Adsorption Processes for Water Treatment || Elements of Surface Chemistry

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Elements of Surface Chemistry

Since the 1960s, an increased awareness of the occurrence of many synthetic and natural organic substances in natural waters has led to the emergence of adsorp-tion by activated carbon a n d / o r porous synthetic resins, as one of the most ef-fective methods of removing these substances from drinking and wastewaters.

PRINCIPLES OF ADSORPTION

Types

Adsorption is a surface phenomenon that is defined as the increase in concen-tration of a particular component at the surface or interface between two phases. In any solid or liquid, a toms at the surface are subject to unbalanced forces of attraction normal to the surface plane. These forces are merely extensions of the forces acting within the body of the material and are ultimately responsible for the phenomenon of adsorption. In discussing the fundamentals of adsorption, it is useful to distinguish between physical adsorption, involving only relatively weak i n t e r m o d u l a r forces, and chemisorption, which involves essentially the forma-tion of a chemical bond between the sorbate molecule and the surface of the adsorbent. Although this distinction is conceptually useful, many cases are in-termediate and it is not always possible to categorize a particular system une-quivocally [1].

Physical adsorption can be distinguished from chemisorption according to one or more of the following criteria:

1. Physical adsorption does not involve the sharing or transfer of electrons and thus always maintains the individuality of interacting species. The interac-tions are fully reversible, enabling desorption to occur at the same temper-ature, although the process may be slow because of diffusion effects. Chemisorption involves chemical bonding and is irreversible.

2. Physical adsorption is not site specific; the adsorbed molecules are free to cover the entire surface. This enables surface area measurements of solid

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2 Adsorption Processes for Water Treatment

adsorbents. In contrast, chemisorption is site specific; chemisorbed mole-cules are fixed at specific sites.

3. The heat of physical adsorption is low compared to that of chemisorption; however, heat of adsorption is not usually a definite criterion. The upper limit for physical adsorption may be higher than 20 kcal /mol for adsorption on adsorbents with very narrow pores. The heat of chemisorption ranges from over 100 kcal /mol to less than 20 kcal /mol . Therefore, only very high or very low heats of adsorption can be used as a criterion for this type of adsorption process [2].

Chemisorption is characterized mainly by large interaction potentials that lead to high heats of adsorption that approach the value of chemical bonds. This fact, coupled with other spectroscopic, electron spin resonance, and magnetic susceptibility measurements, confirms that chemisorption involves the transfer of electrons and the formation of true chemical bonding between the adsorbate and the solid surface [3]. Because chemisorption involves chemical bonding, it often occurs at high temperatures and is usually associated with activation en-ergy. Also, the adsorbed molecules are localized on specific sites and, therefore, are not free to migrate about the surface.

Entropy Changes

The adsorption of solutes from solution by solid adsorbents depends on physical adsorption rather than chemisorption and is, therefore, the focus of this discus-sion. The heat of adsorption provides a direct measure of the strength of the bonding between sorbate and surface. Physical adsorption from the gas phase is invariably exothermic, as may be shown by a simple thermodynamic argument. Since the adsorbed gas molecules have a lower degree of disorder—that is, lower entropy than the surrounding molecules—the process of adsorption is accom-panied by a decrease in entropy. The entropy change on adsorption,

AS = 5 a ds - S g a s, (1.1)

is necessarily negative. For significant adsorption to occur, the free energy change of adsorption, AG, must be negative, and since:

AG = AH - TAS, (1.2)

this requires AH to be negative or an exothermic change. This is usually true also for adsorption from the liquid phase, although some exceptions are possible [1].

Elements of Surface Chemistry 3

ADSORPTION: INTERACTION FORCES

Dispersion Forces

Physical adsorption on nonpolar solids is attributed to forces of interactions be-tween the solid surface and adsorbate molecules that are similar to the van der Waals forces (attraction-repulsion) between molecules. The attractive forces that involve the electrons and nuclei of the system are electrostatic in origin and are termed dispersion forces. These forces exist in all types of matter and always act as an attractive force between adjacent atoms and molecules no matter how dis-similar. They are always present regardless of the nature of other interactions and often account for the major part of the adsorbate-adsorbent potential [3,4]. The nature of the dispersion forces was first recognized in the 1930s by London [5]. Using quantum mechanical calculations, he postulated that the electron mo-tion in an a tom or molecule would lead to a rapidly oscillating dipole moment . At any instant, the lack of symmetry of the electron distribution about the nuclei imparts a transient dipole moment to an a tom or molecule that would average zero over a longer time interval. When in close proximity to a solid surface, each instantaneous dipole of an approaching molecule induces an appropriately ori-ented dipole moment in a surface molecule. These moments interact to produce an instantaneous attraction. These forces are known as dispersion forces because of their relationship, noted by London [5], to optical dispersion. The dipole-dispersion interaction energy can be determined by:

(1.3)

where ED = dispersion energy or potential, C = a constant, and r = distance of separation between the interacting molecules.

In addition to dipole-dipole interactions, other possible dispersion inter-actions contributing to physical adsorption include dipole-quadrapole and quad-rapole-quadrapole interactions. If these two are included, the total dispersion energy becomes [3,5]:

(1.4)

where C = a constant for dipole-quadrapole interactions and C" = a constant for quadrapole-quadrapole interactions.

