Attractive Spheres Research Articles

Ion current on a small spherical attractive probe in a weakly ionized plasma with ion-neutral collisions (kinetic approach)

The ion flux on a small attractive sphere (the sphere radius is much less than the Debye length) and the electric potential distribution around the sphere charged in a stationary weakly ionized plasma are calculated by the direct solution of the kinetic equation with the Bhatnagar–Gross–Krook collision term. Only a weak dependence of the ion flux on the electron temperature is found. An analytical approximation of the calculated ion current–voltage characteristics is proposed for intermediate collisionalities, where neither a collisionless theory nor a continuum fluid approach is valid. This approximation was used for calculation of the floating sphere potential. A reasonable agreement of the calculated floating sphere potential with prior numerical calculations is found.

Theory of gelation, vitrification, and activated barrier hopping in mixtures of hard and sticky spheres

Naive mode coupling theory (NMCT) and the nonlinear stochastic Langevin equation theory of activated dynamics have been generalized to mixtures of spherical particles. Two types of ideal nonergodicity transitions are predicted corresponding to localization of both, or only one, species. The NMCT transition signals a dynamical crossover to activated barrier hopping dynamics. For binary mixtures of equal diameter hard and attractive spheres, a mixture composition sensitive "glass-melting" type of phenomenon is predicted at high total packing fractions and weak attractions. As the total packing fraction decreases, a transition to partial localization occurs corresponding to the coexistence of a tightly localized sticky species in a gel-like state with a fluid of hard spheres. Complex behavior of the localization lengths and shear moduli exist because of the competition between excluded volume caging forces and attraction-induced physical bond formation between sticky particles. Beyond the NMCT transition, a two-dimensional nonequilibrium free energy surface emerges, which quantifies cooperative activated motions. The barrier locations and heights are sensitive to the relative amplitude of the cooperative displacements of the different species.

Ion channels allow atomic control of macroscopic transport

AbstractIon channels are proteins with a hole down their middle that control an enormous range of biological function. Thousands of biologists and clinicians study ion channels every day because of their crucial involvement in disease. Ion channels have a definite structure once open and ions move through them by electrodiffusion. Theories that describe the movement of charged spheres through definite structure are able to account for the experimental behavior of channels in a wide range of conditions with just a few parameters with fixed values. Selectivity is produced by the balance of electrostatic attraction and hard sphere repulsion in at least three types of channels. More ‘chemical’ forces are not involved. The free energy landscapes of these systems are variables. Preformed binding sites are not involved. Indeed, in some cases selectivity is produced by depletion zones, not binding sites. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Simulation studies of a phenomenological model for elongated virus capsid formation

We study a phenomenological model in which the simulated packing of hard, attractive spheres on a prolate spheroid surface with convexity constraints produces structures identical to those of prolate virus capsid structures. Our simulation approach combines the traditional Monte Carlo method with a modified method of random sampling on an ellipsoidal surface and a convex hull searching algorithm. Using this approach we identify the minimum physical requirements for nonicosahedral, elongated virus capsids, such as two aberrant flock house virus particles and the prolate prohead of bacteriophage phi29 , and discuss the implication of our simulation results in the context of recent experimental findings. Our predicted structures may also be experimentally realized by the evaporation-driven assembly of colloidal spheres under appropriate conditions.

Slippery diffusion-limited aggregation

Colloidal particles that interact through strong, short-range, secondary attractions in liquids form irreversible "slippery" bonds that are not shear-rigid. Through event-driven simulations of slippery attractive spheres, we show that space-filling fractal clusters still emerge from the process of "slippery" diffusion-limited aggregation (DLA). Although slippery and classic DLA clusters have the same fractal dimension, d_{f}=2.5 , their average coordination numbers are quite different: z_{S}=6 whereas z_{C}=2 . Local tetrahedral attractive jamming of the particles leads to a structure factor, S(q) , that exhibits dense cluster peaks at higher wave numbers, q , and a fractal power-law rise toward lower q .

The critical endpoint in phase diagrams of attractive hard spheres

We calculate the critical endpoint (cep) in phase diagrams of attractive hard spheres (HS), for both a Yukawa attraction and a polymer depletion potential, using approximate analytical theories. The cep corresponds to the minimum attraction range and the maximum contact potential for which liquid can exist. For both sytems we find essentially the same result: in the cep the attraction range is about one-third of the particle radius, and the attraction strength is around 2 kT. This same cep is found from simulations on particles interacting through a Lennard–Jones-type potential. It thus seems that the cep is essentially independent of the details of the pair potential for any system with a smooth attractive pair potential.

