Determining the partition

We assume that exploring all possible forms for the fields corresponds to exploring the overall usual phase space. To determine the partition function Z the contributions from all the p+ r) and P- r) distributions are summed up with a statistical weight, dependent on p+ r) and p (r), put in the form analogous to the Boltzmann factor exp[—p (F)]], where the effective Hamiltonian p (F)] is a functional of the fields. The... 

In laboratory work the following closely related, but not identical, relationship is used to determine the partition value between phases ... 

The effects of pH on electrokinetic velocities in micellar electrokinetic chromatography was studied by using sodium dodecyl sulfate solutions [179]. Micellar electrokinetic capillary chromatography with a sodium dodecyl sulfate pseudostationary phase has been used to determine the partition constants for nitrophenols, thiazolylazo dyes, and metal chelate compounds [180]. A similar technique was used to separate hydroquinone and some of its ether derivatives. This analysis is suitable for the determination of hydroquinone in skin-toning creams [181]. The ingredients of antipyretic analgesic preparations have also been determined by this technique [182], The addition of sodium dodecyl sulfate improves the peak shapes and resolution in chiral separations by micellar electrokinetic chromatography [183]. 

Thus, given sufEcient detailed knowledge of the internal energy levels of the molecules participating in a reaction, we can calculate the relevant partition functions, and then the equilibrium constant from Eq. (67). This approach is applicable in general Determine the partition function, then estimate the chemical potentials of the reacting species, and the equilibrium constant can be determined. A few examples will illustrate this approach. 

When both the neutral and the n different charged forms of a compound partition into the organic phase, a minimum of n + 1) titrations with different phase volume ratios is necessary to determine the partition coefficient of each species. For a monoprotic substance, for instance, can be related to pK by an empirical equation [119] ... 

Luo et al. (2000) used a somewhat different method for determining the partitioning of Ra by noting that Rn is produced by the total amount of Ra both in solution and on surfaces (and so equal to (1 + K226Ra)( Ra)w) as well as by recoil. " Ra is produced similarly by Ra (through the beta decay of Th) from within the minerals and from the surface. Combining the respective equations (by assuming that the recoil rates for... 

The easiest way to determine the partition coefficient is to extract V cm3 of saturated aqueous solution with Vz cm3 of solvent, and determine the concentration Cj in the latter. The amount left in the aqueous phase is (Ci V — C2V2) = M, so that the partition coefficient is given by... 

Xiang, T.-X. Anderson, B. D., Phospholipid surface density determines the partitioning and permeability of acetic acid in DMPC cholesterol bilayers, J. Membrane Biol. 148, 157-167 (1995). 

In addition to the TDI experiment, the partition ratio measures the TDI efficiency. Specifically, the partition ratio is the number of inactivation kinetic events (k nact) versus the number of substrate turnover events per unit enzyme (kcat) [161], Thus, the most potent partition ratio is zero. The most common experimental setup for determining the partition ratio is the titration method that increases the inhibitor concentration relative to a known amount of enzyme. After the incubations, a secondary incubation containing a probe substrate similar to the TDI experiment is used to define the remaining activity. For accurate determination of the partition ratio from the titration method, it is assumed that the inhibitor is 100% metabolized ... 

It is important to point out once again that explanations (rationalizations) of isotope effects which employ arguments invoking hyperconjugation and/or steric effects are completely equivalent to the standard interpretation of KIE s in terms of isotope independent force constant differences, reactant to transition state. In turn, these force constant differences describe isotope dependent vibrational frequencies and frequency differences which are not the same in reactant and transition states. The vibrational frequencies determine the partition functions and partition function ratios in the two states and thus define KIE. The entire process occurs on an isotope independent potential energy surface. This is not to claim that the... 

Estimation or measurement of pKa is important to understand the state of ionization of the drug under physiological conditions and to evaluate salt-forming ability.27 Log P determines the partitioning of a drug between an aqueous phase and a lipid phase (i.e., lipid bilayer). Log P and acid pKa can be theoretically estimated with reasonable accuracy.14,28,29 High-throughput methods are also available for measurement of log P30 and pKa.31... 

These new methods for determining the partition coefficients of ionized species are still e3q>erimenta1, but they are presented in a spirit that they may stimulate thinking and further refinement. Single-phase titrations with HCl in octanol have only recently been run. A possible concentration dependency of pKa in the single-phase titrations has been suggested by a referee and will be looked for. Further refinement of the two-phase titrations may incorporate ion-pair association constants. 

Ionisation determines the partitioning of drugs across membranes. Unionised molecules can easily cross and reach an equilibrium across a membrane, while the ionised form cannot cross. When the pH is different in the compartments separated by the membrane the total (ionised + unionised) concentration will be different on each side. An acidic drug will become concentrated in a compartment with a high pH and a basic drug in one with a low pH. This is known as ion-trapping, and occurs in the stomach, kidneys, and across the placenta. Urinary acidification accelerates the excretion of weak bases, such as pethidine, while alkalinisation increases the excretion of acidic drugs, such as aspirin. As an example consider pethidine (pKa 8.6) with an unbound plasma concentration of 100 (arbitrary units). At pH 7.4 only 6% of the pethidine will be unionised so that at equilibrium the concentration of unionised pethidine in the urine will be 6 units. In urine at pH 6.5 only 0.8% of the pethidine will be unionised so that the total concentration in the urine will be 744 units. 

Davies, D.T. and White, J.C.D. (1960) The use of ultrafiltration and dialysis in isolating the aqueous phase of milk and in determining the partition of milk constituents between the aqueous and disperse phases. J. Dairy Res., 27, 171-90. 

Molecular Interactions Determining the Partitioning of Organic Compounds Between Different Phases... 

In equilibrium one has, of course, Afik — A y k- These equilibrium conditions are useful for determining the partitioning of the components between the phases, or for determining the %a values (109). 

To test this, we determined the partition coefficients of two different solute extremes - vitamin B-12 and norethindrone. Vitamin B-12 is a relatively large, hydrophilic solute, while norethindrone is a relatively small, hydrophobic solute. Thus we would expect size exclusion to dominate partitioning with vitamin B-12, while hydrophobic interactions should dominate with norethindrone. This behavior is in fact observed in Figs. 19 and 20. The values of K... 

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