Unit-VILIQUID CRYSTALS AND THEIR APPLICATIONS

Introduction: The study of liquid crystals began with an observation made by Austrian botanist, Freindrich Reinitzer in 1888. He observed that solid cholesteryl benzoate on heating becomes a turbid liquid at 1450C which on further heating turns into a clear, transparent liquid at 1780C. The above changes are reversed on cooling. The changes are generally represented as

Cholesteryl benzoate is said to exit a liquid crystal between 1450C and 1780C. The first temperature at which solid changes into turbid liquid is known as transition point and second temperature at which turbid liquid changes in to clear liquid is known as melting point. Thus, liquid crystal is a distinct phase observed between crystalline solid state and isotropic liquid state.

Definition: Liquid crystals may be described as a distinct state of matter in which the degrees of molecular ordering lie intermediate between the ordered crystalline state and the completely disordered isotropic liquid state.

The liquid crystal state is also referred to as mesophase. The compounds which exhibit mesophase are also called mesogens. Liquid crystals exhibit optical anisotropy, i.e., they possess different optical properties when light is incident in different directions. Liquids, however, exhibit optical isotropy i.e., they exhibit same optical property irrespective of the direction of incident light.

Positional and orientational order: Most liquid crystals are composed of organic molecules. In solid state, the molecules are highly ordered. Each molecule occupies a definite position in a more or less rigid arrangement and is immobile. In solid state not only do the molecules occupy specific positions but also tend to orient in a preferred direction which is already existing. In liquid state, however, the molecules neither occupy specific positions nor remain oriented in a particular manner. The molecules are somewhat free to move at random and collide with one another abruptly changing their positions. Intermediate between the solid and the liquid crystal phase, wherein the molecules free to move but are oriented in a particular manner.

Fig.1 Representation of solid, liquid crystal and liquid states (molecules are represented as thin lines)

Thus solid phases possess positional order and orientational order. Liquid phases possess neither positional nor orientational order while in liquid crystal phase some orientational order is retained through there is a loss of positional order as shown in Fig.1

Director: In a liquid crystal, the molecules possess orientational prder i.e., the molecules tend to remain oriented in a particular direction. The direction of preferred orientation in a liquid crystal is called director and may be imagined to be directed towards the top or bottom of the page. Since the molecules are in constant motion, in liquid crystal phase they spend more time pointing along the director than along any other direction. The extent of orientational order can be described by taking the average. A snapshot of the liquid crystal at any instant of time will give the angle made by each molecule with the director at any instant of time. If we consider a representative group of molecules and measure the angles using the snapshot, the average angle gives the measure of orientational order. An average of 00 indicates perfect orientation and can be expected in solids. An average of greater than 450 indicates no orientational order a found in liquids. However, in liquid crystals a smaller average angle with the director is observed which indicates some orientational order (Fig.2).

Fig.2 A snapshot showing the orientation of the molecules in the liquid crystal phase as compared to its solid phase. In the liquid crystal phase, the molecules orient in a preferred direction along the director with an average angle of Ө0. Change in the positional order could be seen.

Classification of liquid crystals: Liquid crystals are classified into two main categories, namely,

1. Thermotropic liquid crystals2. Lyotropic liquid crystals.

1. Thermotropic liquid crystals: The class of compounds that exhibit liquid crystalline behaviour on variation of temperature alone are referred to as thermotropic liquid crystals. The temperature range at which some liquid crystal are stable are given below:

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Solid Liquid crystal LiquidCholesteryl Benzoate 1450 1780

