Adsorption Isotherms To Surface Chemistry Biology Essay

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The surface of a liquid is a state of strain or unsaturation due to the unbalanced or residual forces that act along the surface of a liquid. Similarly, the surface of a solid may also have residual forces acting on it. Thus, the surface of a solid has a tendency to attract and to retain molecules of other species (gas or liquids) when such surfaces come in contact. This phenomenon of surfaces is termed adsorption. As the molecules remain only at the surface, and-do not go deeper into the bulk of the solid, the concentration of adsorbed gas or liquid is higher at the surface than in the bulk of the solid.

According to the Colombia Electronic Encyclopedia, adsorption is a technical term coined to denote the taking up of gas, vapour, liquid by a surface or interface. [1] This term is somewhat different from the more widely used term, absorption. The difference is adsorption is a surface phenomenon whereas absorption is a bulk phenomenon in which the substance assimilated is uniformly distributed throughout the body of a solid or liquid to form a solution or a compound. This difference is illustrated in the figure below.

Image taken from:

Another difference is that in absorption, the concentration of the adsorbed molecules is always found to be greater in the immediate vicinity of the adsorbent than in the adsorbate. Also, in adsorption, the equilibrium is easily attained in a very short time whereas in absorption the equilibrium takes place very slowly. An example of absorption would be a sponge taking up water while adsorption would be the thin layer of moisture that is formed on the surface when a hot crucible is allowed to cool in air.

The material on the surface of which adsorption takes place is called the adsorbent and the substance adsorbed is called the adsorbate. The common surface separating two phases, where the adsorbed molecule concentrates is referred to as the interface. Adsorption takes place more readily when the surface area of the adsorbent is large.

Adsorption stands for different concentrations of a substance at an interface. If the concentration is more at an interface, the adsorption is said to be positive; if the concentration is less at an interface, the adsorption is said to be negative. The reverse process of removal of an adsorbed substance from the surface of a solid is known as desorption. An example of an adsorbent is metals while for adsorbates are gases such as oxygen and nitrogen.

Characteristics of Adsorption

The various characteristics of adsorption are as follows:

1. Adsorption is a spontaneous process and takes place in a very short period of time.

2. Adsorption can occur at all surfaces and five types of interfaces can exist: gas-solid, liquid-solid, liquid-liquid, solid-solid, and gas-liquid.

3. Adsorption accounts for a decrease in the free energy of the system, ΔG. The adsorption will continue to such an extent that ΔG continues to be negative, thus the magnitude of ΔG decreases to zero. When ΔG for further adsorption reaches a value for zero, adsorption equilibrium is said to be established.

4. As the process of adsorption involves loss of degree of freedom of the gas in passing from the free gas to the adsorbed layer there is a decrease in the entropy of the system.

Therefore, considering the Gibbs-Helmholtz equation,


where ΔG is the change in free energy,

ΔH is the change in heat content

ΔS is the change in entropy

T is the temperature of the system.

As the entropy and free energy decrease in adsorption, the value of ΔH decreases. This decrease in ΔH appears as heat. Hence the adsorption process must always be exothermic.

Factors on which adsorption depends

It is generally believed that all gases or vapours are adsorbed on the surface of all solids with which they are in contact. The phenomenon was first described in 1773 by Schcele, who discovered the uptake of gases by charcoal. The phenomenon of adsorption of gases by solids depends upon the following factors:

The amount of the gas adsorbed depends upon the nature of the adsorbent and the gas (adsorbate) which is to be adsorbed. Gases such as ammonia and carbon dioxide which liquefy more easily are adsorbed more readily than the permanent gases such as hydrogen gas and nitrogen gas. This is because the Van der Waals forces of attraction are greater in the easily liquefiable.

The extent of adsorption of gases by solids depends upon the exposed surface area of the adsorbent. The larger the surface area of the adsorbent, the larger will be the extent of adsorption under given conditions of temperature and pressure. Example, vegetable sources become activated because they possess a porous structure.

