization of both individual bottlebrushes and their assemblies. We delineate fundamental correlations between molecular architecture, mesoscopic conformation, and macroscopic properties of polymer melts. Numerical simulations corroborate theoretical predictions for the effect of grafting density and side-chain length on the dimensions and rigidity of bottlebrushes, which effectively behave as a melt of flexible filaments. These findings provide quantitative guidelines for the design of novel materials that allow architectural tuning of their properties in a broad range without changing chemical composition

The Escape Transition of a Compressed Star Polymer: Self-Consistent Field Predictions Tested by Simulation

The escape transition of a polymer “mushroom” (a flexible chain grafted to a flat non-adsorbing substrate surface in a good solvent) occurs when the polymer is compressed by a cylindrical piston of radius R, that by far exceeds the chain gyration radius. At this transition, the chain conformation abruptly changes from a two-dimensional self-avoiding walk of blobs (of diameter H, the height of the piston above the substrate) to a “flower conformation”, i.e. stretched almost one-dimensional string of blobs (with end-to-end distance ≈ R) and an “escaped” part of the chain, the “crown”, outside the piston. The extension of this problem to the case of star polymers with f arms is considered, assuming that the center of the star is grafted to the substrate. The question is considered whether under compression the arms escape all together, or whether there occurs an arm by arm escape under increasing compression. Both self-consistent field calculations and Molecular Dynamics simulations are found to favor the latter scenario

A path integral approach to the dynamics of a random chain with rigid constraints

In this work the dynamics of a freely jointed random chain which fluctuates at constant temperature in some viscous medium is studied. The chain is regarded as a system of small particles which perform a brownian motion and are subjected to rigid constraints which forbid the breaking of the chain. For simplicity, all interactions among the particles have been switched off and the number of dimensions has been limited to two. The problem of describing the fluctuations of the chain in the limit in which it becomes a continuous system is solved using a path integral approach, in which the constraints are imposed with the insertion in the path integral of suitable Dirac delta functions. It is shown that the probability distribution of the possible conformations in which the fluctuating chain can be found during its evolution in time coincides with the partition function of a field theory which is a generalization of the nonlinear sigma model in two dimensions. Both the probability distribution and the generating functional of the correlation functions of the positions of the beads are computed explicitly in a semiclassical approximation for a ring-shaped chain.Comment: 36 pages, 2 figures, LaTeX + REVTeX4 + graphicx, minor changes in the text, reference adde

On a relation between Liouville field theory and a two component scalar field theory passing through the random walk

In this work it is proposed a transformation which is useful in order to simplify non-polynomial potentials given in the form of an exponential. As an application, it is shown that the quantum Liouville field theory may be mapped into a field theory with a polynomial interaction between two scalar fields and a massive vector field.Comment: 15 pages, 4 figures, LaTeX + RevTeX 4. With respect to the previous version an appendix has been added to provide an alternative proof of Eq. (31). Title and abstract have been change