The contribution to ED from the terms in Equation 1.4 clearly depends on the separation, r, between the molecules; therefore, the dipole-dipole interactions will be most significant. Quadrapole interactions involve symmetrical molecules with atoms of different electronegativities like C 0 2 . This molecule has no dipole


moment but does have a quadrapole ( " O - +

C+ - Ο ~ ) that can lead to inter-

actions with polar surfaces. When an adsorbate molecule comes very close to a solid surface molecule

to allow interpénétration of the electron clouds, a repulsive interaction will arise, which is represented semiempirically by the expression:

where ER = repulsion energy and Β = a constant. The total potential energy of van der Waals interactions is the sum of the attractive energy and the repulsion energy:

(1.6)

The inverse sixth energy term falls rapidly with increasing r but not nearly as rapidly as the repulsion term. Thus, the dispersion energy is more important than the repulsion at longer distances.

Potential Energy Curves

The potential energy curve for van der Waals interactions between He atoms is illustrated in Figure 1-1. At separations of more than 3.5 À , the first term in Equation 1.6 predominates. The atoms attract each other and the energy of the two atoms falls to a stabler level as the atoms move closer. If they come closer than 3 À , however, a strong electron pair repulsion predominates over the Lon-don attraction and a large amount of energy is required to push the atoms to-gether. Accordingly, the potential energy curve in Figure 1-1 rises. A balance between attraction and repulsion exists at a 3 À separation, and the two atoms are 18.2 cal /mole stabler than two isolated atoms [6],

The dispersion interaction between a solid and an external a tom or molecule can be determined in a manner analogous to that employed between a pair of atoms or molecules. The usual procedure is to use the property of additivity of the dispersion forces and assume that the atoms of the solid can be thought of as force centers and that the energy of interaction, E, of an external a tom with the solid can be expressed as:

Ε = LEj, (1.7)

where Ej = the energy of interaction between the external a tom and the jth a tom of a solid. The expression of Ej is usually assumed to be of the form in Equation 1.3 or perhaps 1.6. This approach has been used by several investigators [1,3].

(1.5)


R (in angstroms)

Figure 1-1 Potential energy curve for van der Waals attraction between He atoms. Re-produced from Dickerson et al. [6], courtesy of W.A. Benjamin, Inc.

It should be noted that while the additivity of the dispersion energies is strictly valid, it does not necessarily follow that the repulsive contributions are additive, although such an assumption is often made in theoretical calculations of this kind [1].

SURFACE TENSION

The surface of a liquid in contact with its vapor has different properties from those of the bulk phase. A molecule in the interior of a liquid is surrounded on all sides by neighboring molecules of the same substance and, therefore, is at-tracted equally in all directions. A molecule at the surface, however, is subject to a net attraction toward the bulk of the liquid, in a direction normal to the surface, because the number of molecules per unit volume is greater in the bulk of the liquid than in the vapor. Because of the unbalanced attraction, the surface of a liquid always tends to contract to the smallest possible area. To extend the area of the surface, work must be done to bring the molecules from the bulk of the liquid into the surface against the inward attractive force. The surface port ion of a liquid, therefore, has a higher free energy than the bulk liquid.

The work required to increase the area by 1 c m2 is called the surface free

energy. As a result of the tendency to contract, a surface behaves as if it were in a state of tension, and it is possible to ascribe a definite value to this surface


tension, 7 , which is defined as the force in dynes acting at right angles to any line of 1 cm length in the surface. The work done in extending the area of a surface by 1 c m

2 is equal to the surface tension, which is the force per centimeter

opposing the increase, multiplied by 1 cm, the distance through which the point of application of the force is moved. It follows, therefore, that the surface en-ergy, in ergs per square centimeter, is numerically equal to the surface tension in dynes per centimeter. In more general terms, the work, W, done by the surface in extending its area, A, by an amount , dA, is:

dW = -ydA = -dG, (1.8)

whence

dG = ydA9 (1.9)

where dG is the change in free energy. Since the surface energy is a Gibbs free energy, the surface enthalpy, AH,

can be evaluated from change of surface tension y with temperature. From the Gibbs-Helmholtz equation:

(1.10)

The surface enthalpy is given by:

Λ Η - y - T ( f ^ 0 . 1 1 ,

For water at 20°C, 7 = 72.75 e rg / cm2, (dy/dT)P = - 0 . 1 4 8 (the negative sign

is due to the decrease of 7 with increase in temperature), and so AH = 116.2 e rg / cm

2. This is the decrease in enthalpy associated with the destruction of 1 c m

2

of liquid surface. The addition of a solute to a liquid may alter the surface tension consid-

erably. In the case of aqueous solutions, solutes that can markedly lower the surface tension of water are organic compounds that contain both a polar hy-drophilic group and a nonpolar hydrophobic group—for example, organic acids, alcohols, esters, ethers, ketones, and so on. The hydrophilic group makes the molecule reasonably soluble while the hydrocarbon residues have low affinity for water and little work is required to bring them from the interior to the surface. Solutes that lower the surface tension tend to accumulate preferentially at the surface, and hence, there will be a greater proport ion of the solute at the interface than the bulk of the solution. This represents a case of adsorption of the solute at the surface of the solution, and the solute is said to be positively adsorbed at the interface.