For a given gas and a given adsorbent, the extent of adsorption depends on the pressure of the gas. Adsorption of a gas is followed by a decrease of pressure. Therefore, in accordance with Le Chatelier's principle, the magnitude of adsorption decreases with the decrease in pressure and vice-versa. The variation of adsorption with pressure at constant temperature is expressed graphically by a curve known as adsorption isotherm.

For a given adsorbate and an adsorbent, the extent of adsorption depends upon the temperature of the experiment. Adsorption usually takes place with the evolution of heat, therefore, according to the Le Chatelier's principle; the decrease in temperature will increase the adsorption and vice-versa.

Types of Adsorption

Physisorption or Physical Adsorption

Physisorption is whereby the gas molecules are held to the solid via Van der Waals interactions between the adsorbate and the surface. The forces of attraction bringing about physical adsorption are:

Permanent dipole moment in the adsorbed molecule


Dispersion effects

Short range repulsive effect

In case of physisorption, the forces of attraction which hold the gas molecules to the solid are very weak. Therefore it is characterised by a low heat of adsorption, usually of the order of 20 kJmol-1. This value is of the same order of magnitude as the heat of vaporisation of

the adsorbate and lends credence to the concept of a weak 'physical' bonding. Physisorption is usually observed at low temperatures or on relatively 'inert' surfaces. Examples of physisorption are: adsorption of various gases on charcoal and adsorption of nitrogen on mica.

Chemisorption or Chemical Adsorption

In chemisorption, the molecules (or atoms) stick to the surface of the adsorbent by forming a chemical (usually covalent) bond, and tend to find sites that maximize their coordination number with the substrate. The adsorbate undergoes a strong chemical interaction with the unsaturated surface and gives rise to a high heat of adsorption, usually of the order of 200 kJmol-1. Chemisorption is often characterised by taking place at elevated temperatures and is often an activated process. It may be dissociative, non-dissociative or reactive in nature. An example of chemisorption is the adsorption of hydrogen on nickel.

The advent of infrared spectroscopy had led to a better means of distinguishing between these two processes. The infrared spectrum of a molecule arises as a result of the vibrations of the atoms within the molecules. Thus, if the molecule is physically adsorbed, the infrared spectrum is altered only slightly and small frequency shifts, usually less than 1%, are observed. During the chemisorption process, the symmetry of the adsorbed molecule is completely different from that of the gaseous molecule. In this case a completely new infrared spectrum is observed and band shifts and intensities are far removed from those of the gaseous adsorbate.

The observable differences between these two processes are as follows:

Specificity - Physisorptions are non-specific, thus every gas is adsorbed to a lesser or greater extent on all solids, whereas chemisorptions are more specific in nature.

Speed - Physisorptions are instantaneous whereas chemisorptions may sometimes be quite slow depending upon the nature of chemical reaction involved.

Reversibility - Physisorption equilibrium is reversible and is rapidly established whereas chemisorption is irreversible. Physically adsorbed layer can be removed very easily by changing pressure or concentration, whereas, the removal of a chemisorbed layer requires much more rugged conditions such as high temperatures.

Heat of adsorption - Physical adsorption is generally characterised by low heats of adsorption while chemisorption is characterised by high heats of adsorption which indicates that forces are similar to those involved in chemical reactions. Therefore, it is highly probable that gas molecules form a chemical compound with the surface of the adsorbent.

Nature of the adsorbate and adsorbent - Physical adsorption like condensation can occur with any gas-solid system provided only that the conditions of temperature and pressure are suitable. The Chemisorption will take place only if the gas is capable of

forming a chemical bond with the surface atoms.

Effect of pressure - As the pressure of the adsorbate increases, the rate of physical adsorption increases, whereas, the rate of chemisorption decreases with the increase of pressure of adsorbate.

Effect of temperature - Physical adsorption occurs to an appreciable extent at temperatures close to those required for liquefaction of adsorbed gases. Generally, chemisorption occurs at high temperatures where it increases at first and then falls off with rising temperature.

