Langmuir parameter

Table 22.3 The parameters of Langmuir and Freundlich isotherm equations for the adsorption of metobromuron Langmuir parameters...

Significance of Langmuir parameter. Linear increase of 0-vcrsus-/ for low pressures. For low P we have KlP -C 1 so that... 

The values of kinetic and Freundlich parameters (k, Kp, and Ng), obtained from runs carried out with different amounts of catalyst, are reported in Figure 12 vs. the absorbed photon flow per unit mass of catalyst. These values show the same feature of Langmuir parameters obtained for benzyl alcohol oxidation, that is, they decrease by decreasing the photon flow absorbed by the unit mass of catalyst. As in the case of benzyl alcohol, the consideration that the photon flow absorbed by the unit mass of catalyst is the parameter mainly affecting the photoadsorption phenomenon is strengthened by the results reported in Figure 12. 

In Eq. (3). is the flux when intracrystalline transport is rate controlling, Af, is the real flux. 8 AE is the difference between the activation energy for escape from within the crystal to the externally adsorbed layer and the activation energy for diffusion. It is generally a positive quantity [35]. K and K represent the Langmuir parameters for adsorption on the external and internal surfaces, respectively. When internal and external adsorption isotherms are taken to be identical or are within Henry s law range, Eq. (3) becomes... 

The dimensionless parameters of this equation are the Henry coefficients Ht and the dimensionless Langmuir parameters b2 cfeeti,i and b2 cfeea,2- This is the mathematical indication that the feed concentrations are parameters for a certain separation problem, as the H and bt are constant for the chromatographic system. 

In summary, chromatographic batch separation depends on the following dimensionless parameters Peclet and Stanton numbers, dimensionless injection time, Henry coefficients and dimensionless Langmuir parameters. 

Table 3.1 Best bi-Langmuir parameters for Phenol in RPLC...

Figure 4.2 illustrates the best competitive adsorption isotherm model for benzyl alcohol and 2-phenylethanol [16]. The whole set of competitive adsorption data obtained using Frontal Analysis was fitted to obtain the Langmuir parameters column saturation capacity qs =146 g/1), equilibrium constant for benzyl alcohol bsA = 0.0143) and the equilibrium constant for 2-phenylethanol (bpE = 0.0254 1/g). The quality of the fit obtained with this simple model is in part explained by the small variation of the activity coefficients of the two solutes in the mobile phase when the solute concentrations increased from 0 to 50 g/1. The Langmuir competitive adsorption isotherm simplifies also in the case where activity coefficients are of constant value in both phases over the whole concentration range [17]. 

The FA method gives isotherm data. To be useful in preparative chromatography, these data must be fitted to an isotherm model. There are presently no numerical procedures available to smooth the data from multidimensional plots, similar to the 2-D splines or French curves and obtain purely empirical isotherms. Therefore, the major difficulty is the selection of adequate models. The Langmuir isotherm is too simplistic in most cases, and the LeVan-Vermeulen isotherm is complicated and difficult to use as a fitting fimction. Several methods have been described to extract the "best" set of Langmuir parameters which could accormt for a set of competitive adsorption data [108]. These methods have been compared. The most suitable method seems to depend on the aim of the determination and on the deviation of the system from true Langmuir behavior [108]. 

In Eq. 4.79, hi and are the values of the variable k, ahead and behind the shock, respectively. Regression of the experimental values of i/, for different sets of concentrations yields the best Langmuir parameters of all solutes. This method can be used for a mixture of multicomponent solutes. This method, which is based on the measmement of composition velocities, was called MCV [14] (see Eigures 4.26A and 4.26B). 

Table 3. Langmuir parameters for the systems heavy metals-adsorbents at25°C.

Processing the experimental data with the Langmuir model enabled to obtain the Langmuir parameters (see Equations 1-2). In particular C ax turned out to be 2.65 and 1.90 for the systems reported in Figs. 1 and 2, respectively. 

The weighting factor m( y) is very similar to a gaussian function centered on y, as illustrated in Fig. 4.3. Thus the van Bemmelen-Freundlich isotherm can be thought of as the result of a log-normal distribution of Langmuir parameters iC (i.e, a normal distribution of In K) in a soil. The parameter (3 determines the narrowness of this distribution, in that ° ... 

Langmuir Parameters for Diquat and Paraquat Adsorption on Activated Carbons... 

Langmuir Parameters % Adsorption Capacity Langmuir Parameters % Adsorption Capacity... 

Manderscheid et al. [39] determined Langmuir parameters for SO sorption in soils from two forested catchments in Germany. These parameters were included in the chemical equilibrium model. Model of Acidification of Groundwater in Catchments (MAGIC), in order to study the effect of isotherm variability on the prediction of SO fluxes with seepage. Langmuir isotherms are not commonly used in transport models because of the computational burden they introduce due to their nonlinearity and also because many researchers, perhaps unjustifiably, often report just the K. ... 

Table 3.2. Langmuir parameters for N2 and O2 isotherms at 298 K on the adsorbents used...

Zeolites Pure Gas Langmuir Parameters Binary Gas Adsorption ... 

Langmuir parameter, also reciprocal of half-loading partial pressure, cp. (7.16) ... 

Relations (7.37, 7.38) provide an implicit equation to calculate the mass adsorbed (m) from given values of the parameters (b, c, d, k, a, m ,) and sorptive gas pressure (p). Resulting curves can be of lUPAC Type I, IV, V depending on numerical values of parameters b > 0, c 0, d 0, k > 0, a > 0. Here c, d describe admolecular interactions, b is the Langmuir parameter (7.2) and k, a describe the topology of the neighborhood of the admolecule. Hence these parameters are related to the pore structure of the sorbent material. 

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