Partition isotherm

FLUORINECOMPOUNDS,ORGANIC - DIRECTFLUORINATION] (Vol 11) Simple partition isotherm... 

Isotherms. When a fibei is immersed, in a dyebath, dye moves fiom the external phase into the fibei. Initially the late is quick but with time this slows and eventually an equiUbrium is reached between the concentration of dye in the fiber and the concentration of dye in the dyebath. For a given initial dyebath concentration of a dye under given dyebath conditions, eg, temperature, pH, and conductivity, there is an equiUbrium concentration of dye in fiber, Dj and dye in the dyebath external solution, D. Three models describe this relationship simple partition isotherm, Freundhch isotherm, and Langmuir isotherm. 

Essentially, extraction of an analyte from one phase into a second phase is dependent upon two main factors solubility and equilibrium. The principle by which solvent extraction is successful is that like dissolves like . To identify which solvent performs best in which system, a number of chemical properties must be considered to determine the efficiency and success of an extraction [77]. Separation of a solute from solid, liquid or gaseous sample by using a suitable solvent is reliant upon the relationship described by Nemst s distribution or partition law. The traditional distribution or partition coefficient is defined as Kn = Cs/C, where Cs is the concentration of the solute in the solid and Ci is the species concentration in the liquid. A small Kd value stands for a more powerful solvent which is more likely to accumulate the target analyte. The shape of the partition isotherm can be used to deduce the behaviour of the solute in the extracting solvent. In theory, partitioning of the analyte between polymer and solvent prevents complete extraction. However, as the quantity of extracting solvent is much larger than that of the polymeric material, and the partition coefficients usually favour the solvent, in practice at equilibrium very low levels in the polymer will result. 

Suppose we have an ideal chromatographic column, no dispersion, and a linear partition isotherm. The result is only a... 

Describe how nonlinear partition isotherms lead to non-Gaussian bandshapes. Draw the bandshape produced by an overloaded column and a column with tailing. 

Figure 1.9. The dependence of the boundary profile on the form of the partition isotherm. (Courtesy of John Wiley-Interscience. ) c=concentration (cm 5/mole) of solute in gas phase q=concentration in liquid or adsorbed phase t=time for band to emerge from column (1) se1f-sharpening profile (2) diffuse profile (3) gaussian profile.

Factors leading to insolubility in water were discussed in Section 10.2.1.1. Provided they are not highly polymerized, such hydrophobic substances are generally soluble in non-aqueous solvents. In a two-phase system formed by an aqueous phase and a second phase immiscible with it a solute will partition between them until its activity is the same in both. The Nernst partition isotherm quantifies this relationship in the form... 

The Nernst partition isotherm applies to each individual species in an equilibrium mixture. The analyst is more directly concerned with the experimentally determinable distribution ratio, D, defined as... 

With simple partition the situation is comparable to the partition of a solute between two solvents. The bonding forces involved between uncharged dye and uncharged fiber, and uncharged dye and uncharged solvent are considered to be the same. The dye is sometimes referred to as in solid solution in the fiber. The simple partition isotherm is found in practice with disperse dyes on cellulose acetate and polyester. It represents the dyeing situation with the minimum restrictions for the dye to enter the fiber, the only restrielion is when the fiber solution becomes saturated. 

When two immiscible solvents are placed in contact, any substance soluble in both of them will distribute or partition between the two phases in a definite proportion. According to the Nernst partition isotherm, the following relationship holds for a solute partitioning between two phases a and b ... 

Hie subscript M refers to the method of moments. The method of moments is applicable to all chromatographic systems characterized by a linear partition isotherm (that is, for K = constant) irrespective of diffusion processes deforming the elution peak. 

When the partition isotherm is nonlinear (typically when surface adsorption is involved), the elution peaks exhibit long tails. Tailing is also caused by slow diffusion of the probe in the polymer and by technical artifacts mixing in the injection chamber, etc. 

The C-type (constant-partitioning) isotherm, which suggests a constant relative aflSnity of the adsorbate molecules for the adsorbent, is usually observed only at the low range of adsorption. Deviation from the linear isotherm is likely at high adsorption levels. Nevertheless, because many nonpolar organic compounds of interest in soils are adsorbed at quite low concentrations, the linear C-type isotherm is often a reasonable description of adsorption behavior. 

