Solid-liquid distribution coefficient

Ferreira V, Jarauta I, Ortega L, Cacho J (2004) Simple strategy for the optimization of solid-phase extraction procedures through the use of solid-liquid distribution coefficients—application to the determination of aliphatic lactones in wine. J Chromatogr A 1025 147 Rettinger K, Karl V, Schmarr HG, Dettmar F, Hener U, Mosandl A (1991) Chirospecific analysis of 2-alkylbranched alcohols, -acids, and -esters chirality evaluation of 2-methylbutanoates from apples and pineapples. Phytochem Anal 2 184... 

Data sources given in Haack and McCoy (2004). Values in parentheses are calculated initial liquid compositions for elements like Ir and Re with solid/liquid distribution coefficients that are far from unity, meteorite composition may be different from that of the initial liquid core. 

The ranges of solid-liquid distribution coefficients reported for Co in different soil types are rather similar. In general, Kd values from 0.2 to 20,000 L kg l are representative of sand, loam, clay, and organic soils. Sheppard and Thibault (1990) quote median Kd values of 60, 1300, 540, and 990 L kg for each of these soil types, respectively. Soil—plant transfer factors for numerous crop species have been published by the International Union of Radioecologists (lUR, 1989). These values range from 0.037 for cereal grain to 1.1 for alfalfa fodder. For most of the crop types represented in the lUR (1989) database, a range of soil-plant transfer factors from 0.01 to 0.1 seems most applicable. 

Zirconium is polyvalent, but only the 4- - valence state is observed in aqueous environments. In common with other polyvalent elements, it is adsorbed rapidly and relatively intensely by soils and sediments, rendering it relatively poorly available for biological absorption in the terrestrial environment. Solid-liquid distribution coefficients quoted for Zr by Sheppard and Thibault (1990) range from 600 L kg for sandy soil to 7300 L kg for organic soil. 

As expected from the studies cited above, solid-liquid distribution coefficients for " Ru and are highest in organic soils. Sheppard and Thibault (1990)... 

Wauters, J., Elsen, A., Cremers, A., Konoplev, A. V., Bulgakov, A. A., and Comans, R. N. J. (1996). Prediction of solid/liquid distribution coefficients of radiocesium in soils and sediments, 1 A simplified procedure for the solid phase characterisation. Appl. Geochem. 11, 589-594. 

The solid-liquid distribution coefficient of HOCs in the presence of surfactants can be represented as follows (Sun et ai, 1995) ... 

The traditional way to express mobility, e.g. in contaminant/radionuclide transport models, is by means of the solid/liquid distribution coefficient or Kd (L/kg) ... 

Similarly, a bulk rock solid-liquid distribution coefficient, D, for the sum of all minerals in a rock may be defined as... 

The parameter is the solid/liquid distribution coefficient for element m. From a mass balance, the average concentration Cs.m in the solid at the same... 

Figure 9.16 Kinetic fractionation during crystal growth. Steady-state distribution of melt concentrations in the vicinity of a solid growing at the rate v for trace elements with different solid-liquid fractionation coefficients [equation (9.6.5), Tiller et al. (1953)]. The stippled area indicates the steady-state chemical boundary-layer with thickness <5 = <5>/v.

Phase-equilibrium calculations were discussed for vapor-liquid equilibria (VLB), liquid-liquid equilibria (LLE), and solid-solid equilibria (SSE). Results from VLE calculations often take the form of K-factors and relative volatilities, especially when thermodynamic calculations serve as intermediate steps in computer-aided process-design programs. In those situations, K-factors are routinely provided to subprograms that size distillation columns and gas-liquid absorbers. Similarly, the distribution coefficients computed for LLE serve as bases for sizing solvent-extraction columns moreover, liquid-liquid distribution coefficients may be helpful in screening candidate solvents for use in an extraction. 

