Thermodynamics conjugate properties

Figure 11.2 Thermodynamic vectors for a simple fluid, represented in a two-dimensional diagram in which lengths and angles are expressed in terms of experimental properties for example, cos 0St — (Cy/Cp)1 2 and cos 6Sy = aP(TW/CPpT) 2. The thermodynamically conjugate temperature and volume vectors T), V) are perpendicular, as are the pressure and entropy vectors P), S). A number of thermodynamic relationships among the experimental quantities can be read off directly from the diagram.

The first term on the right side of Eq. (1.53) orEq. (1.54) represents heat associated with the thermodynamic temperature T. and the remaining terms are the work terms. The pairs of intensive and extensive properties, such as 1 IT and U, or/, and A, are the conjugate properties. 

There are two approaches for proving the existence of entropy in classical thermodynamics these rely on either molecular-based statistical mechanics or classical thermodynamics. First we employ the latter approach because of its simplicity. It is not necessary to use either approach, because the conjugate property of temperature and entropy is important. In the sense of molecular physics, both the temperature and entropy are an aspect of kinetic movement and the energy level of molecules. 

Modem scaling theory is a quite powerful theoretical tool (appHcable to Hquid crystals, magnets, etc) that has been well estabUshed for several decades and has proven to be particularly useful for multiphase microemulsion systems (46). It describes not just iuterfacial tensions, but virtually any thermodynamic or physical property of a microemulsion system that is reasonably close to a critical poiat. For example, the compositions of a microemulsion and its conjugate phase are described by equations of the foUowiug form ... 

Butadiene, the simplest conjugated diene, has been the subject of intensive theoretical and experimental studies to understand its physical and chemical properties. The conjugation of the double bonds makes it 15 kJ/mole (3.6 kcal/mol) (13) more thermodynamically stable than a molecule with two isolated single bonds. The r-trans isomer, often called the trans form, is more stable than the s-cis form at room temperature. Although there is a 20 kJ/mole (4.8 kcal/mol) rotational barrier (14,15), rapid equiUbrium allows reactions to take place with either the s-cis or r-trans form (16,17). 

Interactions polarize bonds. Trimethylenemethane (TMM) and 2-buten-l,4-diyl (BD) dianions (Scheme 6a, b) are chosen as models for hnear and cross-conjngated dianions. The bond polarization (Scheme 7) is shown to contain cyclic orbital interaction (Scheme 6c) even in non-cyclic conjugation [15]. The orbital phase continnity-discon-tinnity properties (Scheme 6d, e) control the relative thermodynamic stabihties. 

The orbital phase continuity underlies the aromaticity or the thermodynamic stability of cyclic conjugated molecules. Kinetic stability of cyclic conjugate molecules is shown here to be also under the control of the orbital phase property. The continuity conditions can be applied to the design of powerful electron donors and acceptors. 

The cyclic conjugation is continuous if the donors are on one side of the cyclic chain and the acceptors are on the other side (Scheme 14a). Electrons delocalize from a donor Dj to Aj. The electron accepted by Aj can readily delocalize to the neighbor on the other side because it is an acceptor (A ). An electron can delocalize from D, to A. The delocalization can take place along the other path. donates an electron to A. The resulting electron hole in can be supplied with an electron by the neighbor Dj. This is equivalent to the delocalization from Dj to A. Electrons can delocalize in a cyclic manner. Thermodynamic stability of continuously conjugated molecules is under control of the orbital phase property or determined by the number of n electrons. 

Cyclic conjugation is continuous in o-benzoquinone and discontinuous in p-benzoquinone (Scheme 15, cf. Scheme 4). The donors (the C=C bonds) are on one side of the cyclic chain and the acceptors (the C=0 bonds) are on the other side in o-benzoquinone. In p-benzoquinone the donors and the acceptors are alternatively disposed along the chain. The thermodynamic stability of o-benzo-quinone is under control of the orbital phase property. The continuity conditions are not satisfied. o-Benzoquinone is antiaromatic. The thermodynamic stability of p-benzoquinone is free of the orbital phase (neither aromatic nor antiaromatic) and comes from the delocalization between the four pairs of the neighboring donors and acceptors. In fact, p-benzoquinone, which melts at 116 °C, is more stable than o-benzoquinone, which decomposes at 60-70 °C. 

