Second-order transition point temperature

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. 

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,... 

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... 

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]. 

There is no discontinuity in volume, among other variables, at the Curie point, but there is a change in temperature coefficient of V, as evidenced by a change in slope. To understand why this is called a second-order transition, we begin by recalling the definitions of some basic physical properties of matter ... 

Stabilization of the Cellular State. The increase in surface area corresponding to the formation of many ceUs in the plastic phase is accompanied by an increase in the free energy of the system hence the foamed state is inherently unstable. Methods of stabilizing this foamed state can be classified as chemical, eg, the polymerization of a fluid resin into a three-dimensional thermoset polymer, or physical, eg, the cooling of an expanded thermoplastic polymer to a temperature below its second-order transition temperature or its crystalline melting point to prevent polymer flow. 

Modifications separated by a second-order transition can never be coexistent. One typical second-order transition, the displacive structural transition, is characterized by the distortion of bonds rather than their breaking, and the structural changes that occur are usually small. Typically, there is continuous variation in the positional parameters and the unit cell dimensions as a function of temperature. The structural changes in the system occur gradually as the system moves away from the transition point. As well as a structural similarity, a symmetry relationship... 

Fig. 27. Phase diagram of an adsorbed film in- the simple cubic lattice from mean-fleld calculations (full curves - flrst-order transitions, broken curves -second-order transitions) and from a Monte Carlo calculation (dash-dotted curve - only the transition of the first layer is shown). Phases shown are the lattice gas (G), the ordered (2x1) phase in the first layer, lattice fluid in the first layer F(l) and in the bulk F(a>). For the sake of clarity, layering transitions in layers higher than the second layer (which nearly coincide with the layering of the second layer and merge at 7 (2), are not shown. The chemical potential at gas-liquid coexistence is denoted as ttg, and 7 / is the mean-field bulk critical temperature. While the layering transition of the second layer ends in a critical point Tj(2), mean-field theory predicts two tricritical points 7 (1), 7 (1) in the first layer. Parameters of this calculation are R = —0.75, e = 2.5p, 112 = Mi/ = d/2, D = 20, and L varied from 6 to 24. (From Wagner and Binder .)...

Fig. 29. Phase diagram of the model Eq. (22) for coadsorption of two kinds of atoms in the temperature-coverage space. Circles indicate a second-order phase transition, while crosses indicate first-order transitions. Point A is believed to be a tricritical point and point B a bicritical point. The dashed curve shows the boundary from the Blume-Capel model on a square lattice with a nearest-neighbor coupling equal to 7 in the present model (for - 0 Eq. (22) reduces to this model), only the ordered phase I then occurs. From Lee and Landau. )...

The melting point is the temperature range in which total or whole polymer chain mobility occurs. The melting point (T ) is called a first-order transition temperature, and Tg is sometimes referred to as a second-order transition. The values for T are usually 33%-100% greater than for Tg. Symmetrical polymers like HDPE exhibit the greatest difference between T and Tg. The Tg values are low for elastomers and flexible polymers such as PE... 

When the free energies F of the two crystal structures are identical, the system is at a critical point. The identity of F does not imply identical fimctions (otherwise the two phases would be indistinguishable). Therefore, at the critical point first derivatives of F might differ and therefore enthalpy, volume, and entropy of the two phases would be different. These transformations are first-order phase transitions, according to Ehrenfest [105]. A discontinuous enthalpy imphes heat exchange at the transition temperature, which can easily be measured with DSC experiments. A discontinuous volume is evident under the microscope or, more precisely, with diffraction experiments on single crystals or powders. Some phase transitions are however characterized by continuous first derivatives of the free energy, whereas the second derivatives (specific heat, compressibility, or thermal expansivity, etc.) are discontinuous. These transformations are second-order transitions and are clearly softer. 

The fact that the order parameter vanishes above does not mean that Nature does not have an inkling of things to come well below (or above) T. Such indicators are indeed found in many instances in terms of the behaviour of certain vibrational modes. As early as 1940, Raman and Nedungadi discovered that the a-) transition of quartz was accompanied by a decrease in the frequency of a totally symmetric optic mode as the temperature approached the phase transition temperature from below. Historically, this is the first observation of a soft mode. Operationally, a soft mode is a collective excitation whose frequency decreases anomalously as the transition point is reached. In Fig. 4.4, we show the temperature dependence of the soft-mode frequency. While in a second-order transition the soft-mode frequency goes to zero at T, in a first-order transition the change of phase occurs before the mode frequency is able to go to zero. 

Both kinetic and thermodynamic approaches have been used to measure and explain the abrupt change in properties as a polymer changes from a glassy to a leathery state. These involve the coefficient of expansion, the compressibility, the index of refraction, and the specific heat values. In the thermodynamic approach used by Gibbs and DiMarzio, the process is considered to be related to conformational entropy changes with temperature and is related to a second-order transition. There is also an abrupt change from the solid crystalline to the liquid state at the first-order transition or melting point Tm. 

Edgar, O. B., and E. Ellery Structure-property relationships in polyethylene terephthalate co-polyesters. Part. I. Melting points. Part II. Second-order transition temperatures, J. Chem. Soc. (London) 1952, 2633—2643 J. Polymer Sci. 8, 1—22 (1952). 

It can be observed that the agreement of the corresponding temperatures is quite well. As Ehrenstein et al. [16] point out, this deviation is normal and usually Tg(E") Tg(Er) Tg(DSC) holds. The materials where a second temperature value is given in italics do not only possess a glass transition but also show a second order transition. For PP 2500 H, PMMA G7 and G55 these second order transitions which are most likely caused by increased mobility of side-chains... 

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