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LESSON 2.

June 9, 2024

LESSON 2. CALCULATION AN ADSORB ABILITY OF THE SOLID ADSORBENTS. 2. DETERMINATION OF THE SPECIFIC SURFACE AREA OF A SOLID ADSORBENT

Adsorption is the adhesion of atoms, ions, or molecules from a gas, liquid, or dissolved solid to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. This process differs from absorption, in which a fluid (the absorbate) permeatesor is dissolved by a liquid or solid (the absorbent). Note that adsorption is a surface-based process while absorption involves the whole volume of the material. The term sorptionencompasses both processes, while desorption is the reverse of adsorption. It is a surface phenomenon.

Similar to surface tension, adsorption is a consequence of surface energy. In a bulk material, all the bonding requirements (be they ionic, covalent, or metallic) of the constituentatoms of the material are filled by other atoms in the material. However, atoms on the surface of the adsorbent are not wholly surrounded by other adsorbent atoms and therefore can attract adsorbates. The exact nature of the bonding depends on the details of the species involved, but the adsorption process is generally classified as physisorption(characteristic of weak van der Waals forces) or chemisorption (characteristic of covalent bonding). It may also occur due to electrostatic attraction.

Adsorption is present in many natural physical, biological, and chemical systems, and is widely used in industrial applications such asactivated charcoal, capturing and using waste heat to provide cold water for air conditioning and other process requirements (adsorption chillers), synthetic resins, increase storage capacity of carbide-derived carbons, and water purification. Adsorption, ion exchange, andchromatography are sorption processes in which certain adsorbates are selectively transferred from the fluid phase to the surface of insoluble, rigid particles suspended in a vessel or packed in a column. Lesser known, are the pharmaceutical industry applications as a means to prolong neurological exposure to specific drugs or parts there of.

Surface adsorption to a solid falls into two broad categories; physisorption and chemisorption. Physisorption is a non-specific loose binding of the adsorbate to the solid via van der Waals type interactions. Multilayered adsorption is possible and it is easily disrupted by increasing temperatures. Chemisorption involves a more specific binding of the absorbate to the solid. It is a process that is more akin to a chemical reaction and hence, only monolayer adsorption is possible. “The difference between physical and chemisorption is typified by the behavior of nitrogen on iron. At the temperature of liquid nitrogen, -190oC, nitrogen is adsorbed physically on iron as nitrogen molecules, N2. The amount of N2 adsorbed decreases rapidly as the temperature rises. At room temperature iron does not adsorb nitrogen at all. At high temperatures, ~500oC, nitrogen is chemisorbed on the iron surface as nitrogen atoms.” (Castellan 1983) The Langmuir Isotherm best describes chemisorption processes.

The word “adsorption” was coined in 1881 by German physicist Heinrich Kayser (1853-1940).

Adsorption

General. The situation existing at the surface of а liquid or а solid is different from that in the interior. For example, а molecule in the interior of а liquid is completely surrounded by other molecules on all sides and hence the intermolecular forces of attraction are exerted equally in all directions. However, а molecule at the surface of а liquid is surrounded by larger number of molecules in the liquid phase and fewer molecules in the vapour phase i.е. in the space above the liquid surface. As а result, these molecules lying at the surface, experience some net inward force of attraction which causes surface tension. Similar inward forces of attraction exist at the surface of а solid. Alternatively, in case of certain solids such as transition metals (like Ni) there are unutilized free valencies at the surface.

Because of the unbalanced inward forces of attraction or free valencies at the surface, liquids and solids have the property to attract and retain the molecules of а gas or а dissolved substance onto their surfaces with which they come in contact.

The phenomenon of attracting and retaining the molecules of а substance on the surface of а liquid or а solid resulting into a higher concentration of the molecules on the surface is called adsorption. The substance thus adsorbed on the surface is called the adsorbate and the substance on which it is adsorbed is called adsorbent. The reverse process e. removal of the adsorbed substance from the surface is called desorption. The adsorption of gases on the surface of metals is called occlusion.

Difference between adsorption and absorption. The term adsorption differs from the term absorption in the fact that whereas the former refers to the attraction and retention of the molecules of а substance on the surface only, the latter involves passing of the substance through the surface into the bulk of the liquid or the solid. Where there is а doubt whether the process is true adsorption or absorption (i.е. both adsorption and absorption take place) the term sorption is simply used.

Thus in adsorption whereas the concentration is different at the surface than in the bulk, in absorption, the concentration is same throughout. Moreover whereas adsorption is fast in the beginning and then the rate decreases till equilibrium is attained, absorption takes place at uniform speed. Thus the main points of difference between adsorption and absorption may be summed up as follows:

Adsorption:

1. It is а surface phenomenon i.е. it occurs only at the surface of the adsorbent.

2. In this phenomenon, the concentration on the surface of adsorbent is different from that in the bulk.

3. Its rate is high in the beginning and then decreases till equilibrium is attained.

Absorption:

1. It is а bulk phenomenon i.e. occurs throughout the body of the material.

2. In this phenomenon, the concentration is same throughout the material.

3. Its rate remains same throughout the process.

Examples of adsorption, absorption and sorption.

(i) If silica gel is placed in а vessel containing water vapours, the latter are adsorbed on the former. On the other hand, if anhydrous CaCl₂ is kept in place of silica gel, absorption takes place as the water vapours are uniformly distributed in CaCl₂ to form hydrated calcium chloride (CaCO₃ ^. 2H₂O).

(ii) Ammonia gas placed in contact with charcoal gets adsorbed on the charcoal whereas ammonia gas placed in contact with water gets absorbed into water, giving NH₄OH solution of uniform concentration.

(iii) Dyes get adsorbed as well as absorbed in the cotton fibres i.е. sorption takes place.

Positive and Negative Adsorption. In case of adsorption by solids from the solutions, mostly the solute is adsorbed on the surface of the solid adsorbent so that the concentration of solute on the surface of the adsorbent is greater than in the bulk. This is called positive adsorption. However in some cases, the solvent from the solution may be adsorbed by the adsorbent so that the concentration of the solution increases than the initial concentration. This is called negative adsorption. For example, when а concentrated solution of KCI is shaken with blood charcoal, it shows positive adsorption but with а dilute solution of КС1, it shows negative adsorption. To sum up:

When the concentration of the adsorbate is more on the surface of the adsorbent than in the bulk. it is called positive adsorption. If the concentration of the adsorbate is less relative to its concentration in the bulk, it is called negative adsorption.

Factors affecting adsorption of gases by solids. Almost all solids adsorb gases to some extent. However, the exact amount of а gas adsorbed depends upon а number of factors, as briefly explained below:

(i) Nature and Surface area of the adsorbent. If is observed that the same gas is adsorbed to different extents by different solids at the same temperature. Further, as may be expected, the greater the surface area of the adsorbent, greater is the volume of the gas adsorbed. It is for this reason that substances like charcoal and silica gel are excellent adsorbents because they have highly porous structures and hence large surface areas.

For the same reason, finely divided substances have larger adsorption power than when they are present in the compact form.

Since the surface area of adsorbents cannot always be determined readily, the common practice is to express the gas adsorbed per gram of the adsorbent (The surface area per gram of the adsorbent is called specific area).

(ii) Nature of the gas being adsorbed. Different gases are adsorbed to different extents by the same adsorbent at the same temperature.

(iii) Temperature. Studying the adsorption of any particular gas by some particular adsorbent. It is observed that the adsorption decreases with increase of temperature and vice versa. For example, one gram of charcoal adsorbs about 10 cm³ of N₂ at 273 K, 20 cm³ at 244 K and 45 cm³ at 195 K. The decrease of adsorption with increase of temperature may be explained as follows:

Like any other equilibrium, adsorption is а process involving а true equilibrium. The two opposing processes involved are condensation (i.е. adsorption) of the gas molecules on the surface of the solid and evaporation (i.е. desorption) of the gas molecules from the surface of the solid into the gaseous phase. Moreover, the process of condensation (or adsorption) is exothermic so that the equilibrium may be represented as:

Applying be Chatelier’s principle, it can be seen that increase of temperature decreases the adsorption and vice versa.

The amount of heat evolved when one mole of the gas is adsorbed on the adsorbent is called the heat of adsorption.

(iv) Pressure. At constant temperature, the adsorption of а gas increases with increase of pressure. It is observed that at low temperature, the adsorption of а gas increases very rapidly as the pressure is increased from small values.

