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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Effective conductivity of hard-sphere dispersions

A simulation technique is used to compute zeta(2), the key three-point microstructural parameter which arises in three-point conductivity bounds on the effective conductivity sigma(e) of isotropic two-phase composites. Using the new algorithm, the zeta(2) parameter is computed for dispersions of hard spheres by Monte Carlo simulation, and the results are compared with those of several analytical calculations of zeta(2). The simulation data on zeta(2) are then used to compute three-point bounds on the conductivity sigma(e) and Torquato's (1985) approximation for sigma(e).

Miller, C. A.↗
NASA NTRS1994

Dynamics of hard sphere colloidal dispersions

Our objective is to perform on homogeneous, fully equilibrated dispersions the full set of experiments characterizing the transition from fluid to solid and the properties of the crystalline and glassy solid. These include measurements quantifying the nucleation and growth of crystallites, the structure of the initial fluid and the fully crystalline solid, and Brownian motion of particles within the crystal, and the elasticity of the crystal and the glass. Experiments are being built and tested for ideal microgravity environment. Here we describe the ground based effort, which exploits a fluidized bed to create a homogeneous, steady dispersion for the studies. The differences between the microgravity environment and the fluidized bed is gauged by the Peclet number Pe, which measures the rate of convection/sedimentation relative to Brownian motion. We have designed our experiment to accomplish three types of measurements on hard sphere suspensions in a fluidized bed: the static scattering intensity as a function of angle to determine the structure factor, the temporal autocorrelation function at all scattering angles to probe the dynamics, and the amplitude of the response to an oscillatory forcing to deduce the low frequency viscoelasticity. Thus the scattering instrument and the colloidal dispersion were chosen such as that the important features of each physical property lie within the detectable range for each measurement.

Zhu, J. X.↗
NASA NTRS2005

An Automatic Phase-Change Detection Technique for Colloidal Hard Sphere Suspensions

Colloidal suspensions of monodisperse spheres are used as physical models of thermodynamic phase transitions and as precursors to photonic band gap materials. However, current image analysis techniques are not able to distinguish between densely packed phases within conventional microscope images, which are mainly characterized by degrees of randomness or order with similar grayscale value properties. Current techniques for identifying the phase boundaries involve manually identifying the phase transitions, which is very tedious and time consuming. We have developed an intelligent machine vision technique that automatically identifies colloidal phase boundaries. The algorithm utilizes intelligent image processing techniques that accurately identify and track phase changes vertically or horizontally for a sequence of colloidal hard sphere suspension images. This technique is readily adaptable to any imaging application where regions of interest are distinguished from the background by differing patterns of motion over time.

McDowell, Mark↗
NASA NTRS1996

Dynamics of Disorder-Order Transitions in Hard Sphere Colloidal Dispersions in micro-g

We performed a series of experiments on 0.518 millimeter PMMA spheres suspended in an index matching mixture of decalin and tetralin the microgravity environment provided by the Shuttle Columbia on mission STS-73. The samples ranged in concentration from 0.49 to 0.62. volume fraction (phi) of spheres, which covers the range in which liquid, coexistence, solid and glass phases are expected from Earth bound experiments. Light scattering was used to probe the static structure, and the particle dynamics. Digital and 35 mm photos provided information on the morphology of the crystals. In general, the crystallites grew considerably larger (roughly an order of magnitude larger) than the same samples with identical treatment in 1 g. The dynamic light scattering shows the typical short time diffusion and long time caging effects found in 1 g. The surprises that were encountered in microgravity include the preponderance of random hexagonal close packed (RHCP) structures and the complete absence of the expected face centered cubic (FCC) structure, existence of large dendritic crystals floating in the coexistence samples (where liquid and solid phases coexist) and the rapid crystallization of samples which exist only in glass phase under the influence of one g. These results suggest that colloidal crystal growth is profoundly effected by gravity in yet unrecognized ways. We suspect that the RCHP structure is related to the nonequilibrium growth that is evident from the presence of dendrites. An analysis of the dendritic growth instabilities is presented within the framework of the Ackerson-Schatzel equation.

