Single particle characterization

The model developed above serves as a convenient starting point for carrying out a dynamical analysis of the nucleation problem from the perspective of the variational principle of section 2.3.3. A nice discussion of this analysis can be found in Suo (1997). As with the two-dimensional model considered in section 2.3.3, we idealize our analysis to the case of a single particle characterized by one degree of freedom. In the present setting, we restrict our attention to spherical particles of radius r. We recall that the function which presides over our variational statement of this problem can be written genetically as... 

Up-to-date analytical techniques used in nuclear forensics for safeguards in support of non-proliferation, including single particle characterization... 

Kostka M, Hogen T, Danzer KM, et al. Single particle characterization of iron-induced pore-forming alpha-synuclein oligomers. / Biol Chem. 2008 283(16) 10992-11003. 

In a liquid that is in thermodynamic equilibrium and which contains only one chemical species, the particles are in translational motion due to thermal agitation. The term for this motion, which can be characterized as a random walk of the particles, is self-diffusion. It can be quantified by observing the molecular displacements of the single particles. The self-diffusion coefficient is introduced by the Einstein relationship... 

Smectic A and C phases are characterized by a translational order in one dimension and a liquid-like positional order in two others. In the smectic A phase the molecules are oriented on average in the direction perpendicular to the layers, whereas in the smectic C phase the director is tilted with respect to the layer normal. A simple model of the smectic A phase has been proposed by McMillan [8] and Kobayashi [9] by extending the Maier-Saupe approach for the case of one-dimensional density modulation. The corresponding mean field, single particle potential can be expanded in a Fourier series retaining only the leading term ... 

The respirable powders of a DPI cannot be characterized adequately by single-particle studies alone bulk properties must also be assessed since they contribute to ease of manufacture and affect system performance. Primary bulk properties include particle size, particle size distribution, bulk density, and surface area. These properties, along with particle electrostatics, shape, surface morphology, etc., affect secondary bulk-powder characteristics such as powder fiow, handling, consolidation, and dispersibility. 

In order to have an expression for the mixed-system exchange energy (192) in terms of the single-particle KS orbitals we need such an expression for the ensemble DM - the diagonal of pP. When the ensemble density operator is characterized by the following decompc ition into its pure-state contributions... 

With these simplifications, W and X can be generated as functions of T, with the particle characterized by a single dimensionless parameter, either Rejs, A d or Rqj. Figure 11.13 shows predictions for a particle released from rest W = X = 0 at T = 0), while Fig. 11.14 gives trajectories for particles projected vertically upwards such that the particle comes to rest at T = 0. Figures 11.13 and 11.14 enable rapid estimations for many problems involving unsteady motion of particles in gases. 

Dale, J. M M. Yang, W. B. Whitten, and J. M. Ramsey, Chemical Characterization of Single Particles by Laser Ablation/Desorp-tion in a Quadrupole Ion Trap Mass Spectrometer, Anal. Chem., 66, 3431-3435 (1994). 

Schrader, B., Micro Raman, Fluorescence, and Scattering Spectroscopy of Single Particles, in Physical and Chemical Characterization of Individual Airborne Particles (K. R. Spurny, Ed.), Chap. 19, pp. 358-379, Ellis Horwood, Chichester, 1986. 

Aerosol Instrument Classification. Friedlander (34) classified the range of aerosol instrumentation in terms of resolution of particle size, time, and chemical composition. This classification scheme is illustrated in Figure 3. The ideal instrument would be a single-particle counter-sizer-analyzer. Operating perfectly, this mythical instrument would fully characterize the aerosol, with no lumping of size or composition classes, and would make such measurements sufficiently rapidly to follow any transients occurring in the aerosol system. 

If the processes just described are assumed to characterize the transfer of mass and energy in a fixed-bed adsorber, the conservation principles may be applied to them to describe the temperature and concentration as a function of time and position. Presenting the equations for a fixed-bed geometry has the advantage of including also equations, as special cases, for transient adsorption in single particles or groups of particles in batch systems. 

We will formulate the problem simply but generally. Consider a system of structureless, classical particles, characterized macroscopically by a set of thermodynamic coordinates (such as the temperature T) and microscopically by a set of model parameters that prescribe their interactions. The two sets of parameters play a strategically similar role it is therefore convenient to denote them, collectively, by a single label, c (for conditions or constraints or control parameters in thermodynamic-and-model space). 

X-ray powder diffraction data may be helpful but are often hard to interpret for complex mixtures use of computer data file search programs (6) and microcamera methods for single particle analysis (7) may be useful for identification. Comparative sample identification is generally less often possible than for metals since the latter are manufactured while the nonmetallic inorganic solids are often unprocessed materials with large property variations. However, where applicable, the following are some examples of determinations which might be made (a) particle size by microscopy (b) microstructure and sub-microstructure characterization... 

Just as DENs particle sizes have some distribution (albeit relatively narrow), there is surely some distribution in particle compositions for bimetallic DENs. This is a fundamentally important aspect of DENs, particularly with regard to their catalytic properties however, there are presently no reliable characterization methods for evaluating particle composition distributions. One method that has been applied to PdAu [21] and PtPd [19] DENs, as well as dendrimer-templated PtAu [24] is to collect single particle EDS spectra from several (15-20) nanoparticles. These experiments indicate that individual particle composition distributions may vary widely, but the difficulty in obtaining data from the smallest particles may skew the results somewhat. EDS spectra collected over large areas, which sample tens or hundreds of particles, generally agree well with the bulk composition measurements [24] and with stoichiometries set in nanoparticle synthesis [19,21,24]. 

Zuleta, M., Bjornbom, P., and Lundblad, A. Characterization of the electrochemical and ion-transport properties of a nanoporous carbon at negative polarization by the single-particle method../. Electrochem. Soc. 153, 2006 A48-A57. 

The single-particle wave function for the free photoelectron may be expressed as an expansion in angular momentum partial waves characterized by an orbital angular momentum quantum number l and and associated quantum number X for the projection of l on the molecular frame (MF) z axis [22, 23, 63-66],... 

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