(v) Activation of the solid Adsorbent. It constant temperature, the adsorbing power of an adsorbent. This is usually done by increasing the surface area (or the specific area) of the adsorbent which can be achieved in any of the following ways:

(а) By making the surface of the adsorbent rough e.g. by mechanical rubbing or by chemical action or by depositing finely dispersed metals on the surface of the adsorbent by electroplating.

(b) By subdividing the adsorbent into smaller pieces or drains. No doubt this method increases the surface area but it has а practical limitation, that is, if the adsorbent is broken into too fine particles that it becomes almost powder, then the penetration of the gas becomes difficult and this will obstruct adsorption.

(с) By removing the gases already adsorbed e.g. charcoal is activated by heating in superheated steam or in vacuum at а temperature between 623 to 1273 К.

Types of adsorption. An experimental study of the adsorption of various types on solids shows that there are two main types of adsorption. These are briefly explained below:

(i) Physical adsorption or van der Waal’s adsorption or physicosorption. When а gas is held (adsorbed) on the surface of а solid by van-der-Waal’s forces (which are weak intermolecular forces of attraction) without resulting into the formation of any chemical bond between the adsorbate and the adsorbent, it is called “physical adsorption” or “van-der-Waal’s adsorption” or “physicosorption”. This type of adsorption is characterized by low heats of adsorption i.e. about 40 kJ per mole. Further, physical adsorption of а gas by а solid is generally reversible. Increase of pressure causes more gas to be adsorbed and the release of pressure frees the adsorbed gas. Similarly, decrease of temperature increases adsorption but the gas adsorbed at low temperature can be freed again by heating.

(ii) Chemical adsorption or Chemisorption or Langmuir adsorption. When а gas is held on to the surface of а solid by forces similar to those of а chemical bond, the type of adsorption is called chemical adsorption or chemisorption. This type of adsorption results into the formation of what is called а “surface compound”. That the forces involved are similar to those of chemical bond is confirmed by the fact that the heats evolved during chemisorption are high (i.е. about 400 kJ/mole) which are of the same magnitude as those involved in chemical reactions. Further, as chemisorption is something similar to а chemical change, it is usually irreversible. The efforts to free the adsorbed gas often gives some definite compound instead of the free gas. For example, oxygen adsorbed on tungsten or carbon is liberated as tungsten oxide or as carbon monoxide and carbon dioxide.

Another aspect in which chemisorption differs from physical adsorption is the fact that whereas physical adsorption takes place between every gas and а solid i.е. is not specific iature (because it involves van der Waal’s forces which exist among the molecules of every two substances), the chemisorption is specific iature and occurs only where there is а tendency towards compound formation between the gas and the adsorbent. Further unlike physical adsorption, the chemisorption like the most of chemical changes, increases with increase of temperature. For this reason, а gas may be physically adsorbed at low temperature but chemisorbed at higher temperature. For example, it happens in case of adsorption of hydrogen on nickel. When chemisorption takes place by raising the temperature i.е. by supplying activation energy, the process is called “activated adsorption”.

Physical adsorption:

1. The forces operating in these cases are weak van-der-Waal’s forces.

2. The heats of adsorption are low viz. about 20 – 40 kJ/mol

3. No compound formation takes place in these cases.

4. The process is reversible i.е. desorption of the gas occurs by increasing the temperature or decreasing the pressure.

5. It does not require any а activation energy.

б. This type of adsorption decreases with increase of temperature.

7. It is not specific iature i.е. all gases are adsorbed on all solids to some extent.

8. The amount of the gas adsorbed is related to the ease of liquefaction of the gas.

9. It forms multimolecular layer.

Chemisorption:

1. The forces operating in these cases are similar to those of а chemical bond.

2. The heats of adsorption are high viz. about 400-400 kJ/mol

3. Surface compounds are formed.

4. The process is irreversible. Efforts to free the adsorbed gas give some definite compound.

5. It requires activation energy.

6. This type of adsorption first increases with increase of temperature. The effect is called activated adsorption.

7. It is specific iature and occurs only when there is some possibility of compound formation between the gas being adsorbed and the solid adsorbent.

8. There is no such correlation.

9. It forms unimolecular layer.

Adsorption of gases-Freundlich’s. Adsorption isotherm. The extent of adsorption on а given surface generally increases with increase in pressure (for gases) and concentration (for solution) at constant temperature. At low temperatures, the adsorption of а gas increases very rapidly as the pressure rises. When the temperature is high, the increase in adsorption is relatively less.

To understand the effect of pressure on adsorption, we should consider adsorption as an equilibrium process. When the adsorbent and the adsorbate are enclosed in а closed vessel, the amount of gas adsorbed equals the amount desorbed when the equilibrium stage is attained. Therefore, after an initial decrease in the pressure of the gas, gas pressure as well as the amount of gas adsorbed reach constant or equilibrium values.

The amount of gas adsorbed depends on the surface area of the adsorbent or on its mass if the adsorbent is taken in the form of powder.

The extent of adsorption is usually expressed as x/m, where m is the mass of the adsorbent and x is the mass of the adsorbate when adsorption equilibrium is reached.

The specific surface area of а solid (in the form of а powder or porous mass) is the surface area in square meters per gram of the adsorbent. Highly active solids with large surface area (several hundred square meters per gram) are used as adsorbents.

А graph between the amount (х/m) adsorbed by an adsorbent and the equilibrium pressure (or concentration for solutions) of the adsorbate at а constant temperature is called the adsorption isotherm.

The simplest type of adsorption isotherm is shown in Fig. At а value of р_s of equilibrium pressure, x/m reaches its maximum value and then it remains constant even though the pressure p is increased. This is the saturation state and р_s is the saturation pressure. This type of adsorption isotherm is observed when the adsorbate forms а uniform molecular layer of it on the surface of the adsorbent.

Fig. Variation of x/m with increase in pressure at constant temperature (General adsorption isotherm)

А relationship between the amount adsorbed (х/m) and the equilibrium pressure (р) can be obtained as follows:

At low values of р, the graph is nearly straight and sloping. This is represented by the following equation:

x/m µ p¹ or x/m = constant x p¹

At high pressure х/m becomes independent of the values of p. In this range of pressure

x/m µ p⁰ or x/m = constant x p⁰

In the intermediate range of pressure, х/m will depend on p raised to powers between 1 and 0 i.е. fractions. For а small range of pressure values, we can write:

x/m µ p^1/n or x/m = Kp^1/n

whereis а positive integer andand К are constants depending upon the nature of the adsorbate and adsorbent.

This relationship was originally put forward by Freundlich and is known as Freundlich adsorption isotherm.

To test the validity of this equation, taking logarithms of both sides, we get

log x/m = log K + 1/n log p

А graph between log x/m against log p should, therefore, give а straight 1inе with slope equal to 1/n and ordinate intercept equal to log К. The experimental values, when plotted, however, show some deviation from linearity, specially at high pressures. The relation is hence considered as an approximate one and is suitable at low pressures.

Fig. Freundlich adsorption isotherm. Linear graph between log x/m and log p.

Chemisorption of Hydrogen and Halogens

Hydrogen (H₂)

In the H₂ molecule, the valence electrons are all involved in the H-H -bond and there are no additional electrons which may interact with the substrate atoms. Consequently, chemisorption of hydrogen on metals is almost invariably a dissociative process in which the H-H bond is broken, thereby permitting the hydrogen atoms to independently interact with the substrate (see Section 2.4 for a description of the energetics of this process). The adsorbed species in this instance therefore are hydrogen atoms.

The exact nature of the adsorbed hydrogen atom complex is generally difficult to determine experimentally, and the very small size of the hydrogen atom does mean that migration of hydrogen from the interface into sub-surface layers of the substrate can occur with relative ease on some metals (e.g. Pd, rare earth metals).

The possibility of molecular H₂ chemisorption at low temperatures cannot be entirely excluded, however, as demonstrated by the discovery of molecular hydrogen transition metal compounds, such as W( ²-H₂)(CO)₃(Pi-Pr₃)₃ , in which both atoms of the hydrogen molecule are coordinated to a single metal centre.

Halogens (F₂, Cl₂, Br₂ etc.)

Halogens also chemisorb in a dissociative fashion to give adsorbed halogen atoms. The reasons for this are fairly clear – in principle a halogen molecule could act as a Lewis base and bind to the surface without breakage of the X-X bond, in practice the lone pairs are strongly held by the highly electronegative halogen atom so any such interaction would be very weak and the thermodynamics lie very heavily in favour of dissociative adsorption [ i.e. D(X-X) + D(M-X₂) << 2 D(M-X^(-) ) ]. Clearly the kinetic barrier to dissociation must also be low or non-existent for the dissociative adsorption to occur readily.

