Second-order transition point

Here the coefficients G2, G, and so on, are frinctions ofp and T, presumably expandable in Taylor series around p p and T- T. However, it is frequently overlooked that the derivation is accompanied by the connnent that since. . . the second-order transition point must be some singular point of tlie themiodynamic potential, there is every reason to suppose that such an expansion camiot be carried out up to temis of arbitrary order , but that tliere are grounds to suppose that its singularity is of higher order than that of the temis of the expansion used . The theory developed below was based on this assumption. 

Since Eqs. (4.48) and (4.49) both describe the same limit, they must be equal at the second-order transition point ... 

For many applications low-temperature flexibility of the plasticized composition is also important. Plasticizers of low viscosity and low viscosity-temperature gradient are usually effective at low temperature. There is also a close relationship betv/een rate of oil extraction and low-temperature flexibility plasticizers effective at low temperature are usually rather readily extracted from the resin. Plasticizers containing linear alkyl chains are generally more effective at low temperature than those containing rings. Low-temperature performance is evaluated by measuremen t of stiffness in flexure or torsion or by measurement of second-order transition point, brittle point or peak dielectric loss factor. 

Alfrey, T., G. Goldfinger and H. Mark The apparent second-order transition point of polystyrene. J. Appl. Phys. 14,700—705 (1943). 

Formulas and Data Sheets, issued yearly, containing all newly established fundamental equations and numerical data on basic properties of polymers. These would include new equations to express viscosity as a function of temperature, concentration, or shear rate new relations between intrinsic viscosity and molecular weight new formulas on the kinetics of polymerization and copolymerization data on second-order transition points of new polymers or copolymers heat and entropy of solution, dilution, melting, and swelling of macromolecules and similar fundamental data as they are contained in the articles appearing during the reference year. They would be similar in purpose to the Technical Data Sheets and complement them in regard to fundamental information. 

Thermal study of the anionically polymerized homopolymers showed glass-transition temperatures from 40° to 120°C. The samples partly changed on heating on second heating, the second-order transition points were often higher. 

The plot of U versus 1/T (at constant volume) shows the characteristic sigmoid shape (fig. 2.6.1). The curves for the ordered and disordered phases meet at the apparent second order transition point T, which is also the temperature at which the short-range order parameter ( P icos 6 )y in the isotropic phase = l/(z — 1). The first order transition point is the temperature at which the shaded areas are equal, i.e., when the Helmholtz free energies of the ordered and disordered phases are the same. The calculation gives (2J,— T )/2J, = 0.062 for z = 8,0.04 for z = 4 and 0.03 for z = 3. This is an improvement over the Maier-Saupe value of 0.092, though still much higher than the experimental value of 0.003. 

From symmetry considerations it is clear that only even powers of y/ may be included. The coefficient P is always positive. At a certain temperature T, which is the second order transition point, a = 0. Accordingly, as explained in 2.5.1, we set in the mean field approximation,... 

In most plastic articles accidental orientation occurs due to the fact that they are usually made from the melt. During the flow and deformation of the melt in extrusion dies and in moulds the material is sheared, with molecular orientation in the shear direction. Part of this orientation relaxes before the material is cooled below the apparent second-order transition point or melting point. Another part, however, remains and is still observable in the final product. 

THERMAL CONDUCTIVITY OF FOAMED POLYSTYRENE IN A REGION OF THE SECOND ORDER TRANSITION POINT. 

When cooling such brittle macromolecular substances further, another transition point can be observed, the second-order transition point Tm. It may be supposed that here the oscillations of certain molecules around their equilibrium positions become stopped, just as is observed with low-molecular crystallising substances below their melting points. ... 

Scaling for polymers is based just on the fact that fluctuations of segment concentration of a flexible macromolecnle are of the same order of magnitude as segment concentration it.self. Hence, we notice at once a similarity to magnetics or some other systems in which giant fluctuations appear as these systems approach the second-order transition point (or rather the critical point which term is presently preferred since the 2-nd order transitions arc continuous ). 

Figure 13.11 illustrates the change in torsional stiffness that can occur as the temperature drops and compares polyurethane with other rubbers. There is only a small increase in the torsional stiffness as the temperature is decreased from -2(fC to about — 25" C, but then the increase in stiffness occurs very rapidly. The second-order transition point is between — 30 and —40°C and it is dependent upon the regularity of the molecular structure. Lower transition temperatures can be obtained by the use of mixed glycol polyadipates in place of the common polyethylene glycol adipate. For example, it is common commercial practice to use a blend of polyethylene... 

Nakamura, K. and Ookawa, T., Studies on viscoelasticiti of cellulose derivatives films. III. Second-order transition points of cellulose nitrates, Chem. High Polym. Japan, 1957, vol. 14, no. 150, pp. 544-550. 

Second order transition point. Tg (glass temp.)... 

Transition temperatures TniN) of conformational transitions for small elastic polymers with chain lengths W = 13,..., 309 in the liquid-solid and solid-solid transition regimes, obtained from inflection-point analysis. First-order transition points are marked by symbols, second-order transition points by symbols x. Also shown is a fit for the liquid-solid transition temperature towards the thermodynamic limit W oo (dashed line). From [61]. 

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