Second-order transition definition

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 ... 

The transitions between the bottom five phases of Fig. 2 may occur close to equilibrium and can be described as thermodynamic first order transitions (Ehrenfest definition 17)). The transitions to and from the glassy states are limited to the corresponding pairs of mobile and solid phases. In a given time frame, they approach a second order transition (no heat or entropy of transition, but a jump in heat capacity, see Fig. 1). 

Both spin-crossover transitions (HS < LS, FO LS) are first order accompanied by definite jumps of populations, while the cooperative Jahn-Teller transition (HS FO) is weak first-order (very close to a second-order transition). It suggests a possibility of observation of hidden cooperative Jahn-Teller transition (the broken line in Fig. 7) between the metastable HS and FO phases, if the HS phase could be supercooled enough below the spin-crossover transition temperature Tc by a rapid cooling. 

Figure A2.5.4 shows for this two-component system the same thermodynamic functions as in figure A2.5.2, the molar Gibbs free energy G= XjPj + X2P25 the molar enthalpy "w and the molar heat capacity C , again all at constant pressure, but now also at constant composition, x = 1/2. Now the enthalpy is continuous because the vaporization extends over an appreciable temperature range. Moreover, the heat capacity, while discontinuous at the beginning and at the end of the transition, is not a delta function. Indeed the graph appears to satisfy the definition of a second-order transition (or rather two, since there are two discontinuities).

The DSC of the polymers can obtained from 50 to 1600°C to observe any first- or second-order transitions and the onset of chemical reactions. The DSC and TGA curves can be superimposed to differentiate between definite melting or glass transitions and the onset of degradation or cure. 

In a ferromagnetic system the order parameter is given by the spontaneous magnetization, M, which in an ideal second-order transition rises from zero at 7J-(see, e.g., Belov 1959). As mentioned in sect. 2, and are related by C, — TdM IQ T and therefore, if the temperature of the maximum of is taken as the thermodynamical definition of T., it corresponds to the maximum slope of M. Many authors define TJ- (T for us) as the temperature where the maximum slope of extrapolates to Ms = 0. Although this is not a thermodynamical definition, the difference ATc = 7 — Tc is a measure of the fluctuations above Tq as was mentioned in sect. 2. 

Before reviewing in detail the fundamental aspects of elastomer blends, it would be appropriate to first review the basic principles of polymer science. Polymers fall into three basic classes plastics, fibers, and elastomers. Elastomers are generally unsaturated (though can be saturated as in the case of ethylene-propylene copolymers or polyisobutylene) and operate above their glass transition temperature (Tg). The International Institute of Synthetic Rubber Producers has prepared a list of abbreviations for all elastomers [3], For example, BR denotes polybutadiene, IRis synthetic polyisoprene, and NBR is acrylonitrile-butadiene rubber (Table 4.1). There are also several definitions that merit discussion. The glass transition temperature (Tg) defines the temperature at which an elastomer undergoes a transition from a rubbery to a glassy state at the molecular level. This transition is due to a cessation of molecular motion as temperature drops. An increase in the Tg, also known as the second-order transition temperature, leads to an increase in compound hysteretic properties, and in tires to an improvement in tire traction... 

Dimarzio [18] identified this state of vanishing entropy as the entropy catastrophe introduced by Kauzmann [19], and regarded T2 as the glass transition temperature Tg of the polymer. Because the temperature derivative of the entropy is discontinuous if the entropy is kept constant at A5" = 0 below T2, the glass transition on the basis of this picture is classified into a second-order transition by Ehrenfest s definition. 

All in all- at this time a first order thermodynamic glass transition can definitely be excluded. However, the controversy over the existence of a second order transition (even though a hypothetical one) in the... 

Sometimes it is stiU debated whether the glass transition is a purely kinetic transition or a second-order thermodynamic transition (van Krevelen 2003). On one hand, it is true that the crystallization process for a number of (atactic) polymers would not take place even at infinite time, and this transition possesses the characteristics of a second-order thermodynamic transition (at least formally, in the Ehrenfest sense see definition of the phase transition in Section 2.2). But the absence of crystallization does not prove that the glass transition is a thermodynamic second-order transition, and it is also true that the glass transition does not occur as a definite sharp transition as would be required by equilibrium thermodynamics. Therefore, the glass transition must be considered a kinetic transition. 

Unfortunately, there is no way to verify experimentally the validity of these two theories. Although the zero conformational entropy can be calculated, the second-order transition temperature, Ti, is experimentally nonverifiable because of the foregoing kinetic freeze-in phenomenon. On the other hand, the free volume , responsible for the experimentally observed glass transition, cannot be quantified because, depending on the definition used, the estimated values of the critical free volumes differ by several orders of magnitude [18]. 

The results indicated that the final hardening appears like a second order transition and that the definition of hardening temperature is complicated because hardening occurs within either a wider or a narrower temperature range, which varies with the technique. Therefore, Yin, et al., ] defined the hardening temperature as the one at which the rate of... 

Order of the Paramagnetic-Antiferromagnetic Transition. A second-order transition is indicated by various studies with neutrons, Ott, Kjems [14], and the behavior of thermal expansion and heat capacity around the N6el temperature [5].The temperature dependence of critical scattering definitely excludes the existence of a smeared-out first-order phase transition [14]. How-... 

Another type of transition is the second-order phase transition in which the first derivative of the chemical potential is continuous while the second derivative is not. This means that enthalpy, volume, and entropy vary continuously with temperature through a second-order phase transition temperature. This behavior is qualitatively different from that of a first-order phase transition, as illustrated in Figure 4.5. Whereas first-order phase transitions occur at a definite temperature for a given pressure, and with separation of the phases, second-order transitions do not exhibit a separation of phases and occur over a range of temperatures. The transition from superfluid helium to normal liquid helium and the transition from being a superconducting metal to being an ordinary conductor are examples of second-order transitions. 

Thermodynamic Transitions and Glasses 10.2.2.1 Definitions of first- and second-order transitions... 

In 1951, The Council of the International Union of Pure and Applied Chemistry (lUPAC) adopted the following definition of a plasticizer a substance or material incorporated in a material (usually a plastic or elastomer) to increase its flexibility, workability, or distensibility. In addition, it is noted that a plasticizer may reduce the melt viscosity, lower the temperature of a second-order transition, or lower the elastic modulus of the product, but it does not alter the chemical nature of the macromolecule. 

Figure 3-11 is a schematic representation of a DSC measurement in which a glass transition and a melting process are shown. A glass transition is not a second-order transition between two defined equilibrium states. It therefore occurs over a relatively wide temperature range and depends upon the rate of temperature change. For this reason a number of different definitions of the glass transition temperature can... 

In 1965, Walter C. McCrone introduced the term pseudo-polymorphism [ 18]. By his definition, pseudo-polymorphic effects included desolvation/dehydration products, second-order transitions and dynamic isomerism however, today the term is generally limited to all phenomena connected with solvates and hydrates. Any substance used in the pharmaceutical industry has the ability to form so-called crystalline hydrates or solvates. In these structures, volatiles (either water or solvent) are not only physisorbed at the solid-air interface but also incorporated into the crystal lattice structure (chemisorbed) as a guest molecule, either in stoichiometric or in non-stoichiometric amounts. Careful consideration must be... 

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