Transition temperatures, equilibrium

Figure 5. Logarithm of the retractive force at 49% strain (lower curve) and sample temperature (upper curve) plotted against logarithm of time reduced to 263 K. Cross-links are introduced at log t/aT is 3 in the glassy state where the spike on the force curve is due to thermal contraction upon cooling below the glass transition temperature. Equilibrium force at 263 K after cross-linking is feQ. (Reproduced, with permission, from Ref. 27. Copyright 1981, Journal of Chemical Physics.)...

Studies carried out on melt-extmded films prepared from iPP/HOCP blends showed that the addition of HOCP causes the formation of smectic phase of iPP at temperature where the iPP crystallizes in the monoclinic a-form (9). These phenomena are attributed to the effect of HOCP on the glass transition temperature, equilibrium melting temperature, crystallization temperature, and rate of crystallization of iPP. Properties and plastic deformation of the oriented films were also investigated (10). 

Many substances exist in two or more solid allotropic fomis. At 0 K, the themiodynamically stable fomi is of course the one of lowest energy, but in many cases it is possible to make themiodynamic measurements on another (metastable) fomi down to very low temperatures. Using the measured entropy of transition at equilibrium, the measured heat capacities of both fomis and equation (A2.1.73) to extrapolate to 0 K, one can obtain the entropy of transition at 0 K. Within experimental... 

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The glassy state does not represent a true equilibrium phase. Below the transition into a glass phase, the material is regarded as being in a metastable state. If one holds the substances at temperatures somewhat below the glass transition temperature, heat evolution can often be observed over time as the molecules slowly orient themselves into the lower energy, stable crystalline phase. 

The equilibrium pressure when (solid + vapor) equilibrium occurs is known as the sublimation pressure, (The sublimation temperature is the temperature at which the vapor pressure of the solid equals the pressure of the atmosphere.) A norma) sublimation temperature is the temperature at which the sublimation pressure equals one atmosphere (0.101325 MPa). Two solid phases can be in equilibrium at a transition temperature (solid + solid) equilibrium, and (liquid + liquid) equilibrium occurs when two liquids are mixed that are not miscible and separate into two phases. Again, "normal" refers to the condition of one atmosphere (0.101325 MPa) pressure. Thus, the normal transition temperature is the transition temperature when the pressure is one atmosphere (0.101325 MPa) and at the normal (liquid + liquid) solubility condition, the composition of the liquid phases are those that are in equilibrium at an external pressure of one atmosphere (0.101325 MPa). 

Again using C02 as an example, Figure 8.12 shows the discontinuity in Cp, m at the equilibrium transition temperature where C02 changes from solid to gas. A similar discontinuity is found for the compressibility k.1... 

For AG = AH — TAS = 0 the conversion between the two spin states has achieved thermal equilibrium, and the fractions of both states have become equal, % = = 2 - The transition temperature may be thus defined as = AH/AS. 

Temperature has a complex effect on crystallization rate. Initially, as the temperature falls below the equilibrium melting temperature, the crystallization rate increases because nucleation is favored. However, as the temperature continues to fall, the polymer s viscosity increases, which hampers crystallization. As a rule of thumb, a polymer crystallizes fastest at a temperature approximately mid-way between its glass transition temperature and its equilibrium melting temperature. 

The method (27) can best be explained with reference to Figure 2. After stretching to 10, the force f is measured as a function of time. The strain is kept constant throughout the entire experiment. At a certain time, the sample is quenched to a temperature well below the glass-transition temperature, Tg, and cross-linked. Then the temperature is raised to the relaxation temperature, and the equilibrium force is determined. A direct comparison of the equilibrium force to the non-equilibrium stress-relaxation force can then be made. The experimental set-up is shown in Figure 4. 

The important quantities AH and AS are assumed to be temperature independent. This is often quite a good approximation, but the vibrational component of the entropy, which has been neglected altogether, will become increasingly important at high temperatures. The effects of these factors can cause the major defect type present to change as the temperature increases. Near to the transition temperature a complex equilibrium between both defect types will be present. 

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