Collision frequency total

The product of the collision energy E(L) and collision frequency f L) is integrated over all crystals in the distribution to obtain the total rate of energy transfer. Different approaches have been used to estimate E(L) and f L), both for particle impacts and turbulent fluid induced attrition. 

Thus, the steric factor may be explained with the help of entropy change. When two molecules come together to produce the activated complex, the total translational degrees of freedom are reduced (from 6 to 3) and rotational degrees of freedom also diminish. This is compensated by an increase in vibrational degrees of freedom. But the definite orientation in forming the activated complex necessarily reduced the entropy, i.e. AS is negative. This decrease in entropy is small when reaction takes place between simple atoms. The calculated value of kbT/h corresponds to collision frequency... 

The second factor involves the theory that defines the natural width of the lines. Radiations emitted by atoms are not totally monochromatic. With plasmas in particular, where the collision frequency is high (this greatly reduces the lifetime of the excited states), Heisenberg s uncertainty principle is fully operational (see Fig. 15.4). Moreover, elevated temperatures increase the speed of the atoms, enlarging line widths by the Doppler effect. The natural width of spectral lines at 6000 K is in the order of several picometres. 

From a comparison of the two collision frequency terms, described in detail in the Equations 3 and 6, one obtains the relative contributions of the perikinetic and orthokinetic transport to the total particle agglomeration. The ratio is a function of the radius of the colloid, r, and the absolute value of the velocity gradient du/dz ... 

Figure 6. Frequency dependence of dimensionless absorption. Dimensionless collision frequency y = 0.3. (a) Calculation from rigorous formulas (70a) and (70b) (solid lines) and from the PL-RP approximation, Eqs. (78-80b) (dashed lines). Curves 1 refer to P = ji/8 and curves 2 to (3 = ti/4. Vertical lines mark the values of the absorption-peak frequencies estimated by Eqs. (85) and (86). (b) Comparison of the total absorption (solid line) with contribution of the precessional component (dashed line). Calculation for the PL-RP approximation, P = ji/8.

Figure 62. Solid lines contribution of the structural-dynamical model to the dimensionless absorption Astr(v) calculated in the R-band by the ACF method, (a) Calculation for H20, the dimensionless collision frequency Y = 0.6, r/L = 0.27,/) = 2.07. (b) Calculation for D20 with Y = 1.3, r/L = 0.4,/j = 3.54. Dotted lines total absorption calculated for the composite HC-SD model. Temperature 22.2°C. The peak ordinates are set equal to 1.

Encounters with impact parameter b collision rate those with b> rA + rB do not. The total number of collisions per unit time per unit volume between A and B can be found from kinetic theory, and this collision rate is often called the collision frequency, Zab- This quantity is proportional to the numbers of molecules of A and B per unit volume, nA and nB ... 

The rate constant obtained for G + DMSO in air is slightly more than a factor of 2 slower than the value of (2.0 0.3) xlO 10 cm3 s 1 for the reactiom G + DMS (this laboratory, unpublished results). No effect of the O2 concentration was observed for the reaction of G with DMS. However, this rate constant is already close to the collision frequency and a small O2 effect could remain undetected within the precision of the present experimental method. In air the reaction of G with DMSO leads to the formation of SO , DMSO-), CO, HCHO, and HOOOH with yields of approximately 42% (S), 14% (S), 15% (C), 18% (C), and 2% (C), respectively. As discussed earlier it is not known whether the yield of DMS02 is being over- or underestimated. The total sulfur yield was 56% indicating that probably a major sulfur containing product has not been detected. With the inclusion of the contribution from DMSO the total carbon yield was 63%. The formation of DMSO and SO2 as products indicates that both, addition (13) and abstraction (14) pathways are operative,... 

Let us focus our attention on one such mobile adatom. In unit time, it will travel on average a distance c, and it will collide with all the adatoms whose centres are within a distance o, of the line defining its path. Since there is a total of (A/a), adatoms per unit area, each mobile adatom will have a collision frequency of 2 o, c, (Na),. Further, since it takes two adatoms to make a collision and there are (m A/a), mobile adatoms eligible per unit area, the total collision frequency per unit area is [2o, c, (Na) ]... 