The kinetic stabilities and the donor-acceptor properties of cyclic conjugated molecules [68] have been described (Scheme 12) in the theoretical subsection (Sect. 2.2.2) to be controlled by the phase property. There is a parallelism between the thermodynamic and kinetic stabilities. An aromatic molecule, benzene, is kinetically stable, and an antiaromatic molecule, cyclobutadiene, is kinetically unstable (Scheme 13). 

Stabilities of cyclic conjugated molecules encountered in the laboratory seem to owe much to kinetic rather than thermodynamic properties. Many unstable conjugated molecules including anti-aromatic molecules are now known to be isolated as stable ones when they are protected by bulky substituents from intermolecular reactions. 

According to the theory of cyclic conjugation, the Hueckel rule is applicable only to a continuous cyclic conjugation, but not to a discontinuous one (Schemes 14 and 15). In the discontinuously conjugated molecules, electron donors and acceptors are alternately disposed along the cyclic chain [25].The thermodynamic stability depends neither on the number of n electrons nor the orbital phase properties, but on the number of neighboring donor-acceptor pairs. Chemical consequences of the continuity-discontinuity of cyclic conjugation are reviewed briefly here. 

Next, we used an in-house library design software (see details in Chapter 15) to enumerate the virtual libraries and then calculated various physical properties. Products were removed from consideration if MW is > 300, number of rotatable bonds > 3, and ClogP > 3. For solubility, two in-house model calculations were applied as filters turbidimetric >10 mg/mL and thermodynamic solubility >100 xM. The resulting cherry-picked library was then reviewed by NMR spectroscopists to remove compounds with possible artifacts, likely to be insoluble, or likely to be false positive. These included some conjugated systems and compounds with likelihood of indistinct NMR spectra. 

Comparison of the combined first/second law (4.28) with (4.30) leads to the more general and rigorous thermodynamic definitions for the intensive properties T, —P respectively conjugate to the extensive properties S, V ... 

The property (11.59) then permits one to easily rewrite thermodynamic equations in their conjugate form for example, (11.53) becomes... 

Constantinou, L., S. E. Prickett, and L. Mavrovouniotis, Estimation of Thermodynamic and Physical Properties of Acyclic Hydrocarbons Using the ABC Approach and Conjugation Operators. Ind. Eng. Chem. Res., 1993 32, 1734-1746. 

Acrylonitrile (C3H3N, mol wt = 53.064) is an unsaturated molecule having a carbon-carbon double bond conjugated with a nitrile group. It is a polar molecule because of the presence of the nitrogen heteroatom. Tables 1 and 2 list some physical properties and thermodynamic information, respectively, for acrylonitrile. 

This is the form we have already used to describe the linear responses which define the properties of materials, but in some cases, notably for the temperature T, it is inconvenient to set the initial value To to zero (this would require redefining the thermodynamic temperature scale), and so eq. (3) is used instead (see Table 15.7). In the particular example of a change in temperature, the conjugate response is... 

H is the conjugate acid of eaq" [pKa(H") = 9.1 reactions (1), k = 2.2 x 107 dm3 mol-1 s-1 and (2), k = 23 x 1010 dm3 moU1 s 1 (Buxton et al. 1988), for the thermodynamic properties of this system, see Hickel and Sehested (1985)]. Thus, in pure water, the lifetime of eaq is quite long (Hart et al. 1966), even long enough to monitor its presence spectrophotometrically under steady-state 60Co-y-radi-olysis conditions (Gordon and Hart 1964). 

Since fullerene C60 is one of the participants of reaction (4.4) one may suppose that all the conjugation effects in a fullerene cage are properly considered. The values of thermodynamic properties for fullerene C60, cyclohexane and adamantane have been... 

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