Continuum solutions of the Klein-Gordon equation

We construct explicit solutions of the Klein-Gordon equation for continuum states. The role of the energy in the single-particle Klein-Gordon theory is elucidated. Special emphasis is laid on the determination of resonance states in the continuum for overcritical potentials. As examples for long-range interactions we depict solutions for the Coulomb potential of a point-like nucleus as well as an extended nucleus. The square-well potential and the exponential potential are treated to exemplify peculiarities of short-range interactions. We also derive continuum solutions for a scalar interaction of square-well type. Finally we discuss the behaviour of a spin-0 particle in an external homogeneous magnetic field.     

Correlation between Small-Angle X-ray Scattering spectra and apparent diffusion coefficients in the study of structure and interaction of sodium taurodeoxycholate micelles

Small-Angle X-ray Scattering (SAXS) and Dynamic Light Scattering (DLS) measurements were carried out on aqueous micellar solutions of the ionic biological detergent sodium taurodeoxycholate (NaTDC). Apparent diffusion coefficients (D(app)) and SAXS spectra of NaTDC 0.1 M solutions at different ionic strengths (0.1-0.3 M NaCl) were reported. A comparative analysis of SAXS spectra and D(app) data was performed to infer information on particle structure and interaction potential. Uniform particles with a spherical, an oblate, and a prolate symmetry were used to model the micelles in the data interpretation. A hard-core interaction shell of suitable thickness and a screened Coulomb potential of the electric double layer (EDL potential) were alternatively used to represent the long-range repulsive tail of the interaction potential. The Percus Yevick and the Rescaled Mean Spherical Approximation were applied. To compare the data of the two techniques, for each sample, a D(app) was calculated from the SAXS best-fitting geometrical parameters and interparticle structure factor of the micelles. Hence, a fitting procedure involving both the scattering and D(app) data was performed. The interpretation of SAXS spectra does not allow the discrimination between the oblate and the prolate symmetries of the aggregates. On the other hand, the comparison of calculated and experimental D(app) values indicates that the prolate ellipsoid is better suited to represent the micelle shape. Moreover, the agreement between calculated and experimental D(app) values is sensitively better at the lowest NaCl concentration when the EDL potential is used. A rodlike micellar growth and a progressive screening of the electrostatic interactions is testified by the trends of best-fitting parameters as a function of the added electrolyte.     

Titration of hydrophobic polyelectrolytes using Monte Carlo simulations

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK(0) values (pK(0) represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree alpha of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK(0) value.     

Properties of protein adsorption onto pore surface during microfiltration: Effects of solution environment and membrane hydrophobicity

Properties of bovine serum albumin (BSA) adsorption onto pore surface during the filtration of BSA containing solution with the Sirasu porous glass membrane with a pore size of 0.1 μm were studied. The effects of pH, ionic strength, and surface modification on the flux decline and breakthrough curves were observed. The adsorption properties of BSA were estimated quantitatively by using the internal fouling model, which relates the filtration performance to the adsorption interaction, the adsorption capacity, and the thickness of the adsorption layer. The electrostatic interaction between BSA and pore surface was estimated by the streaming potential measurement. The BSA adsorption involved a rapid adsorption in the early stage of filtration followed by a slow multilayer adsorption that dominates the long-term filtration performance. The electrostatic repulsive force reduced the overall adsorption interaction but the electrostatic attractive force did not affect the adsorption interaction. The effect of ionic strength on the BSA adsorption could be explained in terms of the shift of the IEP of BSA toward lower pH with the increase in ionic strength. The hydrophobicity of membrane did not affect the adsorption properties except for the adsorption interaction in the early stage of the filtration.     