Electrolytes, salts of organic acids, bases of low molecular weight, and cer-tain nonvolatile electrolytes usually increase the surface tension of aqueous so-lutions above the value for pure water. These increases are much smaller than the decreases produced by organic acids and similar compounds. The observed increases are attributed to ion-dipole interactions of the dissolved ions that tend to pull the water molecules into the interior of the solution. Additional work must be done against the electrostatic forces to create a new surface. The surface layers in such solutions have lower concentrations of the solute than in the bulk solution. The solute is said to be negatively adsorbed at the interface [7].

THERMODYNAMICS OF ADSORPTION: GIBBS ADSORPTION ISOTHERM

The thermodynamics of the surface was originally formulated by Gibbs in 1878, and subsequent studies were directed mostly to gas/liquid, gas/solid, and l iquid/ solid interfaces [4,7,9], Considerable progress has been made since the 1950s in understanding the thermodynamics of adsorption from solutions, largely because of the work of Hill [10] and Everette [11,12], The following discussion is based on the method given by Gibbs since more detailed information can be obtained from his formulations [8],

The system considered for Gibbs thermodynamic analysis consists of two phases separated by plane interface. An imaginary surface, constructed within the inter facial region and parallel to the boundary planes, that locates the extent of the separate phases is called the surface phase, σ. The bulk phase, the re-mainder of the solution, is assumed to be homogenous up to the dividing surface phase. A surface phase defined in this way has an area, A, but no thickness. It is strictly two dimensional and occupies a finite region of space within which the concentration is uniform and different from that of the bulk phase. The ther-modynamic properties of the adsorbent are considered to be independent of the temperature and the concentration of the adsorbed molecules; that is, the ad-sorbent is considered thermodynamically inert. Under these conditions, the adsorbed molecules may be regarded as a distinct phase, and the effect of the adsorbent is limited to the creation of force field, the detailed nature of which need not be specified [1,12]. The system, therefore, is considered to be divided into two parts , one consisting of all that portion that comes under the influence of the surface forces, which is the surface phase, and the other is the remainder of the solution, the bulk phase, which is free from the surface effects.

From the thermodynamics of bulk phases, the fundamental relationship of the free energy, G, of a two-component system is given by:

G = μληλ + μ2η2, (1.12)

where μι and μ2 = chemical potentials of components 1 and 2, respectively, and nx and n2 = number of moles of components 1 and 2, respectively. Also:


Then:

dG = -SdT + VdP + μχηχ + μ2η2. (1.13)

where S = entropy, Τ = temperature, V = volume, and Ρ = pressure. In addition to the ordinary state variables describing the bulk phases, new

state variables must be introduced to define the state of the surface phase. To allow for the possibility of a change in free energy resulting from an increase or decrease of the exposed surface, it is necessary to include a term, yA, where y is the interfacial tension—that is, the interfacial energy per square centimeter— and A is the surface area. Therefore, the surface free energy, G°, can be obtained from Equation 1.12 by adding the 7A term:

G° = y A + μ,/ι, 4- μ2η2ί (1.14)

and on differentiation:

dGa — ydA + Ady + μχάηχ + ηχάμχ + μ2άη2 + η2άμ2. (1.15)

Alternatively, adding the term ydA, for an increase of dA in the surface area, to Equation 1.13, the differential of the surface free energy becomes:

dG° = -SdT + VdP + ydA + μ,Λι, + μ2άη2, (1.16)

and by comparing Equations 1.15 and 1.16 yields:

SdT - VdP + Ady + ηχάμχ + η2άμ2 = 0 (1.17)

at constant temperature and pressure:

Ady + ηχάμχ + η2άμ2 = 0 . (1.18)

If n°x and n°2 are the number of moles of the two components in the bulk phase that correspond to nx and n2 in the surface phase, then according to the Gibbs-Duhem equation:

η°χάμχ + η°2άμ2 = 0 . (1.19)

Multiplying Equation 1.19 by nx/n0

x and subtracting from Equation 1.18 gives:

Ady + (n2 - nxn°2/n°x) άμ2 = 0 . (1.20)

(1.21)


The quantity n2 is the number of moles of one component , like the solute, as-sociated with nl moles of solvent in the surface phase, and nxn°2/n°x is the cor-responding number of moles associated with nx moles of solvent in the bulk phase. The right-hand side of Equation 1.21, therefore, may be regarded as the excess concentration of the solute per unit of surface area. This excess concentration is given the symbol Γ 2 and is called the surface concentration of solute per unit area of the interface. It is not strictly a concentration term since it is a number of moles divided by an area, but it is nevertheless a definite quantity defined by the right-hand side of Equation 1.21. Substituting for μ2 in Equation 1.21 yields:

Since μ 2 may be represented by:

(1.23)

where a2 is the activity of the solute, then at constant temperature:

(1.24)

Substituting into Equat ion 1.22 gives:

(1.25)

These two equations are various forms of the Gibbs adsorption isotherm. The isotherm holds equally for either component in a binary system, although in prac-tice it is usually applied to the solute. The subscript can, therefore, be neglected, giving:

(1.26)

For dilute solutions, the activity may be replaced by molar concentration, c, and:

(1.27)

It can be seen that if a solute causes a decrease in surface tension with an increase of concentration—that is dy/dc is negative—then Γ is positive and there will be adsorption on the interface.