p-Azoxyphenetole 1370 1670

p-Azoxyanisole 1160 1350

2. Lyotropic liquid crystals: Some compounds transform to a liquid crystal phase when mixed with a solvent. They have a lyophilc and a lyobhobic end that is they are amphiphilic compounds. They are usually obtained by mixing the compound in a solvent and increasing the concentration of compound till liquid crystal phase is observed. Such liquid crystals are called lyotropic liquid crystals. The formation of lyotropic mesophases is dependent on the concentration of either the component or the solvent. Variation of temperature also affects the formation of these mesogens. Examples: (i) soap (soap-water mixture) molecules(ii) Phospholipids (biologically important molecules where each cell membrane owes its structure to the liquid crystalline nature of the phospholoipid-water mixture).Lyotropic mesogens are typically obtained from amphilic compounds comprising of both lyophilic (solvent attracting) and lyobhobic (solvent repelling) parts in the same molecule. In the presence of solvent the lyophobic ends come together while the lyophilic ends directed towards water forming micelles. The formation of micelles takes place only beyond a particular concentration of the solution called critical micelle concentration (CMC). When the concentration of the solution is increased (beyond cmc) the micelles increase in size and eventually coalesce to form liquid crystalline phase.

Molecular ordering in liquid crystals (Types of mesophases):(1) Nematic phase: Nematic (Greek nematos = thread like) liquid crystals are formed by compounds that are optically inactive. The molecules have elongated shape and are approximately parallel to one another (Fig.3). Nematic phase is characterized by the total loss of positional order and a near normal flow behaviour similar to its liquid phase.

Fig.3 Nematic liquid crystal

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Examples: (i) p-azoxyanisole (116-1350)

(ii) p-azoxyphenetole (137-1670C)

(iii) Anisaldine (165-1800C)

(iv) p-Methoxycinnamic acid (170-1860C)

(2) Chiral (Twisted) Nematic Phase (Fig.4): Chiral nematic liquid crystals, also referred to as cholesteric liquid crystals or twisted nematic liquid crystals (TNLC), re formed from optically active compounds having chiral centres. Unlike in a nematic phase where all the molecules approximately parallel to one another, in chiral nematic phase, the molecules arrange themselves in such a way that they form a helical structure. In this mesophase, the director is therefore not fixed in space as in space as in a nematic phase, but rotates throught the sample forming a helical pattern as it changes its direction just like the motion of a nut on a screw. The distance traveled by the director as it completes one full turn is called the pitch of the liquid crystal. In other words, the pitch length is the distance traveled by the director when it gets turned by 3600C. The twisted pattern repeats itself throught the liquid crystal phase. The most striking feature of choleteric mesophase is its strong optical activity and selective light reflection, which are attributed to the twisted structure. The twist present in chiral nematic liquid crystal imparts spectacular optical properties which are made used of as thermochromic materials. The pitch is also temperature dependent and hence cholesterics are used in thermography.

Examples: (1) Cholesteryl benzoate (2) Cholesteryl myristate and (3) Cholesteryl formate etc.

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(a) (b)Fig.4(a) Illustration of the twisted structure in a chiral nematic phase of a liquid crystal as shown by the change in the direction of the director. Arrows show the orientation of the molecules. Pitch is shown as the distance traveled for the director to come back to its original direction. (b) A nut moves a certain distance when it makes a full turn (one pitch) and comes back to its original direction is as shown by the arrows.

(3) Smectic mesophase: Substances that form smectic phases are soap-like (in Greek, smectos means soap). In fact, the soft substance that is left at the bottom of a soap dish is a kind of smectic liquid crystal phase. In smectic mesophase, there is a small amount of orientational order and also a small amount of positional order. The molecules tend to point along the director and arrange themselves in layers. A snapshot would reveal that more number of molecules position in regularly spaced planes and a few molecules lie between the planes (Fig.5). That is, any one molecule would spend more time in these planes than between the planes. Based on the orientation of the director there are many types of smectic phases. If the director is perpendicular to the planes it is called smectic A (Fig. 5a) and smectic C if the director makes an angle other than 900 (Fig.5b). In smectic B phase, the director is perpendicular to the plane with the molecules arranging themselves into a network of hexagons within the layer.

(a) (b) Fig.5 Schematic representation of smectic mesophase where molecules lie on regularly spaced planes (in the form of layers). (a) Smectic A where molecules is perpendicular to the layer planes. (b) Smectic C where the molecules are tilted with respect to the layer planes.