Various parameters such as adsorption and desorption isotherms, diffusion coefficients, liquid/gas, gas/solid and liquid/solid equilibrium distribution coefficients, as well as mass transfer coefficients and many other physicochemical property values have to be used in the models proposed for supercritical fluid extractions. These parameter values are either obtained from existing correlations, or from independent data sources using parameter estimation. However, in those cases where the above stated means are not sufficient to estimate the values of all parameters used in the model, the researcher(s) may be forced to use the model and the associated data to evaluate best fit or optimal values for the missing parameters. The fact is that, the number of reliable correlation s and methods for the SFE are still quite scarce. 

Component Separation by Progressive Freezing When the distribution coefficient is less than I, the first solid which ciystaUizes contains less solute than the liquid from which it was formed. As the frac tion which is frozen increases, the concentration of the impurity in the remaining liquid is increased and hence the concentration of impurity in the sohd phase increases (for k < 1). The concentration gradient is reversed for k > 1. Consequently, in the absence of diffusion in the solid phase a concentration gradient is estabhshed in the frozen ingot. 

If the bulk-liquid phase is well mixed and no diffusion occurs in the solid phase, a simple expression relating the solid-phase composition to the frac tion frozen can be obtained for the case in which the distribution coefficient is independent of composition and fraction frozen... 

There have been many modifications of this idealized model to account for variables such as the freezing rate and the degree of mix-ingin the liquid phase. For example, Burton et al. [J. Chem. Phy.s., 21, 1987 (1953)] reasoned that the solid rejects solute faster than it can diffuse into the bulk liquid. They proposed that the effect of the freezing rate and stirring could be explained hy the diffusion of solute through a stagnant film next to the solid interface. Their theoiy resulted in an expression for an effective distribution coefficient k f which could be used in Eq. (22-2) instead of k. 

Fig. 4.5. Schematic of top left corner of the "silicon-impurity" phase diagram. To make things simple, we assume that the liquidus and solidus lines ore straight. The impurity concentration in the solid is then always less than that in the liquid by the factor k (called the distribution coefficient).

The dimensionless K. is regarded as a function of system T and P only and not of phase compositions. It must be exfjerimentally determined. Reference 64 provides charts of R (T,P) for a number of paraffinic hydrocarbons. K. is found to increase with an increase in system T and decrease with an increase in P. Away from the critical point, it is invariably assumed that the K, values of component i are independent of the other components present in the system. In the absence of experimental data, caution must be exercised in the use of K-factor charts for a given application. The term distribution coefficient is also used in the context of a solute (solid or liquid) distributed between two immiscible liquid phases yj and x. are then the equilibrium mole fractions of solute i in each liquid phase. 

The impurity, x, builds up at the solid- liquid interface as the liquid zone moves and the solid forms. We can write for the distribution coefficient ... 

Lipophilicity represents the affinity of a molecule or a moiety for a lipophilic environment. It is commonly measured by its distribution behavior in a biphasic system, either liquid-liquid (e.g. partition coefficient in 1-octanol-water) or solid-liquid (retention on reversed-phase high-performance liquid chromatography or thin-layer chromatography system). 

C, is the concentration of impurity or minor component in the solid phase, and Cj is the impurity concentration in the liquid phase. The distribution coefficient generally varies with composition. The value of k is greater than 1 when the solute raises the melting point and less than 1 when the melting point is depressed. In the regions near pure A or B the liquidus and solidus lines become linear i.e., the distribution coefficient becomes constant. This is the basis for the common assumption of constant k in many mathematical treatments of fractional solidification in which ultrapure materials are obtained. 

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. 

Saturated vapor pressure of a pure solid substance (Ps) or of its subcooled liquid (Pl) is an indicator of the substance volatility. These and other physical-chemical properties and distribution coefficients can be found in the handbook (Mackay et al., 1992b). 

Two types of distribution coefficients are commonly measured and used in describing the distribution between solid and liquid phases. The first and simplest is the distribution between total solid and liquid phases. This can be represented by Kd, as given in the equation in Figure 5.11. Here, kg is kilogram and L is liter of soil solution. 

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