In deriving the Gibbs adsorption equation, no assumption was made about the nature of the system or the surface. Its most obvious application, however,


UNIMOLECULAR SURFACE FILMS

Insoluble Surface Films

Certain sparingly soluble substances that possess one polar group can spread on the surface of water to form films one molecule in thickness. These are called unimolecular films, or monolayers. The area covered by a spreading compound such as oleic acid on the surface of water can be varied at will by confining the film between movable barriers placed across a shallow tray filled with water on which the compound is placed. Langmuir [15] devised a method for the direct measurement of the force, the surface pressure exerted by a film using an ap-paratus called the surface balance [7,14]. The dependence of the force exerted by the film, / , in dynes/cm, on the average area occupied by each molecule, in A

2, is known as (f — A) curves. Figure 1-2 shows an (f — A) curve for stearic

acid on distilled water [14]. At large areas, the surface force is relatively small, and it increases very slowly with decreasing area until a value of 20.5 Â

2 per

molecule is reached where the pressure begins to increase extremely rapidly on further compression of the film. Similar curves are obtained for a series of long-chain fatty acids, long-chain amides, alcohols, methyl ketones, monobasic esters, and other substances with polar groups [7]. In each case the minimum area per molecule is observed at 20.5 Â

2.

It is believed that such films consist of monolayers, with the molecules ar-ranged more or less vertically with the polar group attached to the surface of the water and the hydrocarbon chain pointing outward. As the film is compressed, the oriented molecules are so closely packed that any further decrease in area demands the exertion of an appreciable surface force, as in the three-dimensional case where compression of a solid or liquid is much more difficult than com-pression of a gas [14]. The limiting area occupied by each molecule is determined by the cross-sectional area of the hydrocarbon chain and, therefore, will be in-dependent of its length or of the nature of the polar end group provided that the

is to a liquid solution with the interface between the liquid and its vapor (liquid/ vapor interface) or to an interface between a solution and a liquid with which it is immiscible (liquid/liquid interface). The quantity then refers to the interfacial tension. There has not been a direct application of the Gibbs equation for ad-sorption by solids from solution because of the difficulty of determining the solid/ liquid tension and the lack of simple mechanical methods for measuring the sur-face tension of a solid surface. In addition, the simple Gibbs model of a sharp boundary between the surface and bulk phases and the autonomy of the surface phase presents many limitations in complex systems. More detailed discussions of the subject can be found elsewhere [12,13]. However, the discussion of the Gibbs isotherm here serves to illustrate the tendency of a given solute to be ad-sorbed at an interface.


«Λ

15

10

5 M 1 1 1

α— *U It Ι β Κ ) 2 2 2 4 £ 6 2 8 3 0 5 2 5 4 5 6 5 β

1.-so J /yoLecuLE

Figure 1-2 /-Λ isotherm at 20°C. Stearic acid on distilled water. Reproduced from Moore [14], courtesy of Prentice-Hall, Inc.

latter is sufficiently attracted by the water for the chains to be anchored to the surface [ 7 ,14 ] .

Expanded and Gaseous Films

The films described in the last section, consisting of closely packed single layers of molecules, are called condensed films to distinguish them from expanded films that are formed as the temperature is raised. In these films the area occupied per molecule is greater than in the condensed films because of the mutual repulsion of the end groups [17] .

Certain films, known as liquid expanded, have (f — A) curves very similar to the pressure-volume (Ρ — V) curves obtained for a gas undergoing liquefaction in the neighborhood of the critical temperature. Figure 1-3 shows (f — A) curves for a number of fatty acids C „ H 2 n+ i C O O H at 2 5 ° C [14] . There is a section at low pressures corresponding to the high compressibility of a gas. Then there is an intermediate region of areas over which the film exhibits a definite force equiv-alent to surface vapor pressure that is independent of the total area occupied. In this region a very small increase in pressure produces a large decrease in the area. Finally, there is a rapid rise in the (f — A) curve that corresponds to the com-pression of a condensed phase. With lower molecular weights, the quasi-two-phase region (the flat port ion of the curve) becomes less evident, and finally the curve appears to be gaseous throughout as in the dotted curve. At low pressures and, especially at elevated temperatures, when the molecules are relatively far


0 1000 2000 3000 4 0 0 0 6000

A*

Figure 1-3 f-A isotherms at low pressures. Reproduced from Moore [14], courtesy of Prentice-Hall, Inc.

apart , gaseous films are formed, which behave like two-dimensional gases cor-responding to three-dimensional gases. If the product of the force, / , and the average area, A, occupied by each molecule—that is, fA—is plotted against / , curves similar to the PV — Ρ curves for gases are obtained [7]. The molecules probably lie more or less flat on the surface. Therefore, substances with polar groups at each end, like esters of dibasic acids, form such films most readily.

