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Register a new userLike-charge attraction at short distances in a charge-asymmetric two-dimensional two-component plasma: Exact results
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We determine exactly the short-distance effective potential between two guest charges immersed in a two-dimensional two-component charge-asymmetric plasma composed of positively ($q_1 = +1$) and negatively ($q_2 = -1/2$) charged point particles. The result is valid over the whole regime of stability, where the Coulombic coupling (dimensionless inverse temperature) $beta <4$. At high Coulombic coupling $beta>2$, this model features like-charge attraction. Also, there cannot be repulsion between opposite-charges at short-distances, at variance with large-distance interactions.
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We study, via computer simulations, the fluctuations in the net electric charge, in a two dimensional one component plasma (OCP) with uniform background charge density $-e rho$, in a region $Lambda$ inside a much larger overall neutral system. Setting $e=1$ this is the same as the fluctuations in $N_Lambda$, the number of mobile particles of charge $e$. As expected the distribution of $ N_Lambda$ has, for large $Lambda$, a Gaussian form with a variance which grows only as $hat kappa |partial Lambda|$, where $|partial Lambda|$ is the length of the perimeter of $Lambda$. The properties of this system depend only on the coupling parameter $Gamma = kT$ which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter $Gamma$ increases, $hat kappa(Gamma)$ decreases to an asymptotic value $hat kappa(infty) sim hat kappa(2)/2$ which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large $Gamma$, the characteristic length $xi_L = 2hat kappa/rho$ associated with charge fluctuations behaves very differently from that of the Debye length, $xi_D sim 1/sqrt Gamma$, which it approaches as $Gamma to 0$. The pair correlation function of the OCP is also studied.
Two-dimensional systems may admit a hexatic phase and hexatic-liquid transitions of different natures. The determination of their phase diagrams proved challenging, and indeed those of hard-disks, hard regular polygons, and inverse power-law potentials, have been only recently clarified. In this context, the role of attractive forces is currently speculative, despite their prevalence at both the molecular and colloidal scale. Here we demonstrate, via numerical simulations, that attraction promotes a discontinuous melting scenario with no hexatic phase. At high-temperature, Lennard-Jones particles and attractive polygons follow the shape-dominated melting scenario observed in hard-disks and hard polygons, respectively. Conversely, all systems melt via a first-order transition with no hexatic phase at low temperature, where attractive forces dominate. The intermediate temperature melting scenario is shape-dependent. Our results suggest that, in colloidal experiments, the tunability of the strength of the attractive forces allows for the observation of different melting scenario in the same system.
The zero-temperature phase diagram of binary mixtures of particles interacting via a screened Coulomb pair potential is calculated as a function of composition and charge ratio. The potential energy obtained by a Lekner summation is minimized among a variety of candidate two-dimensional crystals. A wealth of different stable crystal structures is identified including $A,B,AB_2, A_2B, AB_4$ structures [$A$ $(B)$ particles correspond to large (small) charge.] Their elementary cells consist of triangular, square or rhombic lattices of the $A$ particles with a basis comprising various structures of $A$ and $B$ particles. For small charge asymmetry there are no intermediate crystals besides the pure $A$ and $B$ triangular crystals.
The interaction force between likely charged particles/surfaces is usually repulsive due to the Coulomb interaction. However, the counterintuitive like-charge attraction in electrolytes has been frequently observed in experiments, which has been theoretically debated for a long time. It is widely known that the mean field Poisson-Boltzmann theory cannot explain or predict this anomalous feature since it ignores many-body properties. In this paper, we develop efficient algorithm and perform the force calculation between two interfaces using a set of self-consistent equations which properly takes into account the electrostatic correlation and the dielectric-boundary effects. By solving the equations and calculating the pressure with the Debye-charging process, we show that the self-consistent equations could be used to study the attraction between like-charge surfaces from weak-coupling to mediate-coupling regime, and that the attraction is due to the electrostatics-driven entropic force which is significantly enhanced by the dielectric depletion of mobile ions. A systematic investigation shows that the interaction forces can be tuned by material permittivity, ionic size and valence, and salt concentration, and that the like-charge attraction exists only for specific regime of these parameters.
The two-body (pair) contribution to the entropy of two-dimensional Yukawa systems is calculated and analyzed. It is demonstrated that in the vicinity of the fluid-solid (freezing) phase transition the pair entropy exhibits an abrupt jump in a narrow temperature range and this can be used to identify the freezing point. Relations to the full excess entropy and some existing freezing indicators are briefly discussed.
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