Critical Endpoint and Analytical Phase Diagram of Attractive Hard-Core Yukawa Spheres

We analytically calculate the gas-liquid critical endpoint (cep) for hard spheres with a Yukawa attraction. This cep is a boundary condition for the existence of a liquid. We use an analytical Helmholtz energy expression for the attractive Yukawa (hard) spheres based on the first-order mean spherical approximation to the attractive Yukawa potential by Tang and Lu (J. Chem. Phys. 1993, 99, 9828). This theory and our analytical simplification of it predict the gas-liquid and fluid-solid phase behavior, as found from computer simulations, very accurately as long as the range 1/kappa of attraction is not too short. We find that the cep is situated at kappasigma approximately 6 and at a contact potential around 2 kT. It follows that a liquid state is only possible when the attraction range is longer than (1/6) of the particle diameter sigma, and the attraction strength is smaller than 2 kT. The liquid region does not span more than 0.6 kT in strength, and there is also a relatively narrow window for the attraction range.

Structure and interaction in dense colloidal systems: evaluation of scattering data by thegeneralized indirect Fourier transformation method

The generalized indirect Fourier transformation (GIFT) technique is a versatile tool for theevaluation of small angle scattering data. It does not depend on models for the size andshape of the particles and requires model assumptions only for the interactioneffects that are typically not as sensitive to the details of the assumptions. Wereview here the development of the technique from its inception, focusing on theincluded interaction models for hard, charged and attractive spheres, and lamellae. Aconsiderable number of applications has also been reported ranging from surfactants,emulsions, microemulsions, food science, and ceramics to melts and block-copolymers.

Tuning short-range attractions in protein solutions: from attractive glasses to equilibriumclusters

We report small-angle scattering experiments with two differenttypes of model proteins, lysozyme and the eye lens proteinγB-crystallin. We discuss the results in the context of recent suggestions thatglobular proteins possess a short-ranged attractive potential, and that simplemodels from colloid science could help to rationalize the best route for obtainingprotein crystals and to interpret their complex phase diagrams. The short-rangeattraction leads to an extremely interesting phase behaviour with a liquid–gascoexistence curve that is metastable with respect to the liquid–solid (crystal)boundary and the occurrence of an attractive glass. We demonstrate that forγB-crystallin, the scattering data are indeed in good agreement with predictions for aninteraction potential consisting of short-ranged attraction and hard sphere repulsion, andwe also provide evidence of a dynamically arrested glass or gel phase at highconcentrations. We also report on a systematic study of the effect of a weak screenedCoulomb repulsion in highly concentrated lysozyme solutions. We demonstratethat combining short-range attraction and long-range repulsion results in theformation of small equilibrium clusters, and we discuss the concentration andtemperature dependence of the cluster size in view of its analogy to micelle formation.

Are thermoresponsive microgels model systems for concentrated colloidal suspensions? A rheology and small-angle neutron scattering study.

The structure of concentrated temperature-sensitive poly(N-isopropylacrylamide) (PNiPAM) microgel suspensions has been investigated employing rheology and small-angle neutron scattering (SANS). A previously described model expression for the particle form factor P(inho)(q) is extended by a model hard sphere structure factor S(q), and the average radial density profiles phi(r) are calculated from the amplitude of the form factor A(q) and the structure factor S(q). By this procedure, a direct real space description of the spatial ordering in the neighborhood of a single particle is obtained. The overall particle size and the correlation length xi of the concentration fluctuations of the internal polymer network decrease with concentration, revealing the increasing compression of the spheres. Thus, the particle form factor P(inho)(q) of the swollen PNiPAM microgels depends on concentration. The particle-particle interaction potential does not change significantly between 25 and 32 degrees C. Even approximately 1 K below the lower critical solution temperature (LCST), the experimental scattering intensity distributions I(q)/c are described very well by the hard sphere structure factor when an equivalent hard sphere particle size R(HS) and volume fraction eta(HS) are used. Microgels with different degrees of cross-linking and particle size resemble true hard sphere behavior up to effective volume fractions of phi(eff) < 0.35. At higher effective volume fractions phi(eff) > 0.35 strong deviations from true hard spheres are observed. Interpenetration of the outer, less cross-linked regions of the soft spheres as well as particle compression occurred at higher concentrations. In agreement with this, the equilibrium colloidal phase behavior and rheology also has some features of soft sphere systems. At temperatures well above the LCST, the interaction potential becomes strongly attractive and the collapsed microgel spheres form aggregates consisting of flocculated particles without significant long-range order. Hence, an attractive interaction potential in concentrated suspensions of PNiPAM microgels leads to distinctively different structures as compared to attractive hard sphere colloids. When the peculiar structural properties of the PNiPAM microgels are considered, they can be used as model systems in colloidal science.