Surface Films of Soluble Substances

Soluble substances that produce a marked decrease in the surface tension of water form monolayers at the surface. Therefore, condensed unimolecular films, with oriented molecules, are equivalent to an extreme case of adsorption of a soluble substance. The force, / , exerted by an insoluble film is equal to the difference between the surface tension of pure water and that of the water covered with the film. This definition can be extended to the surface layers of soluble substances so that / is equal to the difference between the surface tension of pure solvent, 7 0, and of the solution, 7 , that is,

/ = To - 7- (1.28)

Differentiating with respect to C:

(1.29)


Surface Layers and Gas Laws

The similarity between gaseous films of soluble and insoluble substances and ordinary three-dimensional gases is more than a qualitative one. If the molecules in the surface film are supposed to be free to- move in any direction, within the two dimensions of the surface, and it is assumed further that the actual cross-sectional area of the molecules is small in comparison with the area they inhabit and that they do not attract each other, then it can be readily deduced from the kinetic theory of gases that [7]:

fA = kT. (1.33)

This equation is the quantitative equivalent of the gas law equation PV = kT, where V is the average volume occupied by a single molecule. As with gases, Equation 1.33 is obeyed at low values of the surface p re s su re , / , equivalent to low gas pressure. At higher surface pressures, an equation similar to that pro-posed for gases may be employed [7]. Thus:

f(A - b) = kTX, (1.34)

and

Substituting - dy/dC in Gibbs Equat ion 1.27, then:

(1.30)

(1.31)

The area, A, occupied by a single molecule is 1/ΛΤ, where Ν is the Avogadro number. Substitution in Equation 1.31 gives:

where k is the Boltzmann constant.

It is possible, therefore, from measurements of the surface tension of a solution at various concentrations, to plot fA against / , the / being equal to y0 - γ and the fA term evaluated from Equation 1.32. The curves obtained, like those of gaseous films of insoluble substances, are of exactly the same type as the PV — Ρ curves for gases. Surface films formed by spreading insoluble sub-stances and those formed by the positive adsorption of solutes at the surface of a solution are basically alike.


where b allows for the cross-sectional area of the molecules and X for their mu-tual attraction; as the attraction increases, X decreases. For a series of soluble acids, X decreases with increasing chain length, suggesting an increase of mutual attraction between the chains.

The fact that the two-dimensional gas equation holds for a solid unimo-lecular film suggests that even in such films the molecules have freedom of move-ment. In this connection, there is evidence that the molecules in certain adsorbed layers are able to move within the bounds of the surface.

ADSORPTION EQUILIBRIA

Generalizations

Adsorption from aqueous solutions involves concentration of the solute on the solid surface. As the adsorption process proceeds, the sorbed solute tends to de-sorb into the solution. Equal amounts of solute eventually are being adsorbed and desorbed simultaneously. Consequently, the rates of adsorption and desorp-tion will attain an equilibrium state, called adsorption equilibrium. At equilib-rium, no change can be observed in the concentration of the solute on the solid surface or in the bulk solution. The position of equilibrium is characteristic of the entire system, the solute, adsorbent, solvent, temperature, p H , and so on. Adsorbed quantities at equilibrium usually increase with an increase in the solute concentration. The presentation of the amount of solute adsorbed per unit of adsorbent as a function of the equilibrium concentration in bulk solution, at constant temperature, is termed the adsorption isotherm.

The shape of the adsorption isotherm gives qualitative information about the adsorption process and the extent of the surface coverage by the adsorbate. Brunauer classified adsorption isotherms into five basic shapes (Figure 1-4) [16]. Isotherms of Type I are associated with systems where adsorption does not pro-ceed beyond the monomolecular layer. The other types of isotherms involve mul-tilayer formation. The isotherms for adsorption from solution follow Type I, although under certain conditions multilayer adsorption may be encountered. Typical adsorption isotherms for adsorption from water systems are shown in Figure 1-5 [17]. Isotherms of this type are typical for adsorption by activated carbon from aqueous solutions when adsorption does not proceed beyond a mon-omolecular layer, whereas multilayer adsorption in these systems is not usually encountered.

The surface of activated carbon is heterogenous, not only in surface struc-ture but also in the distribution of surface energy. During the course of adsorp-tion, the heat of adsorption is not constant for each incremental increase in adsorption. Usually the initial portions of adsorbed solute have greater differ-ential heats of adsorption than subsequent ones. Thus, a steep initial drop of the heat of adsorption with an increase of the amount adsorbed indicates that the first molecules to arrive at the bare surface are preferentially adsorbed on


Figure 1-4 The five typical shapes of isotherms for physical adsorption. Reproduced from Brunauer et al. [16], courtesy of the American Chemical Society.

Ce. rag/1

Figure 1-5 Adsorption isotherms of phenolic compounds on activated carbon. Repro-duced from Faust and Aly [17], courtesy of Butterworth Publishers.