Another way of looking at the interaction of a halogen molecule with a metal surface is as follows : the significant difference in electronegativity between a typical metal and halogen is such that substantial electron transfer from the metal to halogen is favoured. If a halogen molecule is interacting with a metal surface then this transferred electron density will enter the * antibonding orbital of the molecule, thereby weakening the X-X bond. At the same time the build-up of negative charge on the halogen atoms enhances the strength of the metal-halogen interaction. The net result of these two effects when taken to their limit is that the halogen molecule dissociates and the halogen atoms interact with the metal with a strong ionic contribution to the bonding.

Halogen atoms tend to occupy high co-ordination sites on the surface – for example, the 3-fold hollow site on fcc(111) surfaces (A) and the 4-fold hollow site on fcc(100) surfaces (B).

(A) Plan View (B)

This behaviour is typical of atomic adsorbates which almost invariably endeavour to maximise their co-ordination and hence prefer to occupy the highest-available co-ordination site on the surface.

As a result of the electron transfer from the metal substrate to the halogen atoms, each adsorbed atom is associated with a significant surface dipole.

Cross-section

One consequence of this is that there are repulsive (dipole-dipole) interactions between the adsorbed atoms, which are especially evident at higher surface coverages and which can lead to a substantial reduction in the enthalpy of adsorption at specific coverages (if these coverages mark a watershed, above which the atoms are forced to occupy sites which are much closer together).

Another feature of the halogen adsorption chemistry of some metals is the transition from an adsorbed surface layer to surface compound formation at high gas exposures.

Chemisorption of Nitrogen and Oxygen

Oxygen

Oxygen is an example of a molecule which usually adsorb dissociatively, but are also found to adsorb molecularly on some metals (e.g. Ag, Pt). In those cases where both types of adsorption are observed it is the dissociative process that corresponds to the higher adsorption enthalpy.

As noted above, in the molecular adsorption state the interaction between the molecule and the surface is relatively weak. Molecules aligned such that the internuclear axis is parallel to the surface plane may bond to a single metal atom of the surface via both

1. -donor interaction, in which the charge transfer is from the occupied molecular -bonding molecular orbital of the molecule into vacant orbitals of -symmetry on the metal (i.e. M  O₂ ), and

2. -acceptor interaction, in which an occupied metal d-orbital of the correct symmetry overlaps with empty p* orbitals of the molecule and the charge transfer is from the surface to the molecule (i.e. M  O₂).

Although the interaction of the molecule with the surface is generally weak, one might expect that there might be a substantial barrier to dissociation due to the high strength (and high dissociation enthalpy) of the O=O bond. Nevertheless on most metal surfaces, dissociation of oxygen is observed to be facile which is related to the manner in which the interaction with the surface can mitigate the high intrinsic bond energy and thereby facilitate dissociation.

Once formed, oxygen atoms are strongly bound to the surface and, as noted previously, will tend to occupy the highest available co-ordination site. The strength of the interaction between adsorbate and substrate is such that the adjacent metal atoms are often seen to undergo significant displacements from the equilibrium positions that they occupy on the clean metal surface. This displacement may simply lead to a distortion of the substrate surface in the immediate vicinity of the adsorbed atom (so that, for example, the adjacent metal atoms are drawn in towards the oxygen and the metal-oxygen bond distance is reduced) or to a more extended surface reconstruction

Dissociative oxygen adsorption is frequently irreversible – rather than simply leading to desorption, heating of an adsorbed oxygen overlayer often results in either the gradual removal of oxygen from the surface by diffusion into the bulk of the substrate (e.g. Si(111) or Cu(111)) or to the formation of a surface oxide compound. Even at ambient temperatures, extended oxygen exposure often leads to the nucleation of a surface oxide. Depending on the reactivity of the metal concerned, further exposure at low temperatures may result either in a progressive conversion of the bulk material to oxide or the oxidation process may effectively stop after the formation of a passivating surface oxide film of a specific thickness (e.g. Al).

Nitrogen

The interaction of nitrogen with metal surfaces shows many of the same characteristics as those described above for oxygen. However, in general N₂ is less susceptible to dissociation as a result of the lower M-N bond strength and the substantial kinetic barrier associated with breaking the NN triple bond.

Chemisorption of Carbon Monoxide

Depending upon the metal surface, carbon monoxide may adsorb either in a molecular form or in a dissociative fashion – in some cases both states coexist on particular surface planes and over specific ranges of temperature.

1. On the reactive surfaces of metals from the left-hand side of the periodic table (e.g. Na, Ca, Ti, rare earth metals) the adsorption is almost invariably dissociative, leading to the formation of adsorbed carbon and oxygen atoms (and thereafter to the formation of surface oxide and oxy-carbide compounds).

2. By contrast, on surfaces of the metals from the right hand side of the d-block (e.g. Cu, Ag) the interaction is predominantly molecular; the strength of interaction between the CO molecule and the metal is also much weaker, so the M-CO bond may be readily broken and the CO desorbed from the surface by raising the surface temperature without inducing any dissociation of the molecule.

3. For the majority of the transition metals, however, the nature of the adsorption (dissociative v.’s molecular) is very sensitive to the surface temperature and surface structure (e.g. the Miller index plane, and the presence of any lower co-ordination sites such as step sites and defects).

Molecularly chemisorbed CO has been found to bond in various ways to single crystal metal surfaces – analogous to its behaviour in isolated metal carbonyl complexes.

scat2_5d

scat2_5e

scat2_5f

Terminal (“Linear”)
(all surfaces)

Bridging ( 2f site )
(all surfaces)

Bridging / 3f hollow
( fcc(111) )

Bridging / 4f hollow
(rare – fcc(100) ?)

scat2_5g

scat2_5h

scat2_5i

scat2_5j

Whilst the above structural diagrams amply demonstrate the inadequacies of a simple valence bond description of the bonding of molecules to surface, they do to an extent also illustrate one of its features and strengths – namely that a given element, in this case carbon, tends to have a specific valence. Consequently, as the number of metal atoms to which the carbon is co-ordinated increases, so there is a corresponding reduction in the C-O bond order.

However, it must be emphasised that a molecule such as CO does not necessarily prefer to bind at the highest available co-ordination site. So, for example, the fact that there are 3-fold hollow sites on an fcc(111) surface does not mean that CO will necessarily adopt this site – the preferred site may still be a terminal or 2-fold bridging site, and the site or site(s) which is(are) occupied may change with either surface coverage or temperature. The energy difference between the various adsorption sites available for molecular CO chemisorption appears therefore to be very small.

Chemisorption of Ammonia and other Group V/VI Hydrides

Ammonia has lone pairs available for bonding on the central nitrogen atom and may bond without dissociation to a single metal atom of a surface, acting as a Lewis base, to give a pseudo-tetrahedral co-ordination for the nitrogen atom.

Alternatively, progressive dehydrogenation may occur to give surface NH_x (x = 2,1,0) species and adsorbed hydrogen atoms, i.e.

NH₃  NH_{2 (ads)} + H_(ads)  NH_(ads) + 2 H_(ads)  N_(ads) + 3 H_(ads)

As the number of hydrogens bonded to the nitrogen atom is reduced, the adsorbed species will tend to move into a higher co-ordination site on the surface (thereby tending to maintain the valence of nitrogen).

Other Group V and Group VI hydrides (e.g. PH₃ , H₂O, H₂S) exhibit similar adsorption characteristics to ammonia.

Chemisorption of Unsaturated Hydrocarbons

Unsaturated hydrocarbons (alkenes, alkynes, aromatic molecules etc.) all tend to interact fairly strongly with metal atom surfaces. At low temperatures (and on less reactive metal surfaces) the adsorption may be molecular, albeit perhaps with some distortion of bond angles around the carbon atom.

Ethene, for example, may bond to give both a -complex (A) or a di-adsorption complex (B):

(A) Chemisorbed (B)
Ethene

As the temperature is raised, or even at low temperatures on more reactive surfaces (in particular those that bind hydrogen strongly), a stepwise dehydrogenation may occur. One particularly stable surface intermediate found in the dehydrogenation of ethene is the ethylidyne complex, whose formation also involves H-atom transfer between the carbon atoms.

scat2_5n

Ethylidyne :
this adsorbate preferentially occupies a 3-fold hollow site to give pseudo-tetrahedral co-ordination for the carbon atom.

The ultimate product of complete dehydrogenation, and the loss of molecular hydrogen by desorption, is usually either carbidic or graphitic surface carbon.

