Surface and Interfacial Phenomenon

Chapter 3

Surface and Interfacial Phenomenon

Liquid Interface

• The term surface is used to represent the boundary between solid-gas and liquid-gas phases. The two words surface, and interface often used synonymously, although interface is preferred for the boundary between two condensed phases i.e., liquid liquid. The cases where the two phases are formed explicitly for example, solid-gas and liquid-gas interface, the term surface is used as illustrated.

• The boundary that exists between two immiscible phases is called as interface. Several types of interfaces are possible depending on whether the two adjacent phases are in the solid, liquid or gaseous state as shown. The interface is further divided into solid interface and liquid interface. Solid interface is associated with solid and gas phases, solid and liquid phases or solid and solid, while liquid interface deals with association of liquid-gas phase or liquid-liquid phase. The word surface is used to designate the limit between a condensed phase and a gas phase, whereas the term interface is used for the boundary between two condensed phases.

• The interface has applications such as adhesion between particles or granules, manufacturing of multilayer tablets, application of powders to body, flow of materials, and adsorption of colours etc. Whereas, solid-liquid interface has applications in the biopharmaceutical study, filtration processes, chemical interaction, adsorption studies, preparation of dispersed systems like colloids, emulsions, suspensions, wetting of solids etc.   

Surface Tension 

• The tension that exists between solid-gas phase and liquid-gas phase is known as surface tension. The origin of surface tension in a liquid is the cohesive force of attraction between the molecules that make-up the liquid. In the absence of other forces, this mutual force of attraction of the molecules causes the liquid to coalesce in accordance with the LaPlace law. In the bulk of liquid each molecule is pulled equally in all direction by neighboring liquid molecule resulting in a net force of zero.

• The molecules at the deep inside the bulk of the liquid pulls the molecules present at surface inwards, but there are no liquid molecules on the outside to balance these forces. There may be a small outward adhesive force of attraction caused by air molecule, but as air is much less dense than the liquid, this force is negligible. All of the molecules at the surface are therefore subject an inward force of cohesive molecular attraction leading to squeezing of liquid together until it has the lowest surface area possible. This force is the surface tension, defined as the magnitude of the force acting perpendicular to a unit length of a line at the surface. According to definition, surface tension is expressed as: γ = F L Where, the symbol γ represent surface tension and F is the force perpendicular to the length l. Surface tension is represented by different symbols like γ, τ or σ. A few examples of liquids with their surface tensions and interfacial tensions against water.

• SPHERICAL DROP: As seen in previous section liquids has tendency to reduce its exposed surface to the smallest possible area and hence a drop of liquid tends to assume the shape of sphere. This phenomenon is attributed to cohesion, i.e. stronger attractive force acting between the molecules of the liquid.

• The molecules within the liquid are attracted equally from all sides, but those near the surface experience unequal attractions and thus are drawn toward the centre of the liquid mass by this net force. The surface then appears to act like an extremely thin membrane, and the small volume of water that makes-up a drop assumes the shape of sphere. The spherical shape held constant with equilibrium between the internal pressures due to surface tension. 

• Unit of Surface Tension: The CGS unit of surface tension is dyne/cm and SI unit is N/m. The relation between these units is as N/m is equal to 1 × 103 dyne/cm or dyne/cm is equal to m N/m.  

Interfacial Tension

• When two miscible liquids combined together no interface exist between them for example, ethyl alcohol and water mixture. Wherever, if two immiscible liquids combined there exists an interface between them. The tension exerted at the interface between them is due to difference in forces acting on molecules of immiscible liquids for example, chloroform and water, olive oil and water etc. Interfacial tension is defined as the force per unit length acting at right angle over the interface between two immiscible liquids. Interfacial tension represents the strength of adhesive forces at the boundary between two immiscible liquids. Interfacial tension is useful in analyzing fluid reforming, spreading, emulsification, washability and other liquid characteristics. The surface tensions of some liquids and their interfacial tensions against water at 20 °C are given.

• Unit of Surface and Interfacial Tension: Interfacial tension has units that of surface tension, that is dyne/cm or N/m.

Surface Free Energy

• The situation shown in Fig. 3.5 describe that free energy is present in the form of tension at the surface. Tension at the surface is helpful in maintaining the minimum surface possible. This energy is called as surface free energy. It can be defined, as the work required in increasing the area by one cm2 . The surface free energy can be derived from the following illustration. ABCD is a three-sided frame with a movable bar CD of length L. A soap film is formed over the area ABCD. Applying a force F to movable bar, the film stretches to the downward.

• To break the film some force is required. If the applied force is less than what is required to break the film then the film retract due to surface tension. If the force F is applied on a movable bar CD, it shifts by a distance d to C’D’. The work done W is expressed as; W = F × d … (3.2)

• While stretching of the film the force acts against the surface tension of the liquid as it try to contract the liquid. The soap film has liquid–gas interface. The total length of contact of the film is equal to double length of the bar because film has two surfaces on either side. Therefore, force acting on surface is expressed mathematically as F = γ × 2L … (3.3) Substituting values of downward force F, in equation, gives; W = γ × 2L × d … (3.4) 

• The quantity 2L is equal to increased surface area ∆A produced by extending the film. Then the equation changes to: W = γ × ∆A or ∆G = γ × ∆A … where, W is work done or increased surface energy expressed in ergs. In the thermodynamic sense any form of energy can be split into two factors namely, intensity factor and capacity factor. In film stretching surface tension is the capacity factor. The equation is applied in gas adsorption studies on the solid surfaces, in studying physical instability of suspensions and thermodynamic instability of emulsions. The dimensional analysis of work energy theorem shows that the unit of surface tension (N/m or dyne/cm) is equivalent to J/m2. This means surface tension also can be considered as surface free energy. 

• Surface Free Energy Measurement: Following are some methods used to measure free energy of solid materials.

• Dyne Pen Method: This method involves use of set of commercially available felt-tip pens containing a range of inks of known surface tension. One of the pens is used to apply a thin film of ink over area of test surface may be solid or liquid. If the ink film breaks-up into droplets in less than two seconds, the process is repeated using a pen with ink having a lower surface tension. This procedure is used to establish the lowest surface tension ink that yield a film that remains intact for at least two seconds. The value of the surface tension of the ink is taken as the surface free energy of the substrate. 

• Contact Angle Method: In this method, a drop of liquid of known surface tension is placed on the test surface and then observed through a movable eyepiece. The eyepiece is connected to an electronic protractor, which displays the viewed angle. The construction of the angle is such that while viewing, angle equals the contact angle; the illumination viewed through the eyepiece is maximized. The contact angle and the surface tension of the liquid can then be used to calculate the surface energy of the test surface. 

• Interfacial Tensiometer Method: The method involves use of tensiometer in which the solid is dipped into and retracted from a liquid of known surface tension. The variation of contact angle with immersion depth is measured and these values are used to calculate surface free energy of the solid. This method is used for the solids where all exposed faces have same composition.   

