Colloidal Materials: Part II

Transcription

1 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 Colloidal Materials: Part II Dr. Pallab Ghosh Associate Professor Department of Chemical Engineering IIT Guwahati, Guwahati India Joint Initiative of IITs and IISc Funded by MHRD 1/18

2 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 Table of Contents Section/Subsection Page No Brownian motion Osmotic pressure Determination of number average molecular weight Donnan equilibrium Optical properties of colloids 12 Exercise 16 Suggested reading 17 Joint Initiative of IITs and IISc Funded by MHRD 2/18

3 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture Brownian motion In 1827, the English botanist Robert Brown observed under a microscope that pollen grains suspended in water had a ceaseless chaotic movement. Pollen grains which had been stored for a century moved in the same way. Colloid particles when examined under an ultramicroscope through light scattering were also found to execute ceaseless random motion. This motion is known as Brownian motion (Fig ). Fig Brownian movement. Even when all possible causes which may lead to motion (such as heat, light, mechanical vibrations and other disturbances) are carefully eliminated, the particles still move about ceaselessly. Therefore, it can be concluded that the Brownian motion is due to the molecular impacts from the medium on all sides of these dispersed particles. Brownian motion becomes less vigorous with the increase in size of the particles. It is a fundamental property of the colloidal systems. Increase in viscosity of the medium can reduce the vigor of the movement. Brownian motion is often cited as an indirect evidence of the existence of the molecules and their incessant thermal motion. At any instant, the numerous impacts suffered by a colloid particle on all sides are not evenly matched. This results in a net displacement. This displacement is, however, random. The random movements result in self-diffusion of the particles in the fluid. The works of Albert Einstein and Marian Smoluchowski about a Joint Initiative of IITs and IISc Funded by MHRD 3/18

4 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 century ago have formed the basis of the theory of Brownian motion. They derived a relationship between the distance moved by a particle (as a result of Brownian motion) and its diffusion coefficient D by treating Brownian movement as a random-walk process. They obtained, 2 x 2Dt (1.3.1) where 2 x is the mean square displacement of the particle during a period t. Equation (1.3.1) is known as EinsteinSmoluchowski equation. This equation provides us with a means to calculate the diffusion coefficient of colloid particles which can be viewed under a microscope. The actual displacement of a particle in time t is measured by a microscope. From a large number of observations, the mean square displacement is calculated statistically. The diffusion coefficient of a spherical dispersed particle can be related to its diameter (d) and the viscosity of the liquid () as, RT D (1.3.2) 3πμNAd where R is gas constant, N A is Avogadro s number and T is temperature. Equation (1.3.2) is known as StokesEinstein equation. This equation has been found to be quite successful for describing the diffusion of large spherical molecules. Example 1.3.1: The diffusion coefficient of a colloid particle in water at 293 K is m 2 /s. Estimate its diffusion coefficient in ethylene glycol at 313 K. Given: viscosity of ethylene glycol at 313 K is 12.5 mpa s. Solution: From StokesEinstein equation, D T μ. Therefore, we can write, 3 D2 T2 μ D T μ D m 2 /s Joint Initiative of IITs and IISc Funded by MHRD 4/18

5 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 Equation (1.3.2) can be used to determine the value of Avogadro s number. In 1908, Jean Perrin and his collaborators performed studies with monodisperse spheres of natural colloids (e.g., gamboge). The mean square displacement was measured as follows. The particles of the dispersion were focused under a microscope, which carried the design of a previously-calibrated square paper within its eye-piece. The Brownian displacement along the x-axis was read by noting its position on the square design. A large number of observations were made on a single particle, noting its displacement at every 30 s interval. This was repeated for a large number of particles. The magnitude of determined. 2 x in 30 s was thus The value of Avogadro s number obtained by Perrin and collaborators varied between mol and 8 10 mol. Later, Theodor Svedberg studied monodispersed gold sols of known particle size in ultramicroscope and obtained N A mol. These results are considered as strong evidences in favor of the kinetic theory Osmotic pressure French physicist Jean Antoine Nollet discovered in 1748 that when alcohol and water were separated by a pig s bladder membrane, the water passed through the membrane into the alcohol, causing an increase of pressure. However, the alcohol was not able to pass out into the water. This happened because the bladder was semipermeable. It allowed the water to pass through it, but the alcohol was not allowed to pass. The phenomenon of transport of a solvent through a semipermeable membrane from the solvent to a solution, or from a dilute solution to a concentrated solution is known as osmosis. In biology, there are many instances of semipermeable Joint Initiative of IITs and IISc Funded by MHRD 5/18

