The Freundlich Adsorption Isotherm

It is often found that the simple Langmuir isotherm does not adequately describe adsorption systems of theoretical and practical interest. Another classic isotherm that has found apphcation in describing adsorption, especially at moderate pressures, is the so-called Freundhch adsorption isotherm 

Obviously, a plot of In E versus In p should give a straight line. Although originally derived empirically, the Freundhch equation can also be derived theoretically using a model in which it is assumed that the heat of adsorption is not constant but varies exponentially with the extent of surface coverage, a condition that is probably closer to reahty than the Langmuir assumption in most cases. 

A major assumption of the Langmuir isotherm model is that adsorption stops at monolayer coverage. However, since the van der Waals forces leading to physical adsorption are the same as those involved in the formation of the liquid state, it should not be surprising to find that the limitation of adsorption to a single monolayer is unrealistic in many cases. As mentioned previously, such a case is expected only when the interactions among adsorbate molecules are very much weaker than those between adsorbate and adsorbent. 

Assuming the formation of a multilayer of adsorbed molecules, Brunauer, Emmett, and Teller (BET) modified the Langmuir approach of balancing the rates of adsorption and desorption for the various molecular layers. The BET model assumes that the adsorption of the first monolayer has a characteristic heat of adsorption but that subsequent layers are controlled by the heat of condensation of the vapor in question, A//l. 

The BET equation will not be derived here, but the most common linearized form of the final equation is 

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The adsorption coefficients (K) were determined using the equation for the Freundlich adsorption isotherm ... 

Figure 15.4(A) shows the effect of the R = Zn2+/Al3+ ratio, which determines the charge density of the LDH layer, on the Freundlich adsorption isotherms. K values are far higher than those measured for smectite or other inorganic matrices. The increase in Kf with the charge density (Kf= 215, 228, 325mg/g, respectively, for R = 4, 3 and 2) is supported by a mechanism of adsorption based on an anion exchange reaction. The desorption isotherms confirm that urease is chemically adsorbed by the LDH surface. The aggregation of the LDH platelets can affect noticeably their adsorption capacity for enzymes and the preparation of LDH adsorbant appears to be a determinant step for the immobilization efficiency. [ZnRAl]-urease hybrid LDH was also prepared by coprecipitation with R = 2, 3 and 4 and Q= urease/ZnRAl from 1 /3 up to 2.5. For Q < 1.0,100 % of the urease is retained by the LDH matrix whatever the R value while for higher Q values an increase in the enzyme/LDH weight ratio leads to a decrease in the percentage of the immobilized amount.

These figures are in approximate agreement with values calculated -with the aid of the Freundlich adsorption isotherm (see p. 134) but no definite conclusions may be drawn from them since the actual area of liquid-liquid interface in all probability was variable being dependent on the amount of emulsifying agent present. More recently the quantity of various soaps required to form a stable emulsion of kerosene in water has been determined by Grifiin (J.A.C.8. XLV. 1648, 1923) for sodium oleate, potassium stearate and potassium palmitate and by der Meulen and Riemann ibid. XLVI. 876, 1924) for sodium ricinoleate. 

Equation (135) is the well-known Freundlich adsorption isotherm. In a number of instances this isotherm accurately describes experimental data. The interpretation of the Freundlich adsorption isotherm as resulting from exponential nonuniformity of surface is due to Zel dovich 43). 

In the Freundlich adsorption isotherm, the amount adsorbed is proportional to a fractional power of the pressure of the adsorptive. For a particular system, the fractional power and the constant of proportionality are functions of temperature. In terms of coverage the isotherm assumes the form... 

Freundlich adsorption isotherm — The empirical adsorption isotherm 0 = bcn (0 surface coverage, b and n are constant, 0 < n < 1, and c is the solution concentration) was initially proposed by Boedecker in 1895 [i], however it was popularized by -> Freundlich [ii], and today is generally referred to as the Freundlich adsorption isotherm [iii]. 

Molecular or ion-pair adsorption The adsorption of potassium bromate on the surface of barium sulfate appears to involve the simultaneous occupation of adjacent sites on the crystal surface by potassium ions and bromate ions this is called an equivalent adsorption because equal amounts of the two ions are adsorbed. Such adsorptions, and in fact many molecular adsorption processes, follow an empirical equation known as the Freundlich adsorption isotherm ... 

I.2. Freundlich Adsorption Isotherm Equation The Freundlich adsorption isotherm equation is the oldest of the nonlinear isotherms, and its use implies heterogeneity of adsorption sites. The Freundlich isotherm equation is... 

Due to the effects of molecular size and shape and pore structure on the kinetics, the model cannot be used for general predictive purposes. In practice, in order to predict PAC adsorption, a series of experiments must first be carried out using the compound of interest, the activated carbon to be applied, and the water in which it is to be used. Equilibrium parameters, determined from the Freundlich adsorption isotherm equation, are used as input into a computer-based HSDM, which uses the method of least squares to minimize the difference between the experimental kinetic data points and the HSDM fit of the data [10]. When the best fit is achieved, the resultant kinetic parameters (liquid film mass transfer coefficient, k(, and the surface diffusion coefficient, DJ can then be used for the prediction of adsorption behavior under different conditions. 

The foregoing procedure will suffice to serve the needs of most general routine. In any fundamental study, however, it can be very helpful to know and fully understand a principle of measuring adsorption that is embodied in the Freundlich adsorption isotherm.1 6 This isotherm expresses the fact that for data on adsorption... 

If the Freundlich adsorption isotherm is valid than the adsorption rate is proportional to pressure and inversely proportional to a fractional power of surface coverage, giving the Bangham equation... 

Plots of the Freundlich adsorption isotherms for Sevin, 1-naphthol, baygon, pyrolan, and dimetilan on kaolinite are shown in Figure 7 similar plots were obtained for the bentonite system. All the insecticides studied showed equilibrium adsorption on the clay minerals according to... 

This expression was derived assuming the Freundlich adsorption isotherm [86] and estimates the concentration ratio of the inhibitor to chloride that destroys passivity is more important to initiate pitting than the absolute value of inhibitor concentration. In the initial pitting stages, replacement of aggressive ions from the adsorption layer by inhibiting anions explains the inhibition mechanism. 

Umpleby II, R.J. Baxter, S.C. Bode, M. Berch, J.K. Shah, R.N. Shimizu, K.D. Application of the Freundlich adsorption isotherm in the characterization of molecularly imprinted polymers. Anal. Chim. Acta 2001, 435, 35-42. 

The relation between minimum anion activity necessary to inhibit pitting of 18-8 stainless steel in a solution of given CT activity follows the relation log (CT) = k log (anion) -i- const. The same relation apphes to inhibition of pitting of aluminum. The equation can be derived assuming that ions adsorb competitively in accord with the Freundlich adsorption isotherm [26]. 

Derive the relation log(Cl ) = k log(anion) + const, where (anion) is the minimum activity of anion necessary to inhibit pitting of a passive metal in a chloride solution of activity (CT). Assume that the amount of ion a adsorbed per unit area follows the Freundlich adsorption isotherm, a = ki(anion) ", where and ni are constants, and that at a critical ratio of adsorbed Cl" to adsorbed anion the passive film is displaced by CT, allowing a pit to initiate. 

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