• Example 3.1: If the length of bar is 5 cm and the force required to break a soap film is 0.4 g. What is surface tension of soap solution? What is the work required to pull the wire by 1 cm? Solution: γ = Force 2 × L = 0.4 × 980.655 2 × 5 = 39.226 dyne/cm Work = γ × ∆A = 39.226 × (2 × 5) = 392.26 ergs. 

Classification of Methods

• Capillary Rise Method: This is a good method because the parallel walls of the test tube allow better viewing of the two meniscuses that need to be seen. Consider the simple situation as depicted in which the end of a capillary tube of radius r, is immersed in a liquid of density ρ. For sufficiently small capillaries, one observes a substantial rise of liquid up to height h, in the capillary as the force exerted on the liquid due to surface tension. The balance point can be used to measure surface tension. The surface tension acting along the inner circumference of the tube exactly counterbalances the weight of the liquid. The surface tension at surface of the meniscuses is due to the force acting per unit length at a tangent. If θ is the angle between capillary wall and the tangent, then the upward vertical component of the surface tension is γ cos θ. The total surface tension along the circular contact of meniscus is 2πr times γ cos θ. Therefore.

• Upward force = (2πrγ) cos θ … (3.6) Since, for most liquids θ is equal to zero, then cos θ = 1, and upward component reduces to 2πrγ. The liquid is pulled downward by the weight of the liquid column. Thus, Downward force = Weight = Mass × g = hπr 2 ρg … (3.7) At balance point, upward force is equal to downward force, Upward force = Downward force Substituting values of equation (3.6) and (3.7), we get, (2πrγ) cos θ = hπr 2 ρg 

• where, r is radius of capillary, h is the capillary rise, ρ is liquid density, g is acceleration due to gravity and γ is the surface tension of the liquid. Rearrangement of equation (3.8) gives a simple expression for surface tension: γ = ρ grh 2 

• A careful look at Fig. 3.6 (a) and (b), the meniscus boundary shows that the liquid surface in the tube is not perfectly flat. Instead it curves-up (or sometimes down, for example, mercury) at the wall to form a meniscus. The material in this region also contributes to the force of gravity, so one often finds correction to equation (3.9) to yield γ = ρgr       h + r 3 2 … (3.10) 

• A careful look at Fig. 3.6 (a) and (b), the meniscus boundary shows that the liquid surface in the tube is not perfectly flat. Instead it curves-up (or sometimes down, for example, mercury) at the wall to form a meniscus. The material in this region also contributes to the force of gravity, so one often finds correction to equation (3.9) to yield γ = ρgr       h + r 3 2 … (3.10) 

• By this method surface tension against the air is determined. The liquid in the capillary must be raised and lowered several times before making the first reading. To get good results the cleaned capillary should be soaked in nitric acid for several minutes, following by washing with deionized water. When not in use, the capillary should be stored in polyethylene bottle containing deionized water. The apparatus is shown in Fig. 3.7. A test tube is fitted with a two-hole stopper. Through one hole the capillary tube is fitted. The tube is fitted through a glass slave and held in place by a piece of rubber tubing. In the second By this method surface tension against the air is determined. The liquid in the capillary must be raised and lowered several times before making the first reading. To get good results the cleaned capillary should be soaked in nitric acid for several minutes, following by washing with deionized water. When not in use, the capillary should be stored in polyethylene bottle containing deionized water. The apparatus is shown in Fig. 3.7. A test tube is fitted with a two-hole stopper. Through one hole the capillary tube is fitted. The tube is fitted through a glass slave and held in place by a piece of rubber tubing. In the second.

•  The radius of a given capillary is 0.105 mm. A liquid whose density is 0.8 g/mL rises in this capillary to height of 6.25 cm; calculate the surface tension of the liquid. Solution: The formula for calculation of surface tension by capillary rise method is γ = ½ ρ g r h γ = ½ (0.8 × 0.0105 × 6.25 × 980.655) [∴ 0.105 mm = 0.015 cm] γ = 25.74 dyne/cm The surface tension of liquid by capillary rise method is 25.74 dyne/cm. 

• Tensiometer: Tensiometers are used to determine surface or interfacial tension with the help of an optimally wettable probe suspended from a precision balance. The probe is either a ring or a plate. A height adjustable sample carrier is used to bring the liquid to be measured into contact with the probe. A force acts on the balance as soon as the probe touches the surface. If the length of the plate or circumference of the ring is known, the force measured can be used to calculate the surface or interfacial tension. The probe must have a very high surface energy. The ring is made of platinum iridium alloy and plate is made of platinum.

• DuNouy Ring Tensiometer: Historically the ring method was the first to be developed; hence many of the values for interfacial and surface tension given in the literature are the results of the ring method. In this method, the liquid is raised until contact with the surface is observed. The sample is then lowered again so that the liquid film produced beneath the ring is stretched as shown in Fig. 3.8.

• As the film is stretched, a maximum force is experienced; this is recorded in the measurement. At the maximum, the force vector is exactly parallel to the direction of motion; at this moment, the contact angle θ is zero. The illustration in Fig. 3.9 shows the force change as the function of distance of ring from the surface of liquid. In practice the distance is first increased until the area of maximum force has been passed through. The sample trough containing the liquid is then moved back so that the maximum point is passed through a second time. The maximum force is only determined exactly on this return movement and used to calculate the surface tension. The following equation (3.11) is used for the calculation; γ = [Fmax − Fv] [L × cos θ] 

• As the film is stretched, a maximum force is experienced; this is recorded in the measurement. At the maximum, the force vector is exactly parallel to the direction of motion; at this moment, the contact angle θ is zero. The illustration in Fig. 3.9 shows the force change as the function of distance of ring from the surface of liquid. In practice the distance is first increased until the area of maximum force has been passed through. The sample trough containing the liquid is then moved back so that the maximum point is passed through a second time. The maximum force is only determined exactly on this return movement and used to calculate the surface tension. The following equation (3.11) is used for the calculation; γ = [Fmax − Fv] [L × cos θ] 

• Correction for the ring method: The weight of the volume of the liquid lifted beneath the ring, expressed by the term Fv, must be subtracted from measured maximum force (Fmax) as it also affects the balance. The curve of the film is greater at the inside of the ring than at outside. This means that maximum force (at contact of angle = 0°) is reached at different ring distances for the inside and outside of the ring; thus, the measured maximum force does not agree exactly with the actual value. Harkins and Jordan, have a drawn-up tables of correction values by determining different surface tensions of standard liquid with rings of different diameters. Zuidema and Waters scientists also obtained correction values for small interfacial tensions by extrapolating data given by Harkins and Jordan to cover the range of tensions accurately.

• Advantages: 1. Many values in the literature have been obtained with the ring method; this means that in many cases the ring method should be preferred for comparison purposes. 2. As the wetted length of the ring is high it leads to a higher force on the balances so there has a better accuracy. 3. Small interfacial tensions can be obtained more accurately. 4. Cationic surfactants, which show poor wetting properties on platinum, the surface line between ring and liquid is more than that of plate.

