Elastic constants temperature dependence

Let us consider the same mechanical characteristics prediction technique attesting temperature T variation. For the dependences (7) estimation the authors [201] modified the Eq. (15 8) by the simplest mode, assuming that the coefficient in this equation is a function of testing temperature of general view CIT, where C is constant, equal to 205°K, if T is given in K. In Fig. 88 comparison of experimental and calculated by the indicated mode dependences E T) for two PASF film samples, prepared from solutions in chloroform and methylene chloride, is adduced. This comparison shows applicability of the stated above approximation for prediction of the elasticity modulus temperature dependence. 

The elastic constants are dependent upon the temperature T and are commonly of the order 10 dynes to lO" dynes in cgs units, equivalent to aroimd the order of 10 N to 10 N (newtons) in SI units, with often being two or three times larger than Ki or K2 (recall that 1 dyne = 10 N). For the nematic liquid crystal PAA at T = 125°C, the experimental work of ZwetkoflF (Tsvetkov), in 1937, established the values in SI units (originally quoted in dynes)... 

Thermal Properties at Low Temperatures For sohds, the Debye model developed with the aid of statistical mechanics and quantum theoiy gives a satisfactoiy representation of the specific heat with temperature. Procedures for calculating values of d, ihe Debye characteristic temperature, using either elastic constants, the compressibility, the melting point, or the temperature dependence of the expansion coefficient are outlined by Barron (Cryogenic Systems, 2d ed., Oxford University Press, 1985, pp 24-29). 

The thermal conductivity plateau has traditionally been considered by most workers as a separate issue from the TLS. In addition to the rapidly growing magnitude of phonon scattering at the plateau, an excess of density of states is observed in the form of the so-called bump in the heat capacity temperature dependence divided by T. The plateau is interesting from several perspectives. For one thing, it is nonuniversal if scaled by the elastic constants (say, co/)... 

Thus, the model predicts that thermal fluctuations in the tilt and curvature change the way that the tubule radius scales with chiral elastic constant— instead of r oc (THp) 1, the scaling has an anomalous, temperature-dependent exponent. This anomalous exponent might be detectable in the scaling of tubule radius as a function of enantiomeric excess in a mixture of enantiomers or as a function of chiral fraction in a chiral-achiral mixture. 

Figure 5.2 Temperature dependence of the isothermal elastic stiffness constants of aluminium [10].

Finally, it behaves like a liquid provided the chain length is not too long. Just around T some physical properties change distinctively such as the specific volume, the expansion coefficient, the specific heat, the elastic modulus, and the dielectric constant. Determination of the temperature dependence of these quantities can thus be used to determine Tg. 

Instead of measuring the force-temperature dependence at constant volume and length, one can measure this dependence at constant pressure and length but in this case it is necessary to introduce the corresponding corrections. The corrections include such thermomechanical coefficients as iso-baric volumetric expansion coefficient, the thermal pressure coefficient or the pressure coefficient of elastic force at constant length 22,23,42). 

A surprising disappearance of the thermomechanical inversion of heat at elevated temperatures has been observed by Kilian 9,88). At 90 °C, the thermomechanical inversion in SBR and NR is found to disappeare in spite of the constant value of the thermal expansion coefficient. This means that the temperature dependence of elastic force should be negative from the initial deformations, which is in contradiction with experiment. This very unusual phenomenon was supposed to be closely related to rotational freedom which will continuously be activated above some characteristic temperature 9,88). 

Kundu B, PratibhaR, MadhusudanaNV (2007) Anomalous temperature dependence of elastic constants in the nematic phase of binary mixtures made of rodlike and bent-core molecules. Phys Rev Lett 99 247802-1-4... 

The Debye temperature can also be obtained from the elastic constants. The measurement of the elastic constants of polycrystalline AIN was used by Slack et al [8] to derive the Debye temperature, giving 0D = 950 K. Therefore, Slack et al have criticised the value of the AIN Debye temperature 0D = 800 + 2 K, derived from the heat capacity measurements by Koshchenko et al [6], as too low. Also, Slack s value differs considerably from Meng s result [7]. Since the cubic dependence T3 approximates the Debye specific heat well in the temperature range below T = 0d/5O [9], it is likely that the upper temperature limit used by Meng is too high and led to error and the difference from the results of Slack et al [8],... 

Stress relaxation is the time-dependent change in stress after an instantaneous and constant deformation and constant temperature. As the shape of the specimen does not change during stress relaxation, this is a pure relaxation phenomenon in the sense defined at the beginning of this section. It is common use to call the time dependent ratio of tensile stress to strain the relaxation modulus, E, and to present the results of the experiments in the form of E as a function of time. This quantity should be distinguished, however, from the tensile modulus E as determined in elastic deformations, because stress relaxation does not occur upon deformation of an ideal rubber. 

Background At elevated temperatures the rapid application of a sustained creep load to a fiber-reinforced ceramic typically produces an instantaneous elastic strain, followed by time-dependent creep deformation. Because the elastic constants, creep rates and stress-relaxation behavior of the fibers and matrix typically differ, a time-dependent redistribution in stress between the fibers and matrix will occur during creep. Even in the absence of an applied load, stress redistribution can occur if differences in the thermal expansion coefficients of the fibers and matrix generate residual stresses when a component is heated. For temperatures sufficient to cause the creep deformation of either constituent, this mismatch in creep resistance causes a progres-... 

The main difference between a solid and a liquid is that the molecules in a solid are not mobile. Therefore, as Gibbs already noted, the work required to create new surface area depends on the way the new solid surface is formed [ 121. Plastic deformations are possible for solids too. An example is the cleavage of a crystal. Plastic deformations are described by the surface tension y also called superficial work, The surface tension may be defined as the reversible work at constant elastic strain, temperature, electric field, and chemical potential required to form a unit area of new surface. It is a scalar quantity. The surface tension is usually measured in adhesion and adsorption experiments. 

At constant chemical potentials, electric potential, and elastic strain, the dependence of the surface tension on temperature is given by the surface entropy. Inserting into Eq. (I9) yields 192,931... 

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