The Desorption Process

An adsorbed species present on a surface at low temperatures may remain almost indefinitely in that state. As the temperature of the substrate is increased, however, there will come a point at which the thermal energy of the adsorbed species is such that one of several things may occur :

1. a molecular species may decompose to yield either gas phase products or other surface species.

2. an atomic adsorbate may react with the substrate to yield a specific surface compound, or diffuse into the bulk of the underlying solid.

3. the species may desorb from the surface and return into the gas phase.

The last of these options is the desorption process. In the absence of decomposition the desorbing species will generally be the same as that originally adsorbed but this is not necessarily always the case.

(An example where it is not is found in the adsorption of some alkali metals on metallic substrates exhibiting a high work function where, at low coverages, the desorbing species is the alkali metal ion as opposed to the neutral atom. Other examples would include certain isomerisation reactions.)

Desorption Kinetics

The rate of desorption of an adsorbate from a surface can be expressed in the general form :

R_des = k N^x

where

x – kinetic order of desorption

k – rate constant for the desorption process

N – surface concentration of adsorbed species

The order of desorption can usually be predicted because we are concerned with an elementary step of a “reaction” : specifically,

I. Atomic or Simple Molecular Desorption

A_(ads)  A_(g)

M_(ads)  M_(g)

– will usually be a first order process ( i.e. x = 1 ). Examples include …

W / Cu_(ads)  W_(s) + Cu_(g)

; desorption of Cu atoms from a W surface

Cu / CO_(ads)  Cu_(s) + CO_(g)

; desorption of CO molecules from a Cu surface

II. Recombinative Molecular Desorption

2 A_(ads)  A_{2 (g)}

– will usually be a second order process ( i.e. x = 2 ). Examples include …

Pt / O_(ads)  Pt_(s) + O_{2 (g)}

; desorption of O atoms as O₂ from a Pt surface

Ni / H_(ads)  Ni_(s) + H_{2 (g)}

; desorption of H atoms as H₂ from a Ni surface

The rate constant for the desorption process may be expressed in an Arrhenius form,

k_des = A exp ( -E_a^des / RT )

where

E_a^des is the activation energy for desorption , and

A is the pre-exponential factor; this can also be considered to be the “attempt frequency”,  , at overcoming the barrier to desorption.

This then gives the following general expression for the rate of desorption

In the particular case of simple molecular adsorption, the pre-exponential/frequency factor () may also be equated with the frequency of vibration of the bond between the molecule and substrate; this is because every time this bond is stretched during the course of a vibrational cycle can be considered an attempt to break the bond and hence an attempt at desorption.

Adsorption from solutions. Solid surfaces can also adsorb solutes from the solutions. An application of adsorption from solution is the use of activated charcoal for decolorising sugar solutions. Activated charcoal can adsorb colouring impurities from the solutions of organic compounds. Adsorption from solution can also involve colourless solutions. Adsorption of ammonia from ammonium hydroxide solution and acetic acid from its solution in water by activated charcoal are such examples.

This type of adsorption is also affected by temperature and concentration. The extent of adsorption decreases with increase in temperature and increases with increase in concentration. The isotherm for the adsorption of solutes from solutions (by the solid adsorbents) is found to be similar to that shown in Fig. 2. Hence the relationship between x/m (mass of the solute adsorbed per gram of the adsorbent) and the equilibrium concentration, С of the solute in the solution is also similar i.e:

X/m =KC^1/n

Taking logarithms of both sides of the equation, we get:

log x/m = log К + 1/n log C

This equation implies that а plot of log x/m against log С should be а straight line with slope1/n and intercept log Х. This is found to be so over small ranges of concentration.

The equation for adsorption from solutions is found to give better results than for adsorption of gases by solids.

Adsorption isobars. As already discussed, adsorption is а case of dynamic equilibrium in which forward process (adsorption) is exothermic while backward process (desorption) is endothermic. Thus applying be Chatelier’s principle, increase of temperature will favour the backward process i.е., adsorption decreases.

А graph drawn between the amount adsorbed (x/m) and temperature ‘t’ at а constant equilibrium pressure of adsorbate gas is known as adsorption isobar.

Adsorption isobars of physical adsorption and chemical adsorption show important difference [Fig.3 (а) and (b)] and this difference is helpful in distinguishing these two types of adsorption. The physical adsorption isobar shows а с1есгеаье in х/m throughout with rise in temperature, the chemisorption isobar shows an initial increase with temperature and then the expected decrease. The initial increase is because of the fact that the heat supplied acts as activation energy required in chemisorption (like chemical reactions).

Fig.3. (а) Physical adsorption isobar. (b) Chemisorption isobar.

Adsorbents

Characteristics and general requirements

Activated carbon is used as an adsorbent

Adsorbents are used usually in the form of spherical pellets, rods, moldings, or monoliths with hydrodynamic diameters between 0.5 and 10 mm. They must have high abrasion resistance, high thermal stability and small pore diameters, which results in higher exposed surface area and hence high surface capacity for adsorption. The adsorbents must also have a distinct pore structure that enables fast transport of the gaseous vapors.

Most industrial adsorbents fall into one of three classes:

· Oxygen-containing compounds – Are typically hydrophilic and polar, including materials such as silica gel and zeolites.

· Carbon-based compounds – Are typically hydrophobic and non-polar, including materials such as activated carbon and graphite.

· Polymer-based compounds – Are polar or non-polar functional groups in a porous polymer matrix.

Silica gel

Silica gel is a chemically inert, nontoxic, polar and dimensionally stable (< 400 °C or 750 °F) amorphous form of SiO₂. It is prepared by the reaction between sodium silicate and acetic acid, which is followed by a series of after-treatment processes such as aging, pickling, etc. These after treatment methods results in various pore size distributions.

Silica is used for drying of process air (e.g. oxygen, natural gas) and adsorption of heavy (polar) hydrocarbons from natural gas.

Zeolites

Zeolites are natural or synthetic crystalline aluminosilicates, which have a repeating pore network and release water at high temperature. Zeolites are polar iature.

They are manufactured by hydrothermal synthesis of sodium aluminosilicate or another silica source in an autoclave followed by ion exchange with certain cations (Na⁺, Li⁺, Ca²⁺, K⁺, NH₄⁺). The channel diameter of zeolite cages usually ranges from 2 to 9 Å (200 to 900 pm). The ion exchange process is followed by drying of the crystals, which can be pelletized with a binder to form macroporous pellets.

Zeolites are applied in drying of process air, CO₂ removal from natural gas, CO removal from reforming gas, air separation, catalytic cracking, and catalytic synthesis and reforming.

Non-polar (siliceous) zeolites are synthesized from aluminum-free silica sources or by dealumination of aluminum-containing zeolites. The dealumination process is done by treating the zeolite with steam at elevated temperatures, typically greater than 500 °C (930 °F). This high temperature heat treatment breaks the aluminum-oxygen bonds and the aluminum atom is expelled from the zeolite framework.

Activated carbon

Activated carbon is a highly porous, amorphous solid consisting of microcrystallites with a graphite lattice, usually prepared in small pellets or a powder. It is non-polar and cheap. One of its main drawbacks is that it is reacts with oxygen at moderate temperatures (over 300 °C).

Activated carboitrogen isotherm showing a marked microporous type I behavior

Activated carbon can be manufactured from carbonaceous material, including coal (bituminous, subbituminous, and lignite), peat, wood, or nutshells (e.g., coconut). The manufacturing process consists of two phases, carbonization and activation. The carbonization process includes drying and then heating to separate by-products, including tars and other hydrocarbons from the raw material, as well as to drive off any gases generated. The process is completed by heating the material over 400 °C (750 °F) in an oxygen-free atmosphere that cannot support combustion. The carbonized particles are then “activated” by exposing them to an oxidizing agent, usually steam or carbon dioxide at high temperature. This agent burns off the pore blocking structures created during the carbonization phase and so, they develop a porous, three-dimensional graphite lattice structure. The size of the pores developed during activation is a function of the time that they spend in this stage. Longer exposure times result in larger pore sizes. The most popular aqueous phase carbons are bituminous based because of their hardness, abrasion resistance, pore size distribution, and low cost, but their effectiveness needs to be tested in each application to determine the optimal product.

Activated carbon is used for adsorption of organic substances and non-polar adsorbates and it is also usually used for waste gas (and waste water) treatment. It is the most widely used adsorbent since most of its chemical (e.g. surface groups) and physical properties (e.g. pore size distribution and surface area) can be tuned according to what is needed. Its usefulness also derives from its large micropore (and sometimes mesopore) volume and the resulting high surface area.

