Short-range Attractive Potential Research Articles

Mode-coupling theory of colloids with short-range attractions

Within the framework of the mode-coupling theory of super-cooledliquids, we investigate new phenomena in colloidal systems on approachto their glass transitions. When the inter-particle potentialcontains an attractive part, besides the usual repulsive hard core,two intersecting liquid-glass transition lines appear, one of whichextends to low densities, while the other one, at high densities,shows a re-entrant behaviour. In the glassy region a newtype of transition appears between two different types ofglasses. The complex phenomenology can be described in terms of higherorder glass transition singularities. The various glass phases arecharacterized by means of their viscoelastic properties.The glass driven by attractions has been associatedwith particle gels, andthe other glass is the well known repulsive colloidal glass. Thesecorrespondences, in association with the new predictions of glassybehaviour, mean that such phenomena may be expected in colloidal systemswith, for example, strong depletion or other short-ranged attractivepotentials.

Localization on short-range potentials in dissipative quantum mechanics.

In this Letter, the problem of the existence of a state localized on a weak short-range attractive potential in the presence of dissipation is considered. It is shown that, contrary to the pure quantum case, a localized state is produced in any number of dimensions, while in low dimensions dissipation leads to much stronger localization. The results have physical implications for the dissipative dynamics of objects such as heavy particles in Fermi liquids and for superconductivity in high- T(c) materials.

Thermophysical properties of gases, liquids, and solids composed of particles interacting with a short-range attractive potential.

A short-range polynomial interaction potential is introduced which has both a repulsive core and an attractive part. It is cut off smoothly such that its first and second derivatives vanish at the cutoff distance. The potential therefore enables efficient simulation studies of a model material that exhibits similarities to a full (but computationally expensive) classical Lennard-Jones system. Thermophysical properties of the model are calculated by (nonequilibrium) molecular dynamics computer simulations and compared with analytical results. Among the quantities studied is the pressure as a function of the density for various temperatures. Equations of state for the fluid and the solid are tested. The coexistence of gaseous, (metastable) liquid, and fcc solid phases is found for a range of temperatures. Bulk and shear moduli are computed. The response of the system to a shear deformation with a constant shear rate is analyzed. The liquid shows viscoelastic behavior that can be described with a Maxwell model. The solid behaves as an elastic medium up to a finite deformation and then undergoes a transition to plastic flow, which is stick-slip-like at small shear rates and continuous at higher ones.

Fluctuation-induced attraction of vortices in anisotropic superconductors

We study the fluctuation-induced attraction of vortices for continuous anisotropic superconductors by using quantum statistical physics. In the low temperature or quantum limit, only the low-lying modes are relevant, the induced short-range attractive potential is proportional to ( k B T) 3 K 1( ΓR/ λ), while in high temperature or classical limit, the induced attractive potential reduced to long-range van der Waals type k B T/ R 4 for two vortices separated by a distance R.

Effective adiabatic approximation in the problem of three bodies coupled via short-range potentials

The effective adiabatic approximation is constructed for the problem of three bodies on a straight line that are coupled via short-range attractive delta-function potentials. It is shown that, in this system, there arise a nonlocal momentum-dependent long-range effective potential and a polarization potential. A lower bound on the binding energy of the system is obtained to a relative precision of about 10−6. It is shown that, to within 0.03%, this approximation yields a correct asymptotic behavior of solutions and a correct behavior of the phase shift for elastic scattering at relative momenta below the three-body-breakup threshold. A local convergence of the adiabatic expansion in a finite interval of the radial variable is demonstrated.

Interactions and phase transitions in protein solutions

Understanding interactions and phase transitions in protein solutions is essential in order to develop systematic protein crystallisation strategies. Recent studies show that proteins near crystallisation behave as particles interacting via a very short-range attractive potential. The microscopic origin of this attractive term, and its strong dependence on the nature of the crystallisation agent, is, however, still obscure. The interplay of crystal nucleation with formation of weakly bonded amorphous aggregates also deserves further analysis.