Experimental Methods for Determining Adsorption Isotherms

The two principal methods of measuring adsorption equilibrium are classified as volumetric and gravimetric, depending upon whether the amount of adsorped gas is determined by means of experimentally measured pressure and the gas-law relationship of the gas phase or by direct measurement of the weight gained by the adsorbent.

Volumetric or Manometric Method

This is the most widely used technique which makes use of pressure-volume measurements to determine the amount of adsorbate gas before and after exposure to the adsorbent.

The Gravimetric Method of Measuring Adsorption

The gravimetric method of determining the adsorption isotherm, the amount of gas adsorbed is weighed using a vacuum microbalance. Vacuum microbalances, that are suitable for adsorption measurements, have been classified by Rhodin as: Cantilever, Knife-edge, Torsion and Spring type.

Types of Adsorption Isotherms

There are six main types of adsorption isotherms that have been experimentally observed. These are denoted by the following six graphs:

Graphs taken from:

Type I - This type of curve is obtained in cases where mono-molecular layer is formed on the surface of the adsorbent. This curve shows that a saturation state is reached, meaning that there is no change in the amount of molecules adsorbed with the increase in pressure.

Type II - This type of isotherm is the normal for of isotherm obtained with a nonporous or macroporous adsorbent. It has a transition point 'B' which represents the pressure at which the formation of monomolecular layer is complete and that of the multi-molecular layer is being started.

Type III - This reversible type of isotherm occur in systems where the adsorbate-sorbent interaction is small compared to the adsorbate-adsorbate interaction, that is, the strongly associating admolecules.

Type IV - This irreversible type of isotherm describe the adsorption behaviour of special mesoporous materials showing pore condensation together with hysteresis behaviour between the adsorption and the desorption branch.

Type V - This type of isotherm deviate from Type IV curves by nearly perpendicular middle portions of the adsorption and the desorption branches often near relative gas pressures p/ps(T) = 0.5, indicating the existence of mesopores in which phase change like pore condensation may occur.

Type VI - This type of isotherm presents stepwise multilayer adsorption on a uniform non-porous surface. The step height, the sharpness of which depends on the system and the temperature, represents the monolayer capacity for each physisorbed layer and remains nearly constant for two or three adsorbed layers.

Freundlich Adsorption Isotherm

In 1909, Freundlich proposed an empirical equation and was known as Freundlich adsorption isotherm. This equation is as follows:

x/m = kp,/n ...(1)

where x is amount of adsorbate,

m is the amount of adsorbent

p is the pressure

k and n are two constants depending upon the nature of the adsorbent and adsorbate, and n being less than unity.

Equation (1) is applicable to the adsorption of gases and solids. In case of solution, equation (1) takes the form

x/m = kc1/n ...(2)

where c is the concentration of the solute in gm moles per litre.

Equations (1) and (2) predict the effect of pressure (or concentration) on the adsorption of gases (or solution) at constant temperature in a quantitative manner.

Taking logarithms of equations (1) and (2), we get

log (x/m) = log k + (1/n) log p ...(3)

and log (x/m) = log k + (1/n) log c ...(4)

If log x/m is plotted against log p or log c, a straight line should be obtained as shown in the figure below. The slope of the line will give the value of 1/n and the intercept on the Y-axis gives the value of log k.

Thus by using equations (3) and (4), the values of k and n can be calculated from the left graph Analysis of this graph shows that as p increases, x/m also increases and, thus, the Freundlich's equation indicates no limit to this increase. But experimental values, when plotted, show some deviations from linearity especially at low pressures. This is seen in the other graph. Comparing the theoretical (left) and experimental (right) curves, the two agree over a certain range of pressure only. Thus, Freundlich's equation has a limitation that it is valid over a certain range of pressure only.

The first limitation is that it is valid over a certain range of pressure only. The second is the constant k and n vary with temperature and finally, the Freundlich adsorption equation is a purely empirical formula without theoretical foundation.

