Lecture 4 - Surface chemistry Surface and colloid Chemistry PDF

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Surface and colloid Chemistry is a core unit at the undergraduate level for students pursuing chemistry related courses. The unit is aimed at introducing the learners to the various concepts and understanding of the mechanisms of surface reactions. This unit will help the learner to comprehend the c...

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NPTEL  Chemical Engineering  Interfacial Engineering

Module 1: Lecture 4

Colloidal Materials: Part III

Dr. Pallab Ghosh Associate Professor Department of Chemical Engineering IIT Guwahati, Guwahati–781039 India

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Module 1: Lecture 4

Table of Contents

Section/Subsection 1.4.1 Determination of molecular weight by light scattering 1.4.2 Experimental characterization of colloids

Page No. 3 6–9

1.4.2.1 Transmission electron microscopy

6

1.4.2.2 Scanning electron microscopy

7

1.4.2.3 Dynamic light scattering

8

1.4.2.4 Small-angle neutron scattering

8

1.4.3 Electrical properties of colloids

10–19

1.4.3.1 Electrostatic double layer

10

1.4.3.2 Electrokinetic phenomena

12

1.4.3.2.1 Zeta potential

14

1.4.3.2.2 Reciprocal relationship

19

Exercise

20

Suggested reading

22

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1.4.1 Determination of molecular weight by light scattering In liquid dispersions, the scattering of light is due to fluctuations in the solvent density and fluctuations in the particle concentration. The total intensity of the scattered light in all directions is given by,  I s  I0   0



is  2  2 r sin  d I0 



(1.4.1)

The second term inside the integral in Eq. (1.4.1) represents an area on the surface of a sphere, where r is the radius of the sphere and is the angle with the horizontal axis. From the theory of Rayleigh scattering in a solution, the quantity i s I 0 can be determined as shown below. The Rayleigh scattering equation for a solution (at constant temperature) is expressed by, 2

is  I0

2 2

  dnr   nr  dc   kTc    1 cos2   d  r2 4  o   dc 





(1.4.2)

where is is the intensity of the light scattered per unit volume of solution. The gradient of refractive index of the solution n r, is given by dn r dc . The osmotic pressure is given by, c B 2   c    Bc2  , c   RT  M RT M    

  o  RT 

B

B RT

(1.4.3)

Where M is the molecular weight of the solute, c is the concentration, andB is the second virial coefficient. Therefore, the osmotic pressure gradient is given by,

d o  1   RT   2Bc  dc M 

(1.4.4)

From Eq. (1.4.2), we can write,





Kc 1 cos2  is  I 0 r2  1 M  2Bc

(1.4.5)

The quantity K is a constant, which is given by,

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  dn 2  2 2  nr  r     dc   K N A 4

(1.4.6)

From Eqs. (1.4.1) and (1.4.6) we obtain,





2   Is   2 Kc 1  cos  sin  d     I0 0  1 M  2 Bc  





(1.4.7)



The value of the integral:  sin  1  cos2  d is 8 3 . Therefore, Eq. (1.4.7) becomes, 0

Is Hc 16 Kc   I0 3 1 M  2Bc  1 M  2Bc

(1.4.8)

where H   16 K 3 is a constant. It is related to the refractive index, its gradient and

the wavelength of light in the medium by the following equation. H

32 3nr2  dnr dc 

2

(1.4.9)

3N A  4

where  is the wavelength of light in the solution and N A is Avogadro’s number. The quantity I s I 0 is the turbidity,  . Therefore, from Eq. (1.4.8) we have,

Hc





1  2Bc M

(1.4.10)

Equation (1.4.10) is known as Debye equation. It predicts that the plot ofHc  versus c should be a straight line. From the intercept, the molecular weightM can be determined. Example 1.4.1: The variation of Hc  with concentration for a polymeric colloid in

benzene is given below. c (kg/m3)

2.5

4.0

6.5

8.0

10.0

 Hc   103 (mol/kg)

5.6

6.1

6.6

7.2

8.0

From these data, calculate the molecular weight of the polymer.

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Solution: The plot of H c  vs. c is shown in the following figure. The data were fitted by a straight line, as shown in Fig. 1.4.1.

Fig. 1.4.1 Variation of H c  with concentration. The intercept is, 1  0.0048 mol/kg M 

M  208.333 kg/mol

If the system is polydispersed, Eq. (1.4.10) is applicable for each molecular weight fraction. For dilute solutions, we can neglect the second term on the right side of Eq. (1.4.10). For the jth fraction, we can write,

Hc j





j

1 Mj

(1.4.11)

The experimentally measured concentration, turbidity and the average molecular weight are correlated by Equation (1.4.11) as, Hc exp

1 M

(1.4.12)

cexp   c j

(1.4.13)

 exp



where,

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 exp    j

(1.4.14)

From Eqs. (1.4.11)–(1.4.14), we obtain, M

 exp Hcexp



 j H  cj



H  cj M j H  cj



 cj M j  cj

(1.4.15)

Since c j  n j M j Vd , we have, 2

M 

n jM j  n jM j

(1.4.16)

This average molecular weight (i.e., M ) is known as the weight-average molecular

weight.

