Structure and phase behavior of colloidal dumbbells with tunable attractive interactions

We investigate thermodynamic and structural properties of colloidal dumbbells in the framework provided by the Reference Interaction Site Model (RISM) theory of molecular fluids and Monte Carlo simulations. We consider two different models: in the first one we set identical square-well attractions on the two tangent spheres composing the molecule (SW-SW model); in the second scheme, one of square-well interactions is switched off (HS-SW model). Appreciable differences emerge between the physical properties of the two models. Specifically, the $k \to 0$ behavior of SW-SW structure factors $S(k)$ points to the presence of a gas-liquid coexistence, as confirmed by subsequent fluid phase equilibria calculations. Conversely, the HS-SW $S(k)$ develops a low-$k$ peak, signaling the presence of aggregates; such a process destabilizes the gas-liquid phase separation, promoting at low temperatures the formation of a cluster phase, whose structure depends on the system density. We further investigate such differences by studying the phase behavior of a series of intermediate models, obtained from the original SW-SW by progressively reducing the depth of one square-well interaction. RISM structural predictions positively reproduce the simulation data, including the rise of $S(k \to 0$) in the SW-SW model and the low-$k$ peak in the HS-SW structure factor. As for the phase behavior, RISM agrees with Monte Carlo simulations in predicting a gas-liquid coexistence for the SW-SW model (though the critical parameters appears overestimated by the theory) and its progressive disappearance moving toward the HS-SW model.Comment: 12 pages, 13 figures, 1 table, 78 reference

Self-assembly mechanism in colloids: perspectives from Statistical Physics

Motivated by recent experimental findings in chemical synthesis of colloidal particles, we draw an analogy between self-assembly processes occurring in biological systems (e.g. protein folding) and a new exciting possibility in the field of material science. We consider a self-assembly process whose elementary building blocks are decorated patchy colloids of various types, that spontaneously drive the system toward a unique and predetermined targeted macroscopic structure. To this aim, we discuss a simple theoretical model -- the Kern-Frenkel model -- describing a fluid of colloidal spherical particles with a pre-defined number and distribution of solvophobic and solvophilic regions on their surface. The solvophobic and solvophilic regions are described via a short-range square-well and a hard-sphere potentials, respectively. Integral equation and perturbation theories are presented to discuss structural and thermodynamical properties, with particular emphasis on the computation of the fluid-fluid (or gas-liquid) transition in the temperature-density plane. The model allows the description of both one and two attractive caps, as a function of the fraction of covered attractive surface, thus interpolating between a square-well and a hard-sphere fluid, upon changing the coverage. By comparison with Monte Carlo simulations, we assess the pros and the cons of both integral equation and perturbation theories in the present context of patchy colloids, where the computational effort for numerical simulations is rather demanding.Comment: 14 pages, 7 figures, Special issue for the SigmaPhi2011 conferenc

Osmotic pressure induced coupling between cooperativity and stability of a helix-coil transition

Most helix-coil transition theories can be characterized by a set of three parameters: energetic, describing the (free) energy cost of forming a helical state in one repeating unit; entropic, accounting for the decrease of entropy due to the helical state formation; and geometric, indicating how many repeating units are affected by the formation of one helical state. Depending on their effect on the helix-coil transition, solvents or co-solutes can be classified with respect to their action on these parameters. Solvent interactions that alter the entropic cost of helix formation by their osmotic action can affect both the stability (transition temperature) and the cooperativity (transition interval) of the helix-coil transition. A consistent inclusion of osmotic pressure effects in a description of helix-coil transition for poly(L-glutamic acid) in solution with polyethylene glycol can offer an explanation of the experimentally observed linear dependence of transition temperature on osmotic pressure as well as the concurrent changes in the cooperativity of the transition.Comment: 5 pages, 3 figures. To be submitted to Phys.Rev.Let

Microscopic formulation of the Zimm-Bragg model for the helix-coil transition

A microscopic spin model is proposed for the phenomenological Zimm-Bragg model for the helix-coil transition in biopolymers. This model is shown to provide the same thermophysical properties of the original Zimm-Bragg model and it allows a very convenient framework to compute statistical quantities. Physical origins of this spin model are made transparent by an exact mapping into a one-dimensional Ising model with an external field. However, the dependence on temperature of the reduced external field turns out to differ from the standard one-dimensional Ising model and hence it gives rise to different thermophysical properties, despite the exact mapping connecting them. We discuss how this point has been frequently overlooked in the recent literature.Comment: 11 pages, 2 figure