Langmuir Adsorption Isotherm

The Freundlich adsorption isotherm holds good for a certain range of pressure only. To solve this, Langmuir (1916) worked out an adsorption isotherm known as Langmuir's adsorption isotherm. The various assumptions are:

The adsorbed layer on the solid adsorbent is assumed to be unimolecular in thickness. This view is accepted for adsorption at low pressures or at moderately high temperatures. However, the adsorbed molecules can hold other gas molecules by van der Waal's forces, so that multimolecular layers are possible. Such behaviour is apparent only at relatively low temperatures and at pressure approaching the saturation value.

The adsorption is taking place on the fixed sites and there is no interaction between the adsorbed molecules on the surface. One site adsorbs one molecule. When the whole surface is completely covered by a unimolecular layer of the gas, further adsorption is not possible and indicates a maximum of saturation of adsorption.

All sites are equivalent and the surface is uniform meaning the surface is perfectly flat on a microscopic scale.

The process of adsorption is a dynamic process which consists of two opposing processes which are condensation and evaporation. The condensation process involves the condensation of the molecules of the gas on the surface of the solid while the evaporation process involves the evaporation of the molecules of adsorbate from the surface of the adsorbent.

When adsorption starts, the whole adsorbent surface remains bare and so the initial rate of condensation is at a maximum. As the surface becomes gradually covered, the rate of condensation decreases. On the other hand, the initial rate of evaporation (desorption) of the condensed molecules is smallest at the beginning of adsorption, but increases as the surface becomes more and more covered.

Ultimately, when the equilibrium is reached, the rate of the condensation becomes equal to the rate of evaporation. It means that the number of gas molecules condensing on the given surface is equal to the number of molecules evaporating away per unit time from the same surface, that is, the arrangement of the adsorbed molecule on the surface is unidirectional.

Consider the dynamic equilibrium is

A(g) + M(surface) AM(surface)

The rate of change of surface coverage due to adsorption is proportional to the partial pressure, p of A and the number of vacant sites N(1 - θ). In this case, N is the total number of sites. Therefore,

dθ/dt = kapN(1 - θ)

The rate of change of θ due to desorption is proportional to the number of adsorbed species, Nθ:

dθ/dt = kapNθ

At equilibrium there is no net change and solving for θ gives the Langmuir isotherm, where

θ = Kp/(1 + Kp)


K = ka/kd

Where ka is the rate constant for adsorption

kd is the rate constant for desorption

With θ = V/V∞

Where V∞ is the volume corresponding to complete coverage, we get

p/V = p/V∞ + 1/KV∞

From this, a plot of p/V against p should give a straight line of slope 1/V∞ and intercept 1/KV∞. This is represented from the graph as follows:

Image taken from:

Considering the rate of adsorption is proportional to the pressure and to the probability that both atoms will fins sites, we get

dθ/dt = kap{N(1 - θ)}2

The rate of desorption is proportional to the frequency of encounters of atoms on the surface, and is therefore second-order in the number of atoms present

dθ/dt = kap(Nθ)2

The condition for no net change leads to the isotherm

Now, the surface coverage depends more weakly on pressure than for non-dissociative adsorption.

The BET Isotherm

In 1815 de Sanssure suggested that the adsorbed gas or vapour is in the form of a thick compressed polymolecular layer. This concept was formulated quantitatively by Euken and Polanyi a century-later. In contrast to the original views of de Saussure, Polanyi, Brunauer Emmet and Teller extended the Langmuir's approach to the multiple molecular layer adsorptions and their equation is known as the BET equation. The BET equation represents the first effective attempt to explain physical adsorption from monolayer regions through multilayer adsorption.

where p* is the vapour pressure above a layer of adsorbate that is more than on molecule thick and which resembles a pure bulk liquid

Vmon is the volume corresponding to monolayer coverage

c is a constant

The figure below illustrates the shape of the BET isotherms.

There is an indefinite increase as pressure increases due to there being no limit to the amount of material that may condense when multilayer coverage may occur.

The BET equation can also be rearranged to give

Where (c - 1)/cVmon can be obtained from the slope of a plot of the expression on the left against z, and cVmon­ can be found from the intercept at z = 0.

