Gerardo Odriozola

Entropy driven key-lock assembly

The effective interaction between a sphere with an open cavity (lock) and a spherical macroparticle (key), both immersed in a hard sphere fluid, is studied by means of Monte Carlo simulations. As a result, a two-dimensional map of the key-lock effective interaction potential is constructed, which leads to the proposal of a self-assembling mechanism: There exists trajectories through which the key-lock pair could assemble avoiding trespassing potential barriers. Hence, solely the entropic contribution can induce their self-assembling even in the absence of attractive forces. This study points out the solvent contribution within the underlying mechanisms of substrate-protein assemblydisassembly processes, which are important steps of the enzyme catalysis and protein mediated transport.

Revisiting the phase diagram of hard ellipsoids

In this work, the well-known Frenkel-Mulder phase diagram of hard ellipsoids of revolution [D. Frenkel and B. M. Mulder, Mol. Phys. 55, 1171 (1985)] is revisited by means of replica exchange Monte Carlo simulations. The method provides good sampling of dense systems and so, solid phases can be accessed without the need of imposing a given structure. At high densities, we found plastic solids and fcc-like crystals for semi-spherical ellipsoids (prolates and oblates), and SM2 structures [P. Pfleiderer and T. Schilling, Phys. Rev. E 75, 020402 (2007)] for x : 1-prolates and 1 : x-oblates with x ≥ 3. The revised fluid-crystal and isotropic-nematic transitions reasonably agree with those presented in the Frenkel-Mulder diagram. An interesting result is that, for small system sizes (100 particles), we obtained 2:1- and 1.5:1-prolate equations of state without transitions, while some order is developed at large densities. Furthermore, the symmetric oblate cases are also reluctant to form ordered phases.

Equilibrium equation of state of a hard sphere binary mixture at very large densities using replica exchange Monte Carlo simulations

We use replica exchange Monte Carlo simulations to measure the equilibrium equation of state of the disordered fluid state for a binary hard sphere mixture up to very large densities where standard Monte Carlo simulations do not easily reach thermal equilibrium. For the moderate system sizes we use (up to N = 100), we find no sign of a pressure discontinuity near the location of dynamic glass singularities extrapolated using either algebraic or simple exponential divergences, suggesting they do not correspond to genuine thermodynamic glass transitions. Several scenarios are proposed for the fate of the fluid state in the thermodynamic limit.

Dynamic scaling concepts applied to numerical solutions of Smoluchowski's rate equation

Smoluchowski’s equation is widely applied to describe the time evolution of the cluster-size distribution during aggregation processes. Analytical solutions for this equation, however, are known only for a very limited number of kernels. Therefore, numerical methods have to be used for describing the time evolution of the cluster-size distribution. In this work, we present a novel self-consistent method for solving Smoluchowski’s equation for any homogeneous kernel. The method considers dynamic scaling to be valid but does not need to assume a given form for the scaling distribution Φ(x). Moreover, the scaling distribution Φ(x) is obtained as a natural result of the algorithm. Due to the implementation of dynamic scaling concepts, the algorithm converges almost immediately with a minimal calculation effort. Comparing calculated size distributions with the corresponding analytical solutions shows the validity of the method. The method is then used to fit experimental data for diffusion limited aggregation....

Further details on the phase diagram of hard ellipsoids of revolution

In recent work we revisited the phase diagram of hard ellipsoids of revolution (spheroids) by means of replica exchange Monte Carlo simulations. This was done by setting random initial configurations, and allows to confirm the formation of sm2 crystal structures at high densities [P. Pfleiderer and T. Schilling, Phys. Rev. E 75, 020402 (2007)] for large anisotropies and stretched-fcc for small anisotropies. In this work we employed the same technique but setting the starting cells as sm2 crystal structures having the maximum known packing density [A. Donev, F. H. Stillinger, P. M. Chaikin, and S. Torquato, Phys. Rev. Lett. 92, 255506 (2004)]. This procedure yields a very rich behavior for quasi-spherical oblates and prolates. These systems, from low to high pressures, show the following phases: isotropic fluid, plastic solid, stretched-fcc solid, and sm2 solid. The first three transitions are first order, whereas the last one is a subtle, probably high order transition. This picture is consistent with the fact of having the sm2 structure capable of producing the maximally achievable density.