• Disadvantages: 1. Corrections are required for volume of liquid lifted beneath the ring. 2. Densities of the liquids are to be known. 

• Wilhelmy Plate Method: In the Wilhelmy plate method the liquid is raised until the contact between the surface and the plate is observed. The maximum tension acts on the balance at this instance; this means that the sample does not need to be moved again during the measurement. shows the illustrative diagram of Wilhelmy plate. The surface tension calculation where, γ is surface or interfacial tension, F is force acting on the balance, L is the wetted length and θ is contact angle. The plate is made of roughened platinum and is optimally wetted so that contact angle is virtually a 0°. This means the term cos θ has a value of approximately the measured force and the length of plate need to be taken into consideration. Correction calculations are not necessary with plate method.

• Advantages: 1. No correction is required for measured values obtained by this method. 2. The densities of the liquids don’t have to be known. Advantages: 1. No correction is required for measured values obtained by this method. 2. The densities of the liquids don’t have to be known.

• Disadvantages: 1. The wetted length surface is small, so small force is required leading to variation in results. 2. Not suitable for cationic surfactants as platinum has poor wetting properties.

• Maximum Bubble Pressure Method: This is an easy method also called Jaegers method, for determining dynamic surface tensions of the liquids at short surface edges. The air pressure is applied slowly through a capillary tube immersed in the test liquid as shown in Fig. 3.11 (a). The gas bubble enters the liquid through a capillary whose radius is known. As pressure is applied gas bubble is formed at exactly defined rate at the end of the capillary. Initially the pressure is below maximum pressure (Pmax) the radius of curvature of the air bubble is larger than the radius of the capillary. When the pressure inside the tube is increased the pressure, curve passes through maximum and it is recorded by manometer attached to capillary tube. 

• At this stage, the air bubble radius is same as that of capillary, and it is of an exact hemisphere. At this point the force due to maximum pressure is equal to that of opposing forces the hydrostatic pressure (Ph) and the surface tension (γ) at the circumference (2πr) of the capillary. This relation between two opposing forces is expressed as: Pmax πr 2 = Ph + 2π r γ … (3.13) Pmax = Ph + 2γ r … (3.14) Pmax = h ρ g + 2γ r … (3.15) where, r is radius of capillary tube, ρ is density of the liquid and h is the length of capillary tube immersed in liquid. After the maximum pressure, the ‘dead time’ of measurement starts.

• The pressure decreases again and the radius of air bubble becomes larger, Fig. 3.12. The bubble finally escapes from the capillary. The cycle begins again with the formation of new bubble. Knowing the values of Pmax, h, ρ and r, surface tension of the liquid can be obtained. 

• The shape of a drop of liquid hanging from a syringe tip in immiscible liquid of different density is determined from surface tension of that liquid. The surface or interfacial tension at the liquid interface can be related to the drop shape through the following equation: γ = ∆ρ g r2 β … (3.16) where, γ is surface tension, ∆ρ is difference in density between liquids at interface, g is gravitational constant, r2 is radius of drop curvature at apex and β is shape factor. The shape factor can be defined through the Young-LaPlace equation expressed as three dimensionless first order equations as shown in the equation (3.17) below. dθ ds = 2 + β z − sin θ x Modern computational methods with interactive approximations use the Young-LaPlace equation to determine β. Thus, for any pendant drop where the densities of the two liquids in contact are known, the surface tension may be measured based upon the Young-LaPlace equation.

Advantages: 

• Easy and accurate compared to traditional methods 
• Able to use very small volumes. 
• Measures low interfacial tensions.
• Measures surface tensions of molten materials easily.
• High quality surface and interfacial measurements can be made. 

• Drop Weight Method: The apparatus used in this method is stalagmometer. It is pipette-having capillary below and above the bulb. About twenty drops of test liquid are collected from the stalagmometer in a weighing bottle and weighed to determine average weight of a drop. Similar type of determinations is carried out for the reference liquid after properly cleaning the apparatus. When the drop is formed at the tip of the stalagmometer, it is supported in upward direction by force of surface tension (γ) acting at the outer circumference (2πr) of the stalagmometer tip, while the downward force acting on the drop is its weight (m × g).

• Using stalagmometer 10 mL each of water and test liquid formed 35 and 46 drops, respectively. If density of liquid is 0.913 g/mL and surface tension of water is 72.75 dyne/cm, calculate surface tension of test liquid. Solution: γ2 =      η1ρ2 η2ρ1 × γ1 =      35 × 0.913 46 × 1 × 72.75 = 50.53 dyne/cm

• Number Drop Method: In this method number of drops of some fixed volume of reference liquid and test liquid are determined by using Stalagmometer. If V is the volume of liquid between two marks A and B as shown in Fig. 3.14, ρ1 and ρ2 are densities and n1 and n2 are number of drops oreference liquid and test liquid, respectively, the volume of one drop of liquid is V/n and the mass is equal to (V/n) ρ. Thus, as per equation (3.21) For reference liquid1 2π r γ1 = (V/n1) ρ1g … (3.23) And for the test liquid2 2π r γ2 = (V/n2) ρ2g … (3.24) Dividing equation (3.23) by (3.24) and on simplification we get γ2 =      n1 ρ2 n2 ρ1 γ1 … (3.25) where, γ1 and γ2 are surface tensions of the liquid1 and liquid2, respectively. If surface tension of one liquid is known the surface tension of other liquid can be calculated by equation (3.25).         

Measurement of Surface Tension

• In addition to the Dupouy ring, pendant drop and number drop methods used for determining surface tension and interfacial tensions, the drop volume method and the spinning drop method are exclusively used for interfacial tension determination.

• Drop Volume Method: A drop volume tensiometer is an instrument for determining the dynamic interfacial tension. Drops of a liquid are produced in a vertical capillary in a surrounding second liquid. The volume at which the drops detach from the tip of the capillary is measured. The dynamic surface tension can also be measured if measurements are made in air as the bulk phase. In the drop volume method, a liquid is introduced into a bulk phase through a capillary. A drop, which tries to move upwards due to buoyancy, forms at the tip of the capillary. The reverse arrangement, in which drops of the heavy phase drop from the tip of the capillary, is also possible. 

• Because of the interfacial tension (γ) the drop tries to keep the interface with the bulk phase as small as possible. As a new interface comes into being when the drop detaches from the capillary outlet, it is necessary to overcome the corresponding interfacial tension. The drop does not detach until the lifting force or weight compensates for the force resulting from the interfacial tension on the wetted length of the capillary, the circumference. The formula for this relationship is: σ = V∆ρg πd … (3.26) g = Acceleration due to gravity, V = Drop volume, d = Inside diameter of capillary, ∆ρ = Difference in density between the phases. 

