Hard Sphere Structure Research Articles

Small-Angle Neutron Scattering Investigation of the Temperature-Dependent Aggregation Behavior of the Block Copolymer Pluronic L64 in Aqueous Solution

Small-angle neutron scattering (SANS) was used to investigate the temperature dependence of the structure of micelles formed by the poly(ethylene oxide)−poly(propylene oxide)−poly(ethylene oxide) Pluronic L64 amphiphilic block copolymer in aqueous (D2O) solution. Different models for the form factor and the structure factor have been considered for fitting the SANS scattering patterns. By comparing the various models, we found that in the intermediate block copolymer concentration range, e.g., 2.5 wt % Pluronic L64, the micelles are well separated while the intermicellar interaction remains strong. Thus the more appropriate model was that of core−corona form factor and hard sphere structure factor, which allowed the determination of the core, micelle, and hard sphere interaction radii, the micelle association number, and the solvent volume fraction in the micelle core and corona. Upon an increase of temperature (in the range 35−55 °C) the micelle radius increased by ≈10%, accompanied by the loss of water in the micelle core. These trends coincide with the second relaxation process (attributed to the micelle core dehydration) observed in recent kinetics studies (Kositza, et al. Macromolecules 1999, 32, 5539). The SANS data also indicated a stronger increase of the micelle association number occurring above 47 °C, reflecting a strong increase of the intermicellar interactions. These results support the attribution of the third relaxation process observed in the aforementioned kinetic studies to micelle clustering.

A relationship between structural, thermodynamic, transport and surface properties of liquid metals: a hard-sphere description

Using the values of the self-diffusion coefficient, D HS, in the hard-sphere fluid obtained by computer simulations, we have investigated a relationship between structural, thermodynamic, transport and surface properties of liquid metals near the melting point. The packing fraction, ξ, used in this D HS were determined from the excess entropy including a contribution arising from the softness of the interatomic forces. The value of ξ thus determined is 0.463, by which the hard-sphere structure factor can well describe experimental structure factor data of liquid metals near the melting point. Then, the viscosity coefficient, η, and the surface tension, γ, were calculated using D HS. The surface entropy and the temperature derivative of η at constant volume were also calculated with ξ=0.463. Predicted values of the transport and the surface properties are reasonable in comparison with available experimental data.

Aggregate Structure in Aqueous Solutions of Brij-35 Nonionic Surfactant Studied by Small-Angle Neutron Scattering

The aggregate formation in aqueous solutions of Brij-35 (C12EO23) nonionic surfactant has been studied in the concentration range from 5 to 200 g/L at 20, 40, and 60 °C. The structure of micelles was modeled by a spherical core with tethered polymer chains to the surface, while the intermicellar interaction was described by a hard sphere structure factor. The mean aggregation number was found to increase substantially with both concentration and temperature from 34 (5 g/L, 20 °C) to 64 (200 g/L, 60 °C). The average core radii obtained are between 18 and 19 A. On the basis of the above two parameters, 35−50% of the core volume is occupied by hydrated poly(ethylene oxide) (PEO) chains. The radius of gyration of tethered chains, Rgc, is in agreement with the theoretical value for Gaussian conformation (11.6 A) at the smaller concentrations measured but increases significantly with increasing concentration. It reveals considerable stretching of the chains that is attributed to sterical constraints. At higher ...

Influence of protein surface morphology on the ultrafiltration flux resistance of bovine serum albumin.

The effect of added ethanol and (NH(4))(2)SO(4) on the flux decline index (FDI) of bovine serum albumin (BSA) and a fatty acid-poor derivative (BSA/FAP) was examined. Ternary phase diagrams of the two protein species indicated that the concentration polarization (CP) layer on the surface of a nonadsorbing 10 000 MWCO regenerated cellulose membrane had principally a packed bed structure up to 33 wt % ethanol and 21 wt % (NH(4))(2)SO(4). Intrinsic viscosity and turbidity analysis were conducted to determine the degree of intra- and interprotein interactions within this packed bed morphology. With BSA/FAP, the effects of these two interactions tended to counterbalance each other, so the FDI of this protein was not strongly influenced by solute addition. In contrast, the adsorption of fatty acids to BSA caused the protein to expand, producing a less rigid CP layer with a higher FDI. However, the addition of ethanol led to protein compression, reducing this effect. The presence of fatty acids also produced a more associated BSA in salt solution, which increased flux resistance. The results obtained for both proteins indicate that an FDI minimum is observed when a noninteraction hard sphere structure is present in the CP layer.