Replica exchange Monte Carlo applied to hard spheres

In this work a replica exchange Monte Carlo scheme which considers an extended isobaric-isothermal ensemble with respect to pressure is applied to study hard spheres (HSs). The idea behind the proposal is expanding volume instead of increasing temperature to let crowded systems characterized by dominant repulsive interactions to unblock, and so, to produce sampling from disjoint configurations. The method produces, in a single parallel run, the complete HS equation of state. Thus, the first order fluid-solid transition is captured. The obtained results well agree with previous calculations. This approach seems particularly useful to treat purely entropy-driven systems such as hard body and nonadditive hard mixtures, where temperature plays a trivial role.

Effect of confinement on the interaction between two like-charged rods

Monte Carlo simulations were employed to study two charged rods confined between two unlike charged plates, all immersed in a model electrolyte. Recently, it was shown that two rods immersed in a multivalent counterion solution may show attraction [Phys. Rev. Lett. 78, 2477 (1997)10.1103/PhysRevLett.78.2477]. Here we show for a monovalent electrolyte that rod-rod attraction and repulsion can switch sign depending on confinement and ionic size. We also propose a simple self-assembling mechanism which may be helpful to understand the DNA-lipid bilayers complexation.

Na-montmorillonite hydrates under ethane rich reservoirs: NPzzT and μPzzT simulations

Na-montmorillonite hydrates in presence of ethane molecules are studied by means of hybrid Monte Carlo simulations in the NP(zz)T and muP(zz)T ensembles. The NP(zz)T ensemble allows us to study the interlaminar distance as a function of water and ethane content. These data show clear plateaus for lower ethane contents and mainly for water contents consistent with the formation of a single water layer. In addition, from this ensemble the structure for some of these interlaminar compositions were analyzed. For systems containing few ethane molecules and water enough to complete a single layer, it was observed that ethane mainly situates close to the interlayer midplane and adopts a nearly parallel arrangement to the clay surface. On the other hand, the muP(zz)T ensemble allows us to determine the interlaminar distance and water-ethane content for any specific reservoir. Here, some important findings are the following: the partial exchange of water by ethane molecules that enhances for decreasing the water vapor pressure; the obtention of a practically constant interlaminar space distance as a function of the water vapor pressure; the conservation of ion solvation shells; the enhancement of the water-ethane exchange for burial conditions; and finally, the incapability for a dehydrated clay mineral to swell in a dry and rich ethane atmosphere.

Phase diagram of two-dimensional hard ellipses

We report the phase diagram of two-dimensional hard ellipses as obtained from replica exchange Monte Carlo simulations. The replica exchange is implemented by expanding the isobaric ensemble in pressure. The phase diagram shows four regions: isotropic, nematic, plastic, and solid (letting aside the hexatic phase at the isotropic-plastic two-step transition [E. P. Bernard and W. Krauth, Phys. Rev. Lett. 107, 155704 (2011)]). At low anisotropies, the isotropic fluid turns into a plastic phase which in turn yields a solid for increasing pressure (area fraction). Intermediate anisotropies lead to a single first order transition (isotropic-solid). Finally, large anisotropies yield an isotropic-nematic transition at low pressures and a high-pressure nematic-solid transition. We obtain continuous isotropic-nematic transitions. For the transitions involving quasi-long-range positional ordering, i.e., isotropic-plastic, isotropic-solid, and nematic-solid, we observe bimodal probability density functions. This supports first order transition scenarios.

Electrolyte distribution around two like-charged rods: their effective attractive interaction and angular dependent charge reversal.

A simple model for two like-charged parallel rods immersed in an electrolyte solution is considered. We derived the three point extension (TPE) of the hypernetted chain/mean spherical approximation (TPE-HNC/MSA) and Poisson-Boltzmann (TPE-PB) integral equations. We numerically solve these equations and compare them to our results of Monte Carlo (MC) simulations. The effective interaction force, F(T), the charge distribution profiles, rho(el)(x,y), and the angular dependent integrated charge function, P(theta), are calculated for this system. The analysis of F(T) is carried out in terms of the electrostatic and entropic (depletion) contributions, F(E) and F(C). We studied several cases of monovalent and divalent electrolytes, for which the ionic size and concentration are varied. We find good qualitative agreement between TPE-HNC/MSA and MC in all the cases studied. The rod-rod force is found to be attractive when immersed in large size, monovalent or divalent electrolytes. In general, the TPE-PB has poor agreement with the MC. For large monovalent and divalent electrolytes, we find angular dependent charge reversal charge inversion and polarizability. We discuss the intimate relationship between this angular dependent charge reversal and rod-rod attraction.