• Spinning Drop Method: A spinning drop tensiometer is an instrument for determining the interfacial tension. Here, a horizontally arranged capillary filled with a bulk phase and a specifically lighter drop phase is set in rotation. The diameter of the drop which is elongated by centrifugal force correlates with the interfacial tension.

• When a heavy bulk phase and a light drop phase is situated in a horizontal, rotating capillary, the drop radius perpendicular to the axis of rotation depends on the interfacial tension γ between the phases, the angular frequency ω of the rotation and the density difference ∆ρ. Thus, with a given speed of rotation and with known densities of the two phases, the interfacial tension can be calculated from the measured drop diameter d (= 2r) in accordance with Vonnegut's equation: σ = r 3 ω 2 ∆ρ 4 … (3.27) The drop diameter is determined from the video image of the drop by means of drop shape analysis. The length of the drop along the axis of rotation must be at least four times the diameter of the drop to minimize the error due to the curvature of the interface. Extremely low interfacial tensions can be measured with a spinning drop tensiometer. The spinning drop method is frequently used when the conditions for forming a micro-emulsion are to be investigated, e.g. with surfactant flooding in enhanced oil recovery (EOR) or in solvent-free degreasing. 

• Comparison of Methods: Of the several methods exist for surface and interfacial tension determinations there is no method available which suits all types of systems. Basically, choice depends on accuracy, sample size, whether surface or interfacial tension or effect of time on surface tension is to be determined.    

Spreading Coefficient 

• Spreading can be observed by adding one liquid to surface of other liquid. The supporting liquid for instance is designated with ‘II’ while the liquid being added to the top by ‘I’, since it initially forms a lens. There are two possibilities, first, the liquid can spread over the surface of sublayer liquid or second, the added liquid will contract into a small lens on the surface of sublayer liquid. We can predict what will happen to the system by determining net loss in free energy. The spreading of liquid is controlled by surface tensions of pure immiscible liquids and interfacial tension between them. The concept of work of cohesion and work of adhesion help to understand the spreading of one liquid on another and predict whether it would spread spontaneously or not. There exists a mathematical relationship, which can be used to forecast the outcome of the situation called as spreading coefficient, denoted by S.

• Work of Cohesion: Let’s consider a column of some liquid as shown in , who’s cross-sectional area is 1 cm2 . On application of force to the liquid it separates with formation of two new surfaces each of 1 cm2 area. The work done in separation of liquids is work of cohesion. It is defined, as a work required in separating the molecules of the spreading liquid so that it can flow over the sub-layer liquid. When the liquid alone is considered, no interfacial tension exists as cohesive forces are operating. Since two new surfaces are created the area becomes 2 cm2 . The work of cohesion is denoted by Wc and is equal to surface tension times the amount of new area created. As per definition the work of cohesion is written as; Wc = 2γ1 … (3.28) where, γL is surface tension of liquid.

• Work of Adhesion: Work of adhesion, Wa, is the work done to destroy the adhesion between unlike molecules. Let’s imagine the situation as shown in Fig 3.17 (b), where the column of liquid is made-up of two immiscible liquids like oil and water. If a force is applied along the liquid column to cause the liquids to separate in to two parts, the work done is work of adhesion. Here by destroying 1 cm2 interface between sublayer and spreading liquid we have created a 1 cm2 surface of sublayer liquid and 1 cm2 surface of spreading liquid. The work of adhesion is then expressed as; Wa = γ1 + γ2 − γ12 … (3.29) where, γL is surface tension of spreading liquid, γ2 is surface tension of sub-layer liquid and γ12 is interfacial tension between them.

• Spreading Coefficient: The spreading coefficient is obtained by following equation S = Wa − Wc … (3.30) Substituting values from equation (3.28) and (3.29) we get S = (γ1 + γ2 − γ12) − 2γ1 … (3.31) The coefficient of each of the term is one because we either created or destroyed 1 cm2 surface or interface respectively. On simplifying equation (3.31) we get S = γ2 − γ1 − γ12 S = γ2 − (γ1 + γ12) … (3.32) A positive value of S means that the liquid will spread and negative means it will not. Water has surface tension of 72.8 dyne/cm, benzene has surface tension of 28.9 dyne/cm, and interfacial tension between them is 35 dyne/cm. If benzene is added to water surface, there exists two possibilities. First, the benzene can spread over the surface of water if S is positive or second, it will contract into small lens on surface of water if S is negative. On substituting these values of surface and interfacial tension of water and benzene in equation (3.32), S = 72.8 − (28.9 + 35) S = 8.9 As the value of spreading coefficient is positive benzene will spread on the surface of water. In spreading of organic liquids on surface of water, the initial spreading coefficient may be positive or negative, but the final spreading coefficient is negative. On addition of benzene to water, even though polar groups are absent in benzene, it spreads over the water due to stronger adhesive forces over the cohesive forces. With time benzene begins to saturate the water and surface tension of water saturated with benzene decreases to 62.0 dyne/cm. Now substituting values in equation (3.32) we get S = 62.2 − (28.9 + 35) S = −1.7 Since value of S is negative, benzene contract on the surface of water and forms a lens. The spreading coefficient of substances depends on their structures, especially presence of  polar functional groups and non-polar carbon chain length. Polar substances such as acids and alcohols spread more freely compared to non-polar hydrocarbons like benzene, octane and liquid petroleum due to presence of polar groups.

• Example 3.6: At 20 °C the surface tension of water and chloroform are 72.75 and 27.10 dyne/cm, respectively while the interfacial tension between the two is 32.8 dyne/cm. Calculate (a) work of cohesion (b) work of adhesion and (c) the spreading coefficient of chloroform on water. Will chloroform spread on water? 

• Solution: (a) Work of cohesion: Wc = γ1 + γ2 + γ12 = 27.10 + 72.75 − 32.8 = 99.85 – 32.8 = 67.05 (b) Work of adhesion: Wa = 2 γ1 = 2 × 27.10 = 54.20 (c) Spreading coefficient: S = γ2 − γ1 − γ12 = 72.75 – 27.10 – 32.8 = 12.85 Since, the value of spreading coefficient is positive, chloroform will spread on the surface of water. 

Adsorption at Liquid Interfaces

• Like surface tension, adsorption is a consequence of surface energy. The molecules from bulk of liquid are brought to the interface. In bulk of liquid, all the bonding requirements, such as ionic or covalent of the constituent atoms of the molecule are fulfilled, but atoms at the clean surface experience a bond deficiency, because they are not wholly surrounded by similar other atoms. Thus, it is energetically favorable for them to bond with whatever happens to be available. The exact nature of bonding depends on the species involved. According to this principle greater the molecules and ions that are dispersed in liquid, they move towards the interface decreasing their concentration in the bulk and accumulates at the interface, this leads to reduction in surface free energy of the system. This phenomenon is known as adsorption. Adsorption is a process that occurs when added molecules partitioned to surface forming a molecular or atomic film. More specifically it is regarded as positive adsorption. It is different from absorption, where added molecules diffuse into a liquid to form solution also called negative adsorption or reverse adsorption. The term sorption encompasses both process namely adsorption and absorption.