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Examples: 4-n-Butyloxybenzylideneamino propiophenone (smecti A)

Terephthalylidene-bis-4-n-butylaniline (smectic B)

4,41-di-n-Heptyloxyazoxybenzene (Smectic C)

Discotic or Columnar Liquid crystalline Phase: Liquid crystals formed by molecules which have disk-like or plate-like structure are referred to as discotic or columnar liquid crystals.

The simplest discotic phase is also called discotic nematic phase because there is orientational order but no positional order (Fig.6a). There is random motion of the molecules, but on an average, the axis perpendicular to the plane of each molecule tends to orient along the director.

In the discotic or columnar phase, in addition to the orientational order present in the nematic discotic phase, most of the molecules tend to position themselves in columns (Fig.6b). The columns are arranged in a hexagonal lattice resembling a set of coins stacked as shown below (note: the coins in a stack have a great deal of positional order i.e., the coins are equidistant whereas the molecules in a columnar phase are stacked in random fashion).

(a) (b)Fig.6 Schematic representation of disc like molecules arranged in (a) Discotic nematic (b) discotic columnar liquid crystal phases

Example: Benzene-hexa-n-alkanoate

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Liquid crystalline behaviour in homologous series: A series of compounds of the same type in which all the members have the

same functional group and molecular formulae of adjacent members differ by CH2

is called a homologous series. The thermal stability of a liquid crystal compound may be altered by altering the molecular structure e.g., by increasing its chain length as in homologues series. PAA (p-azoxyanisole) series: The liquid crystal phase of p-azoxyanisole (PAA) is stable between 1180C and 1350C. PAA has more than 12 homologues which are formed when –CH2 groups are added to its side chain as shown below.

O

OC2H5NNH5C2O 4

.

.

.

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A plot of transition temperatures against number of carbon atoms for PAA is as shown in Fig. 7(a)

(a) (b)Fig.7 Graphical representation of different phases and transition temperatures of the homologous series of (a) p-azoxyanisole (PAA) and (b) p-methoxybenzylidine-p-n-butylaniline (MBBA)

It can be seen from Fig.7(a) that, in general, the transition temperature of the liquid crystal, decreases with the increase in the number of carbon atoms in the side chain. The molecules with even number of carbon atoms generally have higher transition temperature than those having odd number of carbon atoms. When the alkyl group (side chain) contains 1 to 6 carbon atoms, liquid crystals show a nematic phase and when the number of carbon atoms is greater than 6, smectic phase is exhibited. Homologues containing 7 and 8 carbon atoms, however, show a transition from solid to smectic to nematic before melting to a liquid. Molecules with longer alkyl chains exhibit smectic phase.

In PAA series, the alkyl groups are linked to benzene ring through an oxygen atom. In addition, the transition temperature of the PAA series make them unsuitable for display applications.

p-Methoxybenzylidene-p-n-butylaniline (MBBA) series: The structure of which is given below

It may be noted that there is direct linking of alkyl chain to the benzene ring on one side (C4H9) where as the other alkyl (CH3) is linked through oxygen to the benzene ring. The molecules with odd number of carbon atoms generally have higher transition temperature than those having even number of carbon atoms. The transition temperature (21-700C) and various phases of first five homologues of the MBBA obtained by changing the length of the chain that does not contain oxygen (i.e., C4H9) is shown in Fig.7(b).

The members of MBBA series do not exhibit smectic phase. All the members show transition from solid to nematic to isotropic liquid state.

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The transition temperatures of the compounds can thus be altered by changing the length of the flexible side chain at terminal position. Biphenyl and terphenyl systems carrying highly polarizable groups such as nitro and cyano show lower transition temperatures. Such molecules with low transition temperatures have extensive applications in liquid crystal display.

Electro-optic effect of liquid crystals: Nematic liquid crystals have rod like molecular structure and align

themselves spontaneously along the director. Nematic materials have two dielectric constants- one in the direction parallel to the director and the other perpendicular to the director. Dielectric anisotropy (Δε) is defined as the difference between the dielectric constants parallel and perpendicular to the director. Similarly, the optical anisotropy (Δn) is defined as the refractive index parallel to the director minus the refractive index perpendicular to the director. These two properties are important for the electro-optic effects in liquid crystals.