Langmuir Adsorption Isotherm

The basic assumptions underlying Langmuir 's model, which is also called the ideal localized monolayer model, are:

1. The molecules are adsorbed on definite sites on the surface of the adsorbent. 2. Each site can accommodate only one molecule (monolayer). 3. The area of each site is a fixed quantity determined solely by the geometry

of the surface. 4. The adsorption energy is the same at all sites.

In addition, the adsorbed molecules cannot migrate across the surface or interact with neighboring molecules. The Langmuir equation was originally de-rived from kinetic considerations [18]. Later, it was derived on the basis of sta-tistical mechanics, thermodynamics, the law of mass action, theory of absolute reaction rates, and the Maxwell-Boltzmann distribution law [3].

The kinetic derivation considered the adsorbed layer to be in dynamic equi-librium with the gas phase. A certain fraction of the molecules striking the bare sites will condense and be held by the surface forces for a finite time and are regarded as adsorbed; the remainder will be reflected. Those molecules striking sites that are already occupied will immediately re-evaporate as if they had been reflected. If the fraction of the site already filled is 0, then:

Where ka = rate of adsorption, and kd = rate of desorption from a fully

covered surface.

At equilibrium the number of molecules in the adsorbed state at any instant

is constant; therefore:

Rate of adsorption = kaP(l - 0), (1.35)

Rate of desorption = kdd, (1.36)

kj\l - 0) = kde (1.37)

and

the most attractive sites or on positions on the surface where their potential en-ergy will be a minimum [3]. As adsorption proceeds, the less active sites become occupied. Therefore, adsorption occurs on sites of progressively decreasing ac-tivity. Smooth adsorption isotherms are usually obtained because of the presence of a sufficiently large number of sites that may occur in patches of equal energy or randomly distributed sites of unequal energy [3]. Several models can be used for the description of the adsorption data, and Langmuir 's and Freundl iche ad-sorption isotherms are the most commonly used.


Th = ktp "·38>

Taking ka/kd = b, which is the adsorption equilibrium constant, Equat ion 1.38 becomes:

bP = (1.39)

or

• ' TTTP · "·40)

which is known as the Langmuir adsorption isotherm. If V is the volume of gas adsorbed at pressure, P, and VM is the volume

adsorbed at infinite pressure—that is, when all the sites are occupied—then:

and Equat ion 1.40 becomes:

V-TTTP- (1·42>

This expression shows that V approaches VM asymptotically as Ρ ap-proaches infinity. VM is supposed to represent a fixed number of surface sites, and it should, therefore, be a temperature-independent constant while the tem-perature dependence of the equilibrium constant should follow a van ' t Hoff equation:

-AH

b = b0e RT . (1.43)

Since adsorption is exothermic (AH negative), b should decrease with increasing temperature.

For adsorption from solution by solid adsorbents, the Langmuir adsorption isotherm is expressed as:

XmbCe

x = TTTq ' ( L 4 4 )

where X = x/m, the amount of solute adsorbed, x, per unit weight of adsorbent, m; Ce = equilibrium concentration of the solute; Xm = amount of solute ad-sorbed per unit weight of adsorbent required for monolayer coverage of the sur-


face, also called monolayer capacity; and b = a constant related to the heat of adsorption, [b<x(exp(-AH/RT)] [3].

Equat ion 1.44 indicates that X approaches Xm asymptotically as Ce ap-proaches infinity. For linearization of the data, Equation 1.44 can be written in the form:

When Ce/X is plotted against Ce, a straight line, having a slope \/Xm and an intercept \/bXm, should result. Another linear form can be obtained by dividing Equation 1.45 by ex-

ploiting l/X against l/Cet a straight line, having a slope \/bXm and an intercept \/Xm, is obtained.

The monolayer capacity, Xm, determined from the Langmuir isotherm, de-fines the total capacity of the adsorbent for a specific adsorbate. Also, it may be used to determine the specific surface area of the adsorbent by utilizing a solute of known molecular area. Reliable Xm values can be obtained only for systems exhibiting Type I isotherms of the Brunauer 's classification shown in Figure 1-4 [3].

It must be indicated that conformity to the algebraic form of Langmuir 's equation does not constitute conformity to the ideal localized monolayer model, even if reasonable values of b and Xm are obtained. Therefore, a constant value of b may be a result of cancellation of variations in AH. In turn, constancy of AH may be a result of internal compensation of opposing effects such as attrac-tive lateral interactions and surface nonuniformity [3]. In addition, the assump-tion that the area of the sites and, in turn, Xm are determined solely by the nature of the solid and are independent of the nature of the solute is contrary to what is encountered in adsorption systems. However, orientation of solute molecules on the surface of activated carbon has been shown to affect the monolayer ca-pacity, Xmi as determined from the area occupied by the molecules [19,20]. Therefore, nonconformity with the physical model should not detract from the usefulness of the Langmuir isotherm for analytical description of adsorption sys-tems that do not proceed beyond monomolecular layers and conform to Type I isotherms.

Freundlich Adsorption Isotherm

The Freundlich adsorption equation is perhaps the most widely used mathemat-ical description of adsorption in aqueous systems. The Freundlich equation is expressed as [21]:

(1.46)

(1.45)


(1.47)

where χ = the amount of solute adsorbed, m = the weight of adsorbent, Ce = the solute equilibrium concentration, and Κ and \/n = constants characteristic of the system.