• Amphiphiles: Paul Winsor coined the word amphiphile 60 years ago. It comes from Greek roots amphi which means, “double”, “from both sides”, “around”, as in amphitheater or amphibian and philos that expresses friendship or affinity, as in “philanthropist” (the friend of man), “hydrophilic” (compatible with water), or “philosopher” (the friend of wisdom or science). An amphiphilic substance exhibits a double affinity, which can be defined from the physicochemical point of view as a polar/non-polar duality. A typical amphiphilic molecule consists of two parts: on the one hand a polar group which contains heteroatoms such as O, S, P, or N, included in functional groups such as alcohol, thiol, ether, ester, acid, sulfate, sulfonate, phosphate, amine, amide etc. On the other hand, an essentially non-polar group, which is in general a hydrocarbon chain of the alkyl or alkylbenzene type sometimes with halogen atoms and even a few non-ionized oxygen atoms.

• An important case of adsorption on liquid surfaces is that of surface-active molecules. The polar portion exhibits a strong affinity for polar solvents, particularly water, and it is often called hydrophilic part or hydrophile, . The non-polar part is called hydrophobe or lipophile, from Greek roots Phobos (fear) and Lipos (grease). The following structure is an example of amphiphilic molecule commonly used in shampoos.   

Surface Active Agents 

• Because of dual affinity of an amphiphilic molecule, it does not feel “at ease” in any solvent, be it polar or non-polar, since there is always one of the groups which “does not like” the solvent environment. Therefore, amphiphilic molecules exhibit a very strong tendency to migrate to interfaces or surfaces and to orientate so that the polar group lies in water and the non-polar group is placed out of it, and eventually in oil. In English, the term surfactant (surface-active-agent) designates a substance, which exhibits some superficial or interfacial activity. Only the amphiphiles with equilibrated hydrophilic and lipophilic tendencies are likely to migrate to the surface or interface. It does not happen if the amphiphilic molecule is too hydrophilic or too hydrophobic, in which case it stays in one of the phases. In other languages, such as French, German or Spanish the word “surfactant” does not exist, and the actual term used to describe these substances is based on their properties to lower the surface or interface tension, for example, tensioactif (French), tensile (German), denotative (Spanish). This would imply that surface activity is strictly equivalent to tension lowering, which is not general, although it is true in many cases. Amphiphiles exhibit other properties than tension lowering and therefore they are often labelled as per their main use such as: soap, detergent, wetting agent dispersant, emulsifier, foaming agent, bactericide, corrosion inhibitor, antistatic agent etc. In some cases, they are known from the name of the structure they can build, i.e. membrane, microemulsion, liquid crystal, liposome, vesicle or gel.

CLASSIFICATION OF SURFACTANTS 

• From the commercial point of view surfactants are often classified as per their use. The most accepted and scientifically sound classification of surfactants is based on their dissociation in water.

Anionic Surfactants: 

• Anionic Surfactants are dissociated in water in an amphiphilic anion, and a cation, which is in general an alkaline metal (Na + , K+ ) or a quaternary ammonium. They are the most commonly used surfactants. They include alkylbenzene sulfonates (detergents), (fatty acid) soaps, lauryl sulfate (foaming agent), di-alkyl sulfosuccinate (wetting agent), lignosulfonates (dispersants) etc.

Non-ionic Surfactants: 

•  Nonionic Surfactants do not ionize in aqueous solution, because their hydrophilic group is of a non-dissociable type, such as alcohol, phenol, ether, ester, or amide. A large proportion of these nonionic surfactants are made of hydrophilic portion (by the presence of a polyethylene glycol chain) and lipophilic portion (alkyl or alkylbenzene) 

Cationic Surfactants: 

• Cationic Surfactants are dissociated in water into an amphiphilic cation and an anion, most often of the halogen type. A very large proportion of this class corresponds to nitrogen compounds such as fatty amine salts and quaternary ammoniums, with one or several long chains of the alkyl type, often coming from natural fatty acids. They are used as bactericide and as positively charged substance, which can adsorb on negatively charged substrates to produce antistatic and hydrophobia effect. When surfactant molecules exhibit both anionic and cationic dissociations it is called amphoteric or zwitterionic, for example, betaines or sulfacetamides and natural substances such as amino acids and phospholipids.

Polymeric Surfactants: 

• Polymeric surfactants are often not accounted as surfactants. Their importance is growing; however, because they enter in many formulated products as dispersants, emulsifiers, foam boosters, viscosity modifiers, etc. Some of them commonly used are paleopolyploid block copolymers, ethoxylated or sulfonated resins, carboxymethyl cellulose and other polysaccharide derivatives, polyacrylates, xanthan etc.   

HLB Scale 

• The hydrophilic lipophilic balance (HLB) system is based on the concept that some molecules of surfactants are having hydrophilic groups; other molecules have lipophilic groups and some have both hydrophilic and lipophilic groups called amphiphilic molecules. Hydrophilic and lipophilic portions dissolve in aqueous and oily phase. It is useful to correlate and measure these characteristics of the surfactants by some means for their applications in various fields such as to formulate various dispersed systems like lotions and emulsions. A common system, which is used to express the amphiphilic nature as a balance between hydrophilic and lipophilic portion of the molecule is called as HLB system.

• Weight percentage of each type of group in a surfactant molecule or in a mixture of surfactants predicts what behaviour the surfactant molecular structure will exhibit. Griffin in 1949 and its latter development in 1954 introduced the HLB system, a semi-empirical method. It is the number on scale of 1 to 40, as shown in Fig. 3.20. The HLB value for a given surfactant is the relative degree to which the surfactant is water-soluble or oil soluble. An emulsifier having a low HLB number indicates that the number of hydrophilic groups present in the molecule is less and it has a lipophilic character. For example, spans generally have low HLB number and they are also oil soluble. Because of their oil soluble character, spans cause the oil phase to predominate and form a w/o emulsion.

• A higher HLB number indicate that the emulsifier has a large number of hydrophilic groups on the molecule and therefore is more hydrophilic in character. Tweens have higher HLB numbers and they are also water soluble. Because of their water-soluble character, Tweens will cause the water phase to predominate and form an o/w emulsion. The usual HLB range is from 1 to 20, while there is one exception to this range as shown in Table 3.5 at the bottom. Sodium lauryl sulphate, a surfactant dissolves in water very well and is common additive to most of the heterogeneous systems and to almost all common detergents. As HLB value is additive, the blending of surfactants with known HLB values to get a desired one is very easy. The appropriate HLB values are calculated by various methods.

• Methods to Determine HLB: Method I - Alligation or Algebraic manipulations: If a and b are the HLB values of surfactant A and B, respectively, and the c is desired HLB value then proportional parts required of A and B surfactants are x and y, respectively. x y = (c − a) (a − c) … (3.33) Or HLBBlend = f HLBA + (1 − f) HLBB … (3.34) where, f is fraction of surfactant A and (1 − f) is fraction of surfactant B in the surfactant blend. 

