Diffusion constants, rotational

Fig. 18. Plots of rotational diffusion constants D (closed squares), D (closed circles), and Dr (closed triangles), as well as jump constants kx (open squares) and k2 (open circles) versus the temperature in the nematic phase of Azpac. Solid lines are to guide the eyes only. (Adapted from Ref. 179.)...

Size of the particle. Assuming a spherical shape, the value of the rotational diffusion constant Dp can provide an average radius using the following relationship ... 

Rotational diffusion constant Density extrapolated to 20°C, water Density... 

The rotational diffusion constant in water at 25° and neutral pH as measured by electric birefringence (258) is 230 X 105 sec-1 or 0.73 X HT8 sec as a relaxation time. For a hydrodynamic ellipsoid of dimensions 66 X 22 A and a molecular weight of 14,000, the calculated relaxation tilde is 0.72 X 10-8 sec. However, the apparent asymmetry of the molecule from the X-ray structure corresponds to an axial ratio of no more than 2 1 rather than 3 1. 

The interest in alkaloids of the nicotine group continues. Convenient syntheses of 7V-CD3-labelled nicotine and nicotine analogues have been described.38 The 13C n.m.r. spin-lattice relaxation times of nicotine have been analysed in terms of anisotropic rotational diffusion constants. The results agree best with a dihedral angle of H(2 )-C(2 )-C(3)-C(2) of ca 0°.39 Dithiodinicotyrine , obtained... 

The Euler angles between both principal-axis systems may be calculated as optimizable parameters simultaneously with the rotational diffusion constants in a... 

A more rigorous treatment of the variable-temperature, 3C Tl data has been used to describe the overall molecular motion of the glucose derivative, namely 1,6-an-hydro-/3-D-glucopyranose (31) in solution.147 This rigid molecule contains a number of nonequivalent 13C- H vectors and is amenable to a rigorous quantitative treatment by means of Eq. 29. Table VI summarizes the diagonal elements of the rotational diffusion tensor, that is, the rotational diffusion constants Dx,Dy, and Dz obtained upon diagonalization of the rotational diffusion tensor with respect to... 

Rotational Diffusion Constants (x 1010 s" ), Euler Angles, Activation Energies (kj/mol), D Values (x 1012 s" ), Correlation Coefficients (R), and Quotients of the Rotational Diffusion Constants for Compound 31... 

For the set of the Euler angles a = 50°, /3 = 60°, y = 40°, the order of the rotational diffusion constants is Dy> Dz> Dx. This trend is also reflected in the quotients of the rotational diffusion constants, DJDX and DJDX (Table VI), which describe the anisotropy of the rotational diffusion in solution. The principal axes of the rotational diffusion tensor corresponding to the aforementioned set of the Euler angles is shown graphically in Fig. 12. 

Eexp(iut) with effects of torques of the surroundings represented by a rotational diffusion constant D. This model leads to an expression of the form... 

Four different models for the molecular dynamics have been tested to simulate the experimental spectra. Brownian rotational diffusion and jump type diffusion [134, 135] have been used for this analysis, both in their pure forms and in two mixed models. Brownian rotational diffusion is characterized by the rotational diffusion constant D and jump type motion by a residence time t. The motions have been assumed to be isotropic. In the moderate jump model [135], both Brownian and jump type contributions to the motion are eou-pled via the condition Dx=. ... 

S. Broersma, Rotational diffusion constant of a cylindrical particle, J. Chem. Phys., 32 (1960) 1626-1631, 1632-1635... 

D = (Di + D2 + D3)/3, the mean rotational diffusion constant given that Di, D2 and D3 are the rotational diffusion constants around the three ptinc al axes labelled 1, 2 and 3. 

Here D, is the rotational diffusion constant and is given by the Einstein law as 1 kT... 

An important detail of the theory and its experimental verification is the fact that our setup uses isotropic detection (no polarizers) together with polarized excitation. With 2n or 47t detection a correct description of orientational correlation with three eigen- values of the diffusion tensor is obtained. They are sums of the rotational diffusion constants D, Dy, around the individual axes of the rotational ellipsoid [5,7] 2Dz + 4 Dx,y, 5Dz + D y. 

The rotational diffusion constant may be obtained by introducing a constant rotational motion (33) ... 

The rotational diffusion of molecules is investigated by exciting their fluorescence with short pulses of polarized light and by observing the time dependence of the polarized emission. For a symmetric body the anisotropy of the emission (Fig. 9) is characterized by 3 rotational relaxation times each of which is a function of the rotational diffusion constants around the main axes of rotation. The corresponding amplitudes a depend on the position of the absorption vector and the emission vector within the coordinates of the rotating unit. 

The new parameters for restricted anisotropic rotational diffusion are the angular amplitude over which rotation diffusion occurs, Z, and the rotational diffusion constant for restricted anisotropic rotational diffusion, D- r. 

Assuming a spherical shape for the fluorescent molecule, the degree of change in the rotational Brownian motion is given by Eq. (3.25), where v is the volume of the spherical molecule, r)0 is the solvent viscosity, r is the fluorescence lifetime of the chromophore, and T is the temperature. The values of r0 and r/v can be obtained from a plot of Mr versus T/rj0. Thus, if the fluorescence lifetime of the chromophore is known, it is possible to determine the hydrodynamic volume of the rotating molecule and its rotational diffusion constant D,. This data treatment is known as the Perrin-Weber approximation,25 after the two scientists who first derived the equations in the case of protein chromophores. 

---