Counterion Penetration and Effective Electrostatic Interactions in Solutions of Polyelectrolyte Stars and Microgels

Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modelling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of star-branched and microgel macroions. The counterions are found to penetrate stars more easily than microgels, with important implications for screening of bare macroion interactions. The effective pair interactions are Yukawa in form for separated macroions, but are softly repulsive and bounded for overlapping macroions. A one-body volume energy, which depends on the average macroion concentration, emerges naturally in the theory and contributes to the total free energy.Comment: 15 pages, 5 figure

Molecular Dynamics Simulation of Semiflexible Polyampholyte Brushes - The Effect of Charged Monomers Sequence

Planar brushes formed by end-grafted semiflexible polyampholyte chains, each chain containing equal number of positively and negatively charged monomers is studied using molecular dynamics simulations. Keeping the length of the chains fixed, dependence of the average brush thickness and equilibrium statistics of the brush conformations on the grafting density and the salt concentration are obtained with various sequences of charged monomers. When similarly charged monomers of the chains are arranged in longer blocks, the average brush thickness is smaller and dependence of brush properties on the grafting density and the salt concentration is stronger. With such long blocks of similarly charged monomers, the anchored chains bond to each other in the vicinity of the grafting surface at low grafting densities and buckle toward the grafting surface at high grafting densities.Comment: 8 pages,7 figure

Reversible stretching of homopolymers and random heteropolymers

We have analyzed the equilibrium response of chain molecules to stretching. For a homogeneous sequence of monomers, the induced transition from compact globule to extended coil below the $\theta$-temperature is predicted to be sharp. For random sequences, however, the transition may be smoothed by a prevalence of necklace-like structures, in which globular regions and coil regions coexist in a single chain. As we show in the context of a random copolymer, preferential solvation of one monomer type lends stability to such structures. The range of stretching forces over which necklaces are stable is sensitive to chain length as well as sequence statistics.Comment: 14 pages, 4 figure

Weak Segregation Theory and Non-Conventional Morphologies in the Ternary ABC Triblock Copolymers

The Leibler weak segregation theory in molten diblock copolymers is generalized with due regard for the 2nd shell harmonics contributions defined in the paper and the phase diagrams are built for the linear and miktoarm ternary ABC triblock copolymers. The symmetric linear copolymers with the middle block non-selective with respect to the side ones are shown to undergo the continuous ODT not only into the lamellar phase but also into various non-conventional cubic phases (depending on the middle block composition it could be the simple cubic, face-centered cubic or non-centrosymmetric phase revealing the symmetry of space group No.214 first predicted to appear in molten block copolymers). For asymmetric linear ABC copolymers a region of compositions is found where the weakly segregated gyroid (double gyroid) phase exists between the planar hexagonal and lamellar or one of the non-conventional cubic phases up to the very critical point. In contrast, the miktoarm ABC block copolymers with one of its arm non-selective with respect to the two others are shown to reveal a pronounced tendency towards strong segregation, which is preceded by increase of stability of the conventional BCC phase and a peculiar weakly segregated BCC phase (BCC3), where the dominant harmonics belong to the 3rd co-ordination sphere of the reciprocal lattice. The validity region of the developed theory is discussed and outlined in the composition triangles both for linear and miktoarm copolymers.Comment: 61 pages, 12 figure

Diffusive-Ballistic Transition in Random Walks with Long-Range Self-Repulsion

We prove that a class of random walks on $\Z^2$ with long-range self-repulsive interactions have a diffusive-ballistic phase transition.Comment: 7 pages, to appear in Letters in Mathematical Physic

Network development in biological gels: role in lymphatic vessel development

In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the collagen volume fraction, and the evolution of the proton concentration in a collagen implant; as described in experiments of Boardman and Swartz (Circ. Res. 92, 801–808, 2003). Using linear stability analysis, we find that above a critical level of proton concentration, spatial patterns form due to small perturbations in the initially uniform steady state. Using a long wavelength reduction, we can reduce the two coupled partial differential equations to one fourth order equation that is very similar to the Cahn–Hilliard equation; however, it has more complex nonlinearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model

The Persistence Length of a Strongly Charged, Rod-like, Polyelectrolyte in the Presence of Salt

The persistence length of a single, intrinsically rigid polyelectrolyte chain, above the Manning condensation threshold is investigated theoretically in presence of added salt. Using a loop expansion method, the partition function is consistently calculated, taking into account corrections to mean-field theory. Within a mean-field approximation, the well-known results of Odijk, Skolnick and Fixman are reproduced. Beyond mean-field, it is found that density correlations between counterions and thermal fluctuations reduce the stiffness of the chain, indicating an effective attraction between monomers for highly charged chains and multivalent counterions. This attraction results in a possible mechanical instability (collapse), alluding to the phenomenon of DNA condensation. In addition, we find that more counterions condense on slightly bent conformations of the chain than predicted by the Manning model for the case of an infinite cylinder. Finally, our results are compared with previous models and experiments.Comment: 13 pages, 2 ps figure

Nonlinear Elasticity: From Single Chain to Networks and Gels

Biological and polymeric networks show highly nonlinear stress-strain behavior manifested in materials that stiffen with increasing deformation. Using a combination of the theoretical analysis and molecular dynamics simulations, we develop a model of network deformation that describes nonlinear mechanical properties of networks and gels by relating their macroscopic strain-hardening behavior to molecular parameters of the network strands. The starting point of our approach is a nonlinear force/elongation relation for discrete chains with varying bending rigidity. The derived expression for the network free energy is a universal function of the first deformation invariant and chain elongation ratio that depends on a ratio of the unperturbed chain size to chain dimension in a fully extended conformation. The model predictions for the nonlinear shear modulus and differential shear modulus for uniaxial and shear deformations are in very good agreement with both the results of molecular dynamics simulations of networks and with experimental data for biopolymer networks of actin, collagen, fibrin, vimentin, neurofilaments, and pectin. © 2013 American Chemical Society

Adsorption of a polyampholyte on a charged spherical particle

We develop a scaling theory for a single polyampholyte chain adsorbed on a charged spherical particle in a theta-solvent. Adsorption of a polyampholyte molecule is due to its polarization in the electrostatic field of the particle. For large particles with sizes exceeding the thickness of the adsorbed layer, the conformations of the chain are similar to the one found for polyampholyte adsorption on charged planar surface. However, an adsorbed polyampholyte chain forms a self-similar flower-like structure near the particles with sizes smaller than its Gaussian size. These self-similar structures result from the balance of the polarization energy of loops and the excluded volume interactions between monomers. The structure of an adsorbed polyampholyte in the flower-like conformation is similar to that of a neutral star polymer