Effect of electric field: The director in a liquid crystal is free to point in any direction. But when a film of liquid crystal is placed between two plates of certain materials, director is forced to point along a particular direction when an electric field is applied. For example, when a film of liquid is placed between two specially treated glass sheets (such as rubbing with a velvet cloth, or applying a thin coat of a polyamide followed by unidirectional rubbing with a roller), the molecules close to the glass surfaces are forced to orient themselves parallel to the surfaces of the glass sheets.

Fig.8 Liquid crystal film kept between two treated glass plates (a) in the field off state (below the threshold value) all molecules and the director orient parallel to the surface (b) in the field on state (above the threshold value) the molecules near the surface orient parallel to the surface whereas in others it is deformed

In the absence of an electric field, (below a threshold value) the molecules at other layers are also aligned parallel to the surfaces giving a homogeneous arrangement. But when an electric field is applied perpendicular to the glass surface, molecules near the surface are aligned parallel to the surface (perpendicular to the applied field). The molecules near the centre of the liquid crystal layer (away from the surface) are free to orient themselves along the applied field. The crystal undergoes deformity (Fig. 8). The deformity begins at a threshold value of the applied field and increases with increase in the strength of the field. This transition (deformity) is important in the operation of liquid crystal

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displays (LCD) because the transition brings about a significant change in the optical characteristics of the liquid crystal.

Effect of light: When light is incident on two crossed polarizers, no light emerges because the light emerging from the first polarizer id completely absorbed by the second polarizer and hence appears dark. When a film of a liquid crystal is placed between two polarizers, only a part of the light from first polarizer is absorbed by the second polarizer some light emerges giving bright appearance. A cell is assembled such that the direction of alignment at the top surface is perpendicular to that at the lower surface of the cell. Then it filled with a twisted nematic liquid crystal (TNLC) having a positive dielectric anisotropy (dielectric constant parallel to the director is higher). Twisted structure acts like a wave-guide and gradually rotates the plane of polarization of light by 900. Hence a linearly polarized light incident on the cell emerges linearly polarized but in the an orthogonal direction resulting in a bright appearance (Fig. 9).

Fig.9 Bright and dark appearance when light is passed through twisted nematic liquid crystal placed between two crossed polarizers (a) appearance is bright in the absence of electric field (b) appearance is dark in the presence of electric field.

The 900 twist in the cell is lost when a sufficiently strong electric field (2-5V) is applied to the cell. Hence the cell appears dark between two crossed polarizers (Fig. 8b). The following conditions, however should be met to see the electro-optic effect.

(i) The plane of polarization of incident light should be parallel or perpendicular at the surface of the cell.

(ii) The product of optical anisotropy, Δn, (the difference in refractive indices parallel and perpendicular to the director) and pitch P should be greater the wavelength of the incident light. Δn × P > λ.

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Applications of liquid crystals in display systems:The electro-optic effect of liquid crystals controls brightness/darkness of

the light emerging from its elements and is used in information displays. Information is passed into the user using the liquid crystals which control the brightness/darkness of the parts of the display. Numeric display has seven segments whereas alphabets are displayed using fourteen-segments. More complex graphic images are formed using pixels (picture elements) which are closely packed array of dots in two dimensions.

A numeric display consists of seven segments for each digit. Light from the area of each of the seven segments of pixels is controlled independently and is used to create any one of the ten digits. When an electric field is applied to a segment, the liquid crystal in that segment undergoes deformation (is activated) and when polarized light is incident, the light is modulated depending on the deformation in that segment. A typical liquid display cell (reflection mode) is shown in Fig.9.

Fig.9. Schematic representation of a liquid crystal display (reflection mode pixel) where the liquid crystal is embedded between two glass plates.