Probing Static Structure of Colloid–Polymer Suspensions with Multiply Scattered Light

Time-dependent measurements of light propagation were conducted in aqueous dispersions of 523 nm diameter polystyrene at concentrations between 0.1 and 0.4 solids volume fraction in order to assess how particle correlation is influenced by depletion interactions arising from the addition of soluble polyethyleneoxide (PEO). In the absence of polymer, the transport scattering length can be predicted from Mie scattering theory and the Percus–Yevick (P-Y) model for static structure of a dense hard-sphere colloidal solution. Depletion forces arising from the addition of PEO of varying molecular weights influenced the spatial ordering of the dispersion and caused a further increase in the transport scattering length beyond that predicted by hard-sphere static structure factor but similar to that predicted by the mean sphere approximation (MSA) to the P-Y model described by Yeet al.(1996). Onset of flocculation occurred with increased PEO addition and correlated with PEO molecular weight. Phase separation was noted by no further change in the transport scattering length, except when flocculation was induced by the highest molecular weight PEO. The use of time-dependent measurements of light propagation in dense systems provides an alternative to small-angle light, neutron, and X-ray scattering characterization of interaction potentials in dense, multiply scattering samples and promises further fruitful investigation of colloidal particle interactions in suspensions.

Determination of hydrodynamic properties in colloidal systems by static and dynamic light scattering

AbstractThe structure and dynamics of silica hard spheres and charged colloidal systems has been investigated at high concentrations by means of light scattering. The index of refraction at these high volume fractions was matched using a mixture of water/isopropanol for the Yukawa particles and toluene/ethanol for the hard spheres. By simultaneously measuring the dynamic and static properties of the colloidal systems we were able to extract the hydrodynamic function H(Q) at different concentrations. Our results are in good agreement with theoretical calculations over a large concentration range.

Electrical resistivity and absolute thermoelectric power of liquid copper–lead alloys

The absolute thermoelectric power S has been measured for the system Cu–Pb from the liquidus to 1100°C. The whole phase diagram has been explored. The thermoelectric power of these alloys has, to our knowledge, never been measured before. These experimental results as well as those of the electrical resistivity (C. Chaı̈b, J.G. Gasser, Z. Phys. Chem. Neue Folge 156 (1988) S483–S487) are interpreted and discussed in terms of the extended Ziman formula using the t-matrix formalism with hard-sphere structure factors. The concentration and energy dependence of the phase shifts have been taken into account for a complete resistivity and thermopower calculation.

PRELIMINARY COMMUNICATION Orientational structure of quasi-two-dimensional dipolar hard spheres

The orientational structure of dipolar hard spheres with centres of mass and dipole moments confined to a plane is investigated by Monte Carlo simulation as a function of density and temperature. At low temperature the structure is dominated by rings and extended chains. At high density, as well as ring structures, domains of chain segments with parallel and antiparallel arrangement of the dipole moments tend to form. There is no evidence of gas-liquid coexistence.

Evaluation of Free Energy Differences Between Crystalline Phases Using the Lattice-Switch Monte Carlo Method

ABSTRACTA new method [1] of calculating the free energy difference between two crystalline structures is presented. The method involves a single simulation which repeatedly transforms the system between the two crystal phases. Since the configurations of both structures are sampled within a single Monte Carlo process, the difference between their free energies can be evaluated directly from the ratio of the measured probabilities of each. Compared with traditional techniques, the method is most advantageous when applied to highly anharmonic systems. To illustrate the method, an application to the free energy difference between the fee and hep structures of hard spheres is described.

Computation of the free energy for alternative crystal structures of hard spheres

A single-occupancy cell (SO-cell) method has been applied to calculate the free energies of different crystal structures of hard spheres via molecular dynamics (MD). The objectives are (i) to examine the nature of the phase transition in the SO-cell model, (ii) to determine the thermodynamic stability of the bcc crystal phase relative to the fcc and the free fluid, (iii) to establish the relative stability of the fcc and hcp crystal structures, and (iv) to investigate hybrid structures of the unit stacking type ‘–ABCAB–'. MD computations are reported for the pressures of the SO-cell models of all these structures. The SO-cell phase transition for fcc and hcp is first-order, with ordered and disordered phases coexisting at the same p, V and T. The transition is much weaker for bcc. The metastable fluid–bcc phase transition parameters are determined; the bcc phase is everywhere unstable compared with fcc. The bcc solid melts to the metastable fluid at a pressure of 14.5 kBT/σ3, and has a melting volume of 0.95 Nσ3, i.e., very close to that of the fcc crystal. A more precise numerical estimate for the fcc–hcp entropy difference is reported. At close packing the fcc phase is the more stable by 0.0026(1) NkBT; the Gibbs and Helmoltz energy differences are the same at close packing. For expanded volumes close to melting, the hcp crystal has a slightly higher pressure than the fcc; the enthalpy difference at melting is 0.0030(5) NkBT. Consequently the Gibbs energy difference approaching melting becomes less than the uncertainty in the computations, i.e. <0.001 NkBT.