The Freundlich equation is an empirical expression that encompasses the heterogeneity of the surface and the exponential distribution of sites and their energies [3,22]. For linearization of the data , the Freundlich equation is written in logarithmic form:

Plotting log x/m versus log Ce, a straight line is obtained with a slope of l/n, and log Κ is the intercept of log x/m at log Ce = 0 (Ce= 1). The linear form of the isotherm can be obtained conveniently by plotting the data on log-log paper (Figure 1-6). The value of l/n obtained for adsorption of most organic com-pounds by activated carbon is < 1. Steep slopes—that is, l/n close to 1—indicate high adsorptive capacity at high equilibrium concentrations that rapidly dimin-

log — = log Κ + - log C e. m η (1.48)

0 2 ,U | 6 , Tr ich lorophenol • 2,U» Dichlorophenol X 2 , 6 , Dichlorophenol • 2 Chiorophenol A h Chlorophenol Ο Phenol

10

1 12

Figure 1-6 Logarithmic form of Freundlich adsorption isotherms for phenolic com-pounds on activated carbon [23].


ishes at lower equilibrium concentrations covered by the isotherm. Relatively flat slopes—that is, \/n << 1—indicate that the adsorptive capacity is only slightly reduced at the lower equilibrium concentrations. As the Freundlich equation in-dicates, the adsorptive capacity or loading factor on the carbon, x/m, is a func-tion of the equilibrium concentration of the solute. Therefore, higher capacities are obtained at higher equilibrium concentrations.

The Freundlich equation can be used for calculating the amount of acti-vated carbon required to reduce any initial concentration to a predetermined final concentration. By substituting C0 — Ce in Equation 1.48 for x, where CQ = the initial concentration:

log ( C

° ~ C e

) = log Κ + - log Ce. (1.49) V m I η

Equation 1.49 is useful for comparing different activated carbons in removal of different compounds or removal by the same carbon.

BET Adsorption Isotherm

The BET isotherm was developed by Brunauer, Emmett , and Teller (BET) for the generalization of the ideal localized monolayer treatment (Langmuir model) to account for multilayer adsorption [24]. The BET model is based on the sim-plifying assumptions that each molecule in the first adsorbed layer serves as a site for the adsorption of a molecule into the second, and so on. The concept of localization, therefore, prevails throughout the layers, and the forces of mutual interactions are neglected. The heat of adsorption, E, of the second and subse-quent layers is assumed to be equal to the heat of liquefication of the bulk liquid and therefore different from the heat of adsorption of the first layer. The expres-sion of the BET isotherm may be derived by an extension of the kinetic argument presented for the Langmuir isotherm or by a thermodynamic argument [1,3]. The resulting equation for the BET equilibrium isotherm is:

where V and Vm have the same meaning as in the Langmuir isotherm, P0 = saturation vapor pressure of the saturated liquid sorbate, and Β = a constant:

(1.50)

(1.51)

which can be simplified to :


where ax and a2 = rates of condensation on the first and second layers, bx and b2 = rates of evaporation from the first and second layers, Ex = first layer heat of adsorption, and EL = heat of liquefication of the bulk phase.

The term Ex — EL is known as the net heat of adsorption. Thus, the BET equation provides a measure of both the heat of adsorption and the surface area of the solid. Application of the BET equation to the adsorption from solution takes the form:

y XmBC

- (C 5 - Ce) [1 + (B - l)Ce/Cs] '

where X, Xm> and Ce have the same meaning as in Langmuir 's isotherm, and Cs = solubility of the solute in water at a specified temperature. Transforming Equation 1.53 to :

Ce 1 (B - 1) Ce

+ ~^TT7 (1.54) X(CS — Ce) XmB XmB Cs

shows that a plot of the left side against Ce/Cs should give a straight line having slope (B-\)/XmB and intercept \/XmB.

Henry's Law: Linear Adsorption Isotherm

This represents the simplest isotherm in which the amount adsorbed varies di-rectly with the equilibrium concentration of the solute. It is often called Henry 's Law after the analogous isotherm for the solution of gases in liquids. The iso-therm is described by:

X = KhCe (1.55)

where X = x/m, the amount of solute adsorbed by unit mass of adsorbent; Ce = equilibrium concentration; and Kh = a constant.

This isotherm is obtained under conditions of low concentrations of solute. In such systems, the adsorbed layer is extremely dilute and the amount adsorbed is only a fraction of the monolayer capacity. Usually the linear relationship is observed at the lower concentration levels of a total adsorption isotherm. There-fore, the application of Henry 's Law equation should be restricted to that region of the isotherm obtained from experiment. Almost all the adsorption isotherms are reduced to Henry 's Law at low concentrations. For example, for the Lang-muir adsorption isotherm, Equation 1.44, at very low concentrations, bCe is small compared with unity so the equation reduces to :

X = XmbCey (1.56)

which is Henry 's Law.

