Particle currents

The attainable particle current density per solid angle of the beam (ions pm s sr ) is an inherent property of the ion source, the so-called brightness. Because of this, reduction of the beam diameter is effected by reducing the beam current. 

TOWARDS THE HYDRODYNAMIC LIMIT STRUCTURE FACTORS AND SOUND DISPERSION. The collective motions of water molecules give rise to many hydrodynamical phenomena observable in the laboratories. They are most conveniently studied in terms of the spatial Fourier ( ) components of the density, particle currents, stress, and energy fluxes. The time correlation function of those Fourier components detail the decay of density, current, and fluctuation on the length scale of the Ijk. 

The chemical characterization of aerosol particles currently is of great interest in the field of atmospheric chemistry. A major goal is the development of a method for continuous elemental analysis of aerosols, especially for the elements C, N, and S. Chemiluminescence reactions described in this chapter have adequate sensitivity and selectivity for such analyses. In fact, considering that a 1- j.m-diameter particle has a mass of =0.5-1.0 pg, online analysis of single aerosol particles should be achievable, especially for larger particles. 

Right at the disc the convection current perpendicular to the surface vanishes. The transport to the surface is effected by diffusion so the particle current density jp of any species with concentration c and... 

From Eqs.(14.1) - (14.3), show that the particle current density jp of a species A at a rotating disc can be written in the form ... 

The rate of reaction, determined as the sum of two individual particle currents, may be given as... 

The formula (101) can also be proved with the escape-rate theory. We consider the escape of particles by difffusion from a large reservoir, as depicted in Fig. 17. The density of particles is uniform inside the reservoir and linear in the slab where diffusion takes place. The density decreases from the uniform value N/V of the reservoir down to zero at the exit where the particles escape. The width of the diffusive slab is equal to L so that the gradient is given by Vn = —N/ VL) and the particle current density J = —Wn = VN/ VL). Accordingly, the number of particles in the reservoir decreases at the rate... 

Having specified the initial distribution of B reactants about A reactants in eqn. (3), it is necessary to find out what the distribution will be at subsequent times, subject to the two boundary conditions of eqns. (4) and (5). The region where p(r, t) is of interest is shown in Fig. 2. Once p(r,t) has been determined, the flux and hence the particle current of B towards A can be calculated. The rate of reaction is the number of B reactants diffusing towards each A reactant multiplied by the concentration of A reactants. From this, the rate coefficient for reaction may be evaluated. 

The flux of particles is in the opposite sense to the direction of the concentration gradient increase. Equation (6) is Fick s first law, which has been experimentally confirmed by many workers. D is the mutual diffusion coefficient (units of m2 s 1), equal to the sum of diffusion coefficients for both reactants, and for mobile solvents D 10 9 m2 s D = DA + jDb. The diffusion coefficient is approximately inversely dependent upon viscosity and is discussed in Sect. 6.9. As spherical symmetry is appropriate for the diffusion of B towards a spherically symmetric A reactant, the flux of B crossing a spherical surface of radius r is given by eqn. (6) where r is the radial coordinate. The total number of reactant B molecules crossing this surface, of area 4jrr2, per second is the particle current I... 

Equation (10) is a diffusion equation which applies equally well for matter or heat. The solution of this equation has been studied by many workers. As with differential equations in general, one arbitrary constant is required for each derivative. Since the diffusion equation has partial derivatives, the arbitrary constants have to be functions of the variable which is not involved in the derivative. The diffusion equation requires two functions of time at fixed values of space coordinates (the boundary conditions) and one function of distance at a given time (the initial condition). These have already been established [eqns. (3)—(5)]. It is possible to proceed to solve the diffusion equation for p(r,t) now and then calculate the particle current of B towards each A reactant and so determine the rate of reaction. 

In the steady limit (times 10ns or more are usually sufficient to attain this in mobile solvents), the flux of B towards an A reactant a distance r away is [B]0DR/r2, from eqn. (6), and the current is 47rUJ [B]0, from eqn. (7), at any separation between B and A. This constancy reflects the steady concentration of B around A achieved at long times. At shorter times the steady-state concentration of B is not established and the particle current of B is both time- and space-dependent. 

The current of B reactants diffusing towards the A reactant is calculated by substituting eqn. (16) for the density distribution into the expression for the particle current, eqn. (7). As noted above, this is dependent upon the separation between A and B. Very close to A, all the B diffusing toward A will react with A. The number of B molecules diffusing towards A per second at the encounter separation is also the rate of reaction of B reactants with any one A reactant. 