Protein adsorption of biomaterials

Protein adsorption is a process that has a fundamental role in the field of biomaterials. Indeed, biomaterial surfaces in contact with biological media, such as blood or serum, are immediately coated by proteins. Therefore, living cells do not interact directly with the biomaterial surface, but with the adsorbed proteins layer. This protein layer mediates the interaction between biomaterials and cells, translating biomaterial physical and chemical properties into a “biological language”.^[6] In fact, cell membrane receptors bind to protein layer bioactive sites and these receptor-protein binding events are transduced, through the cell membrane, in a manner that stimulates specific intracellular processes that then determine cell adhesion, shape, growth and differentiation. Protein adsorption is influenced by many surface properties such as surface wettability, surface chemical composition ^[7] and surface nanometre-scale morphology.^[8]

Adsorption chillers

Combining an adsorbent with a refrigerant, adsorption chillers use heat to provide a cooling effect. This heat, in the form of hot water, may come from any number of industrial sources including waste heat from industrial processes, prime heat from solar thermal installations or from the exhaust or water jacket heat of a piston engine or turbine.

Although there are similarities between absorption and adsorption refrigeration, the latter is based on the interaction between gases and solids. The adsorption chamber of the chiller is filled with a solid material (for example zeolite, silica gel, alumina, active carbon and certain types of metal salts), which in its neutral state has adsorbed the refrigerant. When heated, the solid desorbs (releases) refrigerant vapour, which subsequently is cooled and liquefied. This liquid refrigerant then provides its cooling effect at the evaporator, byabsorbing external heat and turning back into a vapour. In the final stage the refrigerant vapour is (re)adsorbed into the solid.^[9] As an adsorption chiller requires no moving parts, it is relatively quiet.

Portal site mediated adsorption

Portal site mediated adsorption is a model for site-selective activated gas adsorption in metallic catalytic systems that contain a variety of different adsorption sites. In such systems, low-coordination “edge and corner” defect-like sites can exhibit significantly lower adsorption enthalpies than high-coordination (basal plane) sites. As a result, these sites can serve as “portals” for very rapid adsorption to the rest of the surface. The phenomenon relies on the common “spillover” effect (described below), where certain adsorbed species exhibit high mobility on some surfaces. The model explains seemingly inconsistent observations of gas adsorption thermodynamics and kinetics in catalytic systems where surfaces can exist in a range of coordination structures, and it has been successfully applied to bimetallic catalytic systems where synergistic activity is observed.

In contrast to pure spillover, portal site adsorption refers to surface diffusion to adjacent adsorption sites, not to non-adsorptive support surfaces.

The model appears to have been first proposed for carbon monoxide on silica-supported platinum by Brandt et al. (1993).^[10] A similar, but independent model was developed by King and co-workers^[11]^[12]^[13] to describe hydrogen adsorption on silica-supported alkali promoted ruthenium, silver-ruthenium and copper-ruthenium bimetallic catalysts. The same group applied the model to CO hydrogenation (Fischer-Tropsch synthesis).^[14] Zupanc et al. (2002) subsequently confirmed the same model for hydrogen adsorption on magnesia-supported caesium-ruthenium bimetallic catalysts.^[15] Trens et al. (2009) have similarly described CO surface diffusion on carbon-supported Pt particles of varying morphology.^[16]

Adsorption spillover

In the case catalytic or adsorbent systems where a metal species is dispersed upon a support (or carrier) material (often quasi-inert oxides, such as alumina or silica), it is possible for an adsorptive species to indirectly adsorb to the support surface under conditions where such adsorption is thermodynamically unfavorable. The presence of the metal serves as a lower-energy pathway for gaseous species to first adsorb to the metal and then diffuse on the support surface. This is possible because the adsorbed species attains a lower energy state once it has adsorbed to the metal, thus lowering the activation barrier between the gas phase species and the support-adsorbed species.

Hydrogen spillover is the most common example of an adsorptive spillover. In the case of hydrogen, adsorption is most often accompanied with dissociation of molecular hydrogen (H₂) to atomic hydrogen (H), followed by spillover of the hydrogen atoms present.

The spillover effect has been used to explain many observations in heterogeneous catalysis and adsorption.^[17]

Polymer adsorption

Adsorption of molecules onto polymer surfaces is central to a number of applications, including development of non-stick coatings and in various biomedical devices. Polymers may also be adsorbed to surfaces through polyelectrolyte adsorption.

Adsorption in viruses

Adsorption is the first step in the viral infection cycle. The next steps are penetration, uncoating, synthesis (transcription if needed, and translation), and release. The virus replication cycle, in this respect, is similar for all types of viruses. Factors such as transcription may or may not be needed if the virus is able to integrate its genomic information in the cell’s nucleus, or if the virus can replicate itself directly within the cell’s cytoplasm.

Factors Affecting Adsorption of Gases by Solids:
Almost all the solids adsorb gases to some extent. However, the exact amount of a gas adsorbed depends upon a number of factors, as briefly explained below:

1. Nature of surface area of the adsorbent:
It is observed that the same gas is adsorbed to different extents by different solids at the same temperature. Further, as may be expected, the greater the surface area of the adsorbent, greater is the volume of the gas adsorbed. It is for this reason that substances like charcoal andsilica gel are excellent adsorbents because they have highly porous structures and hence large surface area.
The surface area per gram of the adsorbent is called specific area.

2. Nature of the gas being adsorbed:
Different gases are adsorbed to different extents by the same adsorbent at the same temperature. Higher the critical temperature of a gas, greater is the amount of that gas adsorbed. In other words, a gas which is more easily liquefiable or is more soluble in water is more readily adsorbed.

3. Temperature:

We know that adsorption decreases with increase of temperature and vice versa. For example, one gram of charcoal adsorbs about 10 cm³ of N₂ at 273 K, 20 cm³ at 244 K and 45 cm³ at 195 K. the decrease of adsorption with increase of temperature is explained below:

Like any other equilibrium, adsorption is a process involving a true equilibrium. The two opposing processes involved are condensation i.e. adsorption of the gas molecules on the surface of the solid and evaporation i.e. desorption of the gas molecules from the surface of the solid into the gaseous phase.

The amount of heat evolved when one mole of the gas is adsorbed on the adsorbent is called the heat of adsorption.

4. Pressure:

At constant temperature, the adsorption of a gas increases with increase of pressure. It is observed that at low temperature, the adsorption of a gas increases very rapidly as the pressure is increased from small values.

5. Activation of the solid adsorbent:

It means increasing the adsorbing power of an adsorbent. This is usually done by increasing the surface are of the adsorbent which can be achieved by any of the following ways:

a) By making the surface of the adsorbent rough:
For example: by mechanical rubbing or by chemical action or by depositing finely dispersed metals on the surface of the adsorbent by electroplating.

b) By substituting the adsorbent into smaller pieces or grains:
No doubt this method increases the surface area but it has a limitation that is if the adsorbent is broken into too fine particles that it becomes almost powder, then the penetration of the gasbecomes difficult and this will obstruct adsorption.

c) By removing the gases already adsorbed:
For example: charcoal is activated by heating in superheated steam or in vacuum at atemperature ranges from 623 K to 1273 K.

Thermodynamics and kinetics of adsorption and desorption

The chemist is aware of the synergetic effects arising from a simultaneous application of thermodynamic and kinetic concepts. To give a few examples, the (thermodynamical) Langmuir adsorption isotherm has a simple kinetic derivation, basing on the assumption of a dynamical equilibrium. We evaluate adsorbate binding energies from the temperature-dependence of desorption rates, whereas the basic assumption of the transition state theory (TST) is that of an equilibrium between reactants and activated complex, treated with statistical thermodynamics. In the following, we outline some basic concepts of surface thermodynamics and kinetics which are important for this work and try to emphasize the close relationship between them

Application of adsorption. Adsorption finds extensive applications both in research laboratory and in industry. А few applications are briefly described below:

In preserving vacuum. In Dewar flasks activated charcoal is placed between the walls of the flask so that any gas which enters into the annular space either due to glass imperfection or diffusion through glass is adsorbed.

In gas masks. All gas masks are devices containing suitable adsorbent so that the poisonous gases present in the atmosphere are preferentially adsorbed and the air for breathing is purified.

In clarification of sugar. Sugar is decolorised by treating sugar solution with charcoal powder. The latter adsorbs the undesirable colours present.

In chromatographic analysis. The selective adsorption of certain substances from а solution by а particular solid adsorbent has helped to develop technique for the separation of the components of the mixture. This technique is called chromatographic analysis. For example, in column chromatography, а long and wide vertical tube is filled with а suitable adsorbent and the solution of the mixture poured from the top and then collected one by one from the bottom.