• Method II - Water dispersibility: Approximation of HLB for those surfactants and not described by Griffin can be made either from characterization of their water dispersibility, Table 3.6.

• Method III - Experimental estimation: From experimental estimations blends of unknown surfactants in varying ratio with an emulsifier of known HLB are used to emulsify oil. The blend that performs best is assumed to have a value approximately equal to the required HLB of the oil. 

• Method IV – Group contribution method: Davis and Rideal suggested an empirical calculation of HLB based upon the positive and negative contribution of various functional groups to the overall hydrophilicity of a surfactant. Substituting values given in Table 3.7 for various group numbers in equation 3.35 gives HLB of a surfactant. HLB = ∑ (Hydrophilic group number) − ∑ (Lipophilic group number) + 7 … (3.35)  

• Saponification number is defined as the number of milligrams of potassium hydroxide required to neutralize the acid formed during saponification of one gram of sample. Acid number is the number of milligrams of potassium hydroxide required to neutralize the free acid in one gram of sample. One part of structure of glyceryl monostearate contains a fatty acid stearic acid, which is lipophilic in nature while other part is alcohol, which is hydrophilic in nature. Therefore, analysis of these parts by saponification gives HLB estimates. Factors Affecting HLB Value: 

 1. Nature of immiscible phase 

 2. Presence of additive 

 3. Concentration of surfactant

 4. Phase volume

 5. Temperature

• Drawbacks of HLB system: HLB system provides only information about the hydrophilic and lipophilic nature of the surfactants but concentration of these surfactants is not considered. For optimum stability and therapeutic safety concentrations of the surfactant are equally important. It does not consider the effect of temperature as well as the presence of other additives.

• Example 3.7: Calculate overall HLB value of a mixture of 30% Span 80 and 70% Tween 80. Solution: HLB value of span 80 is 4.3 and that of Tween 80 is 15. Therefore, HLB = (0.3 × 4.3) + (0.7 × 15) HLB = 11.8 The overall HLB of surfactant mixture is 11.8.  

Solubilization 

• When drugs are in development, one property that is essential to its success is its solubility. Although water is widely used, most drugs being organic will not go into an aqueous solution easily. Strongly ionized substances are likely to be freely soluble in water over a wide pH range and cause no problem. Similarly, weakly acidic and weakly basic drugs should be sufficiently soluble at favorable pH. Sometimes soluble but concentration of the solute is very close to its limit of solubility and get precipitated on cooling or evaporation of solvent. This section will briefly discuss ways to enhance solubility of unionized drugs and weak electrolytes. There are several different ways to enhance solubility, but the method of choice depends on the nature of the solute and the degree of solubilization needed. 

• Use of Cosolvents: The cosolvency concept is used for increasing solubility of electrolytes and non-electrolytes in water. This can be achieved by addition cosolvent that is miscible with water and in which the substance in question is soluble. The cosolvents work by modifying affinity of solvent for solutes by decrease in interfacial tension between solute and solvent or by changing dielectric constant. The expected dielectric constant values for the solvent and cosolvent blend should be in the range of 25 to 80. Choice of such solvents for the pharmaceutical use is limited due to toxicity and irritancy characteristics. Ethanol (for paracetamol), isopropylalcohol (betamethasone valetrate), glycerin and propylene glycol (for co-trimazole) are some of the examples of cosolvents used for solubilization of drugs mentioned in brackets. Other examples of cosolvents are glycerin, polyethylene glycol, sorbitol, mannitol, etc. and are used for increasing solubilities of electrolytes and non-electrolytes.

• pH Control: Majority of the drugs are either weak acids or bases, and therefore their solubilities in water can be influenced by the pH of the system. There is a little or no effect of pH on solubility of non-ionizable substances with few exceptions. For ionizable solutes such as carboxylic acid (HA) solubility is function of pH, Fig. 3.21. The solubility of weak acid is increased by an increasing pH where as solubility of weak base increased by decreasing pH.

• If the solute is brought outside its pKa by changing the pH value where half portion is ionized and half portion remains unionized, then the solubility will be changed. This is due to introduction of intermolecular forces, mainly ionic force of attraction. For example, carboxylic acid groups (−COOH) have pKa around pH 4 and if the pH is increased above 4 the −COOH is changed to −COO− . The negative charge introduced is free to have introduction with a partial positive charges of the hydrogen of water. The effect of the pH on solubility of weak electrolytes is described by equation pHp = pKa + log      S − So So … (3.40) where, pHp is the pH below which the drug precipitates from solution as the undissociated acid, S is the total solubility and So is the molar solubility of the undissociated acid. We often consider that ionize form is freely soluble but is not always true. For example, carboxylic acids have pKa ~ 4. For the administration of methyl prednesolone hemisuccinate (solubility <1 mg/ml) if base such as sodium hydroxide is added the carboxylic acid becomes deprotonated and solubility increases to more than 200 mg/ml. The same can be observed for base, therefore, pHp = pKw + pKb + log      S  S − So … (3.41) where, pKw is dissociation constant of water, pKb is dissociation constant of base and pHp is the pH above which the free base precipitates out of solution.

• Solubility of weak electrolytes in buffer solution can be changed by addition of cosolvents. The undissociated species get dissolved by modifying polarity of solvent to a more favourable value. In improving solubility of drugs by pH control it must be ensured that the selected pH does not change the other requirement of the product such as chemical stability that may also depend on pH. Non-ionizable, hydrophobic solutes can have improved solubility by changing the dielectric constant of solvent by use of cosolvent. The maximum solubility must be best achieved by appropriate balance between pH and concentration of cosolvent. The solubilities of the non-electrolytes are not much affected by the pH changes therefore other methods can be tried for their solubility enhancement. 

• Example 3.11: The solubility and pKa of phenobarbital sodium in 15% alcohol solution is 0.22% and 7.6, respectively. What is pH of 2% phenobarbital sodium hydroalcoholic solution? Solution: Given that: S = 2; So = 0.22; pKa = 7.6 pHp = pKa + log      S − So So = 7.6 + log      2 − 0.22 0.22 = 7.6 + log 8.09 = 8.508 The pH of hydroalcoholic phenobarbital sodium solution is 8.508. 

• Surfactants in Solubilization: Surfactants play a vital role in many processes of interest. One important property of surfactants is the formation of colloidal-sized clusters in solutions, known as micelles, which have significance in pharmacy because of their ability to increase the solubility of sparingly soluble substances in water. The solubility of drugs that are insoluble or poorly soluble in water can be improved by incorporation of surfactants above its critical micelle concentration (CMC). This phenomenon is widely used for the solubilization of poorly soluble drugs. Micelles are known to have an anisotropic water distribution within their structure. In other words, the water concentration decreases from the surface towards the core of the micelle, with a completely hydrophobic (water-excluded) core. Consequently, the spatial entrapment of a solubilized drug in a micelle depends on its polarity. The non-polar molecules will be  solubilized in the micellar core, and substances with intermediate polarity will be distributed along the surfactant molecules in certain intermediate positions. Numerous drug delivery and drug targeting systems have been studied to minimize drug degradation and loss, to prevent harmful side effects, and to increase drug bioavailability. Within this context, the utilization of micelles as drug carriers presents some advantages when compared to other alternatives such as soluble polymers and liposomes. Micellar systems can solubilize poorly soluble drugs and thus increase their bioavailability, they can stay in the body (blood) long enough to provide gradual accumulation in the required area, and their sizes permit them to accumulate in areas with leaky vasculature.