Real Space Renormalization Group for Langevin Dynamics in Absence of Translational Invariance

A novel exact dynamical real space renormalization group for a Langevin equation derivable from a Euclidean Gaussian action is presented. It is demonstrated rigorously that an algebraic temporal law holds for the Green function on arbitrary structures of infinite extent. In the case of fractals it is shown on specific examples that two different fixed points are found at variance with periodic structures. Connection with growth dynamics of interfaces is also discussed.Comment: 22 pages, RevTex 3.0, 5 figures available upon request from [email protected], to be published in J.Stat.Phy

A numerical study of a binary Yukawa model in regimes characteristic of globular proteins in solutions

The main goal of this paper is to assess the limits of validity, in the regime of low concentration and strong Coulomb coupling (high molecular charges), for a simple perturbative approximation to the radial distribution functions (RDF), based upon a low-density expansion of the potential of mean force and proposed to describe protein-protein interactions in a recent Small-Angle-Scattering (SAS) experimental study. A highly simplified Yukawa (screened Coulomb) model of monomers and dimers of a charged globular protein ($\beta$-lactoglobulin) in solution is considered. We test the accuracy of the RDF approximation, as a necessary complementary part of the previous experimental investigation, by comparison with the fluid structure predicted by approximate integral equations and exact Monte Carlo (MC) simulations. In the MC calculations, an Ewald construction for Yukawa potentials has been used to take into account the long-range part of the interactions in the weakly screened cases. Our results confirm that the perturbative first-order approximation is valid for this system even at strong Coulomb coupling, provided that the screening is not too weak (i.e., for Debye length smaller than monomer radius). A comparison of the MC results with integral equation calculations shows that both the hypernetted-chain (HNC) and the Percus-Yevick (PY) closures have a satisfactory behavior under these regimes, with the HNC being superior throughout. The relevance of our findings for interpreting SAS results is also discussed.Comment: Physical Review E, in press (2005

Crossover phenomenon in self-organized critical sandpile models

We consider a stochastic sandpile where the sand-grains of unstable sites are randomly distributed to the nearest neighbors. Increasing the value of the threshold condition the stochastic character of the distribution is lost and a crossover to the scaling behavior of a different sandpile model takes place where the sand-grains are equally transferred to the nearest neighbors. The crossover behavior is numerically analyzed in detail, especially we consider the exponents which determine the scaling behavior.Comment: 6 pages, 9 figures, accepted for publication in Physical Review

Critical behavior of loops and biconnected clusters on fractals of dimension d < 2

We solve the O(n) model, defined in terms of self- and mutually avoiding loops coexisting with voids, on a 3-simplex fractal lattice, using an exact real space renormalization group technique. As the density of voids is decreased, the model shows a critical point, and for even lower densities of voids, there is a dense phase showing power-law correlations, with critical exponents that depend on n, but are independent of density. At n=-2 on the dilute branch, a trivalent vertex defect acts as a marginal perturbation. We define a model of biconnected clusters which allows for a finite density of such vertices. As n is varied, we get a line of critical points of this generalized model, emanating from the point of marginality in the original loop model. We also study another perturbation of adding local bending rigidity to the loop model, and find that it does not affect the universality class.Comment: 14 pages,10 figure

Interstellar dust in the BOOMERanG maps

Interstellar dust (ISD) emission is present in the mm-wave maps obtained by the BOOMERanG experiment at intermediate and high Galactic latitudes. We find that, while being sub-dominant at the lower frequencies (90,150, 240 GHz), thermal emission from ISD is dominant at 410 GHz, and is well correlated with the IRAS map at 100 µm. We find also that the angular power spectrum of ISD fluctuations at 410 GHz is a power law, and its level is negligible with respect to the angular power spectrum of the Cosmic Microwave Background (CMB) at 90 and 150 GHz

Statistics of self-avoiding walks on randomly diluted lattice

A comprehensive numerical study of self-avoiding walks (SAW's) on randomly diluted lattices in two and three dimensions is carried out. The critical exponents $\nu$ and $\chi$ are calculated for various different occupation probabilities, disorder configuration ensembles, and walk weighting schemes. These results are analyzed and compared with those previously available. Various subtleties in the calculation and definition of these exponents are discussed. Precise numerical values are given for these exponents in most cases, and many new properties are recognized for them.Comment: 34 pages (+ 12 figures), REVTEX 3.