Relaxation method, rotational viscosity

If the applied magnetic field greatly exceeds the critical strength, the relaxation will be non-exponential. The hyperbola rotation must then be calculated by means of the Leslie-Ericksen equations, and the rotational viscosity Yi is determined by a fit of the calculated hyperbola rotation to the observed one. A disadvantage of this method is that it is difficult to follow the rotation of the interference figure by eye or by means of automatic equipment. 

Rotational viscosities can also be determined by means of electron spin resonance (ESR) or nuclear magnetic resonance (NMR) experiments [69-71]. For low viscosity materials the sample is rotated around an axis perpendicular to the magnetic field. For high viscosity materials the sample is rapidly rotated by a small angle and the relaxation observed. Both methods allow the determination of the angle A between director and field direction. For the continuous rotation with an angular velocity jf smaller than the critical one (see Fq. 38) one obtains [69]... 

By the total internal reflection condition at the liquid-liquid interface, one can observe interfacial reaction in the evanescent layer, a very thin layer of a ca. 100 nm thickness. Fluorometry is an effective method for a sensitive detection of interfacial species and their dynamics [10]. Time-resolved laser spectrofluorometry is a powerful tool for the elucidation of rapid dynamic phenomena at the interface [11]. Time-resolved total reflection fluorometry can be used for the evaluation of rotational relaxation time and the viscosity of the interface [12]. Laser excitation can produce excited states of adsorbed compound. Thus, the triplet-triplet absorption of interfacial species was observed at the interface [13]. 

Attempts have been made to identify primitive motions from measurements of mechanical and dielectric relaxation (89) and to model the short time end of the relaxation spectrum (90). Methods have been developed recently for calculating the complete dynamical behavior of chains with idealized local structure (91,92). An apparent internal chain viscosity has been observed at high frequencies in dilute polymer solutions which is proportional to solvent viscosity (93) and which presumably appears when the external driving frequency is comparable to the frequency of the primitive rotations (94,95). The beginnings of an analysis of dynamics in the rotational isomeric model have been made (96). However, no general solution applicable for all frequency ranges has been found for chains with realistic local structure. 

Nuclease behaves like a typical globular protein in aqueous solution when examined by classic hydrodynamic methods (40) or by measurements of rotational relaxation times for the dimethylaminonaphth-alene sulfonyl derivative (48)- Its intrinsic viscosity, approximately 0.025 dl/g is also consistent with such a conformation. Measurements of its optical rotatory properties, either by estimation of the Moffitt parameter b , or the mean residue rotation at 233 nin, indicate that approximately 15-18% of the polypeptide backbone is in the -helical conformation (47, 48). A similar value is calculated from circular dichroism measurements (48). These estimations agree very closely with the amount of helix actually observed in the electron density map of nuclease, which is discussed in Chapter 7 by Cotton and Hazen, this volume, and Arnone et al. (49). One can state with some assurance, therefore, that the structure of the average molecule of nuclease in neutral, aqueous solution is at least grossly similar to that in the crystalline state. As will be discussed below, this similarity extends to the unique sensitivity to tryptic digestion of a region of the sequence in the presence of ligands (47, 48), which can easily be seen in the solid state as a rather anomalous protrusion from the body of the molecule (19, 49). 

Luminescence of Probe Molecules. These studies permit evaluation of polymer properties. In particular, measurement of the relative Intensities of fluorescence of a probe molecule polarized parallel to and perpendicular to the plane of linearly polarized exciting radiation as a function of orientation of a solid sample yields Information concerning the ordering of polymer chains. In solution, similar polarization studies yield Information on the rotational relaxation of chains and the viscosity of the microenvironment of the probe molecule. More recently, the study of luminescence Intensity of probe molecules as a function of temperature has been used as a method of studying transition temperatures and freeing of subgroup motion in polymers. 

There is a more fundamental difficulty in the method in that it is not clear whether in eq. 51 the macroscopic viscosity of the solvent or solution can be employed, since the movement of a fluorescent group in a flexible polymer chain will certainly not be described adequately by the Stokes-Elnstein equation (84). Rotational relaxation may occur about three axes of rotation, and it has been shown that in cases where r/p >> 1, all three... 

Viscosity is measured with rheometers or viscometers. The methods used include rotational deformation, squeezing deformation, extrusion (capillary) flows, and free surface stretching. For rotational instruments, there are two modes of operation controlled strain and controlled stress. Rotational measurements can be further subdivided into different measuring methods (flow, oscillatory, stress relaxation, and creep) and different measurement devices (spindle, cone-and-plate, parallel plate, concentric cyhnder). As for a capillary rheometer, there are two modes of operation controlled flow (strain) and controlled pressure (stress). 

In the method described by Bock et al. [68], the liquid crystal is filled in an ampulla which is suspended from a torsion wire in a constant magnetic field. The suspension of the wire is rotated by a certain angle and the relaxation of the ampulla to the new equilibrium position is observed. The method is very useful for samples with high viscosity. If the oscillation period of the system is negligible relative to the relaxation time, and if the director orientation is not far from its equilibrium position, an exponential relaxation is observed with the time constant... 

Figure 2.38 shows logarithmic dependences of the q viscosity (registered by rotational viscometer) on the tt test time at 20°C and at shear rate yt=54 sec dming the test. These values were obtained for a sample of oligobutadiene urethane aerylate (OBUA) [226], different methods of preliminary treatment were used for this sample. Curve 1 shows the q = f (xt) function of the initial sample curve 2 shows the initial sample after the Yp preliminary shear influence at Yp = 2 sec" for 90 min. additional 90 min. influence at Yp = 6 sec" is shown on curve 3 finally, curve 4 shows the same sample after a 15 hour relaxation in the meter cell of the device. 

---