Zhu, J. X.↗
NASA NTRS1999

Effective Forces Between Colloidal Particles

Colloidal suspensions have proven to be excellent model systems for the study of condensed matter and its phase behavior. Many of the properties of colloidal suspensions can be investigated with a systematic variation of the characteristics of the systems and, in addition, the energy, length and time scales associated with them allow for experimental probing of otherwise inaccessible regimes. The latter property also makes colloidal systems vulnerable to external influences such as gravity. Experiments performed in micro-ravity by Chaikin and Russell have been invaluable in extracting the true behavior of the systems without an external field. Weitz and Pusey intend to use mixtures of colloidal particles with additives such as polymers to induce aggregation and form weak, tenuous, highly disordered fractal structures that would be stable in the absence of gravitational forces. When dispersed in a polarizable medium, colloidal particles can ionize, emitting counterions into the solution. The standard interaction potential in these charged colloidal suspensions was first obtained by Derjaguin, Landau, Verwey and Overbeek. The DLVO potential is obtained in the mean-field linearized Poisson-Boltzmann approximation and thus has limited applicability. For more precise calculations, we have used ab initio density functional theory. In our model, colloidal particles are charged hard spheres, the counterions are described by a continuum density field and the solvent is treated as a homogeneous medium with a specified dielectric constant. We calculate the effective forces between charged colloidal particles by integrating over the solvent and counterion degrees of freedom, taking into account the direct interactions between the particles as well as particle-counterion, counterion-counterion Coulomb, counterion entropic and correlation contributions. We obtain the effective interaction potential between charged colloidal particles in different configurations. We evaluate two- and three-body forces in the bulk as well as study the influence of soft walls. We qualitatively explain the effects of the walls on the forces and demonstrate that many-body effects are negligible in our system. With adjustments in the parameters, the DLVO pair-potential can describe the results quantitatively. Besides electrostatic interactions, entropic depletion effects that arise from (hard-core) exclusion play an important role in determining the behavior of multi-component colloidal suspensions. A standard theory for depletion forces is due to Asakura and Oosawa and is based on the ideal gas approximation. To go beyond this approximation, we have studied entropic forces in molecular dynamics simulations of systems of hard spheres (the effects of the solvent have been ignored). The effective depletion forces for these systems can be found either from equilibrium distribution functions or from direct momentum transfer calculations. Our results obtained by either method show qualitative differences from the Asakura-Oosawa forces, indicating a longer range, higher value at contact and most importantly a more complicated structure, comprising of several maxima and minima. Our calculations include the determination of effective forces between two spheres, a hard sphere and a wall, and the behavior of a hard sphere near a step-edge and a corner. We also demonstrate that such entropic forces do not necessarily satisfy pairwise additivity.

Tehver, Riina↗
NASA NTRS1992

Maxwell's second- and third-order equations of transfer for non-Maxwellian gases

Condensed algebraic forms for Maxwell's second- and third-order equations of transfer are developed for the case of molecules described by either elastic hard spheres, inverse-power potentials, or by Bird's variable hard-sphere model. These hardly reduced, yet exact, equations provide a new point of origin, when using the moment method, in seeking approximate solutions in the kinetic theory of gases for molecular models that are physically more realistic than that provided by the Maxwell model. An important by-product of the analysis when using these second- and third-order relations is that a clear mathematical connection develops between Bird's variable hard-sphere model and that for the inverse-power potential.

Baganoff, D.↗
NASA NTRS1990

Cavities in molecular liquids and the theory of hydrophobic solubilities

Thermal configurational data on neat liquids are used to obtain the work of formation of hard spherical cavities of atomic size in six molecular solvents: n-hexane, n-dodecane, n-undecyl alcohol, chloroform, carbon tetrachloride, and water. These results are used to test a recent suggestion that the differences between nonaqueous solvents and liquid water in solvation of inert gases are not principally due to the hydrogen-bonded structure of liquid water but rather to the comparatively small size of the water molecule. The frequencies of occurrence of cavities in liquid water can be meaningfully distinguished from those in the organic solvents. Liquid water has a larger fractional free volume, but that free volume is distributed in smaller packets. With respect to cavity work, water is compared to a solvent of the same molecular density and composed of hard spheres of the same size as the water molecule. That comparison indicates that the hard-sphere liquid finds more ways to configure its free volume in order to accommodate an atomic solute of substantial size and thus, would be more favorable solvent for inert gases. The scaled particle model of inert gas solubility in liquid water predicts cavity works 20% below the numerical data for TIP4P water at 300 K and 1.0 g/cm3 for cavity radii near 2.0 angstroms. It is argued that the sign of this difference is just the sign that ought to be expected and that the magnitude of this difference measures structural differences between water and the directly comparable hard-sphere liquid. In conjunction with previous data, these results indicate that atomic sized cavities should be considered submacroscopic.

NASA Discipline Exobiology↗
NASA NTRS1984

Theoretical study of miscibility and glass-forming trends in mixtures of polystyrene spheres

A theoretical study of glass-forming trends and miscibility in mixtures of polystyrene spheres (polyballs) of different diameters, suspended in an aqueous solution, is presented. The polyballs are assumed to be charged and to interact via a Debye-Hueckel screened Coulomb potential. The Helmholtz free energy is calculated from a variational principle based on the Gibbs-Bogoliubov inequality, in which a mixture of hard spheres of different diameters is chosen as the reference system. It is found that when the charges of the two types of polyballs are sufficiently different, the variationally determined ratio of hard-sphere diameters differs substantially, leading to packing difficulties characteristic of glass formation. The experimentally observed range of glass formation corresponds to a ratio of hard-sphere diameters of 0.8 or less. Calculations of the free energy as a function of concentration indicate that the liquid polyball mixture is stable against the phase separation, even for widely different polyball charges.

