Volume-temperature dependence

Molarity (M) mol solute L solution Useful in stoichiometry measure by volume Temperature-dependent must know density to find solvent mass... 

The very large pressure coefficient of the susceptibility (Fig. 14a) and conductivity in the metallic regime (d In room temperature [6]) raises a serious problem for the comparison with theory, which usually computes constant-volume temperature dependences. Hence the temperature dependence at constant pressure that is observed in actual experiments must be transformed into constant-volume data since the change of volume (due to the thermal expansion) cannot be ignored between 300 and 50 K. No detailed determinations of the constant-volume resistivity have been performed so far. However, a crude estimate of the intrinsic temperature dependence can be performed using the thermal expansion and the pressure dependence of the a axis at various temperatures [59] (Fig. 14b). 

A dependence close to a linear law is observed down to 100 K. At low temperature, both the thermal expansion and the pressure coefficient are small. Therefore, the constant-volume temperature dependence of the resistivity does not deviate from the quadratic law observed under constant pressure. At this stage it is interesting to stress that the theory of the resistivity in a half-filled band conductor [63], including the strength of the coulombic repulsions as derived from NMR data (Section III.B), should lead to a more localized behavior than that observed experimentally in Fig. 14. 

Figure 14 (a) Pressure dependence of the spin susceptibility x (T,T)-l/2 from NMR data. (From Ref. 41b.) (b) Constant-pressure and constant-volume temperature dependences of the resistivity of (TMTSF)2AsF6 derived point by point from the constant-pressure data of Fig. 12. The lattice parameters are from Ref. 33 and the pressure coefficient of the conductivity from Ref. 57.

Figure 2.23 Volume-temperature dependence for glassy and highly crystalline polymers.

Specific volume-temperature dependence for semicrystalline poly-... 

Figure 2.26 Specific volume-temperature dependence for poly(vinyl acetate) as a function of cooling rate.

Fig. 22. Schematic representation of the volume temperature dependence, lowing the expansion factor for the glass, a, the liquid, oci, and the occupied volume, o%, and the fractional free volume / at the glass temperature T ...

Utracki, L. A., and Simha, R., Pressure-volume-temperature dependence of polypropy-lene/organoclay nanocomposites. Macromolecules, 37, 10123-10133 (2004). 

The first simplification was suggested by Olabisi and Simha [1977]. Combining Tail s equation (6.10) with the volume-temperature dependence of the S-S equation of state, Eq. (6.23), and the linear dependence observed for the Tail compressibility parameter, — In B = 0.04615 + 49.22T, the authors wrote... 

Fig. 1.2 Schematic of a volume-temperature dependence for a material in various states (after Jones (1956)).

L.A. Utracki, Pressure-volume-temperature dependencies of polystyrenes. Polymer 46, 11548-11556 (2005)... 

Another means of examining fundamental thermodynamic phenomena is the use of high pressure dilatometry to measure the pressure-volume-temperature dependence of polymers. This results in the development of an equation of state describing the variation of specific volume with temperature and pressure. As with DSC, these curves show thermodynamic as... 

Another, though small, error is introduced by temperature differences between subsampling and the volume determination of the sample bottles. The resulting volume error depends very much on the geometry and material of the sample bottles. For high-precision oxygen measurements the determination of the volume-temperature dependence of the type of sample bottle and resulting correction is recommended. 

A first-order transition normally has a discontinuity in the volume-temperature dependence, as well as a heat of transition, AHf, also called the enthalpy of fusion or melting. The most important second-order transition is the glass transition, Chapter 8, in which the volume-temperature dependence undergoes a change in slope, and only the derivative of the expansion coefficient, dVIdT, undergoes a discontinuity. There is no heat of transition at Tg, but rather a change in the heat capacity, ACp. 

Utracki L A, Simha R, Garcia-Rejon A (2003), Pressure-volume-temperature dependence of poly-e-caprolactam/clay nanocomposites , Macromolecules, 36, 2114-21. 

---