Global phase diagrams of the van der Waals–Dieterici and the BMCSL–Dieterici equations of state

Global phase diagrams of a binary mixture of attractive hard spheres described by the van der Waals–Dieterici and Boublik–Mansoori–Carnahan–Starling–Leland–Dieterici equations of state (with a square root combining rule for cross-attraction) are calculated in dependence on the ratio of the hard-sphere diameters and the attraction strength.

Mapping of theoretical equations of state for molecular fluids on a biquadratic equation

A biquadratic equation of state for the attractive hard sphere chain fluid with dipolar interactions is developed. The background of the development is the mapping of molecular model equations onto a simplified mathematical form. In course of this mapping procedure known properties such as virial coefficients and physical limits are accounted for. For the hard sphere reference model a simple theoretical equation is developed, which is almost as accurate as the Carnahan–Starling (CS) equation and includes the nearly correct high density limit. The perturbation of this reference model due to chain formation and dipolar forces is accounted for by variations of the coefficients in the reference model. These coefficients are constant values for the hard sphere reference fluid and become dependent on the chain length parameter or the reduced dipole moment for the chain fluid or the dipolar fluid, respectively. By simple mathematical manipulations one can recover the usual equation of state form which consists of a sum of additive terms for each molecular property.

Post‐alighting responses of Mexican fruit flies (Dipt., Tephritidae) to different insecticides in paint on attractive spheres

Abstract: Two new, comparatively safe insecticides (spinosad and imidacloprid) were compared with dimethoate (each at 1.5% active ingredient) for behavioural and mortality effects on Mexican fruit flies, Anastrepha ludens. Insecticide was mixed with sugar (as a feeding stimulant) and yellow latex paint (as an extending agent) applied to the surface of fruit‐mimicking biodegradable 7 cm spheres made of sugar, flour and glycerin. Flies feeding on spinosad‐treated spheres did not differ from flies feeding on untreated spheres in post‐feeding intra‐tree flight capability, amount of oviposition or mortality. Flies that fed on imidacloprid‐ or dimethoate‐treated spheres for as little as 30 s experienced both high reduction in oviposition and high mortality compared with flies that fed on untreated spheres, and the flies from imidacloprid‐treated spheres also showed a much reduced intra‐tree flight capability. If baited with attractive odour, biodegradable yellow spheres treated with a surface coating of imidacloprid in latex paint and sugar could have potential for suppressing Mexican fruit flies on host trees.

Interaction between macroparticles in a binary fluid mixture: anomalous effects due to the bulk composition

The interaction between macroparticles in a binary fluid mixture has been analysed using the reference hypernetted-chain (RHNC) theory. The mixture is composed of particles interacting through an attractive potential (component 1) and hard spheres (component 2). Particles of different components interact through a hard-sphere potential. Significantly high affinity is assumed between the macroparticle surface and component 1. Two cases have been studied: case 1 where the bulk mixture unavoidably separates into two immiscible phases in the regime x 1p < x 1 < x 1Q (x 1 is the mole fraction of component 1, and x 1p and x 1Q denote values at the spinodal points); and case 2 where the bulk mixture is miscible over the entire composition range. As x 1 increases from x 1 = 0 or x 1 decreases from x 1 = 1 in case 1, the macroparticle interaction always shifts to the more attractive side. As x 1 → x 1R;1—0 or x 1 → x 1S;1 + 0 (x 1R;1 and x 1S;1 are threshold values, and x 1R;1 < x 1P and x 1S;1 > x 1Q), the range of the interaction exhibits sudden growth to a scale that is far longer than molecular dimensions, and the interaction becomes strongly attractive. This behaviour is ascribed to a surface-induced phase transition, the partial wetting of one of the components accompanied by the partial drying of the other. Even in case 2, similar behaviour has been observed as x 1 → x 1R;2—0 or x 1 → x 1S;2 + 0 (x 1R;2 and x 1S;2 are threshold values). Over the regime x 1R;2 < x 1 < x 1S;2 the RHNC theory possesses no solutions. The interaction between unlike macroparticles, whose surfaces have high affinity only with component 1 and only with component 2, respectively, has been analysed also. Although the interaction between like macroparticles is strongly attractive except for very small separations, the interaction between unlike macroparticles is strongly repulsive for all separations.