The seven-segment display shown in Fig.10 is used to display numbers in calculators and watches. The top and bottom glass plates of a display have electrode patterns formed by etching a layer of indium tin oxide using standard photolithographic process. All the seven segments in the bottom glass plate are interconnected as shown in Fig. 10a to form a back plane. Connections to the segments a to g are brought out separately on the other glass plate as shown in Fig. 10b. Liquid crystal mixture is filled in the cell formed by sealing the edges of the top and bottom glass plates. Area of intersection between the electrode patterns on the top and bottom glass plates decides the shape of the segments in the display. The distance between the top and bottom glass plate is called cell thickness. It is usually in the range 4 to 8 µm to ensure that display can switched in milliseconds. The quantity of liquid crystal mixture used in a display is small.

Figure 10c shows a 3 digit numeric display. Application of a voltage between the back plane and the corresponding electrode on the top plate turns ON a segment. For example the segment b is turned ON by applying a voltage about 3 volts between the back plane and the electrode b on the top plate. The ac waveforms applied to the back plane, an ON segment and an OFF segment are as shown in Fig.10d.

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Fig.10. Seven segment liquid crystal display used to display numbers in calculatorsDyes used in liquid crystal displays are called dichroic dyes and give

desired colours to the displays with a good contrast. Liquid crystal displays operate at low voltages (a few volts) and consume less power as compared to other display.Uses: a) Watches, calculators, mobile telephones, laptop computer and related electronic gadgets.b) Indicators used in automobile dashboards, airplane cockpits, traffic signals, advertisement boards and petrol pump indicators.c) Blood pressure instruments, digital thermometers and TV channel indicators.d) pH meters, conductometers, colorimeters, potentiometers and other analytical instruments.

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INSTRUMENTAL METHODS OF ANALYSIS

(1) COLORIMETRYThe variation of the color of a solution with change in concentration of

some solute component in the solution forms the basis of colorimetry.

Thoery: When a monochromatic light of intensity I0 is incident on a transparent

medium, a part of light is absorbed by the media (Ia), a part of light is reflected (Ir) and the remaining part of light is transmitted (It), i.e.,

I0 = Ia + Ir + It

For a glass-air interface, Ir is negligibleTherefore I0 = Ia + It

The investigations on the change of absorption of light with thickness of the medium were carried out by Lambert. Beer later applied similar experiments to solutions of different concentrations. Two separate laws governing absorptions are known as Lambert’s law and Beer’s law. In the combined form, they are referred to as Lambert-Beer law.

Lambert’s law:It states that “when monochromatic light passes through a transparent

medium, the rate of decrease in intensity with thickness of the medium is proportional to the intensity of the light”

i.e., - dI/dt = kI ………………………..(1)

Where I is the intensity of the intensity of the incident light, l is the thickness of the medium and k is a proportionality factor.

On rearranging (1), -dI/I= -kdt…………………………(2)

Integrating (2) between the limits, I = I0 when l = 0, and I = It at l ln(I0/It) = kt It = I0e-kt …………………………..(3)

Where I0 is the intensity of the incident light falling upon an absorbing medium of thickness l, It is the intensity of the transmitted light and k is a constant for the absorbing medium. The equation indicates that the intensity of the emitted light decreases exponentially as the thickness of the absorbing medium increases arithmetically.

By changing into common logarithms, we get:It = I0 10-Kt…………………………. (4)

Where, K = k/2.303, and is termed as absorption coefficient.It/I0 = 10-Kt ………………………….(5)

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The ratio It/I0 is the fraction of the fraction of the incident light transmitted by a thickness t of the medium and is termed the transmittance, T. Its reciprocal, It/I0 is the optical density (opacity).

Therefore, Absorbance A = log (I0/It) = Kt………(6)

Beer’s law:It states that “when monochromatic light passes through a solution, the rate

of decrease in intensity with concentration of the light absorbing species is proportional to the intensity of the light.”

i.e. - dI/dc = k1I ………………………..(7).Where ‘c’ is the concentration of the light absorbing species in the solution and k1

is proportionality constant. On rearranging and integrating between the limits, I = I0 at c = 0, and I = It

at c, It = I0 e-kc log (I0/It) = K1c ……………………….(8)

Where K1 = k1/2.303.