Shih, W.-H.↗
DOE OSTI2024

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

Here, we analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call “complexity reduction”. In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature T g of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2–6 nm at T g . Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

cancer↗
NASA NTRS1992

Local thermodynamic mapping for effective liquid density-functional theory

The structural-mapping approximation introduced by Lutsko and Baus (1990) in the generalized effective-liquid approximation is extended to include a local thermodynamic mapping based on a spatially dependent effective density for approximating the solid phase in terms of the uniform liquid. This latter approximation, called the local generalized effective-liquid approximation (LGELA) yields excellent predictions for the free energy of hard-sphere solids and for the conditions of coexistence of a hard-sphere fcc solid with a liquid. Moreover, the predicted free energy remains single valued for calculations with more loosely packed crystalline structures, such as the diamond lattice. The spatial dependence of the weighted density makes the LGELA useful in the study of inhomogeneous solids.

Kyrlidis, Agathagelos↗
NASA NTRS1979

Further development of ultrasonic techniques for non-destructive evaluation based on Fourier analysis of signals from irregular and inhomogeneous structures

To investigate the use of Fourier analysis techniques model systems had to be designed to test some of the general properties of the interaction of sound with an inhomogeneity. The first models investigated were suspensions of solid spheres in water. These systems allowed comparison between theoretical computation of the frequency dependence of the attenuation coefficient and measurement of the attenuation coefficient over a range of frequencies. Ultrasonic scattering processes in both suspensions of hard spheres in water, and suspensions of hard spheres in polyester resin were investigated. The second model system was constructed to test the applicability of partial wave analysis to the description of an inhomogeneity in a solid, and to test the range of material properties over which the measurement systems were valid.

Miller, J. G.↗
NASA NTRS1998

Study of Atmospheric Nitric Oxide

We investigated the contribution of energetic nitrogen atoms to the production of nitric oxide in the thermosphere and their influence on the infrared emission spectrum. The nitric oxide molecules are important contributors to the cooling of the atmosphere. We first pointed out that in determining the energy distribution of the nitrogen atoms, it is important to take into account the thermal motion of the atmospheric gases. It had been ignored in all earlier studies. The source spectra are broadened considerably by the center of mass motion of the reactants. We worked out the consequences for the production of nitric oxide at night, using as sources of energetic N atoms, NO(+) + e yield N + O, N(D-2) + O yield N + O. The high energy tail is enhanced by orders of magnitude. We had earlier suggested (Sharma et al. 1993) that the reaction of energetic nitrogen atoms with O2 was responsible for the rotationally enhanced NO identified in the infrared spectrum. Our calculations provided quantitative confirmation of the suggestion. We proceeded to explore the validity of another approximation used in earlier analyses, the hard sphere approximation for the energy loss in elastic collisions. We carried out precise quantum mechanical calculations of the elastic 2 differential scattering of nitrogen atoms in collisions with oxygen atoms and showed that although the hard sphere approximation was nowhere of high precision, reasonable results could be obtained with an effective cross section of 6 x 10(exp 15)sq cm. We also initiated a program to include inelastic energy loss processes in the determination of the energy distribution function. We began a calculation of the rotation and vibrational excitation cross sections of molecular nitrogen and nitrogen atoms and developed a method for including inelastic energy loss as a function of scattering angle in the Boltzmann equation. A procedure for obtaining the solution of the Boltzman equation was worked out.

Dalgarno, A.↗
NASA NTRS1982

Energetic O/+/ precipitation

Fluxes of energetic O(+) ions are often observed precipitating into the atmosphere and are possibly a significant energy source for the ionosphere and thermosphere. Models of these events indicate that most of the energy of such an O(+) beam is deposited as neutral heat at F region heights and a significant escape flux of O atoms results. The distribution of this heating with altitude, however, has a major effect on the type and significance of the aeronomical consequences that it can initiate. The particulars of this distribution are very sensitive to the cross sections and scattering parameters used in the modeling. A comparison of hard sphere and classical elastic parameters indicates that using the latter, more realistic formulation not only results in a more penetrating beam but reduces the escape flux by as much as a factor of 2 over the hard sphere treatment.

Kozyra, J. U.↗
NASA NTRS1991

A review of the kinetic detail required for accurate predictions of normal shock waves

Several aspects of the kinetic models used in the collision phase of Monte Carlo direct simulations have been studied. Accurate molecular velocity distribution function predictions require a significantly increased number of computational cells in one maximum slope shock thickness, compared to predictions of macroscopic properties. The shape of the highly repulsive portion of the interatomic potential for argon is not well modeled by conventional interatomic potentials; this portion of the potential controls high Mach number shock thickness predictions, indicating that the specification of the energetic repulsive portion of interatomic or intermolecular potentials must be chosen with care for correct modeling of nonequilibrium flows at high temperatures. It has been shown for inverse power potentials that the assumption of variable hard sphere scattering provides accurate predictions of the macroscopic properties in shock waves, by comparison with simulations in which differential scattering is employed in the collision phase. On the other hand, velocity distribution functions are not well predicted by the variable hard sphere scattering model for softer potentials at higher Mach numbers.

Muntz, E. P.↗