Stationary phase material balance

The major parameter for column selection is the intended application [7, 8]. A balance of mobile phase polarity in comparison with the polarity of the stationary phase and sample polarity is important for pure SEC separations. In general, users will select their columns according to the mobile phase they need to use. Stationary phase materials can be either silica or polymeric based. Table 9.4 shows an overview of stationary phases with different polarities typically used in SEC. 

In a typical slurry bubble column operation, the liquid velocity is one order of magnitude lower than the one of gas, and in general, is very low. This mode of operation can be approximated by a semibatch operation. The semibatch operation is frequently used and is the case where the liquid and the catalyst comprise a stationary phase (sluny) in the reactor. In this case, the material balance, eq. (3.122) is used along with the overall rate based on the bulk gas-phase concentration (see Section 3.4.6). In the following, the semibatch operation is presented. 

Equilibrium The physical process (reaction) of adsorption or ion exchange is considered to be so fast relative to diffusion steps that in and near the solid particles, a local equilibrium exists. Then, the so-called adsorption isotherm of the form q = f(Ce) relates the stationary and mobile-phase concentrations at equilibrium. The surface equilibrium relationship between the solute in solution and on the solid surface can be described by simple analytical equations (see Section 4.1.4). The material balance, rate, and equilibrium equations should be solved simultaneously using the appropriate initial and boundary conditions. This system consists of four equations and four unknown parameters (C, q, q, and Ce). 

Figure 6.1 gives an example for a one-dimensional model. Mass balances for the fluid mobile phase as well as the stationary adsorbent phase are derived on the basis of differential volume elements. Section 6.2.2 gives further information regarding the derivation of the material balance. 

An additional equation for the material balance for the particle phase is necessary (Eqs. 6.4, 6.14 and 6.30), where the accumulation in the stationary phase equals the... 

The reaction characteristic of the present system are best performed in a semicontinuous reactor in which the solid is stationary, as described in the previous section. This easily permits the two steps. In general, however, continuous reactors in which both the gas and solid phases move continuously are more important. We therefore briefly consider in this section the mathematical basis for the design of such a reactor. The chief reactor and operating parameters are gas and solids feed rates, product size distribution, bed size, and so on, and procedures for determining them are described. With a size distribution o(R), an elutriation stream and an arbitrary rate law for the changing particle size, a material balance on solids of size between R and R + dR yields... 

If simple adsorption behavior can be considered (e.g., which is often not the case in bioseparations), the assumption of local adsorption equilibrium (Section 6.2.2.7) is normally valid. In this case Equation 6.31 formally reduces to an isotherm relationship connecting pore concentration a and solid loading a (Equation 6.34). As mentioned in Section 6.2.2.7, the two balances in the stationary phase (Equations 6.5 and 6.6) and the adsorption kinetics (Equation 6.31) can then be replaced by an isotherm equation (Equation 6.34) and the overall material balance for one particle (Equation 6.7). The latter can be derived analogous to Equations 6.81 and 6.82, leading to... 

The last factor is particularly important for the successful utilization of aqueous SEC in the investigation of the micellization process. In order to provide a realistic picture for the micellization equilibrium, the chromatographic system needs to meet several strict requirements The packing material and the eluent should be appropriately chosen to prevent the occurrence of non-size-exclusion phenomena and adsorption of micelles in the stationary phase. In all cases, mass balance of the material injected and recovered from the columns must be performed in order to verify the absence copolymer entrapment. Cross-linked copolymers containing either poly(vinyl alcohol) or polyCglycidyl methacrylate) as the hydrophilic component are the most widely used column packing materials for aqueous SEC. Both Shodex Protein KW (Showa Denko, Japan) and Micropak TSK-gel PW (Toyo Soda, Japan) columns have been reported to afford good information on the micellization behavior of PEO copolymers without... 

Stationary phases containing carboxylic acid functional groups are now frequently used for I EC instead of strong-acid sulfonated resins. The carboxylic acid particles are often a polymethacrylate gel. These materials have found extensive use for the analysis of low concentrations of both cations and anions in acid rain. Acid rain caused by SO2 and NOx in air is a major environmental pollution problem in many parts of the world. The major cationic components of acid rain are Na, NH4, K, Mg and Ca, and the major anionic components are cr, NOg and SO4 . The ionic balance between the total positive charge and negative charge of... 

Generally speaking, for the first and second fractionation classes under the minimum reflux mode, the points of compositions in the zones of constant concentrations (i.e., stationary points of the trajectory bundles) should be arranged at the trajectories of reversible distillation built for the product points. It follows from the conditions of the material balance and the phase equilibrium in the zones of constant concentrations. Figure 2.11b illustrates the partially reversible process (it is reversible in the colunm parts that are from the constant concentration zones for the minimum reflux mode up to the column ends). 

The choice of solvent is dictated by a number of factors. A balance between the adsorption power of the stationary phase and the solvation power of the elution solvent governs the rate of travel of the material down the column. If the material travels rapidly down the column, then too few adsorption-elution cycles will occur and the materials will not separate. If the sample travels too slowly, diffusion broadening takes over and separation is degraded. Solvent choices and elution rates can strike a balance between these factors and maximize the separation. It can take considerable time to develop a solvent or mixture of solvents that produces a satisfactory separation of a particular mixture. 

A proper SEC experiment has to be balanced with respect to polarities. In order to obtain a true and pure SEC separation, the polarity of stationary phase (column material), the polarity of eluent, and the polarity of sample have to be matched. This is visualized by the magic triangle (Fig. 9.6). Dominance of size separation is only maintained in the center of the triangle (bright area), where the overall systan is balanced. Otherwise, specific interactions will occur, which will overlay with the normal SEC elution behavior. 

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