In catalysis. The action of certain solids as catalysts is best explained in terms of adsorption. The theory is called adsorption theory. According to this theory, the gaseous reactants are adsorbed on the surface of the solid catalyst. As а result, the concentration of the reactants increases on the surface and hence the rate of reaction increases. The theory is also able to explain the greater efficiency of а catalyst in the finely divided state, the action of catalytic promoters and poisons.

In paint industry. The paint should not contain dissolved gases as otherwise the paint does not adhere well to the surface to be painted and thus will have а poor covering power. The dissolved gases are, therefore, removed by suitable adsorbents during manufacture. Further, all surfaces are covered with layers of gaseous, liquid or solid films. These have to be removed before the paint is applied. This is done by suitable liquids which adsorb these films. Such liquids are called wetting agents. The use of spirit as wetting agent in furniture painting is well known.

In adsorption indicators. Various dyes, which owe their use to adsorption, have been introduced as indicators particularly in precipitation titrations. For example, KBr is easily titrated with AgNO₃ using eosin as an indicator.

In softening of hard water. The use of ion exchangers for softening of hard water is based upon the principle of competing adsorption just as in chromatography.

In removing moisture from air in the storage of delicate instruments. Such instruments, which may be harmed by contact with the moist air, are kept out of contact with moisture using silica gel.

Adsorption is usually described through isotherms, that is, the amount of adsorbate on the adsorbent as a function of its pressure (if gas) or concentration (if liquid) at constant temperature. The quantity adsorbed is nearly always normalized by the mass of the adsorbent to allow comparison of different materials.

Linear

Freundlich

The Freundlich equation or Freundlich adsorption isotherm is an adsorption isotherm, which is a curve relating the concentrationof a solute on the surface of an adsorbent, to the concentration of the solute in the liquid with which it is in contact. In 1909, Freundlich gave an empirical expression representing the isothermal variation of Adsorption of a quantity of gas adsorbed by unit mass of solid adsorbent with pressure. This equation is known as Freundlich Adsorption Isotherm or Freundlich Adsorption equation. There are basically two well established types of adsorption isotherm: the Freundlich adsorption isotherm and the Langmuir adsorption isotherm. Here the amount of mass that is adsorbed is plotted against the temperature which gives an idea about the variation of adsorption with temperature.

The Freundlich Adsorption Isotherm is mathematically expressed as

It is also written as

where

x = mass of adsorbate

m = mass of adsorbent

p = Equilibrium pressure of adsorbate

c = Equilibrium concentration of adsorbate in solution.

K and n are constants for a given adsorbate and adsorbent at a particular temperature.

At high pressure 1/n = 0, hence extent of adsorption becomes independent of pressure.

It is used in cases where the actual idendity of the solute is not known, such as adsorption of colored material from sugar, vegetable oil etc.

Limitation of Freundlich adsorption isotherm

Experimentally it was determined that extent of adsorption varies directly with pressure till saturation pressure Ps is reached. Beyond that point rate of adsorption saturates even after applying higher pressure. Thus Freundlich Adsorption Isotherm failed at higher pressure.

Langmuir

In 1916, Irving Langmuir published a new model isotherm for gases adsorbed to solids, which retained his name. It is a semi-empirical isotherm derived from a proposed kinetic mechanism. It is based on four assumptions:

1. The surface of the adsorbent is uniform, that is, all the adsorption sites are equivalent.

2. Adsorbed molecules do not interact.

3. All adsorption occurs through the same mechanism.

4. At the maximum adsorption, only a monolayer is formed: molecules of adsorbate do not deposit on other, already adsorbed, molecules of adsorbate, only on the free surface of the adsorbent.

These four assumptions are seldom all true: there are always imperfections on the surface, adsorbed molecules are not necessarily inert, and the mechanism is clearly not the same for the very first molecules to adsorb to a surface as for the last. The fourth condition is the most troublesome, as frequently more molecules will adsorb to the monolayer; this problem is addressed by the BET isotherm for relatively flat (non-microporous) surfaces. The Langmuir isotherm is nonetheless the first choice for most models of adsorption, and has many applications in surface kinetics (usually called Langmuir-Hinshelwood kinetics) and thermodynamics.

The Langmuir equation (also known as the Langmuir isotherm, Langmuir adsorption equation or Hill-Langmuir equation) relates the coverage or adsorption of molecules on a solid surface to gas pressure or concentration of a medium above the solid surface at a fixed temperature. The equation was developed by Irving Langmuir in 1916. The equation is stated as:

θ is the fractional coverage of the surface, P is the gas pressure or concentration, α is a constant.

The constant α is the Langmuir adsorption constant and increases with an increase in the binding energy of adsorption and with a decrease in temperature.

Equation Derivation

The Langmuir equation is derived starting from the equilibrium between empty surface sites (SP), particles () and filled particle sites (S)

The equilibrium constant K is thus given by the equation:

Because the number of filled surface sites (SP) is proportional to θ, the number of unfilled sites (S*) is proportional to 1-θ, and the number of particles is proportional to the gas pressure or concentration (p), the equation can be rewritten as:

where α is a constant.

Rearranging this as follows:

leads to Langmuir equation:

Other equations relating to adsorption exist, such as the Temkin equation or the Freundlich equation. The Langmuir equation (as a relationship between the concentration of a compound adsorbing to binding sites and the fractional occupancy of the binding sites) is equivalent to the Hill equation (biochemistry).

Statistical Derivation

Langmuir isotherm can also be derived using statistical mechanics with the following assumptions:
1. Suppose there are M active sites to which N particles bind.
2. An active site can be occupied only by one particle.
3. Active sites are independent. Probability of one site being occupied is not dependent on the status of adjacent sites.

The partition function for a system of N particles adsorbed to M sites (under the assumption that there are more sites than the particles) is:

with qλ being the distribution function for one particle:

and .

If we allow the number of particles to increase so that all sites are occupied, the partition function becomes (using the binomial theorem in the last step):

And finally:

$\langle s \rangle=\frac{q\lambda}{1+q\lambda}$

Equation Fitting

The Langmuir equation is expressed here as:

where K = Langmuir equilibrium constant, c = aqueous concentration (or gaseous partial pressure), Γ = amount adsorbed, and Γ_max = maximum amount adsorbed as c increases.

The equilibrium constant is actually given by :

The Langmuir equation can be fitted to data by linear regression and nonlinear regression methods. Commonly used linear regression methods are: Lineweaver–Burk, Eadie-Hofstee, Scatchard, and Langmuir.

A plot of (1/Γ) versus (1/c) yields a slope = 1/(Γ_maxK) and an intercept = 1/Γ_max. The Lineweaver-Burk regression is very sensitive to data error and it is strongly biased toward fitting the data in the low concentration range. It was proposed in 1934. Another common linear form of the Langmuir equation is the Eadie-Hofstee equation:

A plot of (Γ) versus (Γ/c) yields a slope = -1/K and an intercept = Γ_max. The Eadie-Hofstee regression has some bias toward fitting the data in the low concentration range. It was proposed in 1942 and 1952. Another rearrangement yields the Scatchard regression:

A plot of (Γ/c) versus (Γ) yields a slope = -K and an intercept = KΓ_max. The Scatchard regression is biased toward fitting the data in the high concentration range. It was proposed in 1949. Note that if you invert the x and y axes, then this regression would convert into the Eadie-Hofstee regression discussed earlier. The last linear regression commonly used is the Langmuir linear regression proposed by Langmuir himself in 1918.

A plot of (c/Γ) versus (c) yields a slope = 1/Γ_max and an intercept = 1/(KΓ_max). This regression is often erroneously called the Hanes-Woolf regression. The Hanes-Woolf regression was proposed in 1932 and 1957 for fitting the Michaelis-Menten equation, which is similar in form to the Langmuir equation. Nevertheless, Langmuir proposed this linear regression technique in 1918, and it should be referred to as the Langmuir linear regression when applied to adsorption isotherms. The Langmuir regression has very little sensitivity to data error. It has some bias toward fitting the data in the middle and high concentration range.

There are two kinds of nonlinear least squares (NLLS) regression techniques that can be used to fit the Langmuir equation to a data set. They differ only on how the goodness-of-fit is defined. In the v-NLLS regression method, the best goodness-of-fit is defined as the curve with the smallest vertical error between the fitted curve and the data. In the n-NLLS regression method, the best goodness-of-fit is defined as the curve with the smallest normal error between the fitted curve and the data. Using the vertical error is the most common form of NLLS regression criteria. Definitions based on the normal error are less common. The normal error is the error of the datum point to the nearest point on the fitted curve. It is called the normal error because the trajectory is normal (that is, perpendicular) to the curve.