(1.53)


REFERENCES

1. Ruthven, D.M. Principles of Adsorption and Adsorption Processes. John Wiley & Sons, New York (1984).

2. Lowell, S. Introduction to Powder Surface Area. John Wiley & Sons, New York (1979).

3. Young, D.M., and A.D. Crowell. Physical Adsorption of Gases. Butter worths, Lon-don (1962).

4. Osipow, L.I. "Physical Adsorption on Solids," Chapter 4 in Principles and Appli-cations of Water Chemistry: Proceedings of the 4th Rudolfs Conference. S.D. Faust and J.V. Hunter, eds. John Wiley & Sons, New York (1976), 75.

5. London, F. Trans. Faraday Soc. 33, 8 (1937). 6. Dickerson, R.E., et al. Chemical Principles. W.A. Benjamin, New York (1970). 7. Glasstone, S. Textbook of Physical Chemistry. Van Nostrand Co., Princeton (1959). 8. Gibbs, J.W. Collected Works. Dover, New York (1961). 9. Kipling, J.J. Adsorption from Solutions of Non-Electrolyte. Academic Press, Lon-

don (1965). 10. Hill, T.L. J. Chem. Phys. 17, 507, 520 (1949). 11. Everette, D.H. Trans. Faraday Soc. 46, 453 (1950). 12. Ottewill, R.H., et al. Adsorption from Solution. Academic Press, London (1983). 13. Goodrich, F.C. "Capillary Thermodynamics Without a Geometric Gibbs Conven-

tion,' ' Chapter 1 in Adsorption from Aqueous Solutions. Advances in Chemistry Series 79. American Chemical Society, Washington, D.C. (1969), 1.

14. Moore, W.J. Physical Chemistry, 2nd ed. Prentice-Hall, Englewood Cliffs, N.J. (1960).

Most of the adsorption studies reported in the literature have been con-ducted in distilled water systems. However, inorganic salts have been shown to affect the adsorptive capacity of activated carbon for certain solutes. Snoeyink et al. [25] and Zogorski [26] reported on the enhancement of adsorptive capacity of activated carbon for some phenolic compounds at high p H values (anionic species) in the presence of inorganic salts. This effect was suggested to be due possibly to a reduction of the repulsive forces between adsorbed molecules and the carbon surface or between anions adsorbed on the surface. Although the concentrations of the inorganic salts used in these studies were too high to be encountered in drinking water supplies, the implication of the potential effects of inorganic ions on the carbon 's adsorptive capacity should not be overlooked. Indeed, Weber et al. [27] showed that the presence of low concentrations of cal-cium and magnesium salts enhances the adsorption of humic acids on activated carbon possibly because of the formation of an ion-humate-carbon complex. Ad-sorption isotherms of humic acid in tap water systems showed higher carbon adsorptive capacities than those in distilled water systems. Therefore, adsorption studies for the application of activated carbon in water treatment plants should be conducted using the natural water or a synthetic medium of equivalent com-position. In addition, the isotherms should be conducted within the concentration range corresponding to the levels likely to be encountered for the compound of interest since extrapolation of the isothermal data can lead to erroneous results.


15. Langmuir, I. J. Amer. Chem. Soc. 39, 1848 (1917). 16. Brunauer, S., et al. J. Amer. Chem. Soc. 62, 1723 (1940). 17. Faust, S.D., and O.M. Aly. Chemistry of Water Treatment. Butterworths, Stone-

ham, Mass. (1983). 18. Langmuir, I. J. Amer. Chem. Soc. 37, 1139 (1915). 19. Puri, R.P. "Carbon Adsorption of Pure Compounds and Mixtures from Solution

Phase,'' Chapter 17 in Activated Carbon Adsorption of Organics from the Aqueous Phase, vol. 1. I.H. Suffet and M.J. McGuire, eds. Ann Arbor Science Publishers, Ann Arbor, Mich. (1980), 353.

20. Morris, J.C., and W.J. Weber, Jr. "Adsorption of Biochemically Resistant Materials from Solution." Environmental Health Series AWTR-9. U.S. Department of Health, Education, and Welfare, Washington, D.C. (1964).

21. Freundlich, H. Colloid and Capillary Chemistry. Methuen and Co., London (1926). 22. Sips, R. J. Chem. Phys. 16, 490 (1948). 23. Aly, O.M., and S.D. Faust. "Sorption of Phenolic Compounds from Aqueous So-

lutions." Paper presented at the Kendall Award Symposium, American Chemical Society, 163rd National Meeting, Boston (1972).

24. Brunauer, S., et al. J. Amer. Chem. Soc. 60, 309 (1938). 25. Snoeyink, V.L., et al. Environ. Sei. Technol. 3, 918 (1969). 26. Zogorski, J.S. "The Adsorption of Phenols onto Granular Activated Carbon from

Aqueous Solutions." Ph.D. dissertation, Rutgers University, Department of Envi-ronmental Science, New Brunswick, N.J. (1975).

27. Weber, W.J., Jr., et al. "Potential Mechanisms for Removal of Humic Acids from Water by Activated Carbon," Chapter 16 in Activated Carbon Adsorption of Or-ganics from the Aqueous Phase, Vol. 1. I.H. Suffet and M.J. McGuire, eds. Ann Arbor Science Publishers, Ann Arbor, Mich. (1980), 317.

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