P. Pincus

Macrocrystal Ordering in Star Polymer Solutions

We show that a solution of f-armed star polymers develops a peak in its scattering structure function S(q), whose height scales as f3/2. The peak is largest when the separation between neighboring stars is about equal to the radius of a star. Our results follow from general scaling properties of polymers in a good solvent. We predict crystalline ordering of the polymers when the functionality f exceeds a universal threshold fc.

Hydrodynamic surface modes on concentrated polymer solutions and gels

We present a coupled two‐fluid model for hydrodynamic surface modes on concentrated polymer solutions and polymer gels. This model is used to investigate such surface modes in the limit of strong coupling. The surface mode dispersion relation ω(k) and the structure factor S(k,ω) of thermally induced surface fluctuations are derived in this limit for materials with a general constitutive relation η(ω). We argue for the existence of several types of surface modes, including Rayleigh elastic waves, capillary waves, and overdamped modes resulting from viscous dissipation in the solvent as well as from polymer diffusion in the case of polymer solutions. The properties of surface modes are discussed separately for the cases of polymer gels and concentrated polymer solutions. Detailed predictions for the form of the normal modes ω(k), and the surface mode structure factor S(k,ω) are given and their dependence on relevant material properties are discussed in each case. Possible experimental scenarios are anticipa...

Strong-Coupling Electrostatics in the Presence of Dielectric Inhomogeneities

We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte Carlo simulations to study the image charge effects induced by multiple dielectric discontinuities in this system. These effects lead to strong counterion crowding in the central region of the intersurface space upon increasing the solvent-membrane dielectric mismatch and change the membrane interactions from attractive to repulsive at small separations. These features agree quantitatively with the SC theory at elevated couplings or dielectric mismatch where the correlation hole around counterions is larger than the thickness of the central counterion layer.

The role of multipoles in counterion-mediated interactions between charged surfaces: strong and weak coupling

We present general arguments for the importance, or lack thereof, of structure in the charge distribution of counterions for counterion-mediated interactions between bounding symmetrically charged surfaces. We show that on the mean field or weak coupling level, the charge quadrupole contributes the lowest order modification to the contact value theorem and thus to the intersurface electrostatic interactions. The image effects are non-existent on the mean field level even with multipoles. On the strong coupling level the quadrupoles and higher order multipoles contribute additional terms to the interaction free energy only in the presence of dielectric inhomogeneities. Without them, the monopole is the only multipole that contributes to the strong coupling electrostatics. We explore the consequences of these statements in all their generality.

Electrostatic attraction of coupled Wigner crystals: finite temperature effects.

In this paper we present a unified physical picture for the electrostatic attraction between two coupled planar Wigner crystals at finite temperature. This model may facilitate our conceptual understanding of counterion-mediated attractions between (highly) similarly charged planes. By adopting an elastic theory, we show that the total attractive force between them can be (approximately) decomposed into a short-ranged and a long-ranged component. They are evaluated below the melting temperature of the Wigner crystals. In particular, we analyze the temperature dependence of the short-ranged attraction, arising from ground-state configuration, and we argue that thermal fluctuations may drastically reduce its strength. Also, the long-range force agrees exactly with that based on the charge-fluctuation approach. Furthermore, we take quantum contributions to the long-ranged (fluctuation-induced) attraction into account and show how the fractional power law, which scales as d(-7/2) for large interplanar distance d at zero temperature, crosses over to the classical regime d(-3) via an intermediate regime of d(-2).

A Phenomenological Description of Case-II Diffusion in Polymeric Materials

In several glassy polymer-solvent systems the observed initial uptake of solvent is linear in time. A sharp front moving at a constant velocity v0 divides the polymer into two regions: ahead of the front the solvent concentration is low and the polymer is still glassy, while behind it the concentration is high and the polymer has been plasticized. Here a simple description of this process is presented. It is based on the idea that the slow plasticization kinetics sets an upper limit for the flux of solvent into the glassy region. Our description predicts that the front velocity will crossover to the usual 1/√t behaviour at t ≈ τ1 = D1/v02 (here D1 is the diffusion coefficient for solvent in the plasticized region) and that an induction time (whose duration depends on the value of the diffusion coefficient D0 in the glassy region) will precede the establishment of the front.

Coiling instabilities of multilamellar tubes

Myelin figures are densely packed stacks of coaxial cylindrical bilayers that are unstable to the formation of coils or double helices. These myelin figures appear to have no intrinsic chirality. We show that such cylindrical membrane stacks can develop an instability when they acquire a spontaneous curvature or when the equilibrium distance between membranes is decreased. This instability breaks the chiral symmetry of the stack and may result in coiling. A unilamellar cylindrical vesicle, on the other hand, will develop an axisymmetric instability, possibly related to the pearling instability.

Surface Modes on a Viscoelastic Medium.

We discuss the surface modes of a linear viscoelastic material with surface tension within the context of a Maxwell fluid model. After deriving a general surface mode dispersion relation, we present a perturbation calculation of viscoelastic surface modes when surface tension is a small effect and discuss the crossover from viscous fluid to elastic behavior as a function of wave vector.

CHARGE-FLUCTUATION-INDUCED NONANALYTIC BENDING RIGIDITY

In this Letter, we consider a neutral system of mobile positive and negative charges confined on the surface of curved films. This may be an appropriate model for: i) a highly charged membrane whose counterions are confined to a sheath near its surface; ii) a membrane composed of an equimolar mixture of anionic and cationic surfactants in aqueous solution. We find that the charge fluctuations contribute a non-analytic term to the bending rigidity that varies logarithmically with the radius of curvature. This may lead to spontaneous vesicle formation, which is indeed observed in similar systems.

Unwinding of Polymer Chains under Forces or Flows

With optical tweezers plus fluorescent labels it is now possible to force, and to observe, the stretching and the relaxation of a single polymer chain. We calculate here the unwinding of a tethered, flexible, chain (N monomers) immersed in a solvent if, at time t = 0 starting from rest, one imposes either a flow (V) of the solvent, or an external force f on the free end.