6 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 membrane, e.g., inner walls of egg-shells, potato-skin, and intestinal walls of some animals. To demonstrate the origin of osmotic pressure, let us perform a thought experiment in the setup shown in Fig Fig Osmosis and osmotic pressure. A semipermeable membrane is placed at the center of the U-tube as shown in the figure. The right part of the tube is filled with a solution and the left part is filled with the pure solvent. In absence of any external field (e.g., electric field) the solvent spontaneously passes through the membrane into the solution (i.e., osmosis). The transport of the solvent into the solution can be counteracted by applying a pressure π o on the solution. This excess pressure on the solution which would just prevent osmosis is called the osmotic pressure of the solution. Therefore, the osmotic pressure of a solution is the pressure required to prevent osmosis when the solution is separated from the pure solvent by a semipermeable membrane. If the pressure on the solution side is greater than π o, the solvent will flow in the reverse direction (i.e., from the solution to the solvent). In this case, the semipermeable membrane functions like a filter that separates the solvent from the solution. This process is known as reverse osmosis, which has large-scale Joint Initiative of IITs and IISc Funded by MHRD 6/18

7 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 industrial applications (e.g., desalination, concentration of fruit juice, and removal of pollutants from water). It is important, however, to note that the concept of osmotic pressure is more general than that discussed above. In fact, one does not have to invoke the presence of a membrane to define osmotic pressure. The osmotic pressure is a property of the solution. For example, in electrostatic double layer (Lecture 4, Module 1), the concentration of the counterions in the vicinity of the surface is larger than their concentration in the bulk solution. This difference in concentration generates osmotic pressure, which maintains the double layer. The van t Hoff s law of osmotic pressure is: πo crt, where c is the concentration of the solute in the solution, R is gas constant and T is temperature. This relationship is very similar to the ideal gas law. Therefore, van t Hoff stated that the osmotic pressure of a solution is the same as the solute would exert if it existed as a gas in the same volume as that occupied by the solution at the same temperature. It was also found by van t Hoff that the dilute aqueous solutions of electrolytes such as NaCl showed considerable departure from the above law. The observed osmotic pressure of salt solutions was found to be much higher than that predicted from the equation: πo crt. To account for this deviation from ideality, van t Hoff introduced a factor i, which is defined as the ratio of the observed and ideal osmotic pressures. Therefore, the modified van t Hoff s law is: πo icrt. The origin of van t Hoff factor greater than unity is the dissociation of the electrolyte in solution. In dilute solution, the dissociation is almost complete. Thus, one NaCl molecule generates two ions in a dilute solution and the value of i approaches 2. Similarly, for H 2 SO 4, the value of i approaches 3 in dilute solution. The osmotic pressure of a non-electrolyte solution may be represented as, Joint Initiative of IITs and IISc Funded by MHRD 7/18