Adsorption of poly(amido amine) (PAMAM) dendrimers on silica: importance of electrostatic three-body attraction

Adsorption of poly(amido amine) (PAMAM) dendrimers to silicon oxide surfaces was studied as a function of pH, ionic strength, and dendrimer generation. By combining optical reflectometry and atomic force microscopy (AFM), the adsorbed layers can be fully characterized and an unequivocal determination of the adsorbed mass becomes possible. For early stages, the adsorption process is transport limited and of first order with respect to the dendrimer solution concentration. For later stages, the surface saturates and the adsorbed dendrimers form loose but correlated liquidlike surface structures. This correlation is evidenced by a peak in the pair correlation function determined by AFM. The maximum adsorbed amount increases with increasing ionic strength and pH. The increase with the ionic strength is explained by the random sequential adsorption (RSA) model and electrostatic repulsion between the dendrimers. The adsorbing dendrimers interact by the repulsive screened Coulomb potential, whose range decreases with increasing ionic strength and thus leads to increasing adsorbed densities. The pH increase is interpreted as an effect of the substrate and is quantitatively explained by the extended three-body RSA model. This model stipulates the importance of a three-body interaction acting between two adsorbing dendrimers and the charged substrate. The presence of the charged substrate weakens the repulsion between the adsorbing dendrimers and thus leads to higher surface densities. This effect can be interpreted as an additional attractive three-body interaction, which acts in addition to the usual two-body repulsion and originates from the additional screening of the Coulomb repulsion by the counterions accumulating in the diffuse layer.     

AFM interaction study of alpha-alumina particle and c-sapphire surfaces at high-ionic-strength electrolyte solutions

Ionic strength dependence of interaction and friction forces between hydrophilic alpha-alumina particles and c-sapphire surfaces (0001) were investigated under basic pH conditions using the colloidal probe method. The compression of the double layer could be seen from force-distance curves as the ionic strength of the solution increased. The forces were repulsive at all ionic strengths measured, even though the interaction distance changed drastically. No jump to contact occurred. The interaction distance decreased from about 20 nm in 10(-3) M KCl solution to about 7 nm in the 1 M KCl case. The lubricating effect of hydrated cations on the lateral friction force was demonstrated at high electrolyte concentrations. This was attributed to more hydrated cations being present in the solution. The friction behavior was closely related to the short-range repulsive forces between the alpha-alumina surfaces at pH 11.     

The Effect of Solute Concentration on Equilibrium Partitioning in Polymeric Gels

The effect of solute concentration on the equilibrium partitioning of sphere-like, colloidal solutes in stiff polymer hydrogels is examined theoretically and experimentally. The theoretical development is a statistical mechanics approach, and allows quantitative calculations to be performed to determine the concentration-dependent partition coefficient correct to first order in solute concentration at specific surface charge densities. The theory predicts that repulsive steric and/or electrostatic solute-fiber interactions exclude solute from the gel phase, but that repulsive solute-solute interactions cause partitioning into the gel to increase with increasing solute concentration. These trends are enhanced for larger solutes, increased fiber volume fractions, or stronger electrostatic repulsion. Partition coefficients have also been measured for two proteins, bovine serum albumin (BSA) and alpha-lactalbumin (ALA), in a system consisting of a salt solution and cubes of agarose hydrogel. To investigate the effect of electrostatic interactions, the experiments were performed at 0.15 M KCl and 0.01 M KCl. The theory underpredicts the strong electrostatic repulsion between BSA macromolecules at the lower ionic strength. The experimental results for ALA show the influence of an attractive interaction between the protein macromolecules, in addition to hard-sphere repulsive and electrostatic interactions. Copyright 2001 Academic Press.     

Small-angle X-ray scattering and light scattering on lysozyme and sodium glycocholate micelles

