Nanoparticle collisions in the gas phase in the presence of singular contact potentials

Collisional growth and ionization is commonplace for gas phase nanoparticles (i.e., in aerosols). Nanoparticle collisions in atmospheric pressure environments occur in the mass transfer transition regime, and further attractive singular contact potentials (which arise when modeling nanoparticles as condensed matter and for which the potential energy approaches -∞ when two entities contact) often have a non-negligible influence on collision processes. For these reasons collision rate calculations for nanoparticles in the gas phase are not straightforward. We use mean first passage time calculations to develop a simple relationship to determine the collision rate in the gas phase, accounting for the influences of both the transition regime and singular contact potentials (specifically the non-retarded van der Waals and image potentials). In the presented analysis, methods to determine the degree of enhancement in collision rate due to attractive singular potentials in the continuum (diffusive) regime, η(C), and the degree of enhancement in the free molecular (ballistic) regime, η(FM), are first reviewed. Accounting for these enhancement factors, with mean first passage time calculations it is found that the collision rate for gas phase nanoparticles with other gas phase entities can be determined from a relationship between the dimensionless collision rate coefficient, H, and the diffusive Knudsen number, Kn(D), i.e., the ratio of the mean collision persistence distance to the collision length scale. This coincides with the H(Kn(D)) relationship found to appropriately describe collisions between entities interacting via a hard-sphere potential, but with η(C) and η(FM) incorporated into the definitions of both H and Kn(D), respectively. The H(Kn(D)) relationship is compared to the predictions of flux matching theory, used prevalently in prior work for collision rate calculation, and through this comparison it is found that at high potential energy to thermal energy ratios, flux matching theory predictions underestimate the true collision rate. Finally, a series of experimental measurements of nanoparticle-nanoparticle collision rates are compared to the determined H(Kn(D)) expression, considering that nanoparticles interact via non-retarded van der Waals potentials. Very good agreement is found with collision rates inferred from experiments, with almost all measured values from four separate studies within 25% of model predictions.     

Sphere packing, helices and the polytope {3, 3, 5}

The packing of tetrahedra in face contact is well-known to be relevant to atomic clustering in many complex alloys. We briefly review some of the structures that can arise in this way, and introduce methods of dealing with the geometry of the polytope {3, 3, 5}, which is highly relevant to an understanding of these structures. Finally, we present a method of projection from S₃ to E₃ that enables coordinates for the key vertices of the collagen model of Sadoc and Rivier to be calculated. Received 27 March 2001     

An alternative method to specify the degree of resonator stability

We present an alternative method to specify the stability of real stable resonators. We introduce the degree of optical stability or the S parameter, which specify the stability of resonators in a numerical scale ranging from 0 to 100%. The value of zero corresponds to marginally stable resonator and S < 0 corresponds to unstable resonator. Also, three definitions of the S parameter are provided: in terms of A&D, B&Z _Ro and g ₁ g ₂. It may be noticed from the present formalism that the maximum degree of stability with S = 1 automatically corresponds to g ₁ g ₂ = 1/2. We also describe the method to measure the S parameter from the output beam characteristics and B parameter. A possible correlation between the S parameter and the misalignment tolerance is also discussed.      

Replacing the hydrogen in the intermolecular hydrogen bond of the cyanuric acid-bipyridyl adduct by Ag(I)

A complex between cyanuric acid (CA), 4,4′-bipyridyl (BP) and Ag(I), with the composition, [Ag₂(C₃H₂N₃O₃-κN)₂ (C₁₀H₈N₂-κN)] has been prepared. Crystal structure analysis shows that it has a chain structure in which the CA molecules are linked to the BP units through silver atoms by the formation of N-Ag-N bonds, wherein one of the hydrogens of CA is replaced by Ag(I), showing thereby the chains connected to one another by N-H...O hydrogen bonds formed between the CA molecules. This intermolecular chain structure resembles the chain structure of the CA.BP adduct where CA-BP-CA chains formed by N-H...N hydrogen bonds are linked to one another by N-H...O hydrogen bonds between the CA molecules.     

Magnetism and transport studies in off-stoichiometric metallic perovskite compounds GdPd3Bx (x=0.25, 0.50 and 0.75)

We report the magnetic and transport properties of the off-stoichiometric metallic perovskite like compounds GdPd₃B_x (x=0.25, 0.50 and 0.75). Our results show that doping with boron in the lattice of parent binary-compound GdPd₃ leads to lattice expansion. Which in turn manifests in contrasting magnetic and transport behaviors of the doped compounds in comparison with the undoped GdPd₃. An attempt has been made to compare and correlate the results of magnetic and transport measurements of GdPd₃B_x with that of stoichiometric compositions GdPd₃B_xC_1−x. The comparative study of GdPd₃B_x and GdPd₃B_xC_1−x confirms that there is a strong correlations between the structural, magnetic and transport properties of these compounds.     

High-performance flow-focusing geometry for spontaneous generation of monodispersed droplets

A high-performance flow-focusing geometry for spontaneous generation of monodispersed droplets is demonstrated. In this geometry, a two-phase flow is forced through a circular orifice integrated inside a silicon-based microchannel. The orifice with its cusp-like edge exerts a ring of maximized stress around the flow and ensures controlled breakup of droplets for a wide range of flow rates, forming highly periodic and reproducible dispersions. The droplet generation can be remarkably rapid, exceeding 10(4) s(-1) for water-in-oil droplets and reaching 10(3) s(-1) for oil-in-water droplets, being largely controlled by flow rate of the continuous phase. The droplet diameter and generation frequency are compared against a quasi-equilibrium model based on the critical Capillary number. The droplets are obtained despite the low Capillary number, below the critical value identified by the ratio of viscosities between the two phases and simple shear-flow.