8 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 RT 2 3 πo cbc Cc (1.3.3) M where c is the concentration, M is the molecular weight of the solute, and B and C are constants related to the second and third virial coefficients, respectively. In dilute solutions (small c), we can drop the terms beyond the second term on the right side of Eq. (1.3.3). Therefore, o RT Bc (1.3.4) c M When o c is plotted against c, a straight line is obtained. From the slope and intercept, we can calculate B and M Determination of number average molecular weight The colloid dispersions are usually polydispersed. For such a system, the average molecular weight can be determined by osmometry. Let us assume that the dispersion behaves ideally. If the experimentally observed values of concentration exp and osmotic pressure are c exp and o, respectively, then, exp o cexp RT (1.3.5) M where M is the average molecular weight. For each of the molecular weight fractions (e.g., the j th fraction) we have, oj cj RT (1.3.6) M j The experimental osmotic pressure is the sum of the pressures exerted by each of the fractions, i.e., exp o oj (1.3.7) Also, the experimental concentration is the sum of the concentrations of the fractions, i.e., cexp cj (1.3.8) Therefore, from Eqs. (1.3.5)(1.3.8) we get, Joint Initiative of IITs and IISc Funded by MHRD 8/18

9 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 M c j (1.3.9) cj M j The concentration, c j, is defined as, nm j j c j (1.3.10) Vd From Eqs. (1.3.9) and (1.3.10) we obtain, nm j j M (1.3.11) n j Therefore, the average molecular weight determined from osmometry is the number-average molecular weight. Example 1.3.2: The variation of osmotic pressure with the concentration of nitrocellulose in methanol is given below. c (kg/m 3 ) o (mol/kg) RTc Determine the molecular weight of nitrocellulose from these data. Solution: From Eq. (1.3.4) we can write, o 1 B c RTc M RT The given data are plotted as shown in Fig Joint Initiative of IITs and IISc Funded by MHRD 9/18

10 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 Fig Plot of RTc o versus concentration. 1 Intercept mol/kg M M kg/mol Donnan equilibrium Sometimes the molecular weight determined by osmometry of a colloid containing macroion is found to be significantly lower than that obtained by other methods. Since the macroion cannot pass through the membrane, its counterion(s) also do not pass through the membrane to maintain the electroneutrality of the solution. Osmotic pressure depends upon the number of solute particles. For a molecule that dissociates as Na + and I, the osmotic pressure is associated with two + particles. If the colloidal electrolyte were Az I z, the osmotic pressure would be associated with z 1 particles. The observed molecular weight from osmometric measurement is the number average molecular weight of the macroion and the ions dissociated from it. So, if we do not consider the presence of the counterions, the molecular weight calculated from Eq. (1.3.4) would be lower than the actual molecular weight. It has been observed that the osmotic pressure of the solution of a substance containing the membrane-impermeable macroion is lowered if the other side of the membrane contains the solution of a salt that has the same counterion as that of the macroion. The reason for this behavior was explained by Irish chemist Joint Initiative of IITs and IISc Funded by MHRD 10/18

11 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 Frederick Donnan in Suppose that the charge of the macroion, I z, is balanced by Na + ions. When the solution of I z is kept separated from a NaCl solution by a semipermeable membrane, it is expected that only the Na + and Cl ions would diffuse through the membrane because the membrane acts as an impermeable barrier towards I z. This perturbs the concentration distributions of the small ions and gives rise to an ionic equilibrium which is different from the equilibrium that would result if I z were absent. The resulting equilibrium is known as Donnan equilibrium. This equilibrium is very important for the biological membranes. Suppose that a semipermeable membrane separates an aqueous NaCl solution from an aqueous solution of an organic salt, Na I (Fig ). All ions except I are permeable through the membrane. Both NaI and NaCl are fully dissociated in the solutions. It can be easily shown [see Ghosh (2009)] that the ratio of the obs observed osmotic pressure o to the true osmotic pressure o is given by, obs o o c1 c2 c1 2c2 (1.3.12) Fig Partitioning of ions by membrane in presence of membrane impermeable ion. Joint Initiative of IITs and IISc Funded by MHRD 11/18