1.4.2 Experimental characterization of colloids  Colloids are characterized by various methods. Some of these are, transmission electron microscopy (TEM), scanning electron microscopy (SEM), dynamic light scattering (DLS), and small-angle neutron scattering (SANS). Depending on the properties of the colloidal matter, the appropriate characterization method is selected.

1.4.2.1 Transmission electron microcopy

 Many colloid particles are too small to be viewed in an optical microscope. The numerical aperture of an optical microscope is generally less than unity, which can be increased up to 1.5 with oil-immersion objectives. Therefore, for light of wavelength 600 nm, the resolution limit is of the order of 200 nm.

 To increase the resolving power of a microscope so that colloidal dimensions can be directly observed, the wavelength of the radiation must be reduced considerably below that of visible light. Electron beams can be produced which have wavelengths of the order of 0.01 nm. These are focused by electric or magnetic fields, which act as the equivalent of lenses. A resolution of the order of 0.2 nm can be attained after smoothing the noise. Single atoms appear to be

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blurred irrespective of the resolution, owing to the rapid fluctuation of their location.

 The TEM can be used for measuring particle size between 1 nm and 5 m. Due to the complexity of calculating the degree of magnification directly, calibration is done using pre-characterized polystyrene latex particles.

 The use of electron microscopy for studying colloid systems is limited by the fact that electrons can travel without any hindrance only in high vacuum. Therefore, the samples need to be dried before observation.

 A small amount of the sample is deposited on an electron-transparent plastic or carbon film (10–20 nm thick) supported on a fine copper mesh grid. The sample scatters electrons out of the field of view, and the final image can be viewed on a fluorescent screen. The amount of scattering depends on the thickness and the atomic number of the atoms of the sample.

 The organic materials are relatively transparent for electrons whereas, the heavy metals make ideal samples. To enhance contrast and obtain three-dimensional effect, various techniques (e.g., shadow-casting) are generally employed.

1.4.2.2 Scanning electron microcopy

 In scanning electron microscopy, a fine beam of medium-energy electrons scans across the sample in a series of parallel tracks. These electrons interact with the sample to produce various types of signals such as secondary electron emission, back-scattered-electrons, cathodoluminescence and X-rays. These are detected, displayed on a fluorescence screen and photographed.

 In the secondary-electron-emission mode, the particles appear to be diffusely illuminated. Their size can be measured and the aggregation behavior can be studied.

 In the back-scattered-electron mode, the particles appear to be illuminated from a point source, and the resulting shadows can provide good impressions of height.

 The resolution limit in SEM is about 5 nm, and the magnification achieved is generally less than that in a TEM. However, the depth of focus is large, which is

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important for studying the contours of solid surfaces, particle shape and orientation.

1.4.2.3 Dynamic light scattering

 If the light is coherent and monochromatic (e.g., a laser), it is possible to observe time-dependent fluctuations in the scattered intensity using a suitable detector such as a photomultiplier capable of operating in photon-counting mode.

 These fluctuations arise because the particles are small, and they undergo Brownian movement. The distance between them varies continuously. Constructive and destructive interference of light scattered by the neighboring particles within the illuminated zone gives rise to the intensity fluctuation at the detector plane.

 From the analysis of the time-dependence of the intensity fluctuation, it is possible to determine the diffusion coefficient of the particles. Then, by using the StokesEinstein equation (see Lecture 3, Module 1), the hydrodynamic radius of the particles can be determined.

 An accurately known temperature is necessary for DLS because knowledge of the viscosity is required (because the viscosity of a liquid is related to its temperature). The temperature also needs to be stable, otherwise convection currents in the sample will cause non-random movements that will ruin the correct interpretation of size.

 Dynamic light scattering is also known as photon correlation spectroscopy (PCS) or quasi-elastic light scattering (QELS). It is a well-established technique for the measurement of the size distribution of proteins, polymers, micelles, carbohydrates,

nanoparticles,

colloidal

dispersions,

emulsions

and

microemulsions.

1.4.2.4 Small-angle neutron scattering

 Neutrons from reactors or accelerators are slowed down in a moderator to kinetic energies corresponding to room temperature or less. The wavelength probed by SANS is quite different from the visible light. A typical range of wavelength is Joint Initiative of IITs and IISc  Funded by MHRD

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0.33 nm. This range is much smaller than that of visible light (i.e., 400700 nm).

 The usefulness of SANS to colloid and polymer science becomes evident when one considers the length scales and energy involved in neutron radiation. Light scattering is indispensable for studying particles having size in the micrometer range. For very small particles, neutrons are useful. The energy of a neutron with 0.1 nm wavelength is 1.3 10 20 J. Due to such low energy, neutron scattering is useful for sensitive materials. For colloidal dispersions, where the distance between the particles is large, the scattering angle is small (~ 20rad or less).

