Torsional oscillations

Tobolsky, A. V. and DuPre, D. B. Macromolecular Relaxation in the Damped Torsional Oscillator and Statistical Segment Models. Vol. 6, pp. 103 — 127. 

New membranes have been developed with significantly enhanced mass-transfer characteristics. These membranes include rotating membrane systems that use a torsional oscillation to produce shear rates as high as 150,000 s. Coiled hollow fibres that exploit Dean vortices to increase solute transport and reduce fouling are receiving attention (Zydney, 2000). 

The transition between crystalline and amorphous polymers is characterized by the so-called glass transition temperature, Tg. This important quantity is defined as the temperature above which the polymer chains have acquired sufficient thermal energy for rotational or torsional oscillations to occur about the majority of bonds in the chain. Below 7"g, the polymer chain has a more or less fixed conformation. On heating through the temperature Tg, there is an abrupt change of the coefficient of thermal expansion (or), compressibility, specific heat, diffusion coefficient, solubility of gases, refractive index, and many other properties including the chemical reactivity. 

There are three modes of free and forced oscillatory deformations which are commonly used experimentally, torsional oscillations, uniaxial extensional oscUlations and flexural oscillations. 

In molecular crystals, the separation between internal and external modes is of importance. Except for torsional oscillations in some types of molecules, the internal modes have much higher frequencies than the external modes. According to expressions such as Eqs. (2.51) and (2.58), the latter are then the dominant... 

Since these processes are strongly dependent on temperature, it is appropriate to carry out torsion-oscillation experiments over a wide range of temperature, and to plot the values for the modulus and d against temperature (see Fig. 2.22). 

The value of the modulus and the shape of the modulus curve allow deductions concerning not only the state of aggregation but also the structure of polymers. Thus, by means of torsion-oscillation measurements, one can determine the proportions of amorphous and crystalline regions, crosslinking and chemical non-uniformity, and can distinguish random copolymers from block copolymers. This procedure is also very suitable for the investigation of plasticized or filled polymers, as well as for the characterization of mixtures of different polymers (polymer blends). 

The hardness of a polymer can also be estimated from the modulus of elasticity E (high E modulus indicates high hardness). The advantage here is that every region of elasticity and every degree of hardness can be detected with a single kind of measurement (determination of stress-strain-behavior or torsional oscillation). 

For POM, a matrix algorithm for the statistical mechanical treatment of an unperturbed -A-B-A-B- polymer chain with energy correlation between first-neighboring skeletal rotations is described. The results of the unperturbed dimensions are in satisfactory agreement with experimental data. In addition, if the same energy data are used, the results are rather close to those obtained by the RIS scheme usually adopted. The RIS scheme is shown to be also adequate for the calculation of the average intramolecular conformational energy, if the torsional oscillation about skeletal bonds is taken into account in the harmonic approximation. 

Apparently, in field depositing reduces also slightly the coercivity (from 6 mT to 4 mT). High-amplitude flexural and torsional-oscillation modes were observed for these films. 

Clark, M.B., Zimm,B.H. A linearized chain model for dielectric loss in polymers. ACS Polymer Preprints 12, 116-120 (1971). See also Tobolsky,A.V., DuPre,D.B. Macromolecular relaxation in the damped torsional oscillator and statistical segment models. Advan. Polymer Sci. 6,103-127 (1969). 

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