Rotary force constant

Dependence of Angular Vibration on Rotary Force Constant... 

Dimensionless rotary force constant Single-particle dipolar ACF and its spectrum Distance between charges of the dimer (see Fig. 39b) Element of phase-space volume Charge of electron... 

Note that this formula allows us to relate the force constant k with the T-band resonance frequency vq by putting Vt = 2n ciightV, where vq 200 cm-1 and Cnght is the speed of light (in other sections of this work Ciight is denoted, as usually, c, while the rotary force constant is denoted crot). 

With decreasing of the rotary force constant c the center of the reorientation line L shifts toward lower frequencies. The ratio of line intensities could be roughly estimated as... 

The first dependence, Aq(x), refers to elastic translation of charges (of a nonrigid dipole) and the second, A (x), to elastic reorientation of H-bonded rigid dipoles. For calculation of dependences (157) the rigorous formulas (138) and (139) are used.19 We take the following values of the rotary force constant c 0.4, 0.2, 0.15, and 0.05. For c = 0.2 the dependences (157) are calculated also from the simplified formulas (148). 

For a sufficiently large constant c, as in Fig. 40a, where c = 0.4, the situation changes in two points (i) The translational peaks shift to the left of the orientational one and (ii) the smaller and larger peaks change places. Since the case (i) does not correspond to experiment, we draw the conclusion that for obtaining reasonable ice/water spectra the rotary force constant c should not be too large. 

Figure 40 (a-d) Frequency dependences of the dimensionless absorption A(x). Solid lines denote absorption due elastic translations of charges and dashed lines due to elastic reorientations. Calculation according to strict theory (a) c = 0.4 (b) c = 0.2 for curves 1 and 2 (c) c = 0.15 for curves 5 and 6 and c — 0.1 for curves 7 and 8 (d) c = 0.05. Approximate calculation (b) for c = 0.2 (curves 3 and 4). Vertical lines refer to the Lorentz line centers estimated as xq = /, xfl = p. (e) Amplitude of angular vibration versus rotary force constant, horizontal line depicts the quantity (158). 

We now estimate the minimum value, cmin, of the rotary force constant c. For c < cmin the above-used approximation of small oscillation amplitudes becomes inapplicable The point is in the following. The root-mean-square angular deflection 0, pertaining to the covalent bond of the lefthand molecule20 (see Fig. 39a), according to (102) and (137), increases with decreasing of c. As follows from the indicated formulas, the limiting deflection is... 

Since experimentally observed spectra give the patterns similar to those represented in Figs. 40b or 40c (and not as in Fig. 40a), we conclude that the effective rotary force constant should not noticeably exceed the value (160). This means that in a reasonable molecular model the average H-bond length l should not be too short. 

The calculations of TSM have recently been extended to include the effects of intermolecular forces by Tasumi and Shimanouchi 35). Estimates for the magnitude of intermolecular force constants for these calculations were obtained from the small splitting observed for higher-frequency modes. It was shown that intermolecular forces split every mode into two components belonging to different symmetry species. The acoustic modes vj and of TSM were also affected by intermolecular forces. For an isolated chain, these correspond to deformation and torsional vibrations respectively, but in crystals, they are mixed. Further, the zero and n phases of the acoustic modes predicted for an isolated chain correspond to zero frequency. In the crystal, non-zero values corresponding to rotary and translational lattice vibrations are obtained. 

For many purposes, it is more convenient to characterize the rotary Brownian movement by another quantity, the relaxation time t. We may imagine the molecules oriented by an external force so that the a axes are all parallel to the x axis (which is fixed in space). If this force is suddenly removed, the Brownian movement leads to their disorientation. The position of any molecule after an interval of time may be characterized by the cosine of the angle between its a axis and the x axis. (The molecule is now considered to be free to turn in any direction in space —its motion is not confined to a single plane, but instead may have components about both the b and c axes.) When the mean value of cosine for the entire system of molecules has fallen to ile(e — 2.718... is the base of natural logarithmus), the elapsed time is defined as the relaxation time r, for motion of the a axis. The relaxation time is greater, the greater the resistance of the medium to rotation of the molecule about this axis, and it is found that a simple reciprocal relation exists between the three relaxation times, Tj, for rotation of each of the axes, and the corresponding rotary diffusion constants defined in equation (i[Pg.138]

We denote the longitudinal force constant by k and the dimensionless rotary constant by c. In terms of these constants the strained-state potential energy is expressed as... 

Normal stress measurements on concentrated solutions of helical polypeptides were conducted by lizuka [1,42]. However he used these to calculate extinction angles, from which the rotary diffusion constant was deduced, and thence an apparent particle size from tables given by Scheraga [43]. In a personal communication to Kiss and Porter, lizuka commented that he had observed negative normal stresses in solutions of PBLG + Ch Br with concentrations of greater than 10% (i.e. probably liquid crystalline) however he ascribed this to the adhesive force of the solution (E. lizuka, personal communication, April 1977). 

The direction of the optical axis of the solution which is determined by the average orientation of macromolecules, as a function of shearing force, gives the rotary difiusion constant of the macromolecules from which their size and shape are estimated by apptylng an appropriate model. 

FIG. 15.24 Schematic representation of the four roller extensional rheometer, designed by Meissner (1972) to attain high Hencky strains. Two sets of rotary clamps are individually driven by two motors at constant rotation rates. The force in the sample is measured by a transducer F mounted on a leaf spring. From Barnes, Hutton and Walters (Gen Ref 1993). Courtesy Elsevier Science Publishers. 

Two time definitions are important contact time and dwell time. Contact time can be defined as the time during which a contact of powder and punches is measurable, for example, when the force exceeds a certain limit of 100N. Dwell time can be defined predominantly for rotary machines as the time during which the punch heads are completely under the compression wheels and thus the applied force is constant. 

Although most rotary tablet presses operate by maintaining fixed roller positions during compression, some designs incorporate a compression compensator system in which the counterforce for compression is air pressure. This system compresses to a constant force and allows roller movement when the preset force is achieved. Under these conditions, potential exists to increase the time that the force is maintained near its peak value (approximately 90% of maximum). Compression to a constant force should theoretically provide a more uniform tablet hardness and more uniform dissolution profiles while allowing a greater variation in tablet thickness. 

During tablet compression, the distance between the rollers remains constant unless a machine adjustment is made to change tablet hardness or thickness. Additionally, all tooling dimensions (tooling length and die cavity size) are constant within established standards. Under these conditions, for a specific material of uniform density, if the same volume of material is delivered to each die, the maximum measured compression force for each punch station is the same. If, on the other hand, different volumes of material are delivered to each die, the maximum measured compression force for each punch station is different. On this basis, adjustment of fill depth (fill volume) to maintain a constant compression force should result in a constant tablet weight. This concept is the general basis of all rotary tablet press force control systems. 

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