Thermodynamics first , order

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 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). 

Secondary crystalline transitions (below Tm) occur if the material transforms from one type of crystal to another. These transitions are, like the melting point, thermodynamic first-order transitions. 

While the melting of crystallites is known as a thermodynamic first-order transition (since it involves a discontinuity, at a characteristic temperature, in a property, such as volume, that is a first derivative of free energy), the glass-rubber transition is often considered as a second-order transition (since it involves a discontinuity at a characteristic temperature in a property, such as coefficient of expansion, that is a second derivative of energy). ... 

Moreover, it is also interesting to find that the unit cell dimensions along the a- and -axes show small, but sudden, changes at the transition temperature of e Sj7->Sg. Their first derivatives with respect to the temperature, the coefficients of mermal expansion of those axes, also exhibit discontinuous changes (S,Jjy This clearly indicates that this transition possesses the characteristics of a thermodynamic first-order transition (4). 

There has been considerable interest in the mechanisms of the a — /3 transition, and this has been modeled for static and dynamic measurements [58-60], X-ray diffraction patterns and infrared (IR) and Raman spectra show specific changes through this a—>/3 transition [42-44,61-63], The stress and strain dependence of the molar fraction of the / -form, X, increases drastically above the critical stress / the fraction is almost linearly proportional to the strain the transition is reversible the stress-strain curve has a plateau of the critical stress /, i.e., the curve is divided into three regions the elastic deformation of the a-phase (0-4% strain), the a — /3 transition (plateau region 4-12% strain), and the elastic deformation of the /3-phase (> 12% strain). These experimental results indicate that this stress-induced phase transition is a thermodynamic first-order transition. 

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. 

In Secs. 4.3 and 4.4 we discussed the thermodynamics of the crystal -> Uquid transition. This and other famiUar phase equilibria are examples of what are called first-order transitions. There are other less familiar but also well-known... 

Another well-known thermodynamic result, the Clapeyron equation, applies to first-order transitions (subscript 1) ... 

According to a kinetic study which included (56), (56a) and some oxaziridines derived from aliphatic aldehydes, hydrolysis follows exactly first order kinetics in 4M HCIO4. Proton catalysis was observed, and there is a linear correlation with Hammett s Ho function. Since only protonated molecules are hydrolyzed, basicities of oxaziridines ranging from pii A = +0.13 to -1.81 were found from the acidity rate profile. Hydrolysis rates were 1.49X 10 min for (56) and 43.4x 10 min for (56a) (7UCS(B)778). O-Protonation is assumed to occur, followed by polar C—O bond cleavage. The question of the place of protonation is independent of the predominant IV-protonation observed spectroscopically under equilibrium conditions all protonated species are thermodynamically equivalent. 

Dihydroxypteridine was expected to undergo hydration but, a priori, it was difficult to decide whether covalent hydration would occur across the 3,4- or the 7,8-position, or both. Kinetic and spectroscopic evidence now indicate that addition of water occurs much more rapidly across the 3,4-positions (and, hence, that the energy of activation must be less for this site), but the 7,8-water-adduct is thermodynamically the more stable. With time, the concentration of the species hydrated in the 3,4-position reaches a maximum (about 64% of the total concentration). Thereafter, it falls steadily and the concentration of the 7,8-adduct rises until, at equilibrium, the latter accounts for 92% of the total and the 3,4-adduct for only 7.6%. In 2,6-dihydroxy-4-methylpteridine, the methyl group drastically reduces the extent of water addition to the 3,4-position but does not significantly affect 7,8-addition, so that, spectroscopically, only a first-order conversion of anhydrous molecule into the 7,8-water-adduct is observed. ... 

The aim of the present study is precisely to investigate the thermodynamical properties of an interface when the bulk transition is of first order. We will consider the case of a binary alloy on the fee lattice which orders according to the LI2 (CuaAu type) structure. 

First law of thermodynamics The statement that the change in energy, AE, of a system, is the sum of the heat flow into the system, q, and the work done on the system, w, 214-217,223q First order reaction A reaction whose rate depends upon reactant concentration raised to the first power, 292-295, 316-317q... 

The best understood compounds are cis- and fra s-RuX2(DMSO)4 (X = Cl, Br). The fra s-isomers are thermodynamically less stable and isomerize in DMSO solution to the m-isomer, with first-order kinetics, probably via a dissociative mechanism. The reverse process, cis to trans, is catalysed by light. Syntheses for these and other DMSO complexes are shown in Figure 1.37 [108],... 

An evaluation of the retardation effects of surfactants on the steady velocity of a single drop (or bubble) under the influence of gravity has been made by Levich (L3) and extended recently by Newman (Nl). A further generalization to the domain of flow around an ensemble of many drops or bubbles in the presence of surfactants has been completed most recently by Waslo and Gal-Or (Wl). The terminal velocity of the ensemble is expressed in terms of the dispersed-phase holdup fraction and reduces to Levich s solution for a single particle when approaches zero. The basic theoretical principles governing these retardation effects will be demonstrated here for the case of a single drop or bubble. Thermodynamically, this is a case where coupling effects between the diffusion of surfactants (first-order tensorial transfer) and viscous flow (second-order tensorial transfer) takes place. Subject to the Curie principle, it demonstrates that this retardation effect occurs on a nonisotropic interface. Therefore, it is necessary to express the concentration of surfactants T, as it varies from point to point on the interface, in terms of the coordinates of the interface, i.e.,... 

The activation parameters from transition state theory are thermodynamic functions of state. To emphasize that, they are sometimes designated A H (or AH%) and A. 3 4 These values are the standard changes in enthalpy or entropy accompanying the transformation of one mole of the reactants, each at a concentration of 1 M, to one mole of the transition state, also at 1 M. A reference state of 1 mole per liter pertains because the rate constants are expressed with concentrations on the molar scale. Were some other unit of concentration used, say the millimolar scale, values of AS would be different for other than a first-order rate constant. 

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