Lambert-Beer law:It states that “when monochromatic light passes through a solution, the rate

of decrease in intensity with thickness of the medium is proportional to the intensity of incident radiation as well as to the concentration of the solution.”

i.e., - dI/dt = k I c ……………………….(9)Where I is the intensity of the intensity of the incident light, t is the thickness, c is the concentration of the medium and k is a proportionality factor.

On rearranging and integrating between the limits, I = I0 at l = 0, and I = It

at l, It = I0 e-ktc …………………….(10).It/I0 = e-ktc It/I0 = 10 -Ktc = T………………(11)

T is the transmittance of light absorbing medium.Inversing the above ratio and taking log we get,

log (I0/It) = Ktc = A …………..(12)A is called absorbance (or optical density) of the light absorbing transparent solution. Therefore if absorbance of a series of solutions are plotted versus their concentrations, a straight line passing through origin results (Fig. 1)

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Photoelectric colorimeter:The essential parts of a photoelectric colorimeter are a light source, a light

filter, a container for the solution, a photocell to receive the transmitted light and means for measuring the response of the photocell. The block diagram is shown in Fig.2.

The function of the filters is to isolate any desired spectral region by filtering off the undesired radiations. Optical filters consist of either thin films of gelatin containing different dyes or colored glass. The filter allows radiations of definite wavelength range to pass through it and reach the sample.

Applications: (i) In quantitative analysis: A large numbers of metal ions, anions and

organic compounds can be determined by colorimetry.(ii) Photometric titrations: Colorimetric measurements have also been used

in locating the equivalence point in a titration.(iii) Determination of the composition of a colored complex.

(2) POTENTIOMETRYPotentiometry is an electroanalytical technique in which the amount of a

substance in solution is determined, either directly or indirectly, from measurement of the emf between two electrodes that are dipped into the solution. When a metal M is immersed in a solution containing its own ions, Mn+, the electrode potential is given by Nernst equation.

E = E0 + (2.303RT/nF) log [Mn+]E can be measured by combining the electrode with a reference electrode and measuring the emf of the cell. The concentration can be calculated, provided E0 of the electrode is known.

The procedure of using single measurement of electrode potential to determine the concentration of an ionic species in solution is referred to as direct potentiometry. The electrode, whose potential is dependent upon the concentration of the ion to be determined, is termed as the indicator electrode. The indicator electrode responds to the change in concentration of the analyte species present in the solution, in which it is in contact with. Measurement of pH and measurement

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of ion concentrations using ion selective electrodes are the examples for direct potentiometry. It requires accurate measurement of the emf.

A potentiometer is used to measure the emf of the cell and emf is measure when no current passes through the circuit, i.e., when neither current is drawn from the cell nor it passes through the cell.

Instrumentation:Potentiometer consists of a reference electrode, an indicator electrode and a

potential measuring device. The indicator electrode responds rapidly to the changes in the concentration of the analyte i.e. the solution under study. A simple arrangement of potentiomeytric titration is depicted in Fig.3. A is reference electrode (say saturated calomel electrode, SCE), B is the indicator electrode (say platinum electrode) and C is a mechanical stirrer. The solution to be titrated (to be estimated) is taken in the beaker. A known volume of analyte is taken and its potential is determined. The titrant is added in increments of 1 ml and emf is measure each time. At the approach of equivalence point, the e.m.f. tends to increase rapidly. At this point, small increments, say, 0.1ml of titrant are added. A few readings are taken beyond the end point. Thus the changes in potential at different volumes are recorded.

Fig.3. Potentiometric titration unit

Location of end point: The important factor in a titration is the recognition of the point at which the quantities of the reacting species are present in equivalent amounts- the equivalence point or end point of a titration. In potentiometric titrations, the end point can be fixed by examination of the titration curves, including derivative curves.