Proteins in solution : from X-ray scattering intensities to interaction potentials

Biological macromolecules in solution interact with each other through medium-range (from a few Å to a few nm) interaction potentials. These potentials control the macromolecular distribution in solution, the macromolecular phase diagram and the crystallization process. We have previously shown that small angle X-ray scattering (SAXS) is a convenient tool to characterize the resulting potential, either attractive or repulsive, and to follow the changes induced by the crystallizing agents. In the present paper SAXS and simulation methods derived from statistical mechanics are coupled to determine the best fit potentials from the comparison of experimental and theoretical intensity curves. The currently used models in the colloid field are derived from the DLVO (Derjaguin, Landau, Verwey, Overbeek) potential where three types of interactions play a major role: hard sphere and electrostatic are repulsive, van der Waals are attractive. A combination of a short-range attractive potential and a coulombic repulsive indeed correctly accounts at low ionic strength for the phase diagram as a function of pH and salt concentration. The origin of the ion specificities at high ionic strength associated with the so-called “Hofmeister series” remain, however, unclear. The whole of the data demonstrates that the colloidal approach may be applied with success to protein crystallization.

Weakly bound states in dimensions

We study the critical behaviour near the threshold where a first bound state appears at some value of coupling constant in an attractive short-range potential in dimensions. We obtain a general expression for the binding energy near the threshold and also demonstrate that the critical region is correctly described by an effective separable potential. The critical exponent of the radius of weakly the bound state is shown to coincide with the correlation length exponent for the spin model in the large-N limit. In two dimensions, where the binding energy is exponentially small in coupling constant, we obtain a general analytic expression for the prefactor.

Three-dimensional Fourier representation of a scattering eigenstate

The unbound momentum-space wavefunction of a negatively charged particle in a short-range attractive potential is calculated numerically after isolating its singularities. The result differs considerably from a Coulomb wave to an effective charge, particularly at low scattering energies.

On the boson-fermion model of superconductivity

The existence of pair excitations in a Fermi gas interacting via a short-range attractive potential is investigated. Within the ladder approximation to the Bethe-Salpeter equation for the effective two-particle interaction, evidence of pair excitation is found at energies slightly larger than the chemical potential. The link between those excitations and a boson-fermion model of superconductivity (Phys. Lett. A,196 (1995) 359) is discussed. In particular it is shown that the charge carrier density dependence of the pair excitation (boson) energy, assumed phenomenologically in the boson-fermion model, is consistent with the properties of the interacting Fermi gas studied. These results give support to the microscopic origin of the phenomenological boson-fermion model of superconductivity.

On the interplay between Coulomb and nuclear states in exotic atoms

Abstract The rearrangement of the Coulomb atomic spectrum in exotic atoms due to nuclear states bound by a real attractive short-range potential, and the coupling between atomic and nuclear states, was discussed and classified many years ago by Zeldovich. Here we generalize the discussion to physical situations for which a complex nuclear potential simulates the additional effects of nuclear absorption. As function of the strength parameter W 0 of the imaginary part of the nuclear potential, then for W 0 ≳ W 0 crit we find an almost complete relaxation of Zeldovich's phenomenon of rearrangement and Coulomb atomic states and nuclear states get decoupled from each other. The critical strength W 0 crit is considerably weaker than the absorptivities encountered in exotic atoms experimentally observed. We briefly mention residual signatures of nuclear states in exotic atoms.

Aggregation processes in self‐associating polymer systems: Computer simulation study of micelles in the superstrong segregation regime

AbstractWe present the results of extensive molecular dynamics and Monte Carlo studies of the self‐organization in the solution of short polymer chains with strongly attracting head groups at their end. The formation of micelles (multiplets) is studied in detail. Both two dimensional (2d) and three‐dimensional (3d) systems are considered. The off‐lattice and lattice models under study incorporate physical factors which control micelle structure and growth in the so‐called superstrong segregation regime. These factors include (i) conformational effects associated with short‐range excluded‐volume interaction between the tails of flexible‐chain molecules and (ii) very strong attraction of head groups. Our computer simulations of 3d micelles, constructed a priori from chains with strong attraction of head groups (with the characteristic energy ≈ 10 kBT), show that size and shape of the micellar core depends crucially on the radius rc of the interaction of head‐groups. If the value of rc is comparable with chain length, then micelles of nearly spherical shape emerges. The decrease of rc can induce a sharp polymorphic transition from the micellar core which is spheric in shape to a disk‐like (bilayer‐shaped) aggregate. Such molecular organization differs from the commonly held notion of a radially symmetric micellar core. On the other hand, these findings fall into line with a recent theory of the super strong segregation regime. When the starting configuration is a random one (i.e., no micelles were a priori formed) the type of final microstructures, emerging as a result of micellization in the superstrong segregation regime, also depends essentially on the radius of head‐head attraction. In the case of three‐dimensional systems and/or short range attractive potentials we always obtain many small spherically shaped aggregates which, once formed at initial stages of micellization, remain stable for all time scales. Such a behavior is due to both the strong head‐head attraction and the screening (repulsive) action of micellar shells creating insurmountable potential barriers. As a result, we deal with kinetically “frozen‐in” microstructures which are not reversible and cannot exchange molecules with one another. In dense systems, we observe the formation of a (quasi) periodic pattern of alternating microdomains.

