Velocity translation

Although this book is devoted to molecular fluorescence in condensed phases, it is worth mentioning the relevance of fluorescence spectroscopy in supersonic jets (Ito et al., 1988). A gas expanded through an orifice from a high-pressure region into a vacuum is cooled by the well-known Joule-Thomson effect. During expansion, collisions between the gas molecules lead to a dramatic decrease in their translational velocities. Translational temperatures of 1 K or less can be attained in this way. The supersonic jet technique is an alternative low-temperature approach to the solid-phase methods described in Section 3.5.2 all of them have a common aim of improving the spectral resolution. 

For LC, the second term in Eq. (12) is often negligible because liquid diffusion coefficients are low ( 10 times lower than for gases). Furthermore, for LC, the parameter A depends on v, and A and C are coupled. For these reasons, LC plate heights increase with velocity for all reasonable operating values of v. One might be tempted to use low velocities in LC to achieve low plate heights however, lower velocities translate into longer retention times. 

Before actually discussing the various algorithms, a few general observations are in order. Suppose that we know the values of the molecular coordinates and velocities (translational and rotational) at time t that is, we have specified the point in phase space. The object of any integration procedure is... 

In the best experiments the translational energy is directly determined by mechanically chopping the beam so that a short pulse of particles is admitted to the detector chamber. The product intensity is then measured as a function of the flight time from the chopper to the detector, thereby giving the velocity distribution. Earlier techniques used mechanical devices to identify and select products of a certain velocity. Translational energy distributions also have been obtained without direct measurement of... 

A bimoleciilar reaction can be regarded as a reactive collision with a reaction cross section a that depends on the relative translational energy of the reactant molecules A and B (masses and m ). The specific rate constant k(E ) can thus fonnally be written in tenns of an effective reaction cross section o, multiplied by the relative centre of mass velocity... 

Magnetic sector instruments typically operate with ion sources held at a potential of between 6 and 10 kV. This results in ions with keV translational kinetic energies. The ion kinetic energy can be written as zt V = Ifur and thus the ion velocity is given by the relationship... 

Molecular beam sample introduction (described in section (Bl.7.2)). followed by the orthogonal extraction of ions, results in improved resolution in TOP instruments over eflfrisive sources. The particles in the molecular beam typically have translational temperatures orthogonal to the beam path of only a few Kelvin. Thus, there is less concern with both the initial velocity of the ions once they are generated and with where in the ion source they are fonned (since the particles are originally confined to the beam path). 

Figure B2.3.6. CM angle-velocity contour plot for the F + D2 reaction at an incident relative translational energy of 1.82 kcal mol [26], Contours are given at equally spaced intensity intervals. This CM differential cross section was used to generate the calculated laboratory angular distributions given in figure B2.3.4. (By pennission from AIP.)...

Figure B2.5.12 shows the energy-level scheme of the fine structure and hyperfme structure levels of iodine. The corresponding absorption spectrum shows six sharp hyperfme structure transitions. The experimental resolution is sufficient to detennine the Doppler line shape associated with the velocity distribution of the I atoms produced in the reaction. In this way, one can detennine either the temperature in an oven—as shown in Figure B2.5.12 —or the primary translational energy distribution of I atoms produced in photolysis, equation B2.5.35.

This actually translates into a fairly simple algorithm, based closely on the standard velocity Verlet method. Written in a Fortran-like pseudo-code, it is as follows. At tire start of the run we calculate both rapidly-varying (1) and slowly-varying (F) forces, then, in the main loop ... 

C3.3.4.2 VELOCITY PROFILES FOR TRANSLATIONAL-ROTATIONAL EXCITATION OF THE BATH... 

Coordin ates of atom s can he set by n orm al translation orrotation of HyperCh cm molecules, fo set initial velocities, however, it is necessary to edit th e H l. file explicitly. The tin it o f velocity in the HIN file is. An gstrom s/picosecon d.. Areact.hin file and a script react.scr are in eluded with HyperChem to illustrate one simple reacting trajectory. In order to have these initial velocities used in a trajectory the Restart check box of the Molecular Dynamics Option s dialog box must he checked. If it is n ot, the in itial velocities in the HIN file will be ignored and a re-equilibration to the tern peratiire f of th e Molecular Dyn am ics Option s dialog box will occur. This destroys any imposed initial conditions on the molecular dynamics trajectory. 

As stated earlier, within C(t) there is also an equilibrium average over translational motion of the molecules. For a gas-phase sample undergoing random collisions and at thermal equilibrium, this average is characterized by the well known Maxwell-Boltzmann velocity distribution ... 

The kinetic or translational energy of the ions is equal to the work done on moving the charged species through the potential, V, i.e., l/2mjVi = zV and l/2m2V2 = zV, where z is the charge on the ions and Vj, V2 are their final velocities. From this, we obtain Equations 33.1 and 33.2. 

Translational spectroscopy. A technique to investigate the distribution of the velocities of product ions from ion/neutral reactions. 

The speed at which a sphere roUs down a cylindrical tube filled with a fluid or down an angled plate covered with a film of the fluid also gives a measure of viscosity. For the cylindrical tube geometry, equation 35, a generalized form of the Stokes equation is used for any given instmment, where p is the translational velocity of the rolling sphere and k is the instmment constant determined by caUbration with standard fluids. 

---