 Light and X-rays are both scattered by the electrons surrounding atomic nuclei, but neutrons are scattered by the nucleus itself. There is, however, no systematic variation of the interaction with the atomic number. The isotopes of the same element can show significant difference in scattering. For example, neutrons can differentiate between hydrogen and deuterium. This has useful applications in biological science in the technique known as contrast matching.

 The interaction of neutrons with most substances is weak, and the absorption of neutrons by most materials is very small. Neutron radiation, therefore, can be very penetrating.

 Neutrons can be used to study the bulk properties of samples with path-length of several centimeters. They can also be used to study samples with somewhat shorter path-lengths but contained inside an apparatus (e.g., cryostat, furnace, pressure cell or shear apparatus).

 The SANS technique provides valuable information over a wide variety of scientific and technological applications such as chemical aggregation, defects in materials, surfactant assemblies, polymers, proteins, biological membranes, and viruses.

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1.4.3 Electrical properties of colloids  The electrical properties of colloidal materials lead to some of the most important phenomena in interfacial engineering. The presence of electrostatic double layer surrounding the particles results in their mutual repulsion so that they do not approach each other closely enough to coagulate. An increase in the size of the particles by coagulation would lead to a decrease of total area, and hence to a decrease of free energy of the system. Therefore, union of colloid particles would be expected to occur, were it not for the repulsion caused by the electrostatic double layer. The stability of the charged colloid particles depends on the presence of electrolytes in the dispersion.

1.4.3.1 Electrostatic double layer

 Let us consider a solidliquid interface. Suppose that the interface is positively charged and the atmosphere of the negatively charged counterions is around it. This visualization of the ionic atmosphere near a charged interface originated the term electrostatic double layer.

 The Coulomb attraction by the charged surface groups pulls the counterions back towards the surface, but the osmotic pressure forces the counterions away from the interface. This results in a diffuse double layer.

 The double layer very near to the interface is divided into two parts: the Stern layer and the GouyChapman diffuse layer. The compact layer of adsorbed ions is known as Stern layer. This layer has a very small thickness (say, 1 nm). The counterions specifically adsorb on the interface in the inner part of the Stern layer, which is known as inner Helmholtz plane (IHP) (see Fig. 1.4.2). The potential drop in this layer is quite sharp, and it depends on the occupancy of the ions.

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Fig. 1.4.2 Electrostatic double layer.

 The outer Helmholtz plane (OHP) is located on the plane of the centers of the next layer of non-specifically adsorbed ions. These two parts of the Stern layer are named so because the Helmholtz condenser model was used as a first approximation of the double layer very close to the interface.

 The diffuse layer begins at the OHP. The potential drop in each of the two layers is assumed to be linear. The dielectric constant of water inside the Stern layer is believed to be much lower (e.g., one-tenth) than its value in the bulk. The value is lowest near the IHP.

 The diffuse part of the electrostatic double layer is known as Gouy Chapman layer. The thickness of the diffuse layer is known as Debye length (represented by 1  ). This length indicates the distance from the OHP into the solution up to the

point where the effect of the surface is felt by the ions.  is known as

Debye Hückel parameter. The Debye length is highly influenced by the concentration of electrolyte in the solution. The extent of the double layer decreases with increase in electrolyte concentration due to the shielding of charge Joint Initiative of IITs and IISc  Funded by MHRD

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at the solidsolution interface. The ions of higher valence are more effective in screening the charge.

1.4.3.2 Electrokinetic phenomena

 The phenomena associated with the movement of charged particles through a continuous medium, or with the movement of a continuous medium over a charged surface are known as electrokinetic phenomena. There are four major types of electrokinetic phenomena, viz. electrophoresis, electroosmosis, streaming potential and sedimentation potential. There is a common origin for all the electrokinetic phenomena, i.e., the electrostatic double layer.

 Electrophoresis refers to the movement of particles relative to a stationary liquid under the influence of an applied electric field. If a dispersion of positively charged particles is subjected to an electric field, the particles move towards the cathode.

Electrophoresis

phenomenon.

Three

is

types

perhaps of

the

most

electrophoresis

important are

usually

electrokinetic used,

viz.

microelectrophoresis, moving-boundary electrophoresis and zone electrophoresis. Electrophoresis is widely used in biochemical analysis for separation of proteins. Another very important application of electrophoresis is electrodeposition. A cylindrical microelectrophoresis cell for studying the movement of air bubbles under electric field is shown in the Fig. 1.4.3.

Fig. 1.4.3 Setup for microelectrophoresis (source: A. Phianmongkhol and J. Varley, J. Coll. Int. Sci., 260, 332, 2003; reproduced by permission from Elsevier Ltd.,  2003). Joint Initiative of IITs and IISc  Funded by MHRD

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 Electroosmosis refers to the movement of the liquid of an electrolyte solution past a charged surface (e.g., a capillary tube or a porous plug) under the influence of an...