Polymer solutions confined in slit-like pores with attractive walls: An off-lattice Monte Carlo study of static properties and chain dynamics

Using a bead spring model of flexible polymer chains, the density profiles and chain configurational properties of polymer solutions confined between parallel plates were studied. A wide range of density ϕ, chain length N, and strength e of a short-range attractive wall potential was investigated. Both a temperature T in the good solvent regime (T > θ, θ being the Theta temperature where a chain in unconfined bulk three-dimensional solution would behave ideally) and a temperature in the bad solvent regime (T θ) show a crossover from two-dimensional excluded volume behavior (Rg ∝ N2ν with ν = 3/4) to ideal random walk behavior (ν = 1/2), the relaxation times show effective exponents Zeff (τ ∝ NZ eff) that clearly deviate from the Rouse prediction in concentrated confined solutions.

Static and Dynamic Properties of Adsorbed Chains at Surfaces: Monte Carlo Simulation of a Bead-Spring Model

The adsorption of flexible polymers from dilute solution in good solvents at attractive walls is studied by Monte Carlo simulation of a coarse-grained off-lattice model, varying chain length N and the strength ε of a short-range attractive wall potential. Unlike many previous studies, no chain end (or other monomer) is held fixed near the wall. In qualitative agreement with previous work on different models, we find an adsorption transition at a critical strength of the wall potential, where the chain configuration changes from three-dimensional to quasi-two-dimensional in the limit of very long chains. The dynamics of the chains is studied both above and below this adsorption threshold εc. Time-dependent mean-square displacements of monomers and the chain center of gravity as well as the associated relaxation times are studied in detail. In the adsorbed phase, relaxation times are found to scale as τ ∝ Nzeff with zeff ≈ 2.65 ± 0.1 and the lateral diffusion constant scales as DN ∝ N-yeff with yeff ≈ 1.1. Also small-scale motions of monomers in different distances from the adsorbing wall are investigated, and a qualitative picture for the dynamics of these partially adsorbed chains is developed.

Linear and/or quadratic confinement, plus short-range Coulomb-type attraction: A second-order analysis

In this paper the Schroedinger equation, involving a confining linear and/or quadratic, plus a short-range Coulomb-type attractive potential, is solved to second order. This simulates, for example, the two-quark system. A special case is also discussed where, to second order, the exact, analytical result can be obtained for a particular confining linear plus attractive Coulomb-type potential.

Effect of short-range potential and coupling with phonons on impurity states

An influence is discussed of a short-range potential and a coupling with phonons on the energy spectrum of donors. It is shown that the increasing attractive short-range potential leads to an additional state of s symmetry, in which the electron is more strongly localized than in the other states. The energy level connected with this state and hydrogen-like donor levels exhibit an anticrossing with a shape dependent on the electron-phonon interaction. For sufficiently small phonon energy, the anticrossing becomes very sharp. This additional state coexists with the hydrogen-like states, which can lead to a metastability of donors.

Three interacting strings in two dimensions: non-universal and multiple unbinding transitions

Three non-intersecting strings in two dimensions which interact via short-ranged attractive potentials are studied using bath transfer matrix methods and Monte Carlo tech- niques. The critical behavior at the unbinding transition and the critical values of the potential strength are determined for symmetric and asymmetric bundles of strings. In the asymmetric case, for which the two outer strings have diiferent hne tensions (or interact via dilferent po- tentials), the strings unbind in two subsequent transitions, which then exhibit universal critical behavior. In the symmetric case, where the two outer strings have the same line tension, trie three strings unbind simultaneously. The critical behavior at this unbinding transition is found to be non-universal for the whole range of accessible length scales, but its parameter dependence is found to be in strong disagreement with trie predictions of trie so-called necklace model. Trie more flexible the inner string, the deeper the critical potential. However, within the numerical error, three identical strings are found to unbind at the same critical potential strength as two strings with the same line tensions.