Mean-field hydrodynamics brownian dynamics simulations of stabilized colloidal liquids under shear

We extend a recently proposed mean-field hydrodynamics (MFH) discrete element simulation technique to consider the effects of a shear velocity profile on a model colloidal liquid containing monodisperse spherical particles in the non-newtonian shear thinning regime. The MFH method adapts Ermak's free draining brownian dynamics algorithm to include a local density approximation for the friction coefficient, semiempirically parametrized to reproduce the experimentally determined short-time diffusion coefficient. We have also generalized further the previous treatment to allow for a friction coefficient that is dependent on local density anisotropy. The behaviour of Ermak's equations of motion and also the “isotropic” and “anisotropic” MFH schemes with shear flow are compared. We show that, at equilibrium, the MFH approaches generate the same static averages as Ermak's method, and give good agreement with the Percus-Yevick prediction for hard-sphere structure factors using an r −36 soft-sphere interaction. However, under shear, the three equations of motion give quite different rheological behaviour. The MFH methods produce higher viscosities, although the structures remain similar (e.g. all give a “string” phase) but at different shear rates. Variation in the specific details of the MFH equations of motion can promote or delay the development of long-range order with Péclet number.

Structure and electrical resistivity of liquid Ni-Ge alloys

Results on neutron diffraction by Ni-Ge liquid alloys are presented. The germanium concentrations were 29, 50, 67 and 80 at.%, and the temperature was 1150 °C. In this paper, the experimental structure factors and those obtained from simple potentials are presented and compared. Partial structure factors are deduced from the ‘concentration’ method. From the Fourier transform of the partial pair structure factors, the partial pair correlation functions and first neighbours of each species are evaluated. Resistivities are calculated with the Faber-Ziman method where the phase-shifts in the transfer matrix are energy-dependent. The resistivity values are calculated using both the hard sphere structure factors and the experimental ones. The influence of the structure factors on electrical resistivity is discussed. Using the experimental structure factors rather than the hard sphere ones gives a resistivity versus concentration curve nearer the measured resistivity.

About entangled networks of worm-like micelles: a rejected hypothesis

We report new results from small-angle neutron scattering ond12-cyclohexane/lecithin/water micellar solutions performed as a function of the water content (w0), temperature (T) and dispersed phase volume fraction (ϕ). The data from dilute samples are interpretable in terms of the existence of giant cylindrical reverse micelles and are well fit with a core-shell model (that provides the micelle structure and dimensions) with values of 28 and 45 A for the inner core and the outer shell radii, almost independent on temperature and concentration. Such a result could appear consistent with the current idea that worm-like micelles are living polymers. On the contrary, the appearance of a sharp interference maximum at high concentrations (ϕ>0.15) suggests arguments against the current hypothesis of an entangled network of giant flexible cylinders. Further arguments against the current hypothesis are given by the close similarity between the above described results and those from free of water micelles (for sure not cylinders). All the data are well fitted in terms of a unique model taking into account the micellar form factor plus a hard sphere structure factor. The data analysis suggests a micellar size distribution determined by the competition between concentration and interaction effects on which temperature plays not a minor role. Following our results, the current hypothesis of a gel structure in terms of an entangled network can be assumed as wrong and some caution has to be taken in assuming wormlike micelles as living polymers.

Stability of the hard-sphere icosahedral quasilattice.

The stability of the hard-sphere icosahedral quasilattice is analyzed using the differential formulation of the generalized effective liquid approximation. We find that the icosahedral quasilattice is metastable with respect to the hard-sphere crystal structures. Our results agree with recent findings by McCarley and Ashcroft [Phys. Rev. B {\bf 49}, 15600 (1994)] carried out using the modified weighted density approximation.

Density profiles of fluids in some special symmetries

A free-energy-functional approximation based on a semi-empirical method is proposed. The main advantage of the free-energy-functional approximation is its accuracy compared with other models and its relative simplicity compared with other well-known weighted-density approximations. The free-energy-functional approximation is applied to predict the density profiles of the hard-sphere fluids and the Lennard–Jones fluids in some special symmetries. For the density profiles near a hard flat wall, the results reproduced the hard-sphere oscillatory structures qualitatively and quantitatively. For the density profiles of hard-sphere fluids confined in a spherical cage, the results are also in a fair agreement with the computer simulations. For Lennard–Jones fluids, two kinds of density-functional perturbation theories, the density-functional mean-field theory (DFMFT) and the density-functional perturbation theory (DFPT), examined. The results show that at higher temperature the DFPT compares well with computer simulations. However, the agreement deteriorates slightly as the temperature of the Lennard–Jones fluids is reduced. These results demonstrate that both the free-energy-functional approximation and the DFPT succesfully describe the inhomogeneous properties of classical fluids.