• Complex Formation: The apparent solubility of some substance in given solvent may be increased or decreased by incorporation of complex forming substances. The degree of complex formation decides the apparent change in solubility of original solute. For example, complex formation between iodine and povidone increases solubility of iodine. Similarly, complex between iodine and potassium iodide to form polyiodides increases solubility of iodine. The interaction of salicylates and benzoates with theophylline or caffeine also increases solubility of these drugs. Other examples of complex forming substances that increases solubility of drugs are nicotinamide and β-cyclodextrins.

• Drug Derivatization: One method to increase solubility of a drug is to alter the chemical structure of the molecule. The addition of polar groups like carboxylic acids, ketones and amines can increase solubility by increasing hydrogen bonding and the interaction with water. Another structure modification can be to reduce intramolecular forces. An example of structure modification to enhance solubility by the latter method is methyl dopa, solubility ~10 mg/ml, and methyl dopate (aprodrug of methyldopa), solubility 10-300 mg/ml depending on pH, Fig. 3.24. The addition of the ethyl ester to methyldopa reduces the intramolecular hydrogen bond between the carboxylic acid and primary amine. Therefore, this addition reduces the melting point and increases solubility. Other examples of chemical modifications for the solubility enhancement include; sodium phosphate salt of hydrocortisone, prednesolone and beta methasone.

• Solid State Manipulation: The size and shape of particle have significant effect of solubilities. Increase in surface area by decrease in particle size provides more area for interaction between solvent and solute causing higher solubilities.   

Deterge

• Detergency is a complex process involving the removal of foreign matter from surfaces. Surfactants are used for the removal of dirt through the detergency effect. Initial wetting of the dirt and of the surface to be cleaned is carried out by deflocculation and suspension or emulsification or solubilization of the dirt particles. It also involves foaming of the agent for entertainment and washing away of the particles. A wetting agent that when dissolved in water, lowers the advancing contact angle, aids in displacing an air phase at the surface and replacing it with a liquid phase. Wetting agents are useful in

• 1. Displacement of air from sulfur, charcoal and other powders for dispersing these drugs in liquid vehicles 2. Displacement of air from the matrix of cotton pads and bandages so that medicinal solutions may be absorbed for application to various body areas. 3. Displacement of dirt and debris using detergents in the washing of wounds. 4. The application of medicinal lotions and sprays to the surface of the skin and mucous membrane.

• Solid surfaces adsorb dissolved or undissolved substances from the solutions. Common example is adsorption of acetic acid on activated charcoal. Fraction of added acid is adsorbed by activated charcoal and the concentration of acid in solution decreases. Other example of adsorption by activated charcoal are removal of solutes from solutions such as ammonia from ammonium hydroxide, phenolphthalein from solutions of acids and bases, high molecular weight non-electrolyte substances from their solutions. Adsorption from solution follows general principle laid down for adsorption of gases and is subject to same factors. Adsorbent is more effective in attracting certain substances to their surface than others. Temperature decreases the extent of adsorption while surface area has opposite effect to that of temperature as increase in surface area adsorption increases. Adsorption from solutions involves equilibrium between amount adsorbed on to surface and amount present in bulk solution. The effect of concentration of adsorbate on extent of adsorption is represented by Freudlich’s isotherm equation as in the following equation y = kC1/b … (3.42) where y is mass of adsorbate per unit mass of adsorbent, C is equilibrium concentration of adsorbate being adsorbed, while k and b are empirical constants. By taking logarithms of both the sides of the equation (3.42) we obtain log y = log k + 1 b log C … (3.43) The plot of log y versus log C is linear with slope equal to 1/b and intercept equal to log k. Clarification of sugar liquors by charcoal, recovery of dyes from solvents, recovery and concentration of vitamins and other biological substances, wetting and detergency are some of the applications of the adsorption at solid liquid interfaces. One of the uses of adsorption  at solid/liquid interface is to remove poisonous levels of drugs and other toxins from the body. Very often activated charcoal is used as an antidote to poisons. This powder is not wet by water but has a high affinity for some types of drugs. As an example, the sulfonylurea such as tolbutamide will concentrate on the surface of the activated charcoal. Another example is the common OTC analgesic acetaminophen. An overdose of this drug can cause severe liver complications leading to death. A dose of 15 g can kill an adult. By administering activated charcoal, we can reduce the amount of the dose that is absorbed into the body and some research have shown that some of the drug will cross from the blood supply into the gut. 

Adsorption at Solid Interface

• The substance in adsorbed state is called adsorbate, while that present in one or other (or both) of the bulk phases and capable of being adsorbed may be distinguished as adsorptive. When adsorption occurs at the interface between liquid and solid, the solid is usually called the adsorbent; for gas-liquid interfaces sometimes the liquid is called adsorbent. The adsorption process is generally classified as physisorption or chemisorption. Adsorption of gases has wide applications as removal of objectionable odors from food, rooms, characterization of powders, adsorption chromatography, prevention of obnoxious gases entering body by gas masks, production of high vacuum, moisture removal etc. Adsorption of gas on solid is like that of adsorption at liquid surfaces, where the surface free energy is reduced. While comparing solids and liquids with respect to adsorption the surface tension determinations are easier for liquids as they are more mobile than the solids. The average lifetime of molecule at liquid surface is very low i.e. 1 sec compared to atoms at the surface of non-volatile metallic surface.

Solid-Gas Adsorption: 

• It is probable that all solids adsorb gases to certain extent, but the phenomenon is not prominent unless adsorbent possess large surface area. The adsorption of gas on to a solid surface is of mainly of two types.

Physisorption: 

• Physisorption is adsorption in which the forces involved are intermolecular forces (van der Waals forces) of the same kind as those responsible for imperfection of real gases, condensation of vapors and which do not cause a significant change in electronic orbital patterns of species involved. The term van der Waals adsorption is synonymous with physical adsorption but its use is not recommended. 

Characteristics of Physisorption: 

• It is a general phenomenon and occurs in any solid/fluid systems. 
• Minimum change in electronic state of adsorbate and adsorbent is observed. 
• Adsorbed species are chemically identical with those in the chemical adsorbent, so the chemical nature of the adsorbent is not changed by adsorption and subsequent desorption. 
• Energy of interaction between the molecules of adsorbate and adsorbent is of same order of magnitude.
• Elementary step in adsorption of gas does not involve activation energy.
• Equilibrium is established with increase in pressure and usually decreases with temperature. 
•  Under appropriate condition of temperature and pressure, molecules of gas can be adsorbed more than those in direct contact with surface. 

