Short-range Square Research Articles

Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres

We propose an Einstein-solid, self-consistent phonon theory for the crystal phase of hard spheres that interact via short-range attractions. The approach is first tested against the known behavior of hard spheres, and then applied to homogeneous particles that interact via short-range square well attractions and the Baxter adhesive hard sphere model. Given the crystal symmetry, packing fraction, and strength and range of attractive interactions, an effective harmonic potential experienced by a particle confined to its Wigner-Seitz cell and corresponding mean square vibrational amplitude are self-consistently calculated. The crystal free energy is then computed and, using separate information about the fluid phase free energy, phase diagrams constructed, including a first-order solid-solid phase transition and its associated critical point. The simple theory qualitatively captures all the many distinctive features of the phase diagram (critical and triple point, crystal-fluid re-entrancy, low-density coexistence curve) as a function of attraction range, and overall is in good semi-quantitative agreement with simulation. Knowledge of the particle localization length allows the crystal shear modulus to be estimated based on elementary ideas. Excellent predictions are obtained for the hard sphere crystal. Expanded and condensed face-centered cubic crystals are found to have qualitatively different elastic responses to varying attraction strength or temperature. As temperature increases, the expanded entropic solid stiffens, while the energy-controlled, fully-bonded dense solid softens.

Percolation transition of short-ranged square well fluids in bulk and confinement

Using grand canonical Monte Carlo simulations, we investigate the percolation behavior of a square-well fluid with an ultra-short range of attraction in three dimension (3D) and in confined geometry. The latter is defined through two parallel and structureless walls (slit-pore). We focus on temperatures above the critical temperature of the (metastable) condensation transition of the 3D system. Investigating a broad range of systems sizes, we first determine the percolation thresholds, i.e., the critical packing fraction for percolation η(c). For the slit-pore systems, η(c) is found to vary with the wall separation L(z) in a continuous but non-monotonic way, η(c)(L(z)→∞)=η(c)(3D). We also report results for critical exponents of the percolation transition, specifically, the exponent ν of the correlation length ξ and the two fisher exponents τ and σ of the cluster-size distribution. These exponents are obtained from a finite-size analysis involving the cluster-size distribution and the radii of gyration distribution at the percolation threshold. Within the accuracy of our simulations, the values of the critical exponents of our 3D system are comparable to those of 3D random percolation theory. For narrow slit-pores, the estimated exponents are found to be close to those obtained from the random percolation theory in two dimensions.

STRINGENT VERIFICATION OF THIRD ORDER + SECOND ORDER PERTURBATION DENSITY FUNCTION THEORY: BASED ON SHORT-RANGE SQUARE WELL POTENTIAL

A recently proposed third order + second order perturbation density functional theory (DFT) approach is made self-contained by using a virial pressure from the Ornstein–Zernike integral equation theory as input to determine the numerical value of an associated physical parameter. An exacting examination is formulated by applying the self-contained perturbation DFT approach to a short-range square well fluid of low temperatures subject to various external fields and comparing the theoretical results for density profiles to the corresponding grand canonical ensemble Monte Carlo simulation results. The comparison seems favorable for the third order + second order perturbation DFT approach as a self-contained and accurate predictive approach. It is surprisingly found that this self-contained third order + second order perturbation DFT approach is displayed outstandingly even if a deep SW perturbation term is being accounted for by a second order perturbation expansion. A discussion is presented about potential opportunity for this perturbation scheme.

Extended law of corresponding states in short-range square wells: A potential energy landscape study

We study the statistical properties of the potential energy landscape of a system of particles interacting via a very short-range square-well potential (of depth -u0) as a function of the range of attraction Delta to provide thermodynamic insights of the Noro and Frenkel [M. G. Noro and D. Frenkel, J. Chem. Phys. 113, 2941 (2000)] scaling. We exactly evaluate the basin free energy and show that it can be separated into a vibrational (Delta dependent) and a floppy (Delta independent) component. We also show that the partition function is a function of Deltaebetauo, explaining the equivalence of the thermodynamics for systems characterized by the same second virial coefficient. An outcome of our approach is the possibility of counting the number of floppy modes (and their entropy).

Thermodynamic properties of short-range square well fluid

The interfacial properties of short-range square well fluid with lambda=1.15, 1.25, and 1.375 were determined by using single canonical Monte Carlo simulations. Simulations were carried out in the vapor-liquid region. The coexistence curves of these models were calculated and compared to those previously reported in the literature and good agreement was found among them. We found that the surface tension curves for any potential model of short range form a single master curve when we plot gamma* vs TT(c). It is demonstrated that the critical reduced second virial coefficient B(2)* as a function of interaction range or T(c)* is not constant.

Scaling of Dynamics with the Range of Interaction in Short-Range Attractive Colloids

We numerically study the dependence of the dynamics on the range of interaction Delta for the short-range square well potential. We find that, for small Delta, dynamics scale exactly in the same way as thermodynamics, both for Newtonian and Brownian microscopic dynamics. For interaction ranges from a few percent down to the Baxter limit, the relative location of the attractive-glass line and the liquid-gas line does not depend on Delta. This proves that, in this class of potentials, disordered arrested states (gels) can be generated only as a result of a kinetically arrested phase separation.

Studies of structural arrest transition inL64/D2O micellar solutions

We summarize the results of analyses of a series of small angle neutron scattering (SANS)experiments on dense L64 copolymer micellar solutions in heavy water. The system ismodelled as a suspension of micellar particles that interact among themselves with a hardcore plus a short range square well attractive interaction. The observed phasebehaviour in the plane of temperature and polymer concentration is described.Characteristic features such as the existence of the glass-to-liquid-to-glass re-entrancetransition and the line of glass-to-glass transition with its associated end point(A3 singularity) are found which are quantitatively consistent with the recent mode couplingtheory calculations using the same model potential. Supplementary to SANS experiments,photon correlation spectroscopy experiments on the same system have been performed.They show that although the Debye–Waller factors (the long time limits of the coherentintermediate scattering functions) of the two glasses do indeed become identical at theA3 point as predicted, the intermediate scattering functions exhibit distinctlydifferent intermediate time relaxations. Furthermore, we show thatthe Debye–Waller factors obtained from volume fractions beyond theA3 point have the same magnitude as for the repulsive glass obtained before theA3 point. In addition, the effect of applied pressure on the kinetic glass transition(KGT) is explored for the first time. We observe that, for the KGT inL64/D2O micellar system, increasing applied pressure at constant temperature has a similar effect toreducing temperature at constant pressure. The preliminary observation of the ageing effecton quenching into the attractive glass state with the SANS technique is reported as well.

Convergence acceleration for the Kohn variational method in the presence of a long-range interaction.

This paper presents a distorted-wave generalization of the S-matrix version of the Kohn variational principle developed by Zhang, Chu, and Miller [J. Chem. Phys. 88, 10 (1988)]. For scattering in the presence of a long-range interaction, the large-r asymptotic solution to the Schr\"odinger equation is built into the Kohn variational principle order by order in an effort to accelerate the convergence of the short-range square integrable part of the basis-set expansion. The improvement in the rate of convergence is demonstrated by applying the method to a long-range model potential. Multichannel scattering is discussed.