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered matrix of hard spheres: attractive wall-hard sphere interaction

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered hard sphere matrix is studied using the inhomogeneous Ornstein-Zernike equation with hypernetted chain closure. In contrast to previous studies, an attractive wall-hard sphere interaction is considered. The adsorption is affected by the attractive interaction both directly by the fluid-wall interaction and indirectly by the change in the structure of the matrix. Density profiles and pair distribution functions are reported. For comparison, grand canonical Monte Carlo simulation data are obtained. The agreement of the theoretical and simulation results is satisfactory but somewhat less pleasing than for the purely repulsive case.

Global phase diagrams of model and real binary fluid mixtures Part II. Non-Lorentz–Berthelot mixtures of attractive hard spheres

The global phase diagram of a binary mixture of attractive hard spheres described by the Boublik–Mansoori–Carnahan–Starling–Leland equation of state with a van der Waals mean field attractive term is investigated in its dependence on the ratio of the hard-sphere diameters and the strength of the attraction. Two values of the energetic combining rule parameter k12, determining the deviation from the geometric mean rule, are considered. In addition to phenomena reported recently for k12=1, the shield region of quadruple points is investigated for k12=0.8, along with its associated azeotropic phenomena. For k12=1.15, the mixture exhibits a rich set of low-temperature azeotropic phenomena: cusps on the p–T projections of azeotropic lines, exchange of branches of azeotropic lines, zero-temperature limited azeotropy, and double critical azeotropic points. Some of these azeotropic phenomena are described here for the first time.

Statistical associating fluid theory for chains of attractive hard-spheres: Optimized equations of state

New equations of state for chain molecules are proposed. The equations of state are physically sound and have a simple mathematical structure. The equations combine the recently developed simplified hard-sphere equations with the first order thermodynamic perturbation theory for chain molecules. The resulting equations of state show almost identical thermodynamic properties compared to the original equation of state for chains of attractive hard spheres. The advantage of the equations proposed here is the simple mathematical structure. They can be written as fourth order or cubic polynomial in the molar volume for which the molar volume can be calculated analytically for given temperature and pressure. This work shows that physically based model equations of state and simple equation structures can be incorporated. Furthermore the equations presented here enlarge the applicability of the statistical associating fluid theory for chain molecules.

The global phase behaviour of binary mixtures of chain molecules: theory and application

In this work the global phase behaviour of binary fluid mixtures of chain molecules is investigated. The underlying model employed for the investigation is based on our recently developed equation of state for chain molecules. This equation is based on the statistical associating fluid theory for chains of attractive hard spheres. It is an optimized equation of state for chain molecules which can be rearranged into a fourth order polynom in the molar volume. With this equation of state the global phase diagram for several mixtures of spherical molecules with non-spherical molecules has been investigated. The non-spherical molecules range from small non-spherical over short chain molecules to long chain polymer molecules. Special attention is paid to mixtures of small spherical molecules with long chain molecules. Such mixtures are employed to model polymer–solvent mixtures. Based on the calculated global phase diagram for polymer solutions, several processes such as co- or anti-solvent processes and polymerisations are discussed. These processes are represented by paths in the global phase diagram.

Global phase diagrams of model and real binary fluid mixtures: Lorentz–Berthelot mixture of attractive hard spheres

The phase behavior and global phase diagram of binary mixtures of attractive hard spheres described by a hard-sphere mixture equation of state with a mean field term and the Lorentz–Berthelot combining rule are examined in detail in dependence on the ratio of (i) the hard-sphere diameters and (ii) the strength of the mean field attraction. It is shown that in addition to the usual phenomena, the studied mixture exhibits also the closed liquid–liquid immiscibility loop (Type VI and VII behavior) and a variety of new azeotropic phenomena. Topology of phase diagrams is discussed in detail with emphasis on the boundary states and is compared with that based on the one-fluid van der Waals equation approach.

Photoconductivity of an Anthracene / 2,2,4,4-Tetramethylpentane Solution: Pressure Effect on the Photoionization of Solute and Solvent

Abstract The photoconductivity spectrum of a solution of anthracene (AN) in 2,2,4,4-tetramethylpentane (TMP) was measured as a function of pressure up to 2 kbar. The threshold energies of photoionization of the solute (AN) and of the solvent (TMP) increase with pressure. The relative quantum yield for charge carrier generation decreased with increasing pressure. The concomitant reduction of the initial separation distance of the geminate charge carrier pairs may be due to an increase of the number of inelastic collisions caused by the increased density of the liquid within the sphere of Coulomb attraction of the positive ion.