The titration curve can be obtained by plotting emf readings obtained with the reference electrode-indicator electrode pair against volume of the titrant added. (Fig. 4)

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Fig.4. Potentiometric titration curve

Over most of the titration ranges, the cell emf varies gradually, but near the end point, the cell emf changes very abruptly as the logarithm of the concentration changes rapidly. The resulting titration curve will be a S-shaped curve as shown in the figure. The end point can be located on the steeply rising portion of the curve, at the point of inflection, the point which corresponds to the maximum rate of change of cell emf per volume of the titrant added. When the curve shows a very clearly marked steep portion, one can give an approximate value of the end point as being mid way along the steep portion of the curve. The end point can be located more precisely by employing derivative methods in which the first derivative curve ( E/ V) against V (Fig. 5a) or second derivative curve ( 2E/

V2) against V (Fig. 5b) are plotted.

Fig.5.Derivative curves for potentiometric titration

The first derivative curve gives a maximum at the point of inflection of the titration curve, i.e., at the end point. In the second derivative curve, is zero at the point of inflection or at the end point.

Applications: (i) Acid base titrations: For an acid base titration, the indicator electrode has to be a pH sensitive or H+ sensitive electrode as it has to respond the change in pH during the titration. Therefore, glass electrode is most commonly used as the indicator electrode. Saturated calomel electrode is generally employed as the reference electrode.

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The accuracy of the method depends upon the magnitude of the change in emf in the neighbourhood of the equivalence point, and this depends upon the concentration and strength of the acid and alkali. The method may be used to titrate a mixture of acids which differ greatly in their strengths.

(ii) Oxidation reduction titrations: Oxidation reduction titration can conveniently be carried out as potentiometric titrations. For example, in the titration of Mohr’s salt solution with potassium dichromate solution, calomel electrode is used as the reference and an inert platinum foil is used to pick up the potential of indicator electrode, which is actually the oxidation reduction electrode involving the redox species present in the solution.

Before the titration is started, the solution contains only ferrous ions in the solution. When a small volume of the dichromate solution is assed, equivalent small quantity of Fe2+ ions are converted into Fe3+ ions. In the process, the Cr6+ ion in dichromate is reduced to Cr3+ ion.

The presence of Fe2+ and Fe3+ ions in the solution gives rise to an oxidation reduction electrode, the potential of which can be picked up by the platinum electrode dipped in the solution (Pt / Fe3+, Fe2+). The electrode potential of the so formed electrode is given by,

E = E0 – 0.0591log {[Fe2+] / [Fe3+]} at 298KThe electrode potential of the indicator electrode depends upon the ratio of

the concentrations of reduced and oxidized species in the solution. As the titration proceeds, the concentration of Fe3+ goes on increasing and that of Fe2+ goes on decreasing. As a result, the ratio in the expression for electrode potential goes on increasing and the increase in the value of the ratio becomes very large near the end point. This results in the large in the electrode potential and in turn, in the measured emf of the cell.

At the equivalence point, all the Fe2+ ions are converted into Fe3+ ions, the Pt / Fe3+, Fe2+ electrode ceases to exist. But addition of a slight excess of dichromate solution introduces Cr6+ ions into the solution, which along with the Cr3+ ions in the solution (formed during the oxidation of Fe2+) form a new oxidation reduction electrode, Pt / Cr6+, Cr3+. This change over of indicator electrode at the end point also contributes to the large increase in potential at the end point, as E0 of the two electrodes differ by a large value. After the end point, therefore it is Pt / Cr6+, Cr3+ acting as the indicator electrode.

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(3) CONDUCTOMETRYIn this method, an alternating voltage is applied across two electrodes

immersed in the same solution. The applied voltage causes a current to flow. The magnitude of current depends on the conductivity of the solution and composition of the sample is deduced from the measurement of the conductivity.

Principle:Electrolytic conductivity: Electrolytic conductivity is a measure of the ability of a solution to carry an electric current. Electrolytic solutions conduct current by the migration of ions under the influence of an electric field. Like a metallic conductor, they obey Ohm’s law,

E = IRWhere, E is the applied potential, I is the current and R is the resistance, which is the measure of the hindrance caused for the flow of current under the potential applied.

The reciprocal of the resistance is called the conductance, C = 1/RIt is expressed in ohm-1, mhos or Siemen (S) in SI units.

The resistance of any conductor is directly proportional to the length and inversely proportional to the area of cross section of the conductor.

