1,721,244 research outputs found
A density-functional theory investigation of cluster formation in an effective-potential model of dendrimers
No full textWe consider a system of particles interacting via a purely repulsive, soft-core potential recently introduced to model effective pair interactions between dendrimers, which is expected to lead to the formation of crystals with multiple occupancy of the lattice sites. The phase diagram is investigated by density-functional theory (DFT) without making any a priori assumption on the functional form of the density profile or on the type of crystal lattice. As the average density rho is increased, the system displays first a transition from a fluid to a bcc phase, and subsequently to hcp and fcc phases. In the inhomogeneous region, the behavior is that found in previous investigations of this class of cluster-forming potentials. Specifically, the particles arrange into clusters strongly localized at the lattice sites, and the lattice constant depends very weakly on rho, leading to an occupancy number of the sites which is a nearly linear function of rho. These results are compared to those predicted by the more widespread approach, in which the DFT minimization is carried out by representing the density profile by a given functional form depending on few variational parameters. We find that for the model potential studied here, the latter approach recovers most of the predictions of the unconstrained minimization
Some general features of mesophase formation in hard-core plus tail potentials
No full textThe formation of mesophases in fluids with hard-core plus tail interactions is investigated and compared with the occurrence of cluster crystals in ultra-soft repulsive potentials by using a simple variational expression for the Helmholtz free energy. The purpose of this study is mostly qualitative, i.e., to explain the origin of the different behavior of these systems, and the reason why, in the hard-core case, interactions which are apparently quite different display a common pattern for the phase diagram, featuring spheres, cylinders, lamellae, inverted cylinders, and inverted spheres as the density is increased. In the limit of zero temperature, our approach also yields some simple predictions for the densities at which the transitions between different mesophases are expected to take place, as well as for the size of their clusters at the transitions. We find that these results compare favorably with those obtained in a former study of a model fluid with competing attractive and repulsive interactions by density-functional theory with numerical minimization
Globally accurate theory of structure and thermodynamics for soft-matter liquids
No full textStandard statistical mechanical approximations (e.g. mean-field approximations) for pair-correlation functions of strongly interacting systems that yield adequate thermodynamics away from critical points typically break down badly in critical regions. The self-consistent Ornstein-Zemike approximation (SCOZA) transcends this difficulty, yielding globally accurate Structure and thermodynamics. The SCOZA has been applied successfully to a variety of Hamiltonian models and the result will be briefly summarized. We end with a progress report on the applications of the SCOZA to some soft-matter systems
Self-Consistent Ornstein-Zernike Approximation (SCOZA) and exact second virial coefficients and their relationship with critical temperature for colloidal or protein suspensions with short-ranged attractive interactions
Full text linkWe focus on the second virial coefficient B2 of fluids with molecules interacting through hard-sphere
potentials plus very short-ranged attractions, namely, with a range of attraction smaller than half
hard-sphere diameter. This kind of interactions is found in colloidal or protein suspensions, while the interest in B2 stems from the relation between this quantity and some other properties of these fluid systems. Since the SCOZA (Self-Consistent Ornstein-Zernike Approximation) integral equation is
known to yield accurate thermodynamic and structural predictions even near phase transitions and in the critical region, we investigate B2_SCOZA and compare it with B2_exact, for some typical potential models. The aim of the paper is however twofold. First, by expanding in powers of density the condition of thermodynamic consistency included in the SCOZA integral equation, a general analytic expression for B2_SCOZA is derived. For a given potential model, a comparison between B2_SCOZA and B2_exact may help to estimate the regimes where the SCOZA closure is reliable. Second, following the Vliegenthart-Lekkerkerker (VL) and Noro-Frenkel suggestions, the relationship between the critical
B2 and the critical temperature Tc is discussed in detail for two prototype models: the square-well (SW) potential and the hard-sphere attractive Yukawa (HSY) one. The known simulation data for
the SW model are revisited, while for the HSY model new SCOZA results have been generated. Although B2_HSY at the critical temperature is found to be a slowly varying function of the range of
Yukawa attraction Delta_Y over a wide interval of Delta_Y, it turns out to diverge as Delta_Y vanishes. For fluids
with very short-ranged attractions, such a behavior contrasts with the VL assumption that B2 at the critical temperature should be nearly independent of the range of attraction. A very simple analytic representation is found for the available Monte Carlo data for Tc_HSY and B2_HSY as functions of the range of attraction, for Delta_Y smaller than half hard-sphere diameter
An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures
