C term

The zeroth-order Hamiltonian and the spin-orbit part of the perturbation are diagonal with respect to the quantum numbers K, E, P, Uj, It, Uc, and Ic-The terms of H involving the parameters aj, ac, and bo aie diagonal with respect to both the Ij and Ic quantum numbers, while the f>2 term connects with one another the basis functions with I j = Ij 2, 4- 2. The c terms... 

Fig. 3. Extreme cases of counterflow heat exchangers having infinite surface area (a) Cf and (b) Cf C. Terms are defined ia text.

When u E, this interstitial mixing effect was considered complete, and the resistance to mass transfer in the mobile phase between the particles becomes very small and the equation again reduces to the Van Deemter equation. However, under these circumstances, the C term in the Van Deemter equation now only describes the resistance to mass transfer in the mobile phase contained in the pores of the particles and, thus, would constitute an additional resistance to mass transfer in the stationary (static mobile) phase. It will be shown later that there is experimental evidence to support this. It is possible, and likely, that this was the rationale that explains why Van Deemter et al. did not include a resistance to mass transfer term for the mobile phase in their original form of the equation. 

The curves represent a plot of log (h ) (reduced plate height) against log (v) (reduced velocity) for two very different columns. The lower the curve, the better the column is packed (the lower the minimum reduced plate height). At low velocities, the (B) term (longitudinal diffusion) dominates, and at high velocities the (C) term (resistance to mass transfer in the stationary phase) dominates, as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, log (h ) is about 0.35. The optimum reduced velocity is in the range of 3 to 5 cm/sec., that is log (v) takes values between 0.3 and 0.5. The Knox... 

In Figure 7, the resistance to mass transfer term (the (C) term from the Van Deemter curve fit) is plotted against the reciprocal of the diffusivity for both solutes. It is seen that the expected linear curves are realized and there is a small, but significant, intercept for both solutes. This shows that there is a small but, nevertheless, significant contribution from the resistance to mass transfer in the stationary phase for these two particular solvent/stationary phase/solute systems. Overall, however, all the results in Figures 5, 6 and 7 support the Van Deemter equation extremely well. 

The Effect of Particle size on the Magnitude of the Van Deemter C Term... 

Katz et al. [1] also examined the effect of particle diameter on resistance to mass transfer constant (C). They employed columns packed with 3.2 im, 4.4 p,m, 7.8 pm, and 17.5 pm, and obtained HETP curves for the solute benzyl acetate in 4.3%w/w of ethyl acetate in n-heptane on each column. The data were curve fitted to the Van Deemter equation and the values for the A, B and C terms for all four columns extracted. A graph relating the value of the (C) term with the square of the particle diameter is shown in Figure 8. 

Figure 8. Graph of C Term against the Square of the Particle Diameter...

In aqueous solution at room temperature the coefficient B is positive for the majority of electrolytes. For some, however, it is negative in such a case the viscosity at moderate concentrations, where the B term is predominant, is less than that of pure water, while at lower concentrations, where the A s/c term becomes predominant, the value of the viscosity rises above that of pure water. An example of this is shown in Fig. 51, where abcissas are /c. The straight line is a plot of A s/c with A = +0.0052, while the lower curve is a plot of Be with B = —0.033. On adding the ordinates of these two curves the middle curve is obtained, which reproduces, within the experimental error, the values of 17/770 obtained for KC1 in aqueous solution at 18°C. 

Value very uncertain because the Ay/c term is masked by an unusually large negative Be term see Table 21. 

In its reduced state, the paramagnetic Rieske cluster shows a temperature-dependent MOD spectrum composed of numerous positive and negative C-terms that originate from the 8 = 1 ground state. The MOD spectra lack the Fe" 8 charge transfer bands that are observed as intense negative bands between 300 and 350 nm and a posi-... 

The A term represents the contribution from eddy diffusion, the B term the contribution from longitudinal diffusion, and the C terms the contributions from mass transfer in the mobile and stationary phases to the total column plate height. By differentiating equation (1.31) with respect to the mobile phase velocity and setting the result equal to zero, the optimum values of mobile phase velocity (u ) and plate height (HETP ) can be obtained. 

Actually, any time a move is proposed to a region outside the bounds of our transition matrix, whether or not it actually takes the system outside of some constraint, the equivalent transition-matrix update is to add the extrinsic acc to the diagonal C term instead. Since the diagonal terms enter in the final calculations only to normalize the transition probabilities [i.e., they appear only in the denominator of (3.63)], adding such data to the diagonal maintains the correct normalization without affecting the results. 

The term II scattering (equation 7) from vibronic activity in allowed electronic transitions mainly results in fundamental transitions of non-totally symmetric vibrations. This term corresponds to the B and C terms of the Albrecht theory25. 

In a more general form of equation 8.4-21 or -22, a AT c, term appears in the denominator for each adsorbing species i in competition for the adsorption sites. Furthermore, if the species dissociates into nt fragments, the appropriate term is (Kici)lln as in equation 8.4-15 for n = 2. Therefore, in the most general case, the expression for Langmuir adsorption of species i from a multispecies gas mixture is ... 

The activity a and the activity coefficient y are both dimensionless quantities, which explains why we must include the additional c term, thereby ensuring that a also has no units. We say the value of ce is 1 mol dm-3 when c is expressed in the usual units of mol dm-3, and 1 molm-3 if c is expressed in the SI units of mol m-3, and so on. 

Mass transfer (the C term), which involves collisions and interactions between molecules, applies differently to both packed and capillary columns. Packed columns are mostly filled with stationary phase so liquid phase diffusion dominates. The mass transfer is minimized by using a small mass of low-viscosity liquid phase. Capillary columns are mostly filled with mobile phase, so mass transfer is important in both the gas and liquid phases. A small mass of low-viscosity liquid phase combined with a low-molecular weight carrier gas will minimize this term. 

---