It is a common misconception to think that NLLS regression methods are free of bias. However, it is important to note that the v-NLLS regression method is biased toward the data in the low concentration range. This is because the Langmuir equation has a sharp rise at low concentration values, which results in a large vertical error if the regression does not fit this region of the graph well. Conversely, the n-NLLS regression method does not have any significant bias toward any region of the adsorption isotherm.

Whereas linear regressions are relatively easy to pursue with simple programs, such as excel or hand-held calculators, the nonlinear regressions are much more difficult to solve. The NLLS regressions are best pursued with any of various computer programs.

Langmuir suggested that adsorption takes place through this mechanism: $A_{g} + S \rightleftharpoons AS$ , where A is a gas molecule and S is an adsorption site. The direct and inverse rate constants are k and k₋₁. If we define surface coverage, , as the fraction of the adsorption sites occupied, in the equilibrium we have:

where is the partial pressure of the gas or the molar concentration of the solution. For very low pressures $\theta\approx KP$ and for high pressures $\theta\approx1$

$\theta$ is difficult to measure experimentally; usually, the adsorbate is a gas and the quantity adsorbed is given in moles, grams, or gas volumes at standard temperature and pressure (STP) per gram of adsorbent. If we call v_mon the STP volume of adsorbate required to form a monolayer on the adsorbent (per gram of adsorbent), $\theta = \frac{v}{v_\mathrm{mon}}$ and we obtain an expression for a straight line:

$\frac{1}{v}=\frac{1}{Kv_\mathrm{mon}}\frac{1}{P}+\frac{1}{v_\mathrm{mon}}$

Through its slope and y-intercept we can obtain v_mon and K, which are constants for each adsorbent/adsorbate pair at a given temperature. v_mon is related to the number of adsorption sites through the ideal gas law. If we assume that the number of sites is just the whole area of the solid divided into the cross section of the adsorbate molecules, we can easily calculate the surface area of the adsorbent. The surface area of an adsorbent depends on its structure; the more pores it has, the greater the area, which has a big influence on reactions on surfaces.

BET

Brunauer-Emmett-Teller (BET) theory aims to explain the physical adsorption of gas molecules on a solid surface and serves as the basis for an important analysis technique for the measurement of the specific surface area of a material. In 1938, Stephen Brunauer,Paul Hugh Emmett, and Edward Teller published an article about the BET theory in a journa for the first time.

Concept

The concept of the theory is an extension of the Langmuir theory, which is a theory for monolayer molecular adsorption, to multilayer adsorption with the following hypotheses: (a) gas molecules physically adsorb on a solid in layers infinitely; (b) there is no interaction between each adsorption layer; and (c) the Langmuir theory can be applied to each layer. The resulting BET equation is expressed by (1):

and are the equilibrium and the saturation pressure of adsorbates at the temperature of adsorption, is the adsorbed gas quantity (for example, in volume units), and is the monolayer adsorbed gas quantity. is the BET constant, which is expressed by (2):

is the heat of adsorption for the first layer, and is that for the second and higher layers and is equal to the heat of liquefaction.

BET plot

Equation (1) is an adsorption isotherm and can be plotted as a straight line with ${1}/{v [ ({p_0}/{p}) -1 ]}$ on the y-axis and $\phi={p}/{p_0}$ on the x-axis according to experimental results. This plot is called a BET plot. The linear relationship of this equation is maintained only in the range of . The value of the slope and the y-intercept of the line are used to calculate the monolayer adsorbed gas quantity and the BET constant . The following equations can be used:

The BET method is widely used in surface science for the calculation ofsurface areas of solids by physical adsorption of gas molecules. A total surface area $S_{total}$ and a specific surface area are evaluated by the following equations:

where is in units of volume which are also the units of the molar volume of the adsorbate gas

Na: Avogadro’s number,

S: adsorption cross section of the adsorbing species,

: molar volume of adsorbate gas

a: mass of adsorbent (in g)

Derivation

Similar to the derivation of Langmuir theory, but by considering multilayered gas molecule adsorption, where it is not required for a layer to be completed before an upper layer formation starts. Furthermore, the authors made five assumptions:

1. Adsorptions occur only on well-defined sites of the sample surface (one per molecule)

2. The only considered molecular interaction is the following one: a molecule can act as a single adsorption site for a molecule of the upper layer.

3. The uppermost molecule layer is in equilibrium with the gas phase, i.e. similar molecule adsorption and desorption rates.

4. The desorption is a kinetically-limited process, i.e. a heat of adsorption must be provided:

4.1. these phenomenon are homogeneous, i.e. same heat of adsorption for a given molecule layer.

4.2. it is E₁ for the first layer, i.e. the heat of adsorption at the solid sample surface

4.3. the other layers are assumed similar and can be represented as condensed species, i.e. liquid state. Hence, the heat of adsorption is E_L is equal to the heat of liquefaction.

5. At the saturation pressure, the molecule layer number tends to infinity (i.e. equivalent to the sample being surrounded by a liquid phase)

Let us consider a given amount of solid sample in a controlled atmosphere. Let θ_i be the fractional coverage of the sample surface covered by a number i of successive molecule layers. Let us assume that the adsorption rate R_ads,i-1 for molecules on a layer (i-1) (i.e. formation of a layer i) is proportional to both its fractional surface θ_i_-1 and to the pressure P; and that the desorption rate R_des,i on a layer i is also proportional to its fractional surface θ_i:

R_ads,i-1 = k_i*P*θ_i_-1 (1)

R_des,i = k_–i*θ_i (2)

Where k_i and k_–i are the kinetic constants (depending on the temperature) for the adsorption on the layer (i-1) and desorption on layer i, respectively. For the adsorptions, these constant are assumed similar whatever the surface. Assuming a Arrhenius law for desorption, the related constants can be expressed as :

k_–i = exp(-E_i/RT)

Where E_i is the heat of adsorption, equals to E₁ at the sample surface and to E_L otherwise.

Cement paste

By application of the BET theory it is possible to determine the inner surface of hardened cement paste. If the quantity of adsorbed water vapor is measured at different levels of relative humidity a BET plot is obtained. From the slope and y-intersection on the plot it is possible to calculate and the BET constant . In case of cement paste hardened in water (T=97°C), the slope of the line is and the y-intersection ; from this follows

From this the specific BET surface area $S_{BET}$ can be calculated by use of the above mentioned equation (one water molecule covers 0,144 nm2). It follows thus which means that hardened cement paste has an inner surface of 156 square meters per g of cement.

Activated Carbon

For example, activated carbon, which is a strong adsorbate and usually has an adsorption cross section of 0.16 nm² for nitrogenadsorption at liquid nitrogen temperature, is revealed from experimental data to have a large surface area around 3000 m² g^-1. Moreover, in the field of solid catalysis, the surface area of catalysts is an important factor in catalytic activity. Porous inorganic materials such asmesoporous silica and layer clay minerals have high surface areas of several hundred m² g^-1 calculated by the BET method, indicating the possibility of application for efficient catalytic materials.

Often molecules do form multilayers, that is, some are adsorbed on already adsorbed molecules and the Langmuir isotherm is not valid. In 1938 Stephen Brunauer, Paul Emmett, and Edward Teller developed a model isotherm that takes that possibility into account. Their theory is called BET theory, after the initials in their last names. They modified Langmuir’s mechanism as follows:

A_(g) + S ⇌ AS

A_(g) + AS ⇌ A₂S

A_(g) + A₂S ⇌ A₃S and so on

The derivation of the formula is more complicated than Langmuir’s (see links for complete derivation).

x is the pressure divided by the vapor pressure for the adsorbate at that temperature (usually denoted ), v is the STP volume of adsorbed adsorbate, v_mon is the STP volume of the amount of adsorbate required to form a monolayer and c is the equilibrium constant K we used in Langmuir isotherm multiplied by the vapor pressure of the adsorbate. The key assumption used in deriving the BET equation that the successive heats of adsorption for all layers except the first are equal to the heat of condensation of the adsorbate.

The Langmuir isotherm is usually better for chemisorption and the BET isotherm works better for physisorption for non-microporous surfaces.

