M. Muthukumar

Polymers at Surfaces and Interfaces

Preface 1. Introduction and overview 2. The surface of a simple polymer melt 3. Experimental techniques 4. Polymer/polymer interfaces 5. Adsorption and surface aggregation from polymer solutions and mixtures 6. Tethered polymer chains in solutions and melts 7. Adhesion and the mechanical properties of polymer interfaces at the molecular level 8. Polymers spread at air/liquid interfaces Index.

Polymer translocation through a hole

The average residence time τ of a polymer of length N passing through a narrow hole under a chemical potential gradient is calculated. In the proposed model, details of the hole parametrize the rate constant k0 for transporting a monomer across the hole, independent of the chain length. We show that any asymmetry in the average conformations of the polymer across the hole is sufficient to generate the driving force for the polymer translocation. If chemical potential gradient is absent, τ∼N2, with the proportionality constant depending on the size exponent of the polymer before and after the translocation. For translocation along the chemical potential gradient Δμ, τ is proportional to N(T/k0Δμ) and N2/k0, respectively, for large and small NΔμ/T. For translocation against the chemical potential gradient, τ∼exp(N) for long polymers.

Thermodynamics of polymer solutions

The free energy of a polmyer solution is derived by a consideration of the monomer density fluctuations and incorporating three‐body interactions. Explicit interpolation formulas are obtained for the concentration dependence of the correlation length for arbitrary strengths of two‐ and three‐body interactions within the random phase approximation. When the ternary interactions are important, as is the case under the conditions of phase separation in polymer solutions, the derived free energy leads to new corresponding‐states equations for the spinodals. The critical volume fraction φc, and ‖φ−φc‖/φc are found to be proportional to n−1/3 and n1/9, respectively, where n is the degree of polymerization of the polymer and φ is the coexistent polymer volume fraction. A comparison is made between the predictions and the experimental results reported in the literature.

Adsorption of a polyelectrolyte chain to a charged surface

The criteria for the adsorption of a polyelectrolyte chain in a salt solution on a uniformly charged planar membrane are derived using mean field arguments. Explicit formulas are obtained to describe the adsorption characteristics for varying surface charge density, charge on the polymer, Debye screening length κ−1, chain length L, and temperature T. The adsorption can be tuned using any one of these parameters. When T is the tuning variable, for example, the chain is adsorbed at T<Tc, where Tc is proportional to κ−3L−1 and κ−11/5L−1/5 in the weak and strong Coulombic screening limits, respectively. The thickness of the adsorbed layer is derived to vary linearly with κ−1 ln(Tc /T) for T<Tc.

Theory of counter-ion condensation on flexible polyelectrolytes: Adsorption mechanism

A new model is presented for counterion distribution around flexible polyelectrolytes by considering (i) free energy of the polyelectrolyte chain, (ii) translational entropy of adsorbed counterions, (iii) adsorption energy, (iv) translational entropy of unadsorbed counterions, (v) fluctuations of dissociated ions, and (vi) correlation among ion-pairs formed by adsorbed counterions on the polymer. The effective charge and size of the polymer are calculated self-consistently. The degree of ionization f of the polymer decreases continuously with 1/epsilonT (epsilon and T are the dielectric constant of the solvent and temperature, respectively), depending sensitively on local dielectric heterogeneity. Further, f decreases with an increase in salt concentration, monomer concentration, or chain flexibility. The polymer size, accompanying the changes in f, depends nonmonotonically on 1/epsilonT. The predictions of the model are consistent with all trends observed previously in simulations and are distinctly different from the Manning argument for rodlike chains.

Polymer escape through a nanopore

Free energy barrier and mean translocation time, τ, are calculated for the movement of a single Gaussian chain from one sphere to another larger sphere through a narrow pore. The potential interaction between the polymer and pore significantly modifies the entropic barrier landscape of translocation. As the pore length increases, the translocation process undergoes a transition from entropic barrier mechanism to a mechanism dominated by the pore–polymer interaction. This shift in mechanism leads to nonmonotonic dependence of τ on the pore length. Explicit formulas are derived for the dependence of τ on chain length, pore length, sizes of the donor and recipient spheres, strength of pore–polymer interaction, applied voltage, and electrochemical potential gradient for translocation. The calculated results provide guidance for tuning the rate of polymer translocation through narrow pores.

Polymer semiconductor crystals

One of the long-standing challenges in the field of polymer semiconductors is to figure out how long interpenetrating and entangled polymer chains self-assemble into single crystals from the solution phase or melt. The ability to produce these crystalline solids has fascinated scientists from a broad range of backgrounds including physicists, chemists, and engineers. Scientists are still on the hunt for determining the mechanism of crystallization in these information-rich materials. Understanding the theory and concept of crystallization of polymer semiconductors will undoubtedly transform this area from an art to an area that will host a bandwagon of scientists and engineers. In this article we describe the basic concept of crystallization and highlight some of the advances in polymer crystallization from crystals to nanocrystalline fibers.

A trapped polymer chain in random porous media

Dynamic and static properties of a polymer chain without self‐excluded volume, which performs Brownian motion between randomly distributed impenetrable fixed obstacles, have been investigated by Monte Carlo simulations and analyzed by scaling considerations. The mean square radius of gyration 〈S2〉, the center‐of‐mass diffusion coefficient D, and the longest relaxation time τ are functions of x=(1−p)(N)1/2 for all chain lengths N and porosities p above the percolation threshold. Simulations have been performed for x≲10. With increasing x the radius of gyration exhibits a crossover from Gaussian statistics 〈S2〉∼N to a collapsed state where 〈S2〉 is independent of N. This phenomenon is attributed to the effects of both the lack of self‐excluded volume and the presence of an effective self‐attractive potential arising from random repulsion between polymer and the solid particles of the medium. The strong dependency upon chain length of D∼N−2.9±0.3 and τ∼N4.0±0.4 is conjectured to result from randomly distribut...

Electrostatic origin of the genome packing in viruses.

Many ssRNA/ssDNA viruses bind their genome by highly basic semiflexible peptide arms of capsid proteins. Here, we show that nonspecific electrostatic interactions control both the length of the genome and genome conformations. Analysis of available experimental data shows that the genome length is linear in the net charge on the capsid peptide arms, irrespective of the actual amino acid sequence, with a proportionality coefficient of 1.61 ± 0.03. This ratio is conserved across all ssRNA/ssDNA viruses with highly basic peptide arms, and is different from the one-to-one charge balance expected of specific binding. Genomic nucleotides are predicted to occupy a radially symmetric spherical shell detached from the viral capsid, in agreement with experimental data.

Langevin dynamics simulations of early stage shish-kebab crystallization of polymers in extensional flow

We have investigated the molecular origins of shish-kebab morphology occurring in polymer crystallization under extensional flow. Emergence of shish-kebabs is intimately related to the discontinuous coil-stretch transition of isolated chains. Our computed free energy landscape shows that there are in general two populations of stretched and coiled conformations at a given flow rate, even for monodisperse chains. While the stretched chains crystallize into shish, the coiled chains first form single-chain lamellae and then adsorb to the shish constituting the kebabs. We have followed the molecular details of formation of the shish and kebabs, and their dependence on initial configurations of chains, polymer concentration, and rate of crystallization. The local inhomogeneity in polymer concentration dramatically alters the population of stretched and coiled conformations, thus significantly influencing the onset of shish-kebab morphology. The propensity of kebabs is reduced by lowering the rate of crystalliz...