By integrating eqn. (272) similarly and noting that there is no particle current at the outer boundary (nor any across the reaction surface) then... 

The four constants in eqn. (327) have to be determined from the two boundary conditions (323a) and 323b) and two further conditions. Since the flux is everywhere non-infinite, the density must be a continuous function, even at the source point, r = r0, Because there is a source of density at r = r0, the particle current is discontinuous at the source point and the gradient of the density must be discontinuous. This may be shown by multiplying eqn. (325) by r and integrating r over the region (r0 — t) < r < (r0 + e) where e is a small distance compared with ra... 

We require furthermore that the particle currents are continuous at an interface point,... 

In the above equation, q has been considered to have only one component that is along the -direction. L is the Hermitian Liouville operator, Q = 1 — P, where P is the projector onto the dynamical quantity A . Aa is component of a four-vector of particle current density and particle density, defined as... 

This chapter begins by summarising the recent review articles on this topic. Other topics such as sources and physico-chemical characteristics of ambient and emerging nanoparticles (i.e. ENPs) are then covered briefly for the completeness of the article. This is then followed by the assessment of nanoparticles in numerous European cities, estimation of respiratory deposition doses and a brief discussion on current and future prospects of their regulatory control. In what follows, the terms airborne nanoparticle and ENP refer to total particles, currently mainly produced by vehicles, and nanomaterials-derived products, respectively. 

Lead, J. R., and Wilkinson, K. J. (2007). Environmental colloids and particles Current knowledge and future developments. IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, 10,1-16. 

Any electrons which reach the oxide—oxygen interface will be quickly utilized in the formation of 0" ions, and similarly, any positive holes which manage to reach the metal—oxide interface will be quickly annihilated by electrons from the parent metal. The asymmetrical surface reactions thus lead us to expect widely different electron concentrations in the oxide at the two interfaces of the oxide. This difference in electron concentration is equivalent to a difference in the chemical potential for the electronic species at the two interfaces. As in the case of the ionic defect species, such differences in concentration (and chemical potential) can be expected to produce particle currents of the defect species in question. If the primary electronic defects are excess electrons, then we can expect an electron particle current from metal to oxygen if the primary electron defects are the positive holes, then we can expect a positive-hole particle current from oxygen to metal. Of course, an intermediate situation is also possible in which electrons flow from the metal towards the oxygen while simultaneously a positive-hole current flows from the oxygen towards the metal, with recombination [8] (partial or total) occurring within the oxide film. 

CONCENTRATION AND ELECTROCHEMICAL POTENTIAL GRADIENTS AS DRIVING FORCES FOR PARTICLE CURRENTS AND OXIDE GROWTH... 

As an example, it is conceivable that in some metal—oxide systems, the cation interstitials entering the oxide at the metal—oxide interface (x = 0) rise to appreciable bulk concentration values C(cl) (0). These defects can then migrate through the oxide layer. Chemical reaction of any such interstitials which happen to reach the oxide—oxygen interface (x = L) will serve to deplete the number at that interface. Thus the bulk concentration C,(d)(L) will be much lower than the number Ccation interstitials from x = 0 to x = L can be expressed as a particle current density J(C1). This particle current density proceeding from the source interface (x = 0) to the sink interface (x — L) can be essentially uniform (i.e. J(ci) independent of position x) if there is no build-up or depletion of the bulk density C(ci) between source and sink. On the other hand, any build-up or depletion of the bulk density C(x) at a position x within the layer will require the current to decrease or increase, respectively, at that position x in order to supply or take away, as the case may be, the requisite number of such defects. 

If the particle current J a) of cation interstitials is flowing from the metal—oxide interface to the oxide—oxygen interface at time t, and if the area of the parent metal surface is A, then a number J(d)A At of cation interstitials is transported in the time increment A t. If the volume of new oxide formed per transported cation interstitial is designated as Ria then a total quantity of new oxide Rici) (J(cl) A At) is formed during the time interval At. The increase AL in oxide thickness is given by the ratio of this volume to the area A. Thus... 

Fig. 8. Schematic diagrams of concentration profiles and the associated particle currents, (a) Cation interstitials or anion vacancies [(dC/dx)<0] and positively directed particle currents ( 0). (b) Cation vacancies or anion interstitials [(dC/dx) > 0] and negatively directed particle currents (J< 0).

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