Replacement collision

As with most methods for studying ion-molecule kinetics and dynamics, numerous variations exist. For low-energy processes, the collision cell can be replaced with a molecular beam perpendicular to the ion beam [106]. This greatly reduces the thennal energy spread of the reactant neutral. Another approach for low energies is to use a merged beam [103]. In this system the supersonic expansion is aimed at the tluoat of the octopole, and the ions are passed tluough... 

For electron-ion or ion-ion collisions, the plane waves exp(i/c. R) are simply replaced by Coulomb waves to... 

An explanation which is advanced for these reactions is that some molecules collide, but do trot immediately separate, and form dimers of dre reactant species which have a long lifetime when compared with the period of vibration of molecules, which is about 10 seconds. In the first-order reaction, the rate of tire reaction is therefore determined by the rate of break-up of tirese dimers. In the thud-order reaction, the highly improbable event of a tluee-body collision which leads to the formation of tire products, is replaced by collisions between dimers of relatively long lifetime widr single reactant molecules which lead to tire formation of product molecules. 

If the interval r is large compared with the time for a collision to be completed (but small compared with macroscopic times), then the arguments of the distribution functions are those appropriate to the positions and velocities before and after a binary collision. The integration over r2 may be replaced by one over the relative distance variable r2 — rx as noted in Section 1.7, collisions taking place during the time r occur in the volume g rbdbde, where g is the relative velocity, and (6,e) are the relative collision coordinates. Incomplete collisions, or motions involving periodic orbits take place in a volume independent of r when Avx(r) and Av2(r) refer to motion for which a collision does not take place (or to the force-field free portion of the... 

For strong collisions (y = 0), is still equal to //to, but qj does not exist and the diffusion mechanism of rotational relaxation is replaced by a hopping mechanism. 

C05-0068. Consider the figure appearing in Problem 5.25. (a) The monatomic gas shown in the figure is replaced by an equal number of molecules of a diatomic gas, all other conditions remaining the same. What is the pressure inside the container Explain in terms of molecular collisions, (b) The external pressure is reduced to 0.75 atm, and the piston moves as a result. Redraw the sketch to show the new situation. 

In order to reduce the complexity of the problem, several approximation schemes have been developed. In the BGK model, the collision integral is replaced by a simple local term ensuring that the well-known Maxwell distribution is reached at thermal equilibrium [16]. The linearization method assumes that the phase space distribution is given by a small perturbation h on top of a (local) Maxwell distribu-tion/o (see, e.g., [17, 18]) ... 

Multiparticle collisions are carried out at time intervals x as described earlier. We can write the equation of motion for the phase space probability density function as a simple generalization of Eq. (15) by replacing the free-streaming operator with streaming in the intermolecular potential. We find... 

Hybrid MPC-MD schemes may be constructed where the mesoscopic dynamics of the bath is coupled to the molecular dynamics of solute species without introducing explicit solute-bath intermolecular forces. In such a hybrid scheme, between multiparticle collision events at times x, solute particles propagate by Newton s equations of motion in the absence of solvent forces. In order to couple solute and bath particles, the solute particles are included in the multiparticle collision step [40]. The above equations describe the dynamics provided the interaction potential is replaced by Vj(rJVs) and interactions between solute and bath particles are neglected. This type of hybrid MD-MPC dynamics also satisfies the conservation laws and preserves phase space volumes. Since bath particles can penetrate solute particles, specific structural solute-bath effects cannot be treated by this rule. However, simulations may be more efficient since the solute-solvent forces do not have to be computed. 

The effect of hydrodynamic interactions on polymer collapse has also been studied using MPC dynamics, where the polymer beads are included in the multiparticle collision step [28, 84]. Hydrodynamic interactions can be turned off by replacing multiparticle collisions in the cells by sampling of the particle velocities from a Boltzmann distribution. Collapse occurs more rapidly in the... 

At low cM, the rate-determining step is the second-order rate of activation by collision, since there is sufficient time between collisions that virtually every activated molecule reacts only the rate constant K appears in the rate law (equation 6.4-22). At high cM, the rate-determining step is the first-order disruption of A molecules, since both activation and deactivation are relatively rapid and at virtual equilibrium. Hence, we have the additional concept of a rapidly established equilibrium in which an elementary process and its reverse are assumed to be at equilibrium, enabling the introduction of an equilibrium constant to replace the ratio of two rate constants. 

The stationary condition allows p[0)(t) to be replaced by pW (t ) in the collision term (40) and the upper limit of the integration over time to be extended to infinity, because the instant t when the system is stationary is very far removed from the initial instant. One then obtains ... 

This basically means that two instruments have been linked together. The first analyser can replace the traditional chromatographic separation step and is used to produce ions of chosen m/z values. Each of the selected ions is then fragmented by collision with a gas, and mass analysis of these product ions effected in the second analyser. The resulting mass spectrum is used for their identification. The potential combinations of the various magnetic sector and quadrupole instruments to form such coupled systems is considerable. Ion traps may also be operated in a tandem MS mode. 

As in scattering theory in general, one can treat the role of V in either a time independent or a time dependent point of view. The latter is simpler if the perturbation V is either explicitly time dependent or can be approximated as such, say by replacing the approach motion during the collision by a classical path. Algebraic methods have been particularly useful in that context,2 where an important aspect is the description of a realistic level structure for H0. Figure 8.3 is a very recent application to electron-molecule scattering. 

LITs capable of scanning, axial or radial excitation of ions, and precursor ion selection for MS/MS experiments [118,134-136] have lately been incorporated in commercial mass spectrometers (Fig. 4.39). The replacement of Q3 in a QqQ instrument with a scanning LIT, for example, enhances its sensitivity and offers new modes of operation (Applied Biosystems Q-Trap). Introduction of a scanning LIT [118,135] as MSI in front of an FT-ICR instrument (Thermo Electron LTQ-FT) shields the ultrahigh vacuum of the FT-ICR from collision gas and decomposition products in order to operate under optimum conditions. In addition, the LIT accumulates and eventually mass-selects ions for the next cycle while the ICR cell is still busy with the previous ion package. 

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