Latent heat, first-order phase transitions

Another approach to liquid glass transition is the self-consistent phonon theory or density functional theory applied to aperiodic structures [112-114]. These theories predict the Lindemann stability criterion for the emergence of a density wave of a given symmetry. Although the finite Lindemann ratio implies a first-order phase transition, the absence of latent heat in glassy systems suggests the presence of an exponentially large number of aperiodic structures that are frozen in at Tg [94,95,110,111],... 

Fig. 2. Isobaric relationship between enthalpy and temperature in the liquid, glassy, and crystalline states. is the melting temperature, and Fg the glass transition temperature. The lower diagram shows the behavior of the isobaric heat capacity. The arrow indicates the -function singularity due to latent heat at a first-order phase transition. (From Debenedetti, 1996.)...

The theory now proceeds as developed in Sections V and VI, essentially unchanged. For example, P v) will have the same bimodal structure as shown in Fig. 14, but will now be continuous. Similar smoothing of all artificially introduced discontinuities will not affect the theory in any essential way. The loss of a sharp distinction between liquid- and solidlike cells could vitiate use of the percolation theory. The nonanalyticity in S will certainly be lost, leading to a communal entropy for which 9S/9p is always less than infinity. However, the first-order phase transition should be preserved, just as it was for most of the parameter space even when )3> 1. The discontinuity in p and v would be reduced, as would be the latent heat. One important effect of this smearing will be the appearance of a critical end point for the liquid, a temperature below which the liquid phase is no longer even metastable. The second-order transition, which is only a small region of parameter space for /8> 1, is now wiped out completely by the restoration of analyticity. Our theory thus leads to a first-order phase transition or no transition at all. However, the entropy catastrophe can be resolved within our theory only if a transition occurs. 

Characteristics of MTDSC Results for Polymer Melting A first-order phase transition is characterised as a change in specific volume accompanied by a latent heat. The most common example studied by DSC is melting. Typically, at the melt temperature, the sample will remain isothermal until the whole sample has melted. The factor that determines the speed of the transition is the rate at which heat can be supplied by the calorimeter. Normally this is fast compared with the overall rate of rise of temperature so the transition is very sharp with a little tail , the length of which is determined by the speed with which the calorimeter can re-establish the heating programme within the sample. The area under the peak is a measure of the latent heat of the transition. 

Melting is an example of a first-order phase transition. There is latent heat and the molar volume is discontinuous at the melting point. One model of melting... 

The experimentally determined values for the heat absorbed during a transition, AQexp. can be compared directly to theoretical estimates AQtn- The value for the latent heat of a first-order phase transition can be calculated from the free energy, yielding... 

More evidence for a critical point comes from adiabatic and nonadiabatic scanning calorimetry measurements [138], [139], a comparison of which yields the latent heat effects associated with a first-order phase transition. Figure 7.19 shows data from both techniques for two chiralities of a CE2 sample. The sharp peaks, which are due to the nonabiatic technique only, represent first-order helical-BPI and BPI-BPIII transitions the BPIII-isotropic peak only shows first-order behavior for X = 0.40. Repeated runs for various chiralities establishes that, for this system, Xc x 0.45. A complete experimental analysis of the rotatory power and calorimetric experiments has been performed by Kutnjak et al. [139], who conclude that the data is consistent with mean field behavior. Since that time, however, new theory has appeared which allows different conclusions. 

Furthermore, assuming a first-order phase transition, the VPT can be detected by caloric methods. With a differential scanning calorimetry (DSC) measurement, flie heat change, which provides information about the internal free energy or latent heat, can be determined (Otake et al. 1990 Hirotsu 1993, 1994). Figure 1 shows two curves of the DSC method for PNIPAAm with different cross-linking concentrations. The cross-linker used for this case was layered siUcates (Haraguchi et al. 2002 Ferse 2007). 

If a first-order phase transition occurs between r(0) and T (oo), there will be a nonexponential T(t) variation due to latent heat effects. This situation can be handled [32, 33] by defining a time-dependent heat capacity C(t)=Plt, where P=Pq-(T-Tq)K, . In this procedure it is possible to obtain the latent heat using ... 

In photoacoustics, as in a.c. calorimetry, relatively small periodic temperature variations (in the mK range) are used, and only small amounts of samples are needed. The small temperature variations allow measurements very close to phase transitions but latent heats of first-order phase transitions can also not be obtained in this way. 

Phase transitions in a material can be classified as first order and continuous (second order). At a first-order phase transition, we observe a discontinuity of some physical property representative of the degree of order in the system. For example, this could be material density or a calculated measure of order in the material (i.e., an order parameter). If we measure this parameter across the phase boundary, there will be a step, or discontinuity, at the transition point. An example of a typical first-order phase transition is ice melting. At the transition point, the density of the material abruptly changes as we go from ice to liquid water. First-order transitions also have a measureable latent heat. Some phase transitions can be described as weakly first order. In this case, the enthalpy change associated with that transition is very small. This is often true of phase transitions in soft matter systems. As a result, the enthalpy change may be difficult to measure, thus making the phase change difficult to detect by thermal properties alone. 

At point C, we can note another interesting feature of the diagram. The line that defines the transition between liquid and gas is discontinuous and ends at this point. This is a critical point. Below the critical point, the phase transition is discontinuous, with an associated latent heat (first order), but above this line there is no defined phase transition from liquid to gas, and the density of the material varies continuously. 

Different liquid crystal phase transitions will be more or less difficult to detect using DSC. If the transition is first order, meaning that the order parameter is discontinuous across the phase boundary, a significant latent heat will be measurable, and usually a clear peak can be observed. An example of a first-order phase transition in liquid crystals would be the crystalline-to-smectic or -nematic phase. The nematic-to-isotropic phase is also first order. Some liquid crystal phase transitions are much more... 

Latent heat The change in enthalpy associated with a first-order phase transition. 

First-order phase transitions are those that involve a latent heat. During such a transition, a system either absorbs or releases a fixed (and typically large)... 

Since the depletion region of the entropy has an energetic width Ag > 0 and coimects energetic spaces which are associated with different phases of reduced thermodynamic activity, the extended region in-between accommodates macrostates, in which two phases coexist. It is therefore common to interpret Ag as the latent heat and to associate the entropic suppression in this region with a first-order transition, in analogy to thermodynamic first-order phase transitions in the thermodynamic limit. 

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