Collision number with surfaces

As we are particularly interested in surface reactions and catalysis, we will calculate the rate of collisions between a gas and a surface. For a surface of area A (see Fig. 3.8) the molecules that will be able to hit this surface must have a velocity component orthogonal to the surface v. All molecules with velocity Vx, given by the Max-well-Boltzmann distribution f(v ) in Cartesian coordinates, at a distance v At orthogonal to the surface will collide with the surface. The product VxAtA = V defines a volume and the number of molecules therein with velocity Vx is J vx) V Vx)p where p is the density of molecules. By integrating over all Vx from 0 to infinity we obtain the total number of collisions in time interval At on the area A. Since we are interested in the collision number per time and per area, we calculate... 

Ion scattering spectrometry (ISS) is also a technique which is sensitive for all elements with an atomic number greater than 2, and measures the energy change of the bombarding ions, caused by elastic collisions with surface atoms. Like SIMS, it has limited spatial capabilities. 

Number of collisions per unit area second of gas with surface... 

EXAM PLE 9.6 Rate of Atomic Collisions as a Function of Pressure. Assuming 1019 atoms per square meter as a reasonable estimate of the density of atoms at a solid surface, estimate the time that elapses between collisions of gas molecules at 10 6 torr and 25°C with surface atoms. Use the kinetic molecular theory result that relates collision frequency to gas pressure through the relationship Z = 1/4 vNIV, for which the mean velocity of the molecules v = (BRTI-kM) 12 and NIV is the number density of molecules in the gas phase and equals pNJRT. Repeat the calculation at 10 8 and 10 10 torr. 

Let us establish a relationship between the Stokes numbers of the initial and last collisions and estimate the collision number. The decrease in the Stokes number, which corresponds to the repetitive collision St, can be estimated by substituting the particle velocity v, (at its repetitive touch with the bubble surface) into the equation for St. v, can be determined by inserting the time interval T between two collisions (cf Eq. (11.61)) into Eq. (11.60). The second term in Eq. (11.60) can be neglected and we get co,t = n. Taking this into account, from Eqs (11.59) and (11.68) we obtain... 

We have described the theory of repetitive collision to show that the minimum thickness of the liquid interlayer during a second collision many times exceeds h . Thus, the attachment by a second collision is also impossible with particles with surfaces that are too smooth. The derived equation of the particle trajectory between the first and the second collision is restricted to Stokes numbers St < 1. Only one repetitive collision is possible under this condition. An additional restriction is given by the difference between St and St which must not be too small. 

The model was operated by starting with a bare surface, and evaluating the probabilities of all possible events in a time-slice this was repeated about 30 million times after which steady-state behaviour was found. The probabilities were related to real-time by collision numbers based on kinetic theory, and experimental sticking coefficients values of variable parameters were fixed to give best... 

Suppose B starts as a gas unmixed with A. There are in each second a certain number of collisions between the molecules, which also make a certain number of impacts on the surface of the container. The calculation of the collision numbers has already been given. Reference to the derivation (p. 21) will show that the result would be in no way affected by the assumption that some foreign molecules, of A, were present. The cylindrical space swept out by the representative molecule of B becomes more and more bent as collisions with A increase, but apart from this these extra encoimters of B with A have no relevance either to the collisions of B with B, or to the impacts of B on any surface which it may meet. 

This is the population balance equation (PBE). Its principal form was first given by Smoluchowski (1916). In Eq. (4.1), denotes the aggregate number concentration, while Kjj is a kinetic constant related with the collision between clusters of mass i and j, and Etj is the sticking probability of the sub-clusters. Commonly, it is assumed that any successful collision (i.e. surface contact) leads to a stable particle bond and that Ey can be, thus, set to 1. 

Figure 1 shows the correlation between 0O2 and Pc/P as a function of K (= Kc/Koj). It is obvious that the concentration of adsorbed oxygen decreased with an increase in the equivalent constant, Kc. A physisorption model should be introduced. It is well known that the surface collision number, Z, is given by the following Herz-Knudsen equation,... 

Figure 9.10 Secondary nudeation by collisions induced by the impact will be released by a of crystals with surfaces, that is, with the stirrer, fragmentation, and a number of smaller The flow around the stirrer pushes the particles particles are formed that grow and thus away. Depending on the shear flow, some increase the number density of particles.

Flocculation proceeds by biparticle collision when the surface, covered by the polymer, of one particle interacts with the uncovered surface of another particle. The change in the number of particles in a xmit volume of dispersion is proportional to the surface area of the particle covered by the polymer, S i, the number of these particles, Nj, and the surface area of particles not eovered by the polymer (Sf — S i) ... 

In the reported particle collision experiments with negatively charged latex, polystyrene, and silica spheres, most of the step features in the recorded chronoamperograms showed a cmrent decrease due to the blocking of redox mediator diffusion by adsorbed particles. However, a small number of steps showed a current increase, suggesting removal of a particle from the surface. However, in... 

---