Kisliuk

Two adsorbate nitrogen molecules adsorbing onto a tungsten adsorbent from the precursor state around an island of previously adsorbed adsorbate (left) and via random adsorption (right)

In other instances, molecular interactions between gas molecules previously adsorbed on a solid surface form significant interactions with gas molecules in the gaseous phases. Hence, adsorption of gas molecules to the surface is more likely to occur around gas molecules that are already present on the solid surface, rendering the Langmuir adsorption isotherm ineffective for the purposes of modelling. This effect was studied in a system where nitrogen was the adsorbate and tungsten was the adsorbent by Paul Kisliuk (1922–2008) in 1957. To compensate for the increased probability of adsorption occurring around molecules present on the substrate surface, Kisliuk developed the precursor state theory, whereby molecules would enter a precursor state at the interface between the solid adsorbent and adsorbate in the gaseous phase. From here, adsorbate molecules would either adsorb to the adsorbent or desorb into the gaseous phase. The probability of adsorption occurring from the precursor state is dependent on the adsorbate’s proximity to other adsorbate molecules that have already been adsorbed. If the adsorbate molecule in the precursor state is in close proximity to an adsorbate molecule that has already formed on the surface, it has a sticking probability reflected by the size of the S_E constant and will either be adsorbed from the precursor state at a rate of k_EC or will desorb into the gaseous phase at a rate of k_ES. If an adsorbate molecule enters the precursor state at a location that is remote from any other previously adsorbed adsorbate molecules, the sticking probability is reflected by the size of the S_D constant.

These factors were included as part of a single constant termed a “sticking coefficient,” k_E, described below:

As S_D is dictated by factors that are taken into account by the Langmuir model, S_D can be assumed to be the adsorption rate constant. However, the rate constant for the Kisliuk model (R’) is different to that of the Langmuir model, as R’ is used to represent the impact of diffusion on monolayer formation and is proportional to the square root of the system’s diffusion coefficient. The Kisliuk adsorption isotherm is written as follows, where Θ_(t) is fractional coverage of the adsorbent with adsorbate, and t is immersion time:

Solving for Θ_(t) yields:

Adsorption enthalpy

Adsorption constants are equilibrium constants, therefore they obey van ‘t Hoff’s equation:

As can be seen in the formula, the variation of K must be isosteric, that is, at constant coverage. If we start from the BET isotherm and assume that the entropy change is the same for liquefaction and adsorption we obtain

that is to say, adsorption is more exothermic than liquefaction.

Adsorbents

Characteristics and general requirements

Activated carbon is used as an adsorbent

Most industrial adsorbents fall into one of three classes:

· Oxygen-containing compounds – Are typically hydrophilic and polar, including materials such as silica gel and zeolites.

· Carbon-based compounds – Are typically hydrophobic and non-polar, including materials such as activated carbon and graphite.

· Polymer-based compounds – Are polar or non-polar functional groups in a porous polymer matrix.

[edit]Silica gel

Silica is used for drying of process air (e.g. oxygen, natural gas) and adsorption of heavy (polar) hydrocarbons from natural gas.

[edit]Zeolites

Zeolites are natural or synthetic crystalline aluminosilicates, which have a repeating pore network and release water at high temperature. Zeolites are polar iature.

Zeolites are applied in drying of process air, CO₂ removal from natural gas, CO removal from reforming gas, air separation, catalytic cracking, and catalytic synthesis and reforming.

[edit]Activated carbon

Activated carboitrogen isotherm showing a marked microporous type I behavior

[edit]Protein adsorption of biomaterials

[edit]Adsorption chillers

[edit]Portal site mediated adsorption

In contrast to pure spillover, portal site adsorption refers to surface diffusion to adjacent adsorption sites, not to non-adsorptive support surfaces.

[edit]Adsorption spillover

The spillover effect has been used to explain many observations in heterogeneous catalysis and adsorption.^[17]

[edit]Polymer adsorption

Main article: polymer adsorption

[edit]Adsorption in viruses

3. Temperature:

The amount of heat evolved when one mole of the gas is adsorbed on the adsorbent is called the heat of adsorption.

4. Pressure:

5. Activation of the solid adsorbent:

It means increasing the adsorbing power of an adsorbent. This is usually done by increasing the surface are of the adsorbent which can be achieved by any of the following ways:

a) By making the surface of the adsorbent rough:
For example: by mechanical rubbing or by chemical action or by depositing finely dispersed metals on the surface of the adsorbent by electroplating.

c) By removing the gases already adsorbed:
For example: charcoal is activated by heating in superheated steam or in vacuum at atemperature ranges from 623 K to 1273 K.

Thermodynamics and kinetics of adsorption and desorption

ISOSTERIC HEAT OF ADSORPTION – The temperature-dependence of the adsorption/desorption equilibrium pressure can be described by the Clausius-Clapeyron equation. This equation defines different isothermal heats of adsorption depending on which of the parameters are kept constant. Experimentally it is often convenient to fix the coverage, Θ = nA/nS (with the number of adsorption sites, nS, and the number of adsorbate particles, nA). In this case, the differential equilibrium condition between adsorbate and gas phase, dµS = dµG (with the chemical potential of the gas phase, µG, and of the condensed phase, µS) leads, by neglection of the volume of the condensed phase, to

Eq. 3.1 describes adsorption isosters and defines the isosteric heat of adsorption, Qst, which is the negative partial molar adsorption enthalpy, i.e

with the partial molar enthalpies of the gas phase, Hg, and of the adsorbate, Hads, and the adsorption enthalpy, ∆adsh = hads – hg.

Showed that there is no limit to the number of heats of adsorption which can be expressed in terms of equations of the Clausius-Clapeyron type, depending on which state function is fixed.

Eq. 3.1 can be employed for evaluating Qst as a function of coverage from experimental data. For this purpose, we fixed certain pressures, pi, in the gas phase, varied slowly the temperature and measured the corresponding equilibrium coverages by monitoring the adsorbate-induced work function change, ∆ϕ(Θ). This procedure leads to adsorption isobars, )T(ii pp Θ=Θ , which can be rearranged to data triples (p,T,Θ)i . From these triples we obtained, by applying Eq. 3.1, Qst(Θi) from the slope of a linear plot of ln p(Θi) vs. 1/T(Θi). This procedure can be repeated for all coverages Θi of interest.

A relation between Qst and the adsorbate binding energy, E0, follows from equipartition considerations. In the case of a monatomic gas, the enthalpy of the gas phase is Hg = Ug + pVg = (5/2) RT. For estimating the enthalpy of the adsorbate phase, Hads, we must distinguish between mobile and localized adsorption. For mobile adsorption, free translations are restricted to two dimensions (= RT), but there is one vibrational degree of freedom (DOF) normal to the surface (= RT), so that Hads = Uads = – E0 + 2 RT. With Eq. 3.2, we get Qst = E0 + (1/2) RT. In contrast, localized adsorption leads to three vibrational DOFs (= 3 RT), and the isosteric heat amounts to Qst = E0 – (1/2) RT. Thus, Qst is always close to E0 within ± (1/2) RT, if we assume that all adsorbate-substrate vibrations are fully excited. The same considerations, applied to the case of a diatomic molecule, yields Qst = E0 for mobile and Qst = E0 – (3/2) RT for localized adsorption. If adsorption proceeds in equilibrium, the adsorption entropy, ∆Sads, and, thus, the partial molar entropy of the adsorbate, Sads, can be deduced from Qst:

ADSORPTION ISOTHERMS – Instead of measuring adsorption isobars, we may just as well fix the temperature, Ti, and vary p, or we can rearrange the triples (p,T,Θ) in order to get adsorption isotherms. A theoretical adsorption isotherm was first derived by Langmuir under the following assumptions: (a) the adsorption is localized, (b) the surface is saturated at Θ = 1 ML (monolayer), (c) the adsorbate molecules do not interact, (d) all adsorption sites are equivalent. The rates of adsorption, Rads, and desorption, Rdes, are given by:

Applying the dynamical equilibrium condition, Rads = Rdes , we obtain:

References:

1.The abstract of the lecture.

2. intranet.tdmu.edu.ua/auth.php

3. Atkins P.W. Physical chemistry. – New York. – 1994. – P.299-307.

4. Cotton, F. A., Chemical Applications of Group Theory, John Wiley & Sons: New York, 1990

5.Girolami, G. S.; Rauchfuss, T. B. and Angelici, R. J., Synthesis and Technique in Inorganic Chemistry, University Science Books: Mill Valley, CA, 1999

6.John B.Russell. General chemistry. New York.1992. – P. 550-599

7. Lawrence D. Didona. Analytical chemistry. – 1992: New York. – P. 218 – 224.

8. en.wikipedia.org/wiki

9. www.youtube.com/watch?v=cmh1nKCAggA

Prepared by PhD Falfushynska H.