When c >> 1, the BET isotherm takes a simpler form, where

V/Vmon = 1/(1 - z)

This expression is applicable to unreactive gases on polar surfaces, for which c 102 because ΔdesHΘ is then significantly greater than ΔvapHΘ.

However, there have been a few failures in the BET isotherm in at least three aspects. Firstly, it fails below a relative pressure p/p0 of 0-05 and when it is above 0.35. Also, the assumption that was made that the adsorbate has liquid properties was proven incorrect. Finally, the coordination number of molecules in the higher layers also adds the criticism to the B.E.T. equation.

Thus, the equation was further modified in order to correct these approximations which were made in the derivation of B.E.T. equations and to give a better fit to type II isotherms, it is assumed that multilayer formation is limited to n layers and not to the infinity layers. It means that the number of adsorbed layers cannot exceed a finite number, n, and the summation of the rearranged equation cannot be carried out to infinity. Therefore,

V = cz 1(n + 1)nn + nzn+1

Vmon (1 - z) 1 + (c - 1) z - zn+1

The value of n may be considered to be the width of pores, capillaries and surface defects which limit the maximum number of layers even at saturation pressure. If n = 1, the equation gives Langmuir's adsorption isotherm. If n = ∞ then gives B.E.T. equation.

Kisliuk Adsorption Isotherm

As mentioned earlier, the gas molecules that are adsorbed onto the surface of a solid form considerable interactions with molecules in the gaseous phase. Therefore, adsorption will most likely occur around gas molecules that are already formed on the surface. For the purposes of this concept, Langmuir adsorption isotherm proves to be ineffective.

In 1957, Paul Kisliuk derived an experiment where he used nitrogen and tungsten as the adsorbate and adsorbent respectively. He noticed that there was an increased probability of adsorption occurring around molecules present on the surface of the substrate. He compensated for this by developing the precursor state theory. This theory stated that at the interface between the solid adsorbent and adsorbate in the gaseous phase, molecules would enter a precursor state. It is here whereby adsorption or desorption would occur into the gaseous phase. Adsorption is dependent on the proximity of the adsorbate to other adsorbate molecules that have already adsorbed. This leads to the equation,

where SE is the sticking probability where adsorbate molecules in the precursor state are close to the adsorbate molecules to the surface

SD is the sticking probability whereby molecules in the precursor state are away from any other adsorbate molecules

kEC is the rate the molecules are adsorbed from the precursor state

kES is the rate the molecules will desorbed into the gaseous phase.

KE is the sticking coefficient.

However, the rate constant for Kisliuk model (R' )is different from that of Langmuir model. This is represented by the equation below.

where θ(t) is the fractional coverage of the adsorbent with adsorbate.

T is immersion time

Henderson-Kisliuk Adsorption Isotherm

In this type of isotherm, Self Assembling Monolayer (SAM) molecules are adsorbed to the surface of an adsorbent until the SAM molecules' hydrocarbon chains at the surface becomes saturated. These hydrocarbon chains lie flat against the adsorbate and is in turn termed the "lying down" structure. The process of adsorption continues to occur and the hydrocarbon chains begin to be displaced by the thiol groups from the SAM molecules.

During the process, electrostatic forces between the adsorbed SAM molecules and the molecules that were previously adsorbed brings about a new structure known as the "standing up" orientation. As adsorption continues, the entire adsorbent becomes saturated with SAM in a standing up orientation, thus adsorption comes to an end.

These two structures were studied by Andrew P. Henderson in 2009 where he used electrochemical impedance spectroscopy to quantify adsorption and found that both structures had different properties. He therefore suggested four rules that govern this which are:

That the amount of adsorbate on the adsorbent surface was equal to the sum of the adsorbate occupying the "lying down" and "standing up" structure.

The rate of formation of the "lying down" structure is dependent on the availability of potential adsorption sites and intermolecular interactions.

The amount of "lying down" structure is depleted as the "standing up" structure is formed.

The rate of formation of the "standing up" structure is dictated by the amount of adsorbate occupying the "lying down" structure and intermolecular interactions at immersion time, t.

The Henderson-Kisliuk adsorption isotherm equation is shown below,