Free energy terms

As is known, SEC separations require interaction-free conditions. Therefore, the enthalpic contribution to the free energy term vanishes when no enthalpic interaction is postulated between analyte and sorbent ... 

We now discuss the effects of finite chain length. The difficulties arise from the definition of a bulk free energy term, when the very nature of the chains constrains the crystal thickness to be finite. There are two different approaches to this problem the first to be considered is due to Hoffman et al. [31] and is a simple modification of the infinite chain case, but is somewhat lacking in theoretical justification the second, due to Buckley and Kovacs [23], aims to correct this deficiency and suggests that the interpretation of experimental data given by Hoffman s approach is misleading. 

If the two representations are equivalent then Eqs. (3.79) and (3.80) describe how A s and B s must be transformed in terms of a s and /Ts. (These identities are performed explicitly by Sanchez and Di Marzio, [49]. Frank and Tosi [105] further show that if a s and /Ts are chosen to satisfy detailed balance conditions, that is equilibrium behaviour, then the occupation numbers of the two representations are only equivalent if the nv s are in an equilibrium distribution within each stage. This is likely to be true if there is a high fold free energy barrier at the end of each stem deposition, and thus will probably be a good representation for most polymers. In particular, the rate constant for the deposition of the first stem, A0 must contain the high fold free energy term, i.e. ... 

A note on good practice Notice that by using the molar convention, the units match RT is a molar energy (kilojoules per mole), and so too are the two Gibbs free energy terms. 

That is, the equilibrium constant for a reaction is equal to the ratio of the rate constants for the forward and reverse elementary reactions that contribute to the overall reaction. We can now see in kinetic terms rather than thermodynamic (Gibbs free energy) terms when to expect a large equilibrium constant K 1 (and products are favored) when k for the forward direction is much larger than k for the reverse direction. In this case, the fast forward reaction builds up a high concentration of products before reaching equilibrium (Fig. 13.21). In contrast, K 1 (and reactants are favored) when k is much smaller than k. Now the reverse reaction destroys the products rapidly, and so their concentrations are very low. 

In some cases, the enthalpy term may actually oppose the formation of the chelated complex, although the entropy term outweighs it to give an overall favourable free energy term. In general, this situation is the exception rather than the rule. 

Where AG is the free energy term associated with cavity formation, N is Avogadro s number, AA is the change in surface area due to... 

Clearly, this equation can be made more precise by modifying the terms by reference to the crystal geometry. Additionally, the free energy term AGm can be separated into its components, using the following equation ... 

F> obtained by solving the equation is consistent with the F> used to calculate the reaction field. Having established an effective nonlinear Hamiltonian, one may solve the Schrodinger equation by any standard (or nonstandard) manner. The common element is that the electrostatic free energy term Gp is combined with the gas-phase Hamiltonian Hq to produce a nonlinear Schrodinger equation... 

The chemical or intrinsic free energy term is reflected in the pHp2C this pHpzc varies for every oxide depending on each oxide s proton affinity. The Coulombic term, however, is approximately the same for different oxides (AG°ou) = ZF /) at a given ApH and at a given ionic strength. This will be discussed further in Chapter 3.8. 

Since surface pressure is a free energy term, the energies and entropies of first-order phase transitions in the monolayer state may be calculated from the temperature dependence of the ir-A curve using the two-dimensional analog of the Clausius-Clapeyron equation (59), where AH is the molar enthalpy change at temperature T and AA is the net change in molar area ... 

Haq, 2002, has described the overall observed drug-DNA binding free energy as being composed of at least five component free energy terms (the free... 

The free energy term AG is related to the free energy of activation AG" " by... 

Equations 3.121 and 3.122 distinguish the bulk Gibbs free energy of the mixture ( mixture) from the Gibbs free energy term involved in the mixing procedure... 

If mixture (A,B)N is ideal, mixing will take place without any heat loss or heat production. Moreover, the two cations will be fully interchangeable in other words, if they occur in the same amounts in the mixture, we will have an equal opportunity of finding A or B over the same structural position. The Gibbs free energy term involved in the mixing process is... 

If the heat capacity of a chemically complex melt can be obtained by a linear summation of the specific heat of the dissolved oxide constituents at all T (i.e., Stebbins-Carmichael model), the melt is by definition ideal. The addition of excess Gibbs free energy terms thus implies that the Stebbins-Carmichael model calculates only the ideal contribution to the Gibbs free energy of mixing. 

Partial molal volumes can be related to the corresponding Gibbs free energy terms through the partial derivatives on P (see equations 2.28 and 2.33). 

This represents the difference in the second adsorption free energy term in Equation 21, i.e. the two terms on the right hand side each represent the change in free energy when a water-surface molecular contact is replaced with a surfactant-surface molecular contact. It is very reasonable to assume that, at close packing, both surfactants adsorb with only their hydrocarbon moieties (or part of these moieties) in direct contact with the surface. Hence, the two surfactants interact with the latex surface with the same strength and the last term in Equation 17 is equal to zero. 

Equating the molar free-energy terms in (12.24) and (12.25) affords an expression which relates the hydraulic pressure P required to force mercury into pores to the relative pressure, PJPq, exerted by the liquid with radius of curvature, r. That is. 

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