Stabilization quotient

Leggett, D. J., SQUAD Stability quotients from absorbance data, in Leggett, D. J. (ed.), Computational Methods for the Determination of Formation Constants, Plenum Press, New York, 1985, pp. 158-217. 

The intrinsic constants are thermod3mamic constants written for reactions occurring at a hypothetical isolated site on the surface. Actual activities on the surface cannot be directly determined but Q or apparent stability quotients can be calculated based on measurable bulk concentrations. The intrinsic constants and apparent stability quotients are related by considering the electrostatic correction for an ion in solution near the surface compared to an isolated ion on the surface. In an idealized planar model, is the mean potential at the plane of surface charge created by the ionization of the surface functional groups and the formation of surface complexes and is the mean potential at the plane of adsorbed counter ions at a distance 3 from the surface (17). The electrostatic interaction energies at the surface and at a distance 3 are expressed as exponentials. Therefore ... 

K = intrinsic equilibrium constant Q = apparent stability quotient... 

The apparent stability quotients are determined by utilizing the potentiometric titration data and the value for the... 

Using these approximations the apparent stability quotient for Na is ... 

The concentrations of the various surface sites (Fe-0H25 Fe-OH, Fe-O", Fe-0 Na, Fe-O K", Fe-0 MgOH, Fe-0 CaOH+, Fe-0H C1 , Fe-OH HSOj ) were determined by simultaneously solving the apparent stability quotients describing the formation of these sites and the equation describing the total surface sites (Equation 18). 

Refinement refers to efforts to make experimental design as painless and efficient as possible in order to minimise the suffering of each animal subject. One of these refinements consist of non-invasive resonance frequency analysis (RFA) to assess the osseointegration of implants. Roze, Hoornaert and Layrolle (2014) found good correlation between the histomorphometric parameters implant stability quotient (ISQ) and bone growth around the implants (bone surface/tissue surface BS/TS 0.5 mm), and RFA of cylindrical Ti implants inserted bilaterally into the femoral epiphyses of rabbits, thus confirming that RFA may be a useful technique to determine the quality of bone apposition. 

The closest redox-stable analogue of Ce(IV) is thorium(IV), for which a large data base of thermodynamic parameters is available for the carboxylic add complexes (Martell and Smith 1977). Using the ionic radii of Shannon (1976) and recalling that the stability of lanthanide and actinide complexes is derived almost exclusively from electrostatics, we can estimate that a 16% increase in the log of the stability quotients for thorium (since AG oc Z /r oc log should provide a reasonable estimate for the corresponding complexes of cerium(IV) [rce(CN = 8) = 0.97 A, r iCN = 10) = 1.13 A, (l/rce)/(l/ xh) = 116, CN = coordination number]. 

Figure 11.20 Stabilization quotient Q of nicotinic acid esters (ethyl, isopropyl, butyl, benzyl and hexyl) as a function of percentage binding of ester, (a) to three non-ionic surfactants based on PEG lOCX) O PEG l(X)0-lauryl ether, X PEG l(XX)-myristyl ether, PEG 1000 palmityl ether, and (b) to three stearyl surfactant derivatives, O PEG 900 stearyl ether, X PEG 1400 stearyl ether and PEG 2000 stearyl ether. In both (a) and (b) ionic strength is 0.083, temperature 20.0 0.1° C and borate buffer pH 10.(X) 0.02 used. Redrawn from Lippold et al [137], by permission.

Calculation of the internal cell potential is a very complicated matter because the electrochemistry of all of the species within the protocell would have to be balanced subject to their composition quotient Q, after which the standard free energy would have to be established from tabulations. The transport of Na+ would also change this balance, along with the ionic strength of the solution and the stability of the proteins or prebiotic molecules within the protocell. Such non-equilibrium thermodynamics forms the basis of the protocell metabolism. The construction... 

Stability (or binding) constants Ks are often used instead of dissociation constants (Ks = 1/Kd). These equilibrium constants are concentration quotients as the corresponding activity coefficients are given the value 1. However, in many practical situations, other... 

In the previous section we found that only the relative values of the parameters /1 and k, through their quotient, are important in determining the stationary state. We now consider the local stability of this solution and will find here that ji and k play separate roles. We apply the same recipe as that introduced in 3.2 of the previous chapter beginning from the Jacobian matrix... 

The possible factors involved in the biological selectivity towards metal ions have been considered by Frausto da Silva and Williams3 and by Kustin et al.4 In terms of thermodynamic selectivity a useful formalism for the uptake of any metal ion from a multimetal system is the quotient A Cm, where Km is a relative stability constant and Cm is the concentration of the metal ion. However, as these authors point out,3 a combination of both thermodynamic and kinetic properties must be considered. An appreciation of kinetic factors is often absent in this field, but must be of prime consideration in chelate exchange reactions and in the final irreversible step of metal ion insertion to form the metalloenzymes. 

One other serious criticism regarding the data on Cu speciation is the neglect of the cysteine present in blood plasma. Cu11 and cysteine undergo a facile redox reaction (Chapter 20.2). Since the reaction is irreversible, no quantitative thermodynamic quotient is available for use in the computer calculations. Another assumption often made is that the overwhelming concentration of other amino acids may prevent cysteine coordination and, as a result, stabilize the Cu11 state. Recent studies show that this assumption is totally unjustified48 and so the dilemma still has to be resolved. 

Knowing the stability constants (actually, molarity quotients or stoichiometric constants are more useful here), it is possible to say which... 

By graphically plotting 0 as a function of [A ] one can determine vs. [A cp" and aj are obtained at N values of [A-] in the concentration range used. Thus there are N equations from which the stability constants fij can be evaluated. The quotient between the total concentration of the central group adsorbed on the resin (Cmr) and in solution, Cm at equilibrium is written as... 

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