Intrinsic distribution coefficient

In many extraction systems in practice, species i can exist not only as i, but also in other forms. The effective distribution (or partition) coefficient Kq will then be based on the total concentration of t in all forms in the two phases. The intrinsic distribution coefficient Kq of only the free species i between the two phases in the absence of chemical reactions wiU, in general, be different from k [. The intrinsic distribution coefficient Kq of only the free species i between the two phases in the presence of chemical reactions may be different from Kq. If the presence of other species does not influence the distribution coefficient, then Kq = Kjj. Assume the mutual solubility of water and the organic solvent to be unaffected by any of these reactions. We now study how to determine k," for several different cases. 

It has been determined that there is a distribution coefficient for the impurities between crystal and melt which favors the melt. We can see how this arises when we reflect that impurities tend to cause formation of intrinsic defects within the crystal and lattice strain as a result of their presence. In the melt, no such restriction applies. Actually, each impurity has its own distribution coefficient. However, one can apply an average value to better approximate the behavior of the majority of impurities. 

We return to using the Kp and Kd symbols to represent the partition coefficient and the apparent partition (distribution) coefficient, respectively. The effective, apparent, membrane, and intrinsic permeability coefficients are denoted Pe, Pa, Pm, and P0, respectively, and D refers to the diffusivity of molecules. 

One of the original concepts governing oral absorption of organic molecules is the pH partition hypothesis . This hypothesis states that only the nonionized form of the drug is able to permeate the membranes of epithelial cells lining the GI tract [26], According to the classical pH-partition theory, permeability is expected to correlate not with the intrinsic partition coefficient but with the so-called distribution coefficient D of the solute [27], where D is defined as ... 

The partition coefficient (log P) describes the intrinsic lipophilicitY of the collection of functional groups and carbon skeleton, which combine to make up the structure of the compound, in the absence of dissociation or ionization. Methods to measure partition and distribution coefficients have been described [3,4]. 

Where ko, is the distribution coefficient kg and kj are the intrinsic partition coefficient for species 0 and 1 where species 0 is the most protonated. 

The partition coefficient refers to the intrinsic lipophilicity of the drug, in the context of the equilibrium of unionized drug between the aqueous and organic phases. If the drug has more than one ionization center, the distribution of species present will depend on the pH. The concentration of the ionized drug in the aqueous phase will therefore have an effect on the overall observed partition coefficient. This leads to the definition of the distribution coefficient (log D) of a compound, which takes into account the dissociation of weak acids and bases. 

Lipophilicity can be reported as log P, which is the intrinsic partitioning of the drug between octanol and water when the drug is in the neutral state. However, lipophilicity is often reported as log D (distribution coefficient), which represents the distribution of the drug at a specific pH, typically pH 7.4. 

Both the intrinsic rate constant and the effective diffusivity (KD) can be extracted from measurements of the reaction rate with different size fractions of the zeohte crystals. This approach has been demonstrated by Haag et al. [116] for cracking of n-hexane on HZSM5 and by Post et al. [117] for isomerization of 2,2-dimethylbutane over HZSM-5. It is worth commenting that in Haag s analysis the equilibrium constant (or distribution coefficient K) was omitted, leading to erroneously large apparent diffusivity values. 

For an intrinsic rate-limited reaction in the organic phase, if the rate equation can be expressed as rate = ky[catalyst]oj.g[substrate]o g, then for a given substrate the rate of reaction depends mainly on the concentration of the active catalytic species in the organic phase and on the intrinsic rate coefficient, k . The distribution of catalyst in the organic phase can be determined by the extraction constant for the two-phase organic/aqueous system. If the transferred catalyst is in the form of a catalyst-anion pair, then it is important to take the extent of aggregation into account to obtain the effective concentration of the active catalytic species. 

The intrinsic lipophilidty (P or log P) of a compound refers only to the equilibrium of the unionized drug between the aqueous phase and the organic phase. The overall ratio of drug, ionized and unionized, between the phases has been described as the distribution coefficient (D), to distinguish it from the intrinsic lipophilidty (f. The term can be used to describe the eSective lipophilidty of a compound as it takes into account both its intrinsic lipophilidty and its degree of ionization. Log D values or effective lipophilidty are particularly relevant to permeability since values below zero are likely to show low lipoidal flux. 

The intrinsic separation of lanthanide ions on sulfonic acid resins is minimal. They typically offer only a few parts-per-thousand separation factors (ratio of distribution ratios or extraction equilibrium coefficients) for adjacent lanthanide ions, as is shown in fig. 2 (Marcus 1983, Surls and Choppin 1957). Values reported for gadoliniiun numbers (ratio of distribution coefficients normalized to Gd) in 0.01 M HCIO4 vary almost linearly across the series while the 0.11 M HCIO4 data show better selectivity for the light lanthanides... 

If all the resonance states which fomi a microcanonical ensemble have random i, and are thus intrinsically unassignable, a situation arises which is caWtA. statistical state-specific behaviour [95]. Since the wavefunction coefficients of the i / are Gaussian random variables when projected onto (]). basis fiinctions for any zero-order representation [96], the distribution of the state-specific rate constants will be as statistical as possible. If these within the energy interval E E+ AE fomi a conthuious distribution, Levine [97] has argued that the probability of a particular k is given by the Porter-Thomas [98] distribution... 

Synthetic, nonionic polymers generally elute with little or no adsorption on TSK-PW columns. Characterization of these polymers has been demonstrated successfully using four types of on-line detectors. These include differential refractive index (DRI), differential viscometry (DV), FALLS, and MALLS detection (4-8). Absolute molecular weight, root mean square (RMS) radius of gyration, conformational coefficients, and intrinsic viscosity distributions have... 

Many polymer properties can be expressed as power laws of the molar mass. Some examples for such scaling laws that have already been discussed are the scaling law of the diffusion coefficient (Equation (57)) and the Mark-Houwink-Sakurada equation for the intrinsic viscosity (Equation (36)). Under certain circumstances scaling laws can be employed advantageously for the determination of molar mass distributions, as shown by the following two examples. 

The three-dimensional voidage distribution provides the basic correlation for building a reactor model for fast fluidization, given data on particle-fluid transfer coefficients and intrinsic particle reaction kinetics. 

---