Normal translational energy

Figure 23 Adapted from Guo et al. [83], Initial dissociative adsorption probability as a function of normal translational energy for O2 on Pt(l 0 0)-hex-R0.7° for various surface temperatures, Ts.

Molecular adsorption probabilities for 02 as a function of normal translational energies at Ts = 77 K were also measured by Nolan et al., and are shown in Fig. 24, along with dissociative adsorption probabilities obtained by Guo et al. [83] at Ts = 573 K. 

Kolasinski et al. [70] found that there was no translational energy in excess of that expected at equilibrium, while Park et al. [69] found a higher ratio of normal translational energy than expected at equilibrium. These results appear to contradict each other, though this is not a strict logical necessity. Within their simplest interpretations, both experiments agree that any barrier to adsorption in the normal coordinate is at most a few kilocalories per mole. 

The following derivation is modified from that of Fowler and Guggenheim [10,11]. The adsorbed molecules are considered to differ from gaseous ones in that their potential energy and local partition function (see Section XVI-4A) have been modified and that, instead of possessing normal translational motion, they are confined to localized sites without any interactions between adjacent molecules but with an adsorption energy Q. 

As excited atoms, molecules, or ions come to equilibrium with their surroundings at normal temperatures and pressures, the extra energy is dissipated to the surroundings. This dissipation causes the particles to slow as translational energy is lost, to rotate and vibrate more slowly as rovibrational energy is lost, and to emit light or x-rays as electronic energy is lost. 

In porous media, liquid-gas phase equilibrium depends upon the nature of the adsorbate and adsorbent, gas pressure and temperature [24]. Overlapping attractive potentials of the pore walls readily overcome the translational energy of the adsorbate, leading to enhanced adsorption of gas molecules at low pressures. In addition, condensation of gas in very small pores may occur at a lower pressure than that normally required on a plane surface, as expressed by the Kelvin equation, which relates the radius of a curved surface to the equilibrium vapor pressure [25],... 

Since H-atom products from chemical reactions normally do not carry any internal energy excitation with its first excited state at 10.2 eV, which is out of reach for most chemical activations, the high-resolution translational energy distribution of the H-atom products directly reflects the quantum state distribution of its partner product. For example, in the photodissociation of H2O in a molecular beam condition,... 

In a pore the overlapping potentials of the walls more readily overcome the translational energy of an adsorbate molecule so that condensation will occur at a lower pressure in a pore than that normally required on an open or plane surface. Thus, as the relative pressure is increased, condensation will occur first in pores of smaller radii and will progress into the larger pores until, at a relative pressure of unity, condensation will occur on those surfaces where the radius of curvature is essentially infinite. Conversely, as the relative pressure is decreased, evaporation will occur progressively out of pores with decreasing radii. 

The velocity probability distribution function of Eq. 10.20 is the well-known Maxwell-Boltzmann distribution of velocities. Integrating over vx = —cc — oo shows that P(vx) is normalized. It is also easy to calculate the expectation value for the one-dimensional translational energy of a mole of gas as... 

Molecules A and B react to form the excited (energized) reactive intermediate species C (n) in reaction 10.178. Translational energy of the reactant molecules from their relative motion before collision is converted to internal vibrational energy of C (n). The rate constant for formation of C (n) is assumed to depend on n and the temperature T. The forward rate constant is written as ka,oof(n, T) a constant term times a to-be-determined function f(n, T). This function is the probability of forming C (n) in a given energy state n at some temperature T it is normalized as... 

If these relations were true, then one could compute any autocorrelation function involving a higher power of V or J by just knowing v f(t) or Aj(t). For example, the normalized translation kinetic energy autocorrelation function e2(0> where... 

FIGURE 10. The vibrational distribution of the CS radical derived from TOF measurements and from LIF measurements. All of the measurements have been normalized to v" = 4. The TOF measurements of Lu et al. (178) were obtained by using a logarithmic extrapolation for the S(3P) in the translational energy regime where both S(3P) and S(1D) can be formed. The vibrational distributions were then derived from the observed curves. 

In the hydrate lattice structure, the water molecules are largely restricted from translation or rotation, but they do vibrate anharmonically about a fixed position. This anharmonicity provides a mechanism for the scattering of phonons (which normally transmit energy) providing a lower thermal conductivity. Tse et al. (1983, 1984) and Tse and Klein (1987) used molecular dynamics to show that frequencies of the guest molecule translational and rotational energies are similar to those of the low-frequency lattice (acoustic) modes. Tse and White (1988) indicate that a resonant coupling explains the low thermal conductivity. 

Absorption corresponds to a transition from the low- to the high-energy spin state, that is to a reversal of spin. There will be a net absorption only if there is a greater population of the state of lower energy. Since under normal conditions hv is small compared with translational energies, care must be taken not to saturate the system, and sensitivity is greatly increased on cooling. 

---