Small-angle X-ray scattering (SAXS) together with static (SLS) and dynamic light scattering (DLS) measurements were carried out on aqueous solutions of lysozyme (LY) and of the ionic biological detergent sodium glycocholate (NaGC). Apparent diffusion coefficients (D app), excess Rayleigh ratio, and SAXS spectra were measured for 0.1 M NaGC solutions at different ionic strengths (0.05-0.30 M NaCl). The same data were collected for LY in sodium acetate buffer 50 mM without and with 92 mM NaCl as a function of protein concentration (10-80 g L(-1)). A correlated analysis of SLS data and SAXS spectra was first tested on the LY samples and then extended to the interpretation of the NaGC data to infer information on particle structure and interaction potential. A hard-core (HC) interaction shell of uniform thickness, a screened Coulomb potential of the electric double layer (EDL) or the complete DLVO potential were alternatively used to represent the long-range tail of the interaction potential. Whenever an essentially repulsive tail is expected, all the representations give reasonable results, but the data analysis does not allow the discrimination between the oblate and the prolate symmetries of the NaGC aggregates. The DLVO model allows the interpretation of the data even when the attractive component determines the tail character. With this model an overall fit of the micelle data at all the NaCl concentrations was successfully performed by assuming a simple spherical symmetry of the micelles and invariant values of their ionization degree and Hamaker constant, thus considering just the screening effect of the added electrolyte. Whatever model is used, the results point out that the aggregates are quite hydrated (26-38 water molecules per monomer) and very slightly grow by increasing the NaCl concentration. When spherical symmetry is assumed the aggregate radii for all the samples fall in the range 15-16 A. From the SAXS and SLS, best fitting geometrical parameters, and interparticle structure factor, a D app value was calculated for each sample. An excellent consistence is achieved for LY results. On the contrary, calculated D app values systematically lower than the experimental values are always obtained for the NaGC micelles. Micelle polydispersity and internal dynamics seem to be the most probable reasons of the bad agreement.     

Attraction-driven disorder in a hard-core colloidal monolayer

Monte Carlo simulation techniques were employed to explore the effect of short-range attraction on the orientational ordering in a two-dimensional assembly of monodisperse spherical particles. We find that if the range of square-well attraction is approximately 15% of the particle diameter, the dense attractive fluid shows the same ordering behavior as the same density fluid composed of purely repulsive hard spheres. Fluids with an attraction range larger than 15% show an enhanced tendency to crystallization, while disorder occurs for fluids with an attractive range shorter than 15% of the particle diameter. A possible link with the existence of "repulsive" and "attractive" states in dense colloidal systems is discussed.     

Surface tension and vapor-liquid phase coexistence of confined square-well fluid

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envelope is in agreement with that given in literature. The surface tension of the vapor-liquid interface is calculated via molecular dynamics simulations. GC-TMMC with finite size scaling is also used to calculate the surface tension. The results from molecular dynamics and GC-TMMC methods are in very good mutual agreement. The vapor-liquid surface tension, under confinement, was found to be lower than the bulk surface tension. However, with the increase of the slit width the surface tension increases. For the case of a square-well fluid in an attractive planar slit pore, the vapor-liquid surface tension exhibits a maximum with respect to wall-fluid interaction energy. We also report estimates of critical properties of confined fluids via the rectilinear diameter approach.     

Sensitivity analysis of thermodynamic properties of liquid water: a general approach to improve empirical potentials

A sensitivity analysis of bulk water thermodynamics is presented in an effort to understand the relation between qualitative features of molecular potentials and properties that they predict. The analysis is incorporated in molecular dynamics simulations and investigates the sensitivity of the Helmholtz free energy, internal energy, entropy, heat capacity, pressure, thermal pressure coefficient, and static dielectric constant to components of the potential rather than the parameters of a given functional form. The sensitivities of the properties are calculated with respect to the van der Waals repulsive and the attractive parts, plus short- and long-range Coulomb parts of three four site empirical water potentials: TIP4P, Dang-Chang and TTM2R. The polarization sensitivity is calculated for the polarizable Dang-Chang and TTM2R potentials. This new type of analysis allows direct comparisons of the sensitivities for different potentials that use different functional forms. The analysis indicates that all investigated properties are most sensitive to the van der Waals repulsive, the short-range Coulomb and the polarization components of the potentials. When polarization is included in the potentials, the magnitude of the sensitivity of the Helmholtz free energy, internal energy, and entropy with respect to this part of the potential is comparable in magnitude to the other electrostatic components. In addition similarities in trends of observed sensitivities for nonpolarizable and polarizable potentials lead to the conclusion that the complexity of the model is not of critical importance for the calculation of these thermodynamic properties for bulk water. The van der Waals attractive and the long-range Coulomb sensitivities are relatively small for the entropy, heat capacity, thermal pressure coefficient and the static dielectric constant, while small changes in any of the potential contributions will significantly affect the pressure. The analysis suggests a procedure for modification of the potentials to improve predictions of thermodynamic properties and we demonstrate this general approach for modifying potentials for one of the potentials.     

