Time scale, relaxation process

In this chapter we review experimental and theoretical studies of vibrational population relaxation in liquids. This review is complementary to our previous article in the same series, which treated vibrational phase relaxation (dephasing) in liquids due to vibrationally elastic interactions. A number of reviews have appeared recently on related subjects vibrational relaxation in solid matrices has been covered elsewhere, and several reviews have been devoted to experimental studies of picosecond time-scale relaxation processes in liquids. Diestler has recently reviewed theoretical studies of vibrational relaxation in liquids and solids the focus of the present article is rather different from that of Diestler. 

The preceding chapter closed with a discussion on kinetic methods which presume investigations of non-stationary time dependent relaxation processes of optical polarization of the angular momenta in a molecular ensemble. Another possibility, which also permits us to introduce a time scale, consists of the application of an external magnetic field. Indeed, since an angular momentum J produces a corresponding proportional (collinear) magnetic moment hj ... 

The scaling of time in relaxation processes is achieved by means of the Deborah number, which is defined as... 

We can summarize that the great advantage of NSE spectroscopy lies in investigations of aperiodic relaxation dynamics. On mesoscopic time scales well separated from atomic time scales, these processes show broad quasi-elastic features in frequency space, but a featureless decaying structure in the time domain. 

It follows that there are two kinds of processes required for an arbitrary initial state to relax to an equilibrium state the diagonal elements must redistribute to a Boltzmaim distribution and the off-diagonal elements must decay to zero. The first of these processes is called population decay in two-level systems this time scale is called Ty The second of these processes is called dephasmg, or coherence decay in two-level systems there is a single time scale for this process called T. There is a well-known relationship in two level systems, valid for weak system-bath coupling, that... 

Most chemically reacting systems tliat we encounter are not tliennodynamically controlled since reactions are often carried out under non-equilibrium conditions where flows of matter or energy prevent tire system from relaxing to equilibrium. Almost all biochemical reactions in living systems are of tliis type as are industrial processes carried out in open chemical reactors. In addition, tire transient dynamics of closed systems may occur on long time scales and resemble tire sustained behaviour of systems in non-equilibrium conditions. A reacting system may behave in unusual ways tliere may be more tlian one stable steady state, tire system may oscillate, sometimes witli a complicated pattern of oscillations, or even show chaotic variations of chemical concentrations. 

The simulations also revealed that flapping motions of one of the loops of the avidin monomer play a crucial role in the mechanism of the unbinding of biotin. The fluctuation time for this loop as well as the relaxation time for many of the processes in proteins can be on the order of microseconds and longer (Eaton et al., 1997). The loop has enough time to fluctuate into an open state on experimental time scales (1 ms), but the fluctuation time is too long for this event to take place on the nanosecond time scale of simulations. To facilitate the exit of biotin from its binding pocket, the conformation of this loop was altered (Izrailev et al., 1997) using the interactive molecular dynamics features of MDScope (Nelson et al., 1995 Nelson et al., 1996 Humphrey et al., 1996). 

Luminescence lifetime spectroscopy. In addition to the nanosecond lifetime measurements that are now rather routine, lifetime measurements on a femtosecond time scale are being attained with the intensity correlation method (124), which is an indirect technique for investigating the dynamics of excited states in the time frame of the laser pulse itself. The sample is excited with two laser pulse trains of equal amplitude and frequencies nl and n2 and the time-integrated luminescence at the difference frequency (nl - n2 ) is measured as a function of the relative pulse delay. Hochstrasser (125) has measured inertial motions of rotating molecules in condensed phases on time scales shorter than the collision time, allowing insight into relaxation processes following molecular collisions. 

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