Energy balance, thermodynamic gain

Figure 8. Thermodynamic gain of an idealized LSC using a detailed balance of energy.

In order to understand the thermodynamic issues associated with the nanocomposite formation, Vaia et al. have applied the mean-field statistical lattice model and found that conclusions based on the mean field theory agreed nicely with the experimental results [12,13]. The entropy loss associated with confinement of a polymer melt is not prohibited to nanocomposite formation because an entropy gain associated with the layer separation balances the entropy loss of polymer intercalation, resulting in a net entropy change near to zero. Thus, from the theoretical model, the outcome of nanocomposite formation via polymer melt intercalation depends on energetic factors, which may be determined from the surface energies of the polymer and OMLF. 

When a metal, M, is immersed in a solution containing its ions, M, several reactions may occur. The metal atoms may lose electrons (oxidation reaction) to become metaUic ions, or the metal ions in solution may gain electrons (reduction reaction) to become soHd metal atoms. The equihbrium conditions across the metal-solution interface controls which reaction, if any, will take place. When the metal is immersed in the electrolyte, electrons wiU be transferred across the interface until the electrochemical potentials or chemical potentials (Gibbs ffee-energies) on both sides of the interface are balanced, that is, Absolution electrode Until thermodynamic equihbrium is reached. The charge transfer rate at the electrode-electrolyte interface depends on the electric field across the interface and on the chemical potential gradient. At equihbrium, the net current is zero and the rates of the oxidation and reduction reactions become equal. The potential when the electrode is at equilibrium is known as the reversible half-ceU potential or equihbrium potential, Ceq. The net equivalent current that flows across the interface per unit surface area when there is no external current source is known as the exchange current density, f. 

For the three-dimensional self-avoiding walks, the critical exponent of the polymer coil is 3/5, which is larger than the critical exponent of the ideal chain (1/2). This implies that the volume exclusion of the polymer chain leads to coil expansion. Such an expansion makes chain conformation deviate from its most probable state, causing a recovery force originated from the conformational entropy. Therefore, the single coil could not expand unlimitedly, and there exists a thermodynamic balance between the energy gain of volume exclusion and the entropy loss of chain conformation. 

While the relationship between the electronic properties and the reaction enthalpy is important in understanding energetics, the more important thermodynamic feature to focus on is the free energy. Indeed, in Chapter 4 the maximum for the rate of a zeolite-catalyzed reaction is not found for the zeolite with the smallest pore size (maximum adsorption enthalpy) but for medium-sized micropores where adsorbates have a higher entropy, and as a consequence, their concentration is a maximum. The gain in entropy often balances the loss in adsorption enthalpy. 

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