A chain reaction is defined as a reaction in which the products react with the initial material, and, again, the products of this second step then react with more of the initial material, thus involving a series of reaction cycles. A series of reactions can be built up in such a way as to give an equilibrium or steady state in which the fconcentration of material for the rate-determining step is directly proportional to the concentration of the initial material. These are the conditions required for a unimolecular reaction. Thus we have another way of explaining the independence of reaction rates and total collision frequency. 

Application of these equations, with an appropriate collision frequency constant, results in a family of curves representing concentrations of a set of /c-plets over time and the variation of total particle and aggregate number in the dynamic system. Such a plot is shown in Fig. 4, with aggregate numbers normalized to the total initial concentration of singlets, N(0). 

A necessary condition for the two-term expansion of the distribution function of equation (2) to be valid is that the electron collision frequency for momentum transfer must be larger than the total electron collision frequency for excitation for all values of electron energy. Under these conditions electron-heavy particle momentum-transfer collisions are of major importance in reducing the asymmetry in the distribution function. In many cases as pointed out by Phelps in ref. 34, this condition is not met in the analysis of N2, CO, and C02 transport data primarily because of large vibrational excitation cross sections. The effect on the accuracy of the determination of distribution functions as a result is a factor still remaining to be assessed. 

For low temperature collisions with He, the fit given by the multiquantum jump model was clearly superior to that obtained using the single quantum jump model. Even so, the Av = —I process accounted for more than 70% of the total removal rate constant (a = 1.1). For transfer out of V = 23, the total removal rate constant was around 1.6 x 10" cm s at 5 K. This was roughly an order of magnitude smaller than the He vibrational relaxation rate constant at room temperature (1.7 x 10 cm s ). Part of this difference is from the change in the collision frequency. To compensate for this factor, it is helpful to calculate effective vibrational relaxation cross sections from the relationship = kv-v / v)i where v) is the average... 

How does a change in concentration of reactants affect the rate of a reaction at a constant temperature An increase in concentration cannot alter the fraction of collisions that have sufficient energy, or the fraction of collisions that have the proper orientation it can serve only to increase the total number of collisions. If more molecules are crowded into the same space, they will collide more often and the reaction will go faster. Collision frequency, and hence rate, depends in a very exact way upon concentration. 

Table X contains numerical data concerning the temporal decay of momentum correlation functions (for body 1, i.e., L,). One realizes immediately that in this case the influence of the cage body is much weaker than it was for orientational observables. For Wj = 50 the relaxation of the momentum of body 1 is almost totally decoupled from reorientation of body 2, even for large potentials. For Wj = 5, a cluster of eigenvalues close in value to the collision frequency is present. This is also the case for Wj = 0.5, but librational modes are beginning to play a nonnegligible role.

The complex nature of the slow mode responsible for the long-time behavior of first rank correlation functions for a first rank interaction potential is illustrated by the composition of the eigenvector corresponding to the slow mode 11a in Table XI, for Uj = 3 and o) = 0.5. Note that n 1, tij, ii, J2 describe the magnitudes and the orientations of the momentum vectors Lj and L2 j is referred to the orientation of L, -t- Lj, 7, and J2 are related to the orientations of the two bodies, and the total orientational angular operator defines the quantum number J finally J, which is not included in this table, is the total angular momentum quantum number, and it is always equal to 1 for first rank orientational and momentum correlation functions, and to 2 for second rank correlation functions. In Fig. 11 we show the first rank correlation functions for different collision frequencies of body 1. The second rank correlation function decays are plotted in Fig. 12. The librational motions in the wells are more important than they were in the first rank potential case (since there is now a more accentuated curvature of the potential wells). 

The number of collisions in a time interval, At, for particles moving in the y direction relative to a particle moving in the - -x direction is (2y/2)/2 ndsQ. An estimate of the total number of collision in At is an estimate of the collision frequency ... 

A possible explanation is that in these runs the SO2 concentration in the feed gas was 1% and its partial pressure was a linear function of the total pressure of the feed. Consequently, the decrease of the rate of adsorption is a net result of two opposing effects. Higher pressures, on one hand, increase the number of collisions between gas molecules and the external surface of the adsorbent, and on the other hand decrease the flexibility of the orientation of the gas molecules in the direction that will allow them to enter the adsorbent pores. The last effect is apparently dominant and offsets the gain in adsorption rate due to higher collision frequency. 

Total collision frequency of particles with u, test particle Angular velocity Rotation tensor, Eq. (5.1.16)... 

The total collision frequency with the test particle (collisions s ) is therefore... 

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