Hindered Rotation and Diffusion

As already mentioned, in some molecular crystals, a hindered or nearly free rotation of entire molecules is observed, e.g. of benzene molecules in crystals of benzene, or of molecular groups, e.g. of CH3 groups in crystals of methyl naphthalene. These motions are stochastic and are termed pseudorotations or reorientations. These two terms denote the two limiting approximations, that of free rotation and that of a fixed orientation of the molecules or molecular groups. Experimental methods which have proved useful for the investigation of these stochastic motions are nuclear-spin magnetic resonance (NMR) [24] and quasielastic neutron scattering [35, 36]. 

Furthermore, molecules in molecular crystals can diffuse from their lattice sites to a neighbouring vacancy. This translational or seU-diffusion has been investigated in a number of molecular crystals, e.g. using radioactive tracer molecules [31, 32]. 

In the following sections, we treat briefly or sketch the relevant observable quantities in NMR spectroscopy for the investigation of rotational motions and the examples of molecular or molecular-group rotations mentioned, as well as the tracer methods and their results for translational diffusion. 

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Photolysis of 2,4-diphenylpentan-3-one (meso and d, 1, 6) produces different ratios of products26) in homogeneous and aqueous micellar solutions (Scheme VI). While DPE is the major product in both homogeneous and micellar solutions, only in micelles is the recovered starting material isomerized (meso - d,l d,l - meso). This indicates that while diffusion out of the micelle is hindered, rotation and diffusion inside the micelle is still facile. 

Ha T, Glass J, Enderle T, Chemla D S and Weiss S 1998 Hindered rotational diffusion and rotational ]umps of single molecules Phys. Rev. Lett. 80 2093-7... 

When the solution is dilute, the three diffusion coefficients in Eq. (40a, b) may be calculated only by taking the intramolecular hydrodynamic interaction into account. In what follows, the diffusion coefficients at infinite dilution are signified by the subscript 0 (i.e, D, 0, D10> and Dr0). As the polymer concentration increases, the intermolecular interaction starts to become important to polymer dynamics. The chain incrossability or topological interaction hinders the translational and rotational motions of chains, and slows down the three diffusion processes. These are usually called the entanglement effect on the rotational and transverse diffusions and the jamming effect on the longitudinal diffusion. In solving Eq. (39), these effects are taken into account by use of effective diffusion coefficients as will be discussed in Sect. 6.3. 

To explain the Green function method for the formulation of Dx, D and D, of the fuzzy cylinder [19], we first consider the transverse diffusion process of a test fuzzy cylinder in the solution. As in the case of rodlike polymers [107], we imagine two hypothetical planes which are perpendicular to the axis of the cylinder and touch the bases of the cylinder (see Fig. 15a). The two planes move and rotate as the cylinder moves longitudinally and rotationally. Thus, we can consider the motion of the cylinder to be restricted to transverse diffusion inside the laminar region between the two planes. When some other fuzzy cylinders enter this laminar region, they may hinder the transverse diffusion of the test cylinder. When the test fuzzy cylinder and the portions of such other cylinders are projected onto one of the hypothetical planes, the transverse diffusion process of the test cylinder appears as a two-dimensional translational diffusion of a circle (the projection of the test cylinder) hindered by ribbon-like obstacles (cf. Fig. 15a). 

These thermodynamic approaches to hydrophobic effects are complemented by spectroscopic studies. Tanabe (1993) has studied the Raman spectra manifested during the rotational diffusion of cyclohexane in water. The values of the diffusion coefficients are approximately half those expected from data for other solvents of the same viscosity, and the interpretations made are in terms of hindered rotation arising from the icebergs presumably formed (c/. Frank and Evans) around the cyclohexane. 

In a perfect tetrahedral geometry, the length of the proton jump is equal 2rQH sin (10472) = 1.6 A, because the rotation is around the oxygen atom, the distance rOH is 1 A and the angle HOH is around 104°. So, this jump is, more exactly, a hindered rotation of the whole molecule, where the moving H atom remains attached to the same molecule. This is what I call a molecular diffusion mechanism due to rotational jumps. Within this picture, the permanent dipole oscillates with librational motions and has a different orientation at each jump, but the molecule remains neutral. 

As temperature decreases ASW and WAW signal intensity gets somewhat smaller, which sng-gests that these types of water can be partially frozen. When ice formation process takes place, coordination number of water molecules inside of the crystallites is eqnal to four. Therefore for the nucleation process of ASW and WAW, the formation of 3D water clnsters is necessary. The formation of 3D crystallites in the narrow slits is hindered by steric factors. Before freezing ASW and WAW molecules possess certain mobility, which assists formation of ordered strnctnres of bound water from amorphous to crystalline as a result of rotational and translational diffusion of molecules. It can be suggested that ASW- and WAW-formed ice crystals have small size and slightly... 

Ha, T, Glass, J, Enderle, T, Chemla, DS, and Weiss, S, Hindered rotational diffusion and rotational jumps of single molecules. Physical Review Letters 80 (1998) 2093-2096. 

The termination rate constant for NVK does not satisfy the Arrhenius relationship and becomes markedly reduced when the temperature is lowered to —30 °C. This result has been attributed to a hindered rotation of the stilf PVK macroradicals, which markedly retards the diffusion-controlled termination reaction. 

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