Session L49: Focus Session: Fluctuation-Induced Forces in Soft Matter and Polymeric Systems - Charge, Shape and Nucleation

Ion-induced interactions between charged macroions and dielectric inhomogeneities

We present a theoretical study of the interactions between macroions in ionic solutions, that are induced by the surrounding electrolyte. In a first scenario, we consider responsive nanoparticles with positively and negatively charged surface groups, and predict that thermal fluctuations of the net surface charge are responsible for an effective attraction, as a chemical analogue of the atomic London-forces. In a second scenario, we consider nanoparticles in solvents with a low dielectric permittivity, where the Coulomb interactions between ions easily exceed the thermal energy. We predict an ionic condensation in the confinement between two nearby nanoparticles, where the suppression of fluctuations leads to a locally dense state of ions, and a consequent strong effective attraction between the nanoparticles. The induced potential between the nanoparticles is also related to the ion-nanoparticle interactions, by e.g. Van der Waals, surface charge, or image charge attractions. Recently developed theoretical methods are discussed, based on earlier work [1,2]. \\[4pt] [1] J. W. Zwanikken, and M. Olvera de la Cruz, Phys. Rev. E 82, 050401(R) (2010). \\[0pt] [2] J. W. Zwanikken, P. K. Jha, and M. Olvera de la Cruz, J. Chem. Phys. 135, 064106 (2011);   

Dielectric many-body effects in arrays of charged cylindrical macromolecules

Nonuniform dielectric constants are a ubiquitous aspect of condensed-matter systems, but nevertheless widely ignored in simulations. Analytical work suggests that the polarization effects resulting from these inhomogeneities can produce many-body interactions that qualitatively alter the behavior of systems driven by electrostatic interactions, but such work relies on approximations. Recently, we have developed an algorithm that computes the fluctuating polarization charge at the interface between dielectric materials during a molecular dynamics simulation, without approximation. Here, we apply this approach to investigate arrays of charged cylindrical macromolecules in the presence of explicit counterions. We study the dielectric many-body effects as a function of separation, dielectric constant variation, and counterion valency. Our findings have implications for the aggregation of polyelectrolytes such as F-actin or DNA.   

Influence of probe shape on polymer configurations and entropic forces

The free energy of long polymers is frequently dominated by entropy with the interaction energy playing a minor role. In the absence of an energy scale, the corresponding forces are then governed by the thermal energy scale $k_{B}T$ and by the length scales associated with the experimental set-up. Recent advances in single molecule manipulation techniques have brought the accuracy of position and force determination into the range where the measurement of relatively small deformations becomes possible. In these situations the detailed shape of probes to which the molecule is attached must be taken into account. The behavior of a polymer of size $R_0$ attached to the rounded tip of a probe (sphere, paraboloid, spherocylinder) with radius of curvature $R$, differs qualitatively for large and small values of the ratio $s=R_0/R$. The scaled compliance (inverse force constant) $S/R_0^2$, is anisotropic and quite large in the direction parallel to the surface when $s\sim 1$ [1]. When a cone with a polymer attached to its sharp tip approaches a plate, then for cone-plate separation $h\ll R_0$ the polymer-mediated force between them [2] is given by $F=Ak_{B}T/h$. The coefficient $A$ can be related to geometry-dependent correlation exponents of long polymers. We computed $A$ for phantom polymers, and for self-avoiding polymers by $\epsilon$-expansion, as well as by numerical simulations in 3 dimensions. \\[4pt][1] R. Bubis, Y. Kantor and M. Kardar, Europhys. Lett. \textbf{88}, 48001, 2009. \\[0pt][2] M. F. Maghrebi, Y. Kantor and M. Kardar, Europhys. Lett., \textit{in press}, 2011 (arXiv:1109.5658).   

Topological obstacles and the forces on them in systems of strongly interacting directed polymers

Owing to their extended structure and inpenetrability, polymers are strongly influenced by topological obstacles. To shed light on this issue we consider a model system of noncrossing directed polymers in two dimensions. As first exploited by de Gennes [1], the configurations of this system can be mapped onto the worldlines of noninteracting fermions---an analogy that enables the application to the polymer system of techniques initially developed for one-dimensional quantum systems. Via this approach, we discuss how an obstacle that forces a fixed number of polymers to pass to one side of a single topological constraint is associated with a large fluctuation of the quantum system. In addition, via the use of techniques from quantum hydrodynamics, we find that such a constraint on a system of noncrossing polymers generates an effective, long-ranged repulsion between the polymers. This repulsion causes a void to appear in the polymer fluid and generates a super-Hookean force opposing the constraint. [1] P.-G. de Gennes, J. Chem Phys. 48, 2257-2259 (1968).   

Critical exponents in the presence of a tip

The behavior of Landau-Ginzburg model of a critical system, appropriate to describe SAW polymers, in the presence of a conical boundary is studied within mean field and by epsilon expansion in d=4-epsilon dimensions. New exponents emerge for correlation functions near the boundaries, in this case the tip of the cone. In the limit of a sharp cone we find a new exponent which we interpret for a SAW polymer by using its fractal dimension.   

Trapping fluctuations in confined carbon dioxide near the supercritical ridge

We investigate the properties of a confined supercritical carbon dioxide film. Density fluctuations are theoretically predicted near the critical point and along the supercritical extension of the liquid-gas coexistence line (ridge). We have confined carbon dioxide between two atomically smooth surfaces in a new generation of surface forces apparatus. The nanometers to micrometer films are found to be laterally divided into nano domains of two distinct refractive indices. The two-refractive index structure is apparent, yet different on behavior, above or below the supercritical ridge. This non-equilibrium phase separated film exhibits long-range attractive forces (up to 500 nm), which results from an interfacial energy between the different domains. High refractive nano domains can be trapped and stretched to lengths of several micrometers, until we observe coalescence of the domains. Our observations suggest that density fluctuations can be trapped and pinned between surfaces in the form of nano strings of significantly different molecular order.   

Homogeneous crystal nucleation from the melts of flexible $n$-alkanes by molecular simulation

Homogeneous crystal nucleation from a dense melt is particularly interesting for chain molecules due to their anisotropy and conformational flexibility. We report our molecular simulation study of the homogeneous crystal nucleation from $n$-alkane melts. For short $n$-alkane (C20) (J.Chem.Phys. 135, 024903), the nucleation trajectory was sampled using brute force molecular dynamics (MD) simulations at about 20{\%} supercooling and the nucleation free energy was sampled using the Monte Carlo (MC) umbrella sampling method for temperatures ranging from 10{\%} to 20{\%} supercooling. In the MD simulation, we identified the induction period unambiguously and calculated the nucleation rate through a mean-first-passagetime analysis. A typical critical nucleus consists of a bundle of stretched segments organized into a cylindrical shape. The remaining CH2 groups form a disordered interfacial layer. By fitting the free energy curve sampled by MC to the cylindrical nucleus model, the crystal-melt interfacial free energies are calculated. We have found good agreement between the melting temperature and the interfacial free energies obtained in our simulation and those from experiment. For a long $n$-alkane above the entanglement length (C150), MD simulation of nucleation was performed at super-cooling as small as 15{\%}. Chain folding was observed during the nucleation stage, and thickening of crystallites was observed during the subsequent crystal growth. The resulting crystal-amorphous interface is characterized in terms of loops, bridges and tails.