Structural relaxation time many-molecule dynamics

A model having predictions that are consistent with the aforementioned experimental facts is the Coupling Model (CM) [21-26]. Complex many-body relaxation is necessitated by intermolecular interactions and constraints. The effects of the latter on structural relaxation are the main thrust of the model. The dispersion of structural relaxation times is a consequence of this cooperative dynamics, a conclusion that follows from the presence of fast and slow molecules (or chain segments) interchanging their roles at times on the order of the structural relaxation time Ta [27-29]. The dispersion of the structural relaxation can usually be described by the Kohlrausch-William-Watts (KWW) [30,31] stretched exponential function,... 

The fractional exponent KWW can be rewritten as (1 — n), where n is the coupling parameter of the CM. The breadth of the dispersion is reflected in the magnitude of n and increases with the strength of the intermolecular constraints. The dispersion and the structural relaxation time are simultaneous consequences of the many-molecule dynamics, and hence they are related to each other. The intermolecularly cooperative dynamics are built upon the local independent (primitive) relaxation, and thus a relation between the primitive relaxation time To and Ta is expected to exist. The CM does not solve the many-body relaxation problem but uses a physical principle to derive a relation between Ta and To that involves the dispersion parameter, n. This defining relation of the CM... 

Various types of power law relaxation have been observed experimentally or predicted from models of molecular motion. Each of them is defined in its specific time window and for specific molecular structure and composition. Examples are dynamically induced glass transition [90,161], phase separated block copolymers [162,163], polymer melts with highly entangled linear molecules of uniform length [61,62], and many others. A comprehensive review on power law relaxation has been recently given by Winter [164],... 

Molecular Motions and Dynamic Structures. Molecular motions are of quite general occurrence in the solid state for molecules of high symmetry (22,23). If the motion does not introduce disorder into the crystal lattice (as, for example, the in-plane reorientation of benzene which occurs by 60° jumps between equivalent sites) it is not detected by diffraction measurements which will find a seemingly static lattice. Such molecular motions may be detected by wide-line proton NMR spectroscopy and quantified by relaxation-time measurements which yield activation barriers for the reorientation process. In addition, in some cases, the molecular reorientation may be coupled with a chemical exchange process as, for example, in the case of many fluxional organometallic molecules. ... 

NMR is unique in that it can provide detailed and specific information on molecular dynamics in addition to structural information. The use of relaxation time measurements allows the relative mobility of individual atomic positions within a macromolecule to be determined. The d3mamic information obtained includes not only the rates or frequencies of internal motions but also their amplitudes. Such amplitudes are often expressed by order parameters. Not surprisingly, it is observed in many cases that the termini of proteins are more flexible than internal regions. More interestingly, NMR has provided a number of examples where internal loops in proteins have been shown to have dynamics that may be associated with their function. A good example of this is HIV protease, where NMR studies have identified reduced-order parameters in the flap region of the molecule that may reflect flexibility to allow entry of substrates or inhibitors into the active site. 

The spin-lattice relaxation time 7] as a function of temperature T in liquid water has been studied by many researchers [387-393], and in all the experiments the dependence T (T) showed a distinct non-Arrhenius character. Other dynamic parameters also have a non-Arrhenius temperature dependence, and such a behavior can be explained by both discrete and continuous models of the water structure [394]. In the framework of these models the dynamics of separate water molecules is described by hopping and drift mechanisms of the molecule movement and by rotations of water molecules [360]. However, the cooperative effects during the self-diffusion and the dynamics of hydrogen bonds formation have not been practically considered. 

If the molecule has dynamic motions on the timescale of the EPR experiment, this motion will lead to relaxation effects on the EPR line. Depending on the timescale and size of these motions, these effects may be observable directly in the cw-EPR spectrum or indirectly by pulsed EPR measurements of the relaxation times. In many cases, different dynamics may simultaneously contribute to the relaxation behavior of the electron spin system, as, for example, vibrational and rotational motion, conformational dynamics, phonon coupling to the frozen solvent, and nuclear spin dynamics. In these cases, it will be difficult to obtain specific information from these relaxation measurements. On the other hand, it is possible to highlight a specific time-scale window by the selection of pulse sequences and microwave frequencies that can lead, in favourable cases, to a direct relation between measured relaxation times and interesting molecular dynamics at the paramagnetic site. In these cases, very interesting molecular dynamical aspects of electron-transfer, catalytic, or photo-reactions, unobservable by other structural methods, can be studied directly by pulse-EPR techniques. 

Studies of the dynamic properties of peptides in the sofid state are not very common. The main reason for this is lack in many laboratories access to NMR instruments dedicated for sofid-state measurements. Moreover, lower resolution of sohd-state spectra sometimes can lead to uncertainty in interpretation of the results. On the other hand, in solution the dynamics is defined mainly by overall tumbling of the molecule. Thus, the site-specific structure variations, and consequently local dynamics, are difficult to observe. In the sohd-state, the overall tumbling of species is not present and insight into the local changes is facifitated and deeper. The important NMR observables such as the dipolar and quadrupolar couplings as well CSA interactions in the condensed matter are not averaged by overall tum-bhng and slow internal dynamics. These parameters, combined with measurements of diflerent relaxation times, provide precise information about local molecular dynamics of peptides. 

It is worth remarking that this description implicitly assumes that the i = 1 case is associated with a zero-curvature C layer, which could be provided either by a lamellar liquid-crystal structure with alternating O and W flat layers, or a zero-curvature surface of the Schwartz type, or as a transient and fluctuating combination of Si and S2 structures (see Fig. 9). It is now well recognized that middle-phase microemulsions, that are in equilibrium with both oil and water excess phases, exhibit zero-curvature bicontinuous structures [20-22] that are not far from a mixture of Si and S2 swollen micelles predicted by Winsor. Because the relaxation time for a surfactant molecule to enter or to leave the microemulsion film is of the order of 10 s, it is obvious that these structures could be considered to be in dynamic equilibrium with a fast renewal rate, with many fluctuations so that no clear-cut Si or S2 structure actually exists for more than a very short time, but rather as some average statistical occurrence. 

---