Scattering as a probe of collision dynamics

We begin with an introduction to this method as applied to elastic (energy-state unchanging) collisions. First we look at scattering using classical mechanics and then we provide a quantum mechanical view. 

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To sum up, elastic scattering measurements serve as a probe of the collision dynamics and can reveal detailed information on the intermolecular potential. But to do a complete job we cannot overlook quantal effects. 

In liquids and dense gases where collisions, intramolecular molecular motions and energy relaxation occur on the picosecond timescales, spectroscopic lineshape studies in the frequency domain were for a long time the principle source of dynamical information on the equilibrium state of manybody systems. These interpretations were based on the scattering of incident radiation as a consequence of molecular motion such as vibration, rotation and translation. Spectroscopic lineshape analyses were intepreted through arguments based on the fluctuation-dissipation theorem and linear response theory (9,10). In generating details of the dynamics of molecules, this approach relies on FT techniques, but the statistical physics depends on the fact that the radiation probe is only weakly coupled to the system. If the pertubation does not disturb the system from its equilibrium properties, then linear response theory allows one to evaluate the response in terms of the time correlation functions (TCF) of the equilibrium state. Since each spectroscopic technique probes the expectation value... 

We have seen in Section 2.2.5 how the differential elastic cross-section 1(9) serves as a sensitive probe of the dynamics of the collision of stmctineless particles. In a similar fashion one can introduce the differential reactive cross-section /r(0), except that here we mean the number ofproduct molecules scattered atthe (center-of-mass) angle 6 (per unit time and unit sohd angle) divided by the incident flux of reactant molecules. In other words, we write Eq. (3.5) as... 

Molecular beam experiments, in which molecules of well-defined translational and vibrational energy can be scattered by surfaces, probe details of the reaction path across the potential energy surface. Here we discuss the dynamics of hydrogen dissociation based on theoretical calculations which simulate the collisions of molecules with a surface as occurring in molecular beam experiments. A potential energy diagram for the H2 dissociation is shown in Figure 6.12. 

However, one can not simply accept the Moore model in favor of BSH model since the latter is formulated on a more sound dynamical basis. The only weak point of the BSH model is the assumption that the three-dimensional collision can be reduced to a one-dimensional scattering problem in the direction of the gradient of the potential energy surface. This assumption can be probed by studying an alternative model that chooses a different mode as responsible for the vibrational deactivation. 

Strongly non-linear rheology is characteristic of soft matter. In simple fluids, it is difficult to observe any deviations from Newtonian behavior, which is well described by the hydrodynamic equations of motion with linear transport coefficients that depend only on the thermodynamic state. Indeed, Molecular Dynamics simulations [9] have revealed that a hydrodynamic description is valid down to astonishingly small scales, of the order of a few collisions of an individual molecule. This means that one would have to probe the system with very short wave lengths and very high frequencies, which are typically not accessible to standard experiments (with the exception of neutron scattering [10]), and even less in everyday life. However, in soft-matter systems microstructural components (particles and polymers for example) induce responses that depend very much on frequency and length scale. These systems are often referred to as complex fluids. ... 

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