R = S (l/a), where S is specific resistance or resistivity of the conductor.

Therefore, conductance, C = 1/R = (1/S).(a/l) = қ. (a/l)

Where, қ is the specific conductance or conductivity of the electrolytic solution. When a = 1and l =1, C = қ Or, specific conductance is the conductance of an electrolyte solution kept between two electrodes of 1m2 cross sectional area at 1 m apart. It is the conductance of a meter cube of the solution. The unit of қ in SI units is S.m-1

In electrolytic solutions, the ion concentration is an important variable. It is usual to relate the electrolyte conductance in terms of equivalent conductance or molar conductance.Equivalent conductivity is defined as the conductance of a solution containing one gram equivalent weight of the electrolyte. Molar conductance is defined as the conductance of a solution containing one mole of an electrolyte.

Instrumentation: Conductometer consists of two platinum electrodes and a conductance

measuring device. The two electrodes have unit area of cross section and are placed unit distance apart. The assembly responds rapidly to the changes in the concentration of the analyte (the solution under study). A simple arrangement of

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conductometric titration is depicted in Fig.6. The solution to be titrated (to be estimated) is taken in the beaker.

Fig.6. conductometric titration unit

Conductometric titrations: Conductometric titration is a method of volumetric analysis based on the change in conductance of the solution, at the equivalence point (or end point) during titration. This method is based on the fact that conductance of an aqueous solution, containing an electrolyte, depends upon, (i) the number of free ions in the solution (concentration of the solution), (ii) the charges on the free ions, and (iii) mobility (or speed) of the ions.

During the course of titration (i.e., addition of one electrolytic solution to that of another), the number of free ions in the solution changes. Not only that, even the identity of the ions also changes. As a result of this, conductance of the solution (contained in cell) also undergoes a change.

Acid-base titrations:(a) Titration of a strong acid (like HCl) with a strong base (like NaOH)(Fig.7): Before base is added, the conductivity of acid solution is high (mainly due to the presence of highly mobile H+ ions). This is represented by point A on the curve. On gradual addition of NaOH from the burette, highly mobile H+ ions (of the acid) are removed by the added OH- ions to form nearly non-conducting water molecules.

Hence, the conductivity of the solution decreases progressively, till the equivalence point B is reached. On further addition of NaOH, the conductivity of the solution will rise along the curve BC (due to the addition of highly mobile OH -

ions to the solution). Thus, the descending branch of the curve (i.e AB) give the conductance of a mixture of an acid and salt, and the ascending branch (i.e., BC) gives the conductance of mixture of salt and excess base. At the minimum point B, there is no excess of either acid or base and hence, it corresponds to the equivalence point.

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(b) Titration of a weak acid (say CH3COOH) and a strong base (like NaOH) (Fig. 7): The titration curve has the form of A1B1C1. Acetic acid (a weak acid) has low conductivity, as represented by A1. As NaOH is added, the poorly conducting acid is converted into highly ionized salt, CH3COONa, and

CH3COOH + NaOH CH3COO-Na+ + H2Oconsequently, the conductivity goes up along A1B1. When the acid is neutralized, further addition of alkali causes a sharp rise in conductance along B1C1 (due to addition of more conducting OH- ions). The intersection of A1B1 and B1C1, therefore, represents the equivalence point.

Fig.7. Conductometric titration curves. (a) ABC-strong acid vs. strong base. (b) A1B1C1-weak acid vs. strong base.

(c) In the titration of a mixture of strong acid (HCl) and a weak acid (CH3COOH) with a strong base (NaOH) (Fig. 8), the conductance decreases upon addition of NaOH to acid mixture (due to highly mobile H+ are removed by the added OH-

ions).This trend continues till all the H+ ions of HCl replaced. Continued addition of NaOH rises the conductance moderately (due to poorly conducting acid is converted into highly ionized salt, CH3COONa). Further addition of NaOH increases the conductance steeply due to the presence of free OH - ions. The titration curves in the graph given depict the location of the equivalence points.

Fig.8.Conductometric titration of mixture of a strong acid and a weak acid with a strong base.

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