Full text linkThe formation of microphases in systems of particles interacting by repulsive, bounded potentials is studied by means of density-functional theory (DFT) using a simple, mean-field-like form for the free energy which has already been proven accurate for this class of soft interactions. In an effort not to constrain the configurations available to the system, we do not make any assumption on the functional form of the density profile rho(r), save for its being periodic. We sample rho(r) at a large number of points in the unit cell and minimize the free energy with respect to both the values assumed by rho(r) at these points and the lattice vectors which identify the Bravais lattice. After checking the accuracy of the method by applying it to a one-component generalized exponential model (GEM) fluid with pair potential. exp[-(r/R)(4)], for which extensive DFT and simulation results are already available, we turn to a binary mixture of Gaussian particles which some time ago was shown to support microphase formation [A. J. Archer, C. N. Likos, and R. Evans, J. Phys.: Condens. Matter 16, L297 (2004)], but has not yet been investigated in detail. The phase diagram which we obtain, that supersedes the tentative one proposed by us in a former study [M. Carta, D. Pini, A. Parola, and L. Reatto, J. Phys.: Condens. Matter 24, 284106 (2012)], displays cluster, tubular, and bicontinuous phases similar to those observed in block copolymers or oil/water/surfactant mixtures. Remarkably, bicontinuous phases occupy a rather large portion of the phase diagram. We also find two non-cubic phases, in both of which one species is preferentially located inside the channels left available by the other, forming helices of alternating chirality. The features of cluster formation in this mixture and in GEM potentials are also compared
SCOZA critical exponents and scaling in three dimensions
No full textThe critical behavior of a self-consistent Ornstein-Zernike approach (SCOZA) that describes the pair correlation function and thermodynamics of a classical fluid, lattice gas, or Ising model is analyzed in three dimensions below the critical temperature, complementing our earlier analysis of the supercritical behavior. The SCOZA subcritical exponents describing the coexistence curve, susceptibility (compressibility), and specific heat are obtained analytically (beta=7/20, gamma'=7/5, alpha'=-1/10). These are in remarkable agreement with the exact values (beta approximate to 0.326, gamma' approximate to 1.24, alpha' approximate to 0.11) considering that the SCOZA uses no renormalization group concepts. The scaling behavior that describes the singular parts of the thermodynamic functions as the critical point is approached is also analyzed. The subcritical scaling behavior in the SCOZA is somewhat less simple than that expected in an exact theory, involving two scaling functions rather than one
Fluid-fluid and fluid-solid phase separation in nonadditive asymmetric binary hard-sphere mixtures
No full textVery asymmetric mixtures of hard spheres naturally arise in the modellization of colloidal dispersions. Effective potentials have emerged as a powerful tool for describing these systems and have often been employed to extract the phase diagram in both the additive and nonadditive cases. However, most theoretical investigations have been carried out by means of mean-field-like approaches, so their quantitative accuracy remains to be assessed. Here we employ previously determined effective potentials for nonadditive hard-sphere mixtures to study the fluid-fluid phase transition by the hierarchical reference theory (HRT), which is designed to take realistically into account the effects of long-range fluctuations on phase separation. Fluid-solid equilibrium is addressed by supplementing HRT with thermodynamic perturbation theory for the solid phase. We apply this approach both to a potential with adjustable nonadditivity parameter (Louis et al 2000 Phys. Rev. E 61 R1028) and to the Asakura-Oosawa (AO) potential, which represents an extreme case of nonadditivity. Our results for the phase diagram, including modified hypernetted chain (MHNC) calculations, are compared to those of other liquid-state theories and are found to agree nicely with available simulation data. Unlike commonly adopted liquid-state theories, HRT is capable both of getting arbitrarily close to the fluid-fluid critical point, and of giving nontrivial critical exponents. In particular, the fluid-fluid coexistence curve is much flatter than that obtained via perturbation theory, in agreement with a recent finite-size scaling Monte Carlo analysis of the AO model
Regioselective Alkylation of N,N'-Diethylbenzamides via Lithiation and Copper Transmetalation Procedure
No full textThermodynamically self-consistent theory of structure for three-dimensional lattice gases
No full textRecently, methods were developed to solve with high accuracy the equations that describe a thermodynamically self-consistent theory for the two-body correlation function, and preliminary results were reported for three-dimensional lattice gases with nearest-neighbor attractive interaction [R. Dickman and G. Stell, Phys. Rev. Lett. 77, 996 (1996)]. Here we give a detailed description of our methods and of the results, which are found to be remarkably accurate for both the thermodynamics and structure of these systems. In particular, critical temperatures are predicted to within 0.2% of the best estimates from series expansions. Although above the critical temperature the theory yields the same critical exponents as the spherical model, this asymptotic behavior sets in only in a very narrow region around the critical point, so that the apparent exponents and the thermodynamics are well reproduced up to reduced temperatures of around 10(-2). On the coexistence curve, on the other hand, the exponents are nonspherical, and considerably more accurate than the spherical ones. For instance, the exponent beta(coex) predicted by the theory for the shape of the coexistence curve is beta(coex)=0.35
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