Boltzmann plot

Figure C3.3.5. The upper half of tire figure is a Boltzmann plot of the natural log of tire population scattered into...

The linear Boltzmann plot obtained in the photodissociation of H20 in the first continuum merely reflects the rotational FC distribution for the zero-point bending motion in the electronic ground state. It has nothing to do with energy randomization in a long-lived intermediate complex ... 

Inserting the appropriate parameters yields a temperature of approximately 400 K in reasonable accord with the average of the two measured values. A linear Boltzmann plot of the final rotational state distribution usually indicates that the torque in the exit channel is weak. 

These experiments have been made using the Qj 7 line when exciting several other lines (P or Q) no noticeable variation of the quenching was found. This result validates temperature measurements from Boltzmann plots of relative fluorescence intensities. 

Figure 12 Boltzmann plots of the final rotational state distributions for NO scattered from Pt(l 1 1) at an incidence angle of 45°. The left panels contain the experimental data by Wiskerke et al. [91, 92] right panels contain the corresponding simulations. The indicated temperatures result from a linear least square fit through the data points. The three panels from top to bottom indicate measurements for f = 30°, 55° and 70° and calculations for 3 ranges of 0f. From Lahaye et al. [68].

Figure 16 Rotational energy distributions for desorbed NO (v = 0) of hep hollow species from Pt(l 1 1) in the Boltzmann plot. Filled circle Q, = 1/2, open circle 2 = 3/2. (a) X = 193 nm [60], (b) X = 352nm.

Figure 25 Boltzmann plots for the rotational energy distributions of the fast (filled circle and square) and slow (open circle and square) channels for NO (v = 0) desorption from NiO(0 01) at 100 K [64],...

NO desorption from the alloy surface saturated at 80 K is observed at X = 193 nm and is a singlephoton process. The rotational energy distributions in the Boltzmann plot are shown in Fig. 30 and satisfy an almost linear relation, the gradient of which gives Tt 350 K. The two spin-orbit states look... 

The rotational temperature obtained from a linear relation in the Boltzmann plot of the rotational energy distribution is an index of the lifetime in the intermediate excited state and decreases with decreasing lifetime. The rotational temperature of CO desorbed from Pt(l 1 1) is very low as compared with that of NO desorption, i.e. the lifetime of the excited CO is supposed to be much shorter than that of NO. In the case of CO desorption from Pt(l 11), however, the lifetime is not obtained from the rotational energy distribution, since desorbed molecules are detected by the (2 + 1 )REMPI method in the experiment [ 12] and then the single rotational states are not resolved. On the other hand, the rotational temperature of NO desorbed from Pt(l 1 1)-Ge surface alloy is lower than that from Pt(l 1 1). Then, it is speculated that the lifetime of the excited CO on the alloy is shorter than that on Pt( 111) and the residence time of the excited CO on the alloy is too short to be desorbed. As a consequence, the excited CO molecules are recaptured in the relaxation without desorption. However, it has not been understood why the lifetime of the excited CO molecule (or the excited CO-Pt complex) on Pt( 1 1 1) is shorter than that of the excited NO molecule (complex) on Pt(l 11), and further on the Pt-Ge alloy as compared with Pt(l 1 1). 

By plotting ln[Irem/(/ I J + 1)] versus ] (J + 1) for a series of rotational lines a so-called rotational temperature can be determined. It characterizes the kinetic energy of the molecules and radicals, by which the band spectra are emitted. It is also a good approximation of the temperature reflecting the kinetic energy of the neutrals and ions in a plasma. For the case of a hollow cathode discharge the Boltzmann plot and the temperatures as measured from CN and N) band hyper-fine structures are given in Fig. 3. 

Another nonlinear technique that is potentially applicable to thermometric measurements is DPWM [7,9]. Por instance, a Boltzmann plot constructed out of the relative line intensities of a DPWM spectrum can lead to temperature predictions that can be as accurate as CARS in some cases. An alternative method is to fit theoretical simulations to the experimental spectrum. Nonetheless, the versatility of CARS is not equaled by DPWM. In effect, single pulse measurements seems to be limited to some radical species and mode fluctuations of conventional lasers perturb the data severely. To avoid troubles with such laser intensity fluctuations, saturated DPWM is often employed, but the difficulties of spectral S5mthe-sis remain a serious hindrance to a major role of DPWM thermometry. 

Fig. 19. Boltzmann plots for the CO formed in the 0( / )+CH3C2H and CH2 C=CH2 reactions. Solid lines theoretically predicted population distributions. Reprinted with permission from Chem. Phys., 20, 271 (1977). Copyright by North-Holland Publishing Company.

Analysis of these particular rotational lines in absorption did yield linear Boltzmann plots with well-defined rotational temperatures near 1300°C. The total energy separation of lower levels among all the rotational lines used in the... 

R branch of this band were used for analysis although a Boltzmann plot of these lines did yield a straight line, the rotational temperature determined from the slope of this line was independent of the gas kinetic temperature. Thus the Fulcher band is unsuited for use in measuring the gas kinetic temperature. This example illustrates the difficulty of accurate gas kinetic temperature measurement... 

The ratio of two line intensities or the Boltzmann plot gives an excitation temperature. ... 

To allow us to extract rotational populations from vibrational bands like the v = 5 band of Figure 3, we have written a caiputer code which solves these n coupled non-linear equations. Figure 6 illustrates the results obtainable with this code, ihe calculated and observed CARS spectra are nearly identical. The rotational populations derived from the experimental spectrum by the deconvolution program give a linear Boltzmann plot with a temperature of 299 K and a correlation coefficient of 0.997. Ihe experimental spectrum was taken at an ambient temperature of 295 K. 

Assuming uniform detection efficiency, the equilibrium constant, K, is given by the relative abundances of matrix and analyte ions in the spectrum. Since free energies are known or can be readily calculated for some matrices and analytes, this relationship can be tested. Kinsel et al. ° have recently done so for proton transfer reactions of matrix to amino acids. Their Boltzmann plots were nicely linear, verilying the local equilibrium model in these cases. 

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