Chemisorption: 

•  Chemical adsorption or chemisorption is a process in which valance forces of some kind, operating in the formation of chemical compounds are involved. The difference between chemisorption and physisorption is same as that of difference between physical and chemical interaction in general. 

Characteristics of Chemisorption:

• The phenomenon is characterized by chemical specificity. 
• Change in electronic state may be detectable by suitable physical means (e.g. UV, IR, microwave spectroscopy, conductivity etc.) 
• The chemical nature of the adsorptive may be altered by surface reaction in such a way that on desorption the original surfaces cannot be recovered. 
• Like chemical reactions, chemisorption is either exothermic or endothermic and magnitude of energy changes may vary from small to very large.
• The elementary step in chemisorption involves activation energy.
• The rate of chemisorption increases with increase in temperature and when activation energy of adsorption is small, removal of chemisorbed species from the surface may be possible under extreme conditions of temperature and pressure or by some suitable chemical treatment of the surface. 
•  Adsorbed molecules are linked to the surface by valence bonds that occupy certain adsorption sites on surface forming monolayer. 

Factors Affecting Adsorption: 

•  Surface area of adsorbent: Being surface phenomena extent of adsorption depends on available surface area of adsorbent. Finely divided materials since has large surface area, more adsorption is observed on their surfaces. 

Nature of adsorbate: 

• The amount of adsorbate adsorbed on solids depends on its nature; easily liquefiable gases adsorbed to greater extent.

Temperature: 

•  As seen under the characteristics of physical adsorption, it decreases with increase in temperature, while chemical adsorption increases with increase in temperature. 

Pressure: 

•  Applying Le Chatelier’s principle, dynamic equilibrium exists between adsorbed gas molecules and molecules in contact with adsorbate. In fact, it is observed that increase in pressure increases adsorption. Process characteristics: As physical adsorption, inversely proportional and chemical adsorption is directly proportional to temperature, reversing this process condition adsorption can be decreased. 

Thickness of adsorbed layer: 

• Langmuir from his studies of isotherms showed that at low pressures physically adsorbed gas forms only one layer one molecule thick while at higher pressures forms multilayers with increased extent of adsorption.

• ADSORPTION ISOTHERMS Adsorption isotherm is the relation between the quantity of adsorbate adsorbed and the partial pressure in the gas phase (or composition of bulk phase, in adsorptions from liquids) under equilibrium conditions at constant temperature.

Freudlich’s Adsorption Isotherm: 

• The scientist Freundlich’s studied adsorption of gas on solid and from the experimental data; he gave empirical equation called equation of Freundlich’s adsorption isotherm, y = w m = kP1/b … (3.44) where, y is amount (w) of adsorbate adsorbed by m gram of adsorbent at equilibrium pressure P and are determined from the experiment at constant temperature. The constants k and b depend on nature of adsorbate and adsorbent as well as on temperature. In equation (3.44), b > 1 therefore the amount of adsorbed gas increases less rapidly than the pressure. This equation holds good only for medium pressures of gas. If w/m is plotted against pressure, a curve results of which first part is linear and over this range at low pressures x/m ∝ p. At higher pressures a limiting value x/m is reduced, and curve is parabolic in shape as shown in Fig. 3.25. Equation (3.44) is known as Freudlich’s adsorption isotherm. Taking logarithm on both sides of equation (3.44) log      w m =      1 b log P + log K … (3.45)

Langmuir Adsorption Isotherm:

• In 1916, scientist Irving Langmuir (1916) published a new isotherm for gases adsorbed on solids, which retained his name. It is an empirical isotherm derived from assumptions of his extensive study. 

•  The surface of a solid is made-up of elementary spaces and each space can adsorb one gas molecule. 

• All the elementary spaces are identical in their capacity for adsorbing a gas molecule. 

• The adsorption of a gas molecule in one element of space does not affect the properties of neighboring spaces

• It is possible that the adsorption layers are just of a single molecule thickness because intra-molecular forces fall off rapidly at distance beyond it.

• Due to thermal kinetic energy of some the adsorbed molecule, they get detached and pass back into space. Therefore, adsorption can be considered as consisting of two opposing processes in equilibrium (i.e. condensation and evaporation).

• Initially rate of adsorption is high but as the surface area of adsorbent is covered with adsorbate molecules the rate of removal of adsorbed molecules goes on increasing. (i.e., rate of adsorption and evaporation are equal). 

• Langmuir had developed an equation based on the theory that the molecules or atoms of gas are adsorbed on active sites of the solid to form a layer one molecule thick. If fraction of active centers occupied on surface of adsorbent by gas molecules at pressure P is expressed as θ then the fraction of sites unoccupied is 1 − θ. The rate of adsorption (R1) is proportional to unoccupied spots and the pressure P and the rate of evaporation (R2) of molecule bound on surface is proportional to the fraction of surface occupied, θ. R1 ∝ fraction of sites unoccupied × Pressure R1 = k1 (1 − θ) P … (3.47) R2 ∝ Fraction of sites occupied R2 = k2 θ 

Type-I: 

•  Langmuir and Freundlich isotherms are of Type-I, Fig. 3.27, where adsorption takes place on non-porous solids. It represents behaviour of nitrogen or oxygen on charcoal. Total surface area can be determined from this isotherm by multiplying the total number of molecules in the volume of gas adsorbed by the cross-sectional area of the molecule.

Type-II: 

• In this type of isotherm gases are physically adsorbed on a non-porous solid forming monolayer followed by multilayer formation. The first inflection in the curve represents formation of monolayer and subsequent increase in pressure shows multilayer adsorption. This isotherm is explained by BET (Brandauer, Emmett and Teller) equation      P  y (P0 − P) =      1  yam +      (b − 1) ymb ×      P  P0 … (3.54) where, P is pressure of the adsorbate, y is mass of vapour per gram of adsorbent; P0 is vapor pressure at saturation of adsorbent by adsorbate, ym is amount of vapour adsorbed per unit mass of adsorbent when the surface is covered with monomolecular layer and b is constant equal to difference between heat of adsorption in the first layer and latent heat of condensation in the next layers. This isotherm is sigmoid in shape and observed with adsorption of nitrogen on iron catalysts, on silica gel and other surfaces.

Type-III: 

• This isotherm is rarely observed for example, bromine and iodine on silica gel, where heat of adsorption in the first layer is less than the latent heat of condensation in the next layers. The constant b of the BET equation is less than two. 

Type-IV: 

•  This isotherm is typical of adsorption onto porous solids where if the first point is extrapolated to zero pressure represents the amount of gas required in forming monolayer on solid surface. Condensation within the capillaries is responsible for the further adsorption. The example of this type is adsorption of benzene on ferric oxide and silica gel.