Scattering Measurements—Molecular Beams

The study of individual molecular collisions is a topic of great current interest. The experimental methods are variants of the model experiment outlined in Section 2.2 to illustrate the idea of mean free path. While that experiment determines a total cross section for loss of reactant, with more sophisticated apparatus the nature of the product can be determined, i.e., partial cross sections for elastic, inelastic, and reactive events can be distinguished. Let us reconsider the reaction 

To measure the reaction cross section as a function of relative kinetic energy requires forming beams of A molecules and BC molecules with specified velocities. The beams are oriented so that they collide collision products are monitored as a function of energy and orientation. A representative apparatus is sketched in Fig. 8.1. 

In a molecular beam experiment the rate of product formation is measured as a function of the energy of the products and the direction in which they are scattered. The immediate problem is to interpret these data and deduce the reaction cross section. Consider crossed beams such as those of Fig. 8.1. The beams have fluxes and they collide with a relative energy e for which the reaction cross section is Q(e). Reaction occurs in the small collision volume Vco. As the beam fluxes are kept constant, the number of BC molecules in the collision volume is also a constant, N-qq. The quantity IaQ( ) is the number of A molecules which 

To compute the number of BC molecules in the collision zone requires adapting the molecular flux calculations of Chapters 1 and 2. From the perspective of a viewer in the collision volume, A and BC molecules approach one another with the relative speed Crei- The larger the relative speed, the fewer the molecules that are in the collision zone at any instant. 

In Section 1.5 we showed that, for particles moving in the +x direction, the flux of molecules with x component of velocity between u and u + du is 

---

Before discussing specific cases of reactive scattering of molecular beams, we should understand how such beams are formed and how their intensities may be quantitatively measured. As we describe the rather specialized techniques and procedures, the special suitability of beam studies for elucidating microscopic details of chemical dynamics should become apparent. 

This section discusses how spectroscopy, molecular beam scattering, pressure virial coeflScients, measurements on transport phenomena and even condensed phase data can help detemiine a potential energy surface. 

A molecular beam scattering experiment usually involves the detection of low signal levels. Thus, one of the most important considerations is whether a sufficient flux of product molecules can be generated to allow a precise measurement of the angular and velocity distributions. The rate of fonnation of product molecules, dAVdt, can be expressed as... 

The molecular beam and laser teclmiques described in this section, especially in combination with theoretical treatments using accurate PESs and a quantum mechanical description of the collisional event, have revealed considerable detail about the dynamics of chemical reactions. Several aspects of reactive scattering are currently drawing special attention. The measurement of vector correlations, for example as described in section B2.3.3.5. continue to be of particular interest, especially the interplay between the product angular distribution and rotational polarization. 

The "time of flight" mass spectrometer has been used to confirm that this highly radioactive halogen behaves chemically very much like other halogens, particularly iodine. Astatine is said to be more metallic than iodine, and, like iodine, it probably accumulates in the thyroid gland. Workers at the Brookhaven National Laboratory have recently used reactive scattering in crossed molecular beams to identify and measure elementary reactions involving astatine. 

Our experimental techniques ooitprise static techniques such as TiKKD, thermal desorption lectrosoppy (TDS) and work functicn measurements (A p) and < namic techniques like scattering of and D molecular beams. Details of the experimental methods are ven elseihere (2,3). 

The beams of reactant molecules A and B intersect in a small scattering volume V. The product molecule C is collected in the detector. The detector can be rotated around the scattering centre. Various devices may be inserted in the beam path, i.e. between reactants and scattering volume and between scattering volume and product species to measure velocity or other properties. The angular distribution of the scattered product can be measured by rotating the detector in the plane defined by two molecular beams. The mass spectrophotometer can also be set to measure a specific molecular mass so that the individual product molecules are detected. 

Experiments have also played a critical role in the development of potential energy surfaces and reaction dynamics. In the earliest days of quantum chemistry, experimentally determined thermal rate constants were available to test and improve dynamical theories. Much more detailed information can now be obtained by experimental measurement. Today experimentalists routinely use molecular beam and laser techniques to examine how reaction cross-sections depend upon collision energies, the states of the reactants and products, and scattering angles. 

Fig. 5. Rotational temperatures ofNO desorbing from Pt(l 11). The data are representative of data published for (x) neat thermal desorption , ( +) thermal desorption in the presence of coadsorbed C0 ° (solid squares) and (solid triangles) trapping/desorption in molecular beam scattering, (open triangle) reaction limited desorption from NO-NHj complexes, (open circle) and (open square) NHj oxidation reactions. The solid line is for full accommodation. The dashed curve represents results for translational energy measurements in direct inelastic scattering ...

Combining molecular beam techniques with laser state-resolved detection techniques has allowed state-resolved scattering measurements. 

State-resolved inelastic scattering for a wide range of incident conditions ( ), d,) are measured for this system by combining molecular beam techniques with (2 + 1) ion TOF REMPI detection of the scattered molecules [58]. Energy transfer parallel to the surface is measured from the Doppler broadening of the REMPI spectra. Trapping... 

---