Molecular beams velocity selection

Figure 5.9 shows the time evolution of the radii of selected 2D spherulites from Fig. 5.8. We observe that the process is non-linear and accelerated, (fR/df > 0. It is also interesting to notice that, at a given time, the radial growth velocity Ur = dR/dt (slope) is nearly the same for all spherulites, which implies that it depends on the deposition time and certainly not on the radius of the spherulites. In the case discussed here the thickness of the film is increasing with time because of continuous exposure to the molecular beam. The non-linearity is more pronounced at the beginning of the experiment (roughly between 250 and 350 s) and the velocity nearly tends towards an asymptotic value, so that 2D spherulites that are formed last show almost linear growth.

The subject of molecular beam kinetics is very extensive and in this section, therefore, we will deal only briefly with the relevant aspects of the topic. Molecular beam sources are often thermal, operating as a flow system with a gas or a vapour from a heated oven. The velocity distribution of species in such beams is Maxwell—Boltzmann in form. For many experiments, this does not provide sufficient definition of initial translational energy and some form of velocity selection may be used [30], usually at the expense of beam intensity. 

Figure 1.2 Representation of a simple crossed-molecular-beam source [16]. The primary beam effusing from an oven source (A) is velocity selected (S) and then crosses the thermal beam issuing from a second source (B). This diagram shows the detector (D) positioned at the lab angle 0.

Blythe, Grosser, and Bernstein [151 ] have used crossed molecular beams to observe the J = 2 - 0 rotational deexcitation process in D2. A velocity-selected atomic beam of potassium was made to impinge on a modulated Da beam from an effusive (T = I8PK) source. The scattered K atoms were detected by surface ionization on a hot Pt-W ribbon, from which the ions were drawn into an electron multiplier equipped with lock-in amplification. 

In principle, the diffraction patterns can be quantitatively understood within the Fraunhofer approximation of Kirchhoff s diffraction theory as described in any optics textbook (e.g., [Hecht 1994]). However, Fraunhofer s optical diffraction theory misses an important point of our experiments with matter waves and material gratings the attractive interaction between the molecule and the wall results in an additional phase of the molecular wavefunction [Grisenti 1999], Although the details of the calculations are somewhat involved2, the qualitative effect of this attractive force on far-field diffraction can be understood as a narrowing of the real slit width to an effective slit width [Briihl 2002], For our fullerene molecules the reduction can be as big as 20 nm for the unselected molecular beam and almost 30 nm for the slower, velocity selected beam. The stronger effect on slower molecules is due to the longer and therefore more influential interaction between the molecules and the wall. 

An effusive beam of F atoms was produced by thermally dissociating F2 at 2.0 torr and 920 K in a resistively heated nickel oven. The F beam was velocity selected with a FWHM velocity spread of 11%. The H2 beam was produced by a supersonic expansion of 80 psig through a 70 micron orifice at variable temperatures with a FWHM spread of 3%. Rotational state distributions of H2 in the beam were studied previously using molecular beam photoelectron... 

The beam intensities of oriented molecules using hexapole electric field, however, turn out to be poor because the state selection requires a very large flight-length as compared with conventional molecular beam set-ups. In order to increase the beam intensity, one may propose a way to increase the stagnation pressure of the nozzle. However, the characteristics of the molecnlar beam snch as stream velocity, rotational temperature and the size distribntion of clnsters are generally changed [41]. Motivation of the study of Ref [2] has been to develop a new type of electrostatic state-selector in order to prodnce an intense oriented molecnlar beam. Basic idea of this experiment has been that the beam intensity shonld be simply proportional to the nnmber of beam lines if the molecnlar beams can be focnsed on a point in space. 

The experimental conditions for the spectroscopy of reactive collisions are quite similar to those for the study of inelastic collisions. They range from a determination of the velocity-averaged reaction rates under selective excitation of reactants in cell experiments to a detailed state-to-state spectroscopy of reactive collisions in crossed molecular beams (Sect. 8.5). Some examples shall illustrate the state of the art ... 

The techniques discussed in Sects. 8.2-S.4 allowed the measurement of absolute rate constants of selected collision-induced transitions, which represent integral inelastic cross sections integrated over the angular distribution and averaged over the thermal velocity distribution of the collision partners. Much more detailed information on the interaction potential can be extracted from measured differential cross sections, obtained in crossed molecular beam experiments [958, 1074, 1075]. 

For the reaction A + BC AB + C, the partition of the total angular momentum J between the initial and flnal momentum of the colliding particles L, V and the rotational momenta of the reactant and product molecules j,f has been shown to be very useful in the diagnosis of the reaction dynamics. The main problem is that even if one lets two molecular beams collide with well-defined speeds and directions, one cannot select the impact parameter and its azimuthal orientation about the initial relative velocity vector. A currently popular way to circumvent this lack of resolution is to use vector correlations, particularly in laser studies, photofragmentation dynamics and, more generally, the so-called field of dynamical stereochemistry . One of the most commonly used correlations is that between the product rotation angular momentum and the initial and final relative velocity vectors. 

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