Frictional coefficient, rotational

Mean rotational relaxation time t extrapolated to infinite dilution allows computation of the rotational diffusion coefficient 0 and rotational friction coefficient f of an isolated macromolecule from the relations ... 

Exactly the same procedure can be carried through for the angular momentum memory function.68 Then the rotational friction coefficient is... 

The rotational friction coefficient, is related to the viscosity of the medium, tj, and the radius, a, of the molecule through the equation... 

The rotational friction coefficient of a spherical molecule in solution is calculated applying the Navier-Stokes equation for a continuum solvent with a position-dependent viscosity as a model of "microscopic viscosity." The rotational friction coefficient decreases with decreasing surface viscosity. The results are compared with the translational fnction and viscosity B coefficients which are previously obtained from the same model. The B coefficient is most sensitive to a local viscosity change The Gierer-Wirtz model overestimates the effect of the "microscopic viscosity" on the translational friction coefficient comparing with the present results... 

Figure 1 shows the calculated rotational friction coefficient as a function of the parameter a in the range of 0 < a < 0.5. Since the idea of the "microscopic viscosity" is usually employed to explain the friction coefficient smaller than that predicted by the uniform continuum... 

Figure 2. Correlations (a) betw een the translational and the rotational friction coefficients and (b) betw een the viscosit B and the rotational friction coefficients GW indicates the Gierer-Wirtz theory and other symbols have the same meanings as Figure 1...

The main characteristics determining the rotational mobility of a r id particle (molecule) are its rotational friction coefficient, W, depending on the size and shape (conformation) of the molecule, the viscosity of the solvent tjq and the position of the the axis of rotation. 

Hence, Eq. (18) shows that for a solution of ellipsoidal particles a very general relationship exists between the intrinsic viscosity and the rotational friction coefficient of the jarticle. 

Thus, if the necklace has the shape of a rigid straight rod, its rotational friction coefficient for the rotation about the central axis normal to the tod is given by... 

This result is due to the si cificity of the molecular system of coordinates fbc-ing axes with respect to which the rotational friction coefficient is calculated. 

Equations (20) and (23) show that the average rotational friction coefficient W is proportional to the radius of gyration both for extended and symmetrical conformations. Hence, it is proportional to h (compare Eqs. (3) and (3 )p. 98). According to Eq. (46), optical anisotropy in the random chain conformation is also proportional to h in the Gaussian range (h/L -4 1). Hence, a Gaussian coil obeys the following equation... 

In contrast, the motion in the electric field of kinetically rigid molecules for which tq is less than should be governed by the mechanism of the orientation of the molecule as a whole and the rate of this process should be determined by the rotational friction coefficient W or rotatory diffusion coefficient Dj (Eq. (53)). Hence, the study of the orientation kinetics of kinetically rigid macromolecules in the electric field permits the determination of their rotational mobility (i.e. W and Dj). 

Similarly it can be shown, with the mean rotational friction coefficient, that the rotational diffusion coefficient is... 

Note that, in addition to translational motion, other kinds of motion will be subject to random thermal fluctuations as well. In particular, the tumbling of (macro)molecules in solution can be described in terms of rotational diffusion, for which equivalent rotational diffusion constants can be defined. By analogy with translational diffusion described above, the rotational diffusion coefficient (/>rot) and rotational friction coefficient (/rot) are related by the expression ... 

The rotational diffusion coefficient, 0, obtainable from a variety of experimental methods, as indicated in Table I, may be treated in a similar manner. From 0 it is possible to compute a rotational frictional coefficient, f,of an ellipsoidal particle by means of the equation... 

Translational Frictional Coefficient— Rotational Frictional Coefficient... 

Now we proceed to examine a consequence of the hig-fre-quency motion upon the overall dynamics. We shall begin with the remark that functions like C (t) play the part of a generalized friction coefficient in a Langevin formalism of rotational diffusion, and therefore the spectrum measured in the FIR is nothing but the spectral density of this rotational friction coefficient. 

C. Hu and R. Zwanzig,/. Chem. Phys., 60, 4354 (1974). Rotational Friction Coefficients for Spheroids with the Slipping Boundary Condition. 

Tirado et al. inclnded end effects to assess the friction coefficient of finite rigid cylinders. - These anthors solved the hydrodynamic equations in cylindrical coordinates and found that the translational and rotational friction coefficients are given by... 

Zwanzig, R. (1978). Rotational friction coefficients of a bumpy cylinder with slipping and sticking boundary conditions. J. Chem. Phys. 68 4325-4326. 

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