We consider a fluid of hard spheres bearing one or two uniform circular adhesive patches, distributed so as not to overlap. Two spheres interact via a “sticky” Baxter potential if the line joining the centers of the two spheres intersects a patch on each sphere, and via a hard sphere potential otherwise. We analyze the location of the fluid-fluid transition and of the percolation line as a function of the size of the patch (the fractional coverage of the sphere’s surface) and of the number of patches within a virial expansion up to third order and within the first two terms (C0 and C1) of a class of closures Cn hinging on a density expansion of the direct correlation function. We find that the locations of the two lines depend sensitively on both the total adhesive coverage and its distribution. The treatment is almost fully analytical within the chosen approximate theory. We test our findings by means of specialized Monte Carlo simulations and find the main qualitative features of the critical behavior to be well captured in spite of the low density perturbative nature of the closure. The introduction of anisotropic attractions into a model suspension of spherical particles is a first step toward a more realistic description of globular proteins in solution.

We apply a simple statistical mechanics cluster approximation for studying clustering in the Kern and Frenkel model of Janus fluids. The approach is motivated by recent Monte Carlo simulations work on the same model revealing that the vapor coexisting with the liquid phase contains clusters of different sizes and shapes whose equilibrium concentrations in general depend on the interaction range as well as on thermodynamic parameters. The approximation hinges on a separation between the intra- and inter-cluster contribution to thermodynamics, where only the former is explicitly computed by Monte Carlo simulations. Two level of a simple liquid theory approximations are exploited for the description of the latter. In the first we use the ideal-gas expressions and obtain a qualitative agreement with extensive Monte Carlo bulk simulations. This can be improved to a semi-quantitative agreement, by using a hard-sphere description for the cluster-cluster correlations.

Covariant scalar field quantization, nicknamed $({\phi }^r{)}_n$, where $r$ denotes the power of the interaction term and $n=s+1$ where $s$ is the spatial dimension and 1 adds time. Models such that $r<2n/(n-2)$ can be treated by canonical quantization, while models such that $r>2n/(n-2)$ are nonrenormalizable, leading to perturbative infinities, or, if treated as a unit, emerge as ‘free theories’. Models such as $r=2n/(n-2)$, e.g., $r=n=4$, again using canonical quantization also become ‘free theories’, which must be considered quantum failures. However, there exists a different approach called affine quantization that promotes a different set of classical variables to become the basic quantum operators and it offers different results, such as models for which $r>2n/(n-2)$, which has recently correctly quantized $({\phi }^{12}{)}_3$. In the present paper we show, with the aid of a Monte Carlo analysis, that one of the special cases where $r=2n/(n-2)$, specifically the case $r=n=4$, can be acceptably quantized using affine quantization.

We investigate the dependence of the stickiness parameters $t_{ij}=1∕\left(12{\tau }_{ij}\right)$—where the ${\tau }_{ij}$ are the conventional Baxter parameters—on the solute diameters ${\sigma }_i$ and ${\sigma }_j$ in multicomponent sticky hard sphere (SHS) models for fluid mixtures of mesoscopic neutral particles. A variety of simple but realistic interaction potentials, utilized in the literature to model short-ranged attractions present in real solutions of colloids or reverse micelles, is reviewed. We consider: (i) van der Waals attractions, (ii) hard-sphere-depletion forces, (iii) polymer-coated colloids, and (iv) solvation effects (in particular hydrophobic bonding and attractions between reverse micelles of water-in-oil microemulsions). We map each of these potentials onto an equivalent SHS model by requiring the equality of the second virial coefficients. The main finding is that, for most of the potentials considered, the size-dependence of $t_{ij}(T,{\sigma }_i,{\sigma }_j)$ can be approximated by essentially the same expression, i.e., a simple polynomial in the variable ${\sigma }_i{\sigma }_j∕{\sigma }_{ij}^2$, with coefficients depending on the temperature $T$, or—for depletion interactions—on the packing fraction ${\eta }_0$ of the depletant particles.

We introduce a model of attractive penetrable spheres by adding a short range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact impenetrable counterpart as a starting point. The model is expected to describe star polymers in regimes of good and moderate solvent under dilute conditions. We derive the exact coefficients of a low density expansion up to second order for the radial distribution function and up to fourth order in the virial expansion. These exact results are used as a benchmark to test the reliability of approximate theories (Percus-Yevick and hypernetted chain). Notwithstanding the lack of an exact solution for arbitrary densities, our results are expected to be rather precise within a wide range of temperatures and densities. A detailed analysis of some limiting cases is carried out. In particular we provide a complete solution of the sticky penetrable-sphere model in one dimension up to the same order in density. The issue of Ruelle's thermodynamics stability is analyzed and the region of a well defined thermodynamic limit is identified.Comment: 20 pages, 7 figures, to appear in Physical Review E (2008