12 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 obs obs If c1 c2, o o 1. On the other hand, if c2 c1, then o o 12. If c1 c2, it is easy to see that o obs o 23. Therefore, due to the unequal distribution, addition of an electrolyte with common counterion will reduce the observed osmotic pressure of the salt which is completely dissociated in the solution, but contains a non-permeating ion. Thus, a large amount of salt can swamp out the effect associated with the macroion Optical properties of colloids When a beam of light falls on a colloid dispersion, some of the light may be absorbed, some part may be scattered, and the remaining part is transmitted undisturbed through the sample. If light of certain wavelengths is selectively absorbed by the particles, the dispersion appears to be colored. The wavelength of visible light lies between 400 nm (violet) and 700 nm (red). That is the reason why a gold sol is red when the particles are very fine, but the sol is blue when the dispersed particles are bigger. When light impinges on matter, the electric field of the light induces an oscillating polarization of the electrons in the molecules. The molecules then serve as secondary sources of light, and subsequently radiate light. The shifts in frequency, angular distribution, polarization, and the intensity of the scattered light are determined by the size, shape and molecular interactions in the scattering material. The most ubiquitous manifestation of light-scattering is observed when a beam of light passes through a dark room. The air-borne dust particles are responsible for this scattering. When a strong narrow beam is allowed to pass through a colloid system placed against a dark background, bright specks or flashes of light can be observed against the darkness when viewed from above through a microscope. The specks of light change continuously in the dark field. This proves the heterogeneous nature of the colloid dispersions, light-scattering ability of the colloid particles, and their continuous motion. This effect is known as Tyndall effect (named after the Irish physicist John Tyndall). The scattered beam is polarized, and its Joint Initiative of IITs and IISc Funded by MHRD 12/18

13 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 intensity depends upon factors such as the position of the observer, properties of the system, and the wavelength of light. Quantitave studies of Tyndall effect and other optical properties of colloid dispersions have become possible after the development of ultramicroscope. Particles smaller than about 200 nm cannot be seen directly in ordinary microscopes. However, these particles can scatter light which is visible in the ultramicroscope. The presence of particles as small as 5 10 nm can be discerned by ultramicroscope. A narrow beam of parallel or slightly convergent light (from a powerful source such as an arc-lamp) is passed at right angles to the direction of the microscope through a cell on which the instrument is focused. If no particle is present in the cell, the field will appear completely dark. On the other hand, if the cell contains a colloidal dispersion, the particles will scatter light, some of which will pass vertically into the microscope. Each particle will appear as a small disc of light on a dark background. A schematic of slit ultramicroscope is shown in Fig Fig Slit ultramicroscope. The light-scattering by colloid particles can be divided into three categories. Rayleigh scattering: In Rayleigh scattering, the particles are small so that they can act as point sources of scattered light. The size of the particles is much smaller than the wavelength of light. Debye scattering: In Debye scattering, the particles are relatively large, however, the refractive indices of the dispersed phase and the dispersion medium are similar. Joint Initiative of IITs and IISc Funded by MHRD 13/18

14 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 Mie scattering: In Mie scattering, the particles are relatively large (diameter/wavelength ratio is close to unity), and the refractive index of the dispersed phase is significantly different from the dispersion medium. Rayleigh developed the light-scattering theory by applying the electromagnetic theory of light to the scattering by small, non-absorbing spherical particles in a gaseous medium. According to the Rayleigh theory, when an electromagnetic wave falls on a small particle, oscillating dipoles are induced in the particle. The particle then serves as a secondary source for the emission of scattered radiation of the same wavelength as the incident light. According to the Rayleigh theory, the scattering intensity is inversely proportional to the fourth power of the wavelength. Therefore, blue light is scattered more than red light. If the incident light is white, a colloid will appear to be blue if viewed at right angles to the incident beam, and red when viewed from end-on. This phenomenon is responsible for the blue color of the sky and the yellowish-red color of the rising and setting sun. Some colloidal dispersions show very interesting light-scattering phenomena. For example, Fig shows the Lycurgus Cup (in the British Museum) made of ruby glass. Fig The Lycurgus Cup (source: F. E. Wagner et al., Nature, 407, 691, 2000; reproduced by permission from Macmillan Publishers, 