Correlations between structure and dynamics

These spectroscopic and theoretical developments have stimulated the recent advances on electron-transfer dynamics at ITIES. In addition to the correlation between structure and dynamics of charge transfer, fundamental problems in connection with the energetics of ET reactions remain to be fully addressed. We shall consider these problems primarily before discussing kinetic aspects in full detail. 

In another series of experiments [149] the correlation between structure and dynamics was investigated on dilute solutions of 12-arm PS star systems (Mw = 14.9 104 g/mol) in d-tetrahydrofurane, where either only one or all 12 arms were protonated (labelled). 

A unique feature of SM-FRET experiments is their ability to provide information on the correlations between structure and dynamics. One way of extracting this information is by monitoring the distribution of (R)tw as a function of Tw [30] Correlations between conformational structure and the time scale on which it moves can be obtained from the different values of Tw at which different subsets of the ensemble which are characterized by different values of R reach the ergodic limit. 

Information on the correlation between structure and dynamics can also be obtained from the correlation between D(j Tw) and (R)twU) K l- Eq. (8)]. As mentioned above, D( j Tw ) follows a turnover behavior as a function of Tw, and the value of Tw at the turnover corresponds to a characteristic time scale of conformational dynamics. Thus, one may obtain information on the correlation between structure and dynamics by averaging L)(j] Tw) over the subset of conformations that correspond to the same value of (R)twU)> instead of over the ensemble of all the conformations. We will denote this conditional average by D((R)tw). 

A unique feature of SM-FRET experiments is their ability to provide information on the correlations between structure and dynamics. One way of extracting this information is by monitoring the distribution of (R)tw as a... 

Unfolded state a is characterized by a wide uni-modal and asymmetrical distribution of R, with a slow rise and a sharp drop. The distribution becomes narrower and more symmetrical when the averaging time window is larger than the characteristic time scale of conformational dynamics in this unfolded state. This indicates a correlation between structure and dynamics, where conformations that correspond to shorter R move on faster time scales. 

The correlation between structure and dynamics also persists in the midpoint and unfolded states. In the midpoint states D((R)tw) shows two minima, at the positions of the maxima in the corresponding R distributions of Fig. 4. In the unfolded states, D((R)tw) exhibits wide minima that coincide with the wide maxima of the corresponding R distribution of Fig. 4. 

The universal relaxation mode spectrum a correlation between structure and dynamics... 

Yuan, Q., Yao, J., Huang, L., Chen, X., Shao, Z., 2010. Correlation between structural and dynamic mechanical transitions of regenerated silk fibroin. Polymer 51, 6278-6283. 

The correlations between structures and bowl-to-bowl inversion barriers provide information on the inversion dynamics and design of a static bowl. Increase in the curve of buckybowls may also increase their molecular dipole moment. A high inversion barrier conveys a configurational stability to a chiral buckybowl, avoiding loss of enantiopurity through the bowl-inversion racemization process. 

Relationship Between Structure and Dynamics From the data reported above of the coordination number and the diffusivity, it is evident at a qualitative level that the diffusivity in silicon is correlated with coordination number, with higher coordination number corresponding to larger diffusivity. It has been shown in Ref. [32] that the diffusivity depends quite strongly on coordination number and has only a weak-temperature dependence (see Fig. 31). Scaling the diffusivity to... 

Rather than having a situation where a unit cell consists of one or more molecules, as in small molecule crystals, the situation is reversed a single molecule participates in many unit cells. This has significant ramifications for the correlations, both structural and dynamical, between unit cells. Second, the periodicity of the crystal lattice usually implies a periodicity for the conformation of the polymer chain itself. This condition places a severe restriction on the conformation space available to the chain in a crystalline solid. Polymer chains in crystals are more appropriately described as helices rather than coils. A helix conformation consists of a regular repetition of the torsion angles characteristic of a small subsection of the chain, the helix repeat unit [4,5]. Each helix has an axis and a handedness of rotation (the direction in which the chain backbone winds around the helix axis). The helix itself is characterized by the translational displacement parallel to the helix axis, d, and the angle of rotation about the helix axis, a, executed by a single helix repeat unit. The coordinates of Eq. (1) may be expressed in terms of these helical parameters as follows ... 

One of the first studies of multiple ions at the water/solid interface was by Spohr and Heinzinger, who carried out a simulation of a system of 8 Li" and 81" ions dissolved in 200 water molecules between uncharged flat Lennard-Jones walls.However, the issues discussed in their paper involved water structure and dynamics and the single-ion properties mentioned earlier. No attempt was made to consider the ions distributions and ion-ion correlations. This work has recently been repeated using more realistic water-metal potentials. ... 

B. Audit, C. Vaillant, A. Arneodo, Y. d Aubenton-Carafa, and C. Thermes, Long-range correlations between DNA bending sites Relation to the structure and dynamics of nucleo-somes. J. Mol. Biol. 316, 903-918 (2002). 

In Chapters 7 and 8, one-dimensional NOE experiments and a few two-dimensional experiments are presented. Strategies to minimize adverse paramagnetic effects are discussed, as well as ways to exploit such effects to extract structural and dynamic properties. Partial orientation and cross correlation between the Curie magnetic moment relaxation and nuclear dipolar relaxation are also discussed. Chapter 9 deals with the experimental strategies necessary to achieve the highest level of performance in NMR of paramagnetic compounds in solution. 

The rate constant for the reentry is of the magnitude expected for a diffusion-controlled reaction as in Eq. (5.6). This means that the exit rate is determined by the partition coefficient of the solubilizate in its triplet state between the micelle and the aqueous solution. Table 5.2 shows the exit rate constants k for several systems. The water solubilities of the probes are also given to show the correlation between kt and the solubility in water. These studies give further support to the view that the micelle has a very dynamic structure, which makes it easy for the solubilizate to enter and leave the aggregate. 

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