Negative electron affinities from conventional electronic structure methods

If the potential V describing the interaction between an excess electron and a ground-state neutral or anionic parent is sufficiently attractive at short range, electron-attached states having positive electron affinities (EAs) can arise. Even if the potential is not attractive enough to produce a bound state, metastable electron-attached states may still occur and have lifetimes long enough to give rise to experimentally detectable signatures. Low-energy metastable states arise when the attractive components of V combine with a longer-range repulsive contribution to produce a barrier behind which the excess electron can be temporarily trapped. These repulsive contributions arise from either the centrifugal potential in the excess electron’s angular kinetic energy or long-range Coulomb repulsion in the case of an anionic parent. When there is no barrier, this kind of low-energy metastable state does not arise, but improper theoretical calculations can lead to erroneous predictions of their existence. Conventional electronic structure methods with, at most, minor modifications are described for properly characterizing metastable states and for avoiding incorrectly predicting the existence of metastable states with negative EAs where no barrier is present.     

NaCl介质中盐浓度、pH对α－Al~2O~3表面相互作用力的影响

利用原子显微镜研究NaCl介质浓度及体pH值对氧化铝表面作用力的影响规律。发现较低的盐浓度下,相互作用表示为长程排斥力,双电层厚度的实际值与理论值较好地吻合,随NaCl介质浓度的提高,双电层压缩长程斥力减弱,测定了pHMH4.0变化到9.67的作用力曲线,发现当pH等于7/90时,两表面的相互作用表现为吸引力,通过恒电荷、恒电位拟合,发现氧化铝的等电点在pH8.2处,与Zeta电位的测定结果相一致。     

The structural properties of a two-Yukawa fluid: Simulation and analytical results

Standard Monte Carlo simulations are carried out to assess the accuracy of theoretical predictions for the structural properties of a model fluid interacting through a hard-core two-Yukawa potential composed of a short-range attractive well next to a hard repulsive core, followed by a smooth, long-range repulsive tail. Theoretical calculations are performed in the framework provided by the Ornstein-Zernike equation, solved either analytically with the mean spherical approximation (MSA) or iteratively with the hypernetted-chain (HNC) closure. Our analysis shows that both theories are generally accurate in a thermodynamic region corresponding to a dense vapor phase around the critical point. For a suitable choice of potential parameters, namely, when the attractive well is deep and/or large enough, the static structure factor displays a secondary low-Q peak. In this case HNC predictions closely follow the simulation results, whereas MSA results progressively worsen the more pronounced this low-Q peak is. We discuss the appearance of such a peak, also experimentally observed in colloidal suspensions and protein solutions, in terms of the formation of equilibrium clusters in the homogeneous fluid.     

How short-range attractions impact the structural order, self-diffusivity, and viscosity of a fluid

We present molecular simulation data for viscosity, self-diffusivity, and the local structural ordering of (i) a hard-sphere fluid and (ii) a square-well fluid with short-range attractions. The latter fluid exhibits a region of dynamic anomalies in its phase diagram, where its mobility increases upon isochoric cooling, which is found to be a subset of a larger region of structural anomalies, in which its pair correlations strengthen upon isochoric heating. This "cascade of anomalies" qualitatively resembles that found in recent simulations of liquid water. The results for the hard-sphere and square-well systems also show that the breakdown of the Stokes-Einstein relation upon supercooling occurs for conditions where viscosity and self-diffusivity develop different couplings to the degree of pairwise structural ordering of the liquid. We discuss how these couplings reflect dynamic heterogeneities. Finally, we note that the simulation data suggest how repulsive and attractive glasses may generally be characterized by two distinct levels of short-range structural order.     