Structure Factors of Binary Aluminum-Nickel and Ternary Aluminum-Nickel-Silicon Liquid Alloys

Abstract A calculation of the structure of binary Al—Ni and of ternary Al—Ni—Si alloys based on a multicomponent hard sphere model and a square well like interatomic potential is developed in connection with chemical short range order in these alloys. Maret et al. 1 using the isotopic substitution method, measured the partial structure factors of the binary Al80Ni20 alloy. They obtained a prepeak in the partial Ni—Ni structure factor and a preminimum in the Ni—Al partial structure factor. We obtain the same features with a square well potential, but not with hard spheres. It has been shown by Chenal2 that liquid ternary alloys at an amorphisable composition such as Al65Ni15Si20 present a prepeak in the total structure factor, which is absent at a slightly different compostion of Ni: Al75Ni5Si20. We show here that ternary hard sphere structure factors with additive hard spheres cannot explain any prepeak, while such a feature can be reproduced from square well attractions but only at the right composition.

Structure of complex systems using electronic excitation transport: Theory, Monte Carlo simulations, and experiments on micelle solutions

Monte Carlo (MC) simulations and an analytical theory are presented to describe electronic excitation transport (EET) among static chromophores constrained to lie on the surfaces of spherical micelles. Both donor–trap (DT) and donor–donor (DD) EET are examined for two types of systems: probe molecules on the surfaces of isolated (low concentration) micelles, and probes on the surfaces of interacting (concentrated) micelles. The EET dynamics are described by the function, 〈G s(t)〉, the probability of finding the excitation on the originally excited chromophore. For the isolated micelle calculations, the excitation dynamics depend on the distribution of probes on a single hard sphere surface. For the interacting micelle calculations, the hard sphere structure is accounted for by using the radial pair distribution function, g(r). Both single micelle and many micelle DT calculations do not involve approximations. Consequently, the DT expressions agree exactly with the MC calculations. For the DD calculations, a first order cumulant approximation is used to obtain analytically tractable solutions to 〈G s(t)〉. Padé approximants of the cumulant solution, accurate over a broad range of chromophore number and Förster interaction strengths, are used to describe DD EET on isolated micelles. For DD EET in many micelle systems, the first order cumulant approach is shown to be a suitable method for intermicelle structural studies. Both the cumulant and MC calculations are simultaneously compared to time resolved flourescence depolarization measurements performed on octadecylrhodamine B(ODRB)/triton X-100/water systems made in previous investigations.

Structural study on the micelle formation of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer in aqueous solution

The phase behavior of the triblock copolymers dissolved in water has been studied using SANS. The structural properties have been studied as a function of polymer concentration and temperature. At low temperature (T ≤ 15°C) and low polymer concentrations the unimers are fully dissolved Gaussian chains with radius R g =17 A. Close to ambient temperature, the hydrophobic nature of PPO causes aggregation of the polymers into spherical micelles with core sizes of the order of 40-50 A, somewhat temperature dependent. The concentration of micelles increased roughly linearly with temperature, until either a saturation is reached,where all the polymers are part of a micelle, or the volume density of micelles is so high that they lock into a crystalline structure of hard spheres

The Electrical Resistivity of Liquid Germanium-Nickel Alloys

Abstract The electrical resistivity of the liquid Ni x Ge(l-x) system has been measured from pure Germanium to 77 at. % nickel. The resistivity shows a maximum for nickel rich alloys and a minimum for the resistivity temperature coefficient. The resistivity is interpreted and discussed with the t-matrix formulation using hard-sphere structure factors.

Effect of hard-sphere structure on pure-component equation of state calculations

Hard-sphere fluid structure is shown to be important in describing the thermodynamic properties of the square-well fluid. A simple local composition model using the exponential approximation (EXP) of Anderson and Chandler (1972) for the pair correlation function is developed. The hard-sphere pair correlation function is determined using the analytic solution to the Percus-Yevick theory (Wertheim, 1964). The model is shown to predict the properties of the square-well fluid that are in good agreement with molecular dynamics data. The equation is used to predict the properties of argon and methane. The equation is also incorporated into the Simplified-Perturbed-Hard-Chain Theory (SPHCT), and the new equation improves calculations of vapor pressures and saturated densities for non-polar and polar fluids.