There are certain conditions that must be fulfilled if Eqs. (2.2), (2.3) and (2.4) are to be used to calculate partition coefficients. The basic assumption is that the individual retention mechanisms are independent and additive. This will be true for conditions where the infinite dilution and zero surface coverage approximations apply or, alternatively, at a constant concentration with respect to the ratio of sample size to amount of liquid phase. The infinite dilution and zero surface coverage approximations will apply to small samples where the linearity of the various adsorption and partition isotherms is unperturbed and solute-solute interactions are negligible. The constancy of the solute retention volume with variation of the sample size for low sample amounts and the propagation of symmetrical peaks is a reasonable indication that the above conditions have been met. For asymmetric peaks, however, the constant concentration method must be employed if reliable gas-liquid partition coefficients are to be obtained [191]. It is difficult to state absolutely the conditions for which contributions to retention from the structured liquid phase layer can be neglected. This will occur for some minimum phase loading that depends on the support surface area, the liquid phase... 

Gas chromatography is primarily an analytical separation technique. However, since the basic process is an equilibration of a solute between two immiscible phases, the chromatographic technique may be used to measure such physical properties as activity coefficients, second virial coefficients of gas mixtures, partition coefficients, adsorption and partition isotherms, and complex formation constants. Other properties which can be measured with less accuracy, from secondary measurements or from temperature variation studies, include surface areas, heats of adsorption, and excess enthalpies and excess entropies of solution. A number of reviews and discussions on these measurements have appeared in the literature. The present work is restricted to a review of activity-coefficient measurements. 

The relationship between the concentration of A in the stationary phase (Cs) and the concentration of A in the mobile phase (Cm) with regard to a particular component is measured at constant temperature. For this reason, the curves generated by plotting Cs against Cm are known as partition isotherms (see Fig. 45). 

The shape of the partition isotherms in the chromatographic process has a decisive influence on the shape of the peak. Let us now differentiate between two possible cases ... 

Fig. 46 a - c. Relationship of the shape of the peak profile (change of concentration in the carrier gas over time) to the partition isotherm a = linear b = concave c = convex isotherms (Schomburg)... 

There is a dependency between the shape of the chromatographic peak and the profile of the adsorption isotherm on the stationary phase. Symmetric peaks for which retention time does not depend on the volume of probe injected onto the column, which imply a linear adsorption (partition) isotherm, are usually obtained in the case of non-specific (dispersive) adsorbate—adsorbate and adsorbate-adsorbent interactions. The convex isotherm is usually obtained when the diffusive parts of the dependent peaks overlap and the adsorbate-adsorbent interactions are relatively stronger in comparison with the adsorbate-adsorbate interactions. The concave isotherm is usually obtained when the self-sharpening parts of the dependent peaks superimpose and the adsorbate-adsorbate interactions are relatively stronger in comparison with the adsorbate-adsorbent interactions. 

The effect of sample concentration on the chromatographic behaviour of ionic solutes on Sephadex G-10 can be qualitatively described by means of the partition isotherms derived on the basis of the ion partition model proposed by Shibukawa et al. [ref. 69] (see Sec. 2.2.1). The overall partition isotherms are anticipated to be represented as shown in Fig. 9 from the analogy with typical ion-exchange isotherms [ref. 70], if the partition isotherm of process (A) is linear. It is thus predicted that, in the system where the contribution of the steric exclusion effect can be neglected, the difference in the affinity for the internal gel phase between sample ion, s , and coion Y , that is, the equilibrium constant of ion-exahange process (B), K, determines the sample concentration dependence of the elution behaviour of sample ion in the following manner. When > 1, the elution volume or the distribution coefficient of sample ion decreases and the elution profile is more skewed with sharp leading... 

Partition isotherms. Depending on the state of the stationary phase, gas chromatography is influenced either by the equilibrium of dissolution or by that of adsorption. 

At equilibrium, the dependence of a component concentration in the stationary phase on its concentration in the mobile phase is given by an equation which is called the partition isotherm. For the low concentrations of injected substance employed in gas chromatography there are three types of isotherms, shown in Figure 2.3. 

Fig. 2.3. — The shape of partition isotherms (a) and corresponding elution peaks (b) encountered in gas chromatography 1 — linear isotherms, symmetrical peak ...

The relationships for retention data are valid provided that the partition coefficients are constant, i.e. for linear partition isotherms. If these isotherms are not linear, the data may be interpreted only in the case of very low eonc( ntrations, i.e. on the initial linear section of the isotherm. 

FIGURE 2.9 Dependence of boundary profile on form of partition isotherm. C = concentration (mL/mol) of solute in gas phase Q = concentration in liquid or adsorbed phase T = time for band to emerge from the column 1 = self-sharpening profile, 2 = diffuse profile, 3 = Gaussian profile. (Courtesy of Wiley-Interscience Publishers). 

Figure 2.45. Partition isotherm of iodine between water and carbon disulphide...

Partition chromatography has several valuable features. First of all. the partition coefficient is concentration-independent over a broad range of concentrations. The distribution (partition) isotherm is thus usually linear. In such a case, the zones of substances chromatographed are symmetrical and their position is independent of concentration. 

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