On the coexistence of superconductivity and charge density waves

We study a simple tight-binding (Hubbard) model for electrons interacting via a short range attractive potential. We show that on a cubic lattice, for a half-filled band the ground state may feature both superconductivity and a charge density wave. We examine the response of such a ground state to an external magnetic field and describe the effect of the charge density wave on the Meissner effect.

Critical behavior of three interacting strings.

The unbinding of three strings in a plane which interact via short-ranged attractive potentials is studied using both transfer-matrix methods and Monte Carlo techniques. In the symmetric case, for which the two outer strings have the same line tension, the critical behavior depends on the relative flexibility of the inner string in a nonuniversal fashion. In the asymmetric case, the strings unbind in two successsive unbinding transitions at two different temperatures. Renormalization-group arguments predict that these results are also applicable to the adhesion and unbinding of three membranes.

Application of Baxter's model to the theory of cloud points of nonionic surfactant solutions.

It is argued that asymmetric phase diagrams and other properties of colloidal systems can be generated by a system of spherical particles interacting via a sticky hard-sphere potential (Baxter model). This concept is illustrated by application to the cloud-point transition in nonionic surfactants. A detailed interpretation of neutron-scattering, light-scattering, and phase-diagram results for the n-octylpentaoxyethylene glycol monoether (CsE5) system is presented. In 1968, Baxter formulated the statistical mechanics of a system of particles interacting via a hard-sphere repulsion with surface adhesion. ' He demonstrated that in the Percus-Yevick approximation, the Ornstein-Zernike equation can be solved analytically for a potential consisting of a hard core together with a rectangular attractive well, provided that a certain limit is taken in which the range of the well becomes zero and its depth infinite. The results showed a first-order phase transition similar to that obtained with the Lennard-Jones potential. Despite its ability to quantitatively account for a number of experimental properties, this insightful work has not attracted much attention. The hurdle, possibly, has been that the main approximation, which results in a small range of attractive potential (compared to the size of the particles) combined with an infinite well depth, is inapplicable to the atomic systems. What we propose to argue here is that the Baxter model is just right for colloidal systems in the absence of Coulomb potentials. Under this category comes a wide class of systems, e.g. , water-in-oil microemulsions, nonionic surfactant solutions, and dispersions of oxide particles in nonaqueous liquids (paints). In this paper we demonstrate the use of this model in understanding the phase diagram, smallangle neutron scattering (SANS), and the light-scattering experimental results on nonionic surfactant solutions. Dilute aqueous solutions of nonionic surfactants show the phenomenon of clouding on heating to a well-defined temperature (Te, 8 for phase boundary) called the cloud temperature, and this phenomenon has been associated with a lower consolute point in the binary phase diagram of surfactant-water systems. An excellent summary of these aspects has been given recently by Degiorgio. Understanding this phenomenon represents one of the most challenging problems in the topic of nonionic surfactant solutions. The central role played by the hydration of the head group (normally polyethylene oxide) and the resulting temperature-dependent interaction between the micelles has been clearly identified. This interaction is complex and attempts have been made to model them by Yukawa-type potentials mainly because the OrnsteinZernike equations can be solved for this form of the interaction in the mean-spherical approximation (MSA) and one can obtain the structure factor to correlate the predictions with the results obtained from small-angle neutron-scattering experiments. The main handicap of such attempts has been that the strength of the potential (Uo/kT, ) required to fit the experimental data is of the order of 10 to 30, which clearly is unphysical. The fact that Uo!kT, should be of the order of unity is evident from the direct measurements of forces between mica plates coated with nonionic surfactants and from the measurement of cloud points of mixed ionic-nonionic surfactants. Recently, Reatto and Tau have concluded that the MSA is not suitable for short-ranged attractive potentials. Baxter's sticky hard-sphere model' appears to be ideally suited for these types of systems. The features of this model which appear attractive for its use for the clouding phenomenon are the following. (a) The critical volume fraction is low and is given by g, = 0.12. (b) The interaction U/kT is a slowly varying function