渗透压法对牛血清蛋白在NaCl水溶液中相互作用的研究

测量了牛血清蛋白不同pH值和不同离子强度Nacl水溶液中的渗透压,计算了渗透第二维里系数,按照Prausnitz提出的分子热学模型计算了蛋白质之间的静电排斥能、色散吸引能和离子排斥体积产生的吸引势能,并对这三种势能与溶液pH值和离子强度的变化关系进行讨论。     

The non-equilibrium charge screening effects in diffusion-driven systems with pattern formation

The effects of non-equilibrium charge screening in mixtures of oppositely charged interacting molecules on surfaces are analyzed in a closed system. The dynamics of charge screening and the strong deviation from the standard Debye-Hückel theory are demonstrated via a new formalism based on computing radial distribution functions suited for analyzing both short-range and long-range spacial ordering effects. At long distances the inhomogeneous molecular distribution is limited by diffusion, whereas at short distances (of the order of several coordination spheres) by a balance of short-range (Lennard-Jones) and long-range (Coulomb) interactions. The non-equilibrium charge screening effects in transient pattern formation are further quantified. It is demonstrated that the use of screened potentials, in the spirit of the Debye-Hückel theory, leads to qualitatively incorrect results.     

Aggregation in Quenched Systems Interacting through a Short-Range Attractive,Long-Range Repulsive Potential

The morphology and structure factor of a 2D system of particles interacting through a Lennard-Jones potential, modified to include a long-range repulsive component, are described. Of particular interest are those systems quenched from a stabilized colloidal state to temperatures that, in the pure Lennard-Jones system, correspond to the solid-vapor coexistence region. We find that competition between the short-range attractive forces—which cause aggregation—and the long-range repulsion—which acts to keep the particles apart—encourages the formation of space-filling networks. A characteristic peak in the structure factor is observed which moves toward lower wavevectors as the simulation evolves. However, unlike the pure Lennard-Jones system, which when given enough time will completely phase separate, this peak stops moving once a network has formed. The similarities between our simulations and gel formation are discussed.     

Colloidal phase transition driven by alternating electric field

The transverse two-dimensional assembly of colloidal particles near an electrode surface subjected to ac polarization is studied by varying the frequency and field strength in the absence and presence of an added electrolyte. The variation of the translational and bond-orientational correlation functions with frequency suggests the existence of a hexatic phase in which the particles retain the remnants of the crystalline long-range orientational order, but has a liquidlike translational order. The electrohydrodynamic (EHD) flow is analyzed in the light of the existing theoretical models. The equilibrium distribution of particles is considered to be the resultant of the two opposing forces--Stoke's force due to EHD flow and the screened Coulomb interaction between the colloidal particles. Several features of the experimental results are discussed, such as the role played by the EHD flow in the particle aggregation, the dependence of the equilibrium interparticle separation on ionic strength, zeta potential, and particle size.     

Statistical mechanical theory for discotic liquid crystals Discotic nematic-isotropic transition properties

A statistical mechanical theory is applied to study the equilibrium properties of discotic nematic liquid crystals. We report the calculation of thermodynamic properties for a model system composed of molecules interacting through angle-dependent pair potentials which can be broken up into rapidly varying short-ranged repulsions and weak long-range attractions. The repulsive interaction is represented by a repulsion between hard oblate ellipsoids of revolution and is a short-range, rapidly-varying, potential. The influence of attractive potentials, represented by dispersion and quadrupole interactions on a variety of thermodynamic properties is analysed. It is found that the thermodynamic properties for the discotic nematic-isotropic transition are highly sensitive to the form of effective one-body orientational perturbation potential. The discontinuity in the transition properties is more pronounced in the case of quadrupole interaction than for anisotropic dispersion interaction. A remarkable symmetry in the transition properties between prolate ellipsoids (ordinary nematic) and oblate ellipsoids (discotic nematic) is observed.