First-order transitions polymer thermodynamics

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. 

The most common applications of DSC are to the melting process which, in principle, contains information on both the quality (temperature) and the quantity (peak area) of crystallinity in a polymer [3]. The property changes at Tm are often far more dramatic than those at Tg, particularly if the polymer is highly crystalline. These changes are characteristic of a thermodynamic first-order transition and include a heat of fusion and discontinuous changes in heat capacity, volume or density, refractive index, birefringence, and transparency [3,8], All of these may be used to determine Tm [8],... 

The transition from a glass to a rubberlike state is accompanied by marked changes in the specific volume, the modulus, the heat capacity, the refractive index, and other physical properties of the polymer. The glass transition is not a first-order transition, in the thermodynamic sense, as no discontinuities are observed when the entropy or volume of the polymer is measured as a function of temperature (Figure 12.2). If the first derivative of the property-temperature curve is measured, a change in the vicinity of is found for this reason, it is sometimes called a second-order transition (Figure 12.2). Thus, whereas the change in a physical property can be used to locate Tg, the transition bears many of the characteristics of a relaxation process, and the precise value of can depend on the method used and the rate of the measurement. 

The glass transition and other transitions in polymers can be observed experimentally by measuring any one of several basic thermodynamic, physical, mechanical, or electrical properties as a function of temperature. Recall that in first-order transitions such as melting and boiling, there is a discontinuity in the volume-temperature plot. For second-order transitions such as the glass transition, a change in slope occurs, as illustrated in Figure 8.5 (9). 

In contrast to a change in slope at the glass transition, a thermodynamic property such as specific volume exhibits a discontinuity with temperature at the crystalline melting point in polymers as in other materials (Figure 6.2). The glass transition is therefore known as a second-order thermodynamic transition (where v versus Tis continuous and dv/dT versus T is discontinuous) in contrast to a first-order transition such as the melting point (where v versus T is discontinuous). 

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]. 

A relatively recent field in polymer science and technology is that of the polymeric liquid crystals. Low molecular liquid crystals have been known for a long time already they were discovered almost simultaneously by Reinitzer (1888) and Lehmann (1889). These molecules melt in steps, the so-called mescrphases (phases between the solid crystalline and the isotropic liquid states). All these molecules possess rigid molecular segments, the "mesogenic" groups, which is the reason that these molecules may show spontaneous orientation. Thus the melt shows a pronounced anisotropy and one or more thermodynamic phase transitions of the first order. 

The conformational entropy defined by Eq. 1 is directly related to the flexibility or rigidity of given polymer chains. Thermodynamic properties of the bulk state are known to be largely affected by the flexibility of the polymer chain. The RIS information is fundamentally important in predicting bulk properties of polymers from a given first-order structure. A great deal of effort has been made to elucidate the role of conformational entropy in determining the phase transition behavior of chain molecules. 

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