Publications
2002
We study a generic model of self-assembling chains that can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micelles, dipolar fluids, and microemulsions. The model maps the partition function of a solution of branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg magnet in the mathematical limit of zero spin components. As for the calculation of thermodynamic properties as well as the scattering structure factor, the mapping rigorously accounts for all possible cluster configurations, except for closed rings. The model is solved in the mean-field approximation. It is found that despite the absence of any specific interaction between the chains, the presence of the junctions induces an effective attraction between the monomers, which in the case of threefold junctions leads to a first-order reentrant phase separation between a dilute phase consisting mainly of single chains, and a dense network, or two network phases. The model is then modified to predict the structural properties at the mean-field level. Independent of the phase separation, we predict a percolation (connectivity) transition at which an infinite network is formed. The percolation transition partially overlaps with the first-order transition, and is a continuous, nonthermodynamic transition that describes a change in the topology of the system. Our treatment that predicts both the thermodynamic phase equilibria as well as the spatial correlations in the system allows us to treat both the phase separation and the percolation threshold within the same framework. The density-density correlation has the usual Ornstein-Zernicke form at low monomer densities. At higher densities, a peak emerges in the structure factor, signifying the onset of medium-range order in the system. Implications of the results for different physical systems are discussed.
We predict theoretically that long-wavelength surface charge modulations universally reduce the pressure between the charged surfaces with counterions compared with the case of uniformly charged surfaces with the same average surface charge density. The physical origin of this effect is the fact that surface charge modulations always lead to enhanced counterion localization near the surfaces, and hence, fewer charges at the midplane. We confirm the last prediction with Monte Carlo simulations.
Forces exerted by stationary cells have been investigated on the level of single focal adhesions by combining elastic substrates, fluorescence labeling of focal adhesions, and the assumption of localized force when solving the inverse problem of linear elasticity theory. Data simulation confirms that the inverse problem is ill-posed in the presence of noise and shows that in general a regularization scheme is needed to arrive at a reliable force estimate. Spatial and force resolution are restricted by the smoothing action of the elastic kernel, depend on the details of the force and displacement patterns, and are estimated by data simulation. Corrections arising from the spatial distribution of force and from finite substrate size are treated in the framework of a force multipolar expansion. Our method is computationally cheap and could be used to study mechanical activity of cells in real time.
We predict a condensation phenomenon in an overall neutral system, consisting of a single charged plate and its oppositely charged counterions. Based on the "two-fluid" model, in which the counterions are divided into a "free" and a "condensed" fraction, we argue that for high surface charge, fluctuations can lead to a phase transition in which a large fraction of counterions is condensed. Furthermore, we show that depending on the valence, the condensation is either a first-order or a smooth transition.
We predict a condensation phenomenon in an overall neutral system, consisting of a single charged plate and its oppositely charged counterions. Based on the \u201ctwo-fluid\u201d model, in which the counterions are divided into a \u201cfree\u201d and a \u201ccondensed\u201d fraction, we argue that for high surface charge, fluctuations can lead to a phase transition in which a large fraction of counterions is condensed. Furthermore, we show that depending on the valence, the condensation is either a first-order or a smooth transition.
We review the continuum, statistical thermodynamics of surfaces and interfaces in soft matter where both the energy and entropy of the surface are comparable. These systems include complex fluids that are dominated by either surface tension or the interfacial curvature, such as: fluid and solid interfaces, colloidal dispersions, macromolecular solutions, membranes, and other self-assembling aggregates such as micelles, vesicles, and microemulsions. The primary focus is on the theoretical concepts, their universality, and the role of fluctuations and inhomogeneities with connections to relevant experimental systems.
Recent experimental results demonstrate that it is possible to grow a variety of different multiphase, nested nanotube structures. This paper predicts the structure and energetics of such multiphase nanotubes. There are several distinct contributions to the energetics: the internal and external surface energies, the energy of the interface between the different phases, the long-range (van der Waals) interactions between interfaces, and the elastic bending energy. We perform energy minimizations to compare the energies of two- and three-layer films and nanotubes. We present physical guidelines, quantitative theory, and structure maps that show how materials and geometric parameters influence the stability of competing structures.
Using both small-amplitude and singular-perturbation theories we predict theoretically that the presence of surface charge modulations gives rise to an enhancement of the counterion density near the surface above and beyond that of a uniform, charged surface. We confirm these predictions with Monte Carlo simulations. Our study focuses on the weak-to moderate-coupling regime which is complementary to a similar investigation performed by Moreira and Netz (Europhys. Lett., 57 (2002) 911) in the strong-coupling case.
The possibility of elastic interaction of cells was discussed. The laws for elastic interactions of cells were derived and their dependence on elastic constants, distance, cellular orientations, geometry and boundary conditions was also shown. The elastic interaction on elastic substrates was found to be similar to that of electric quadrupoles in two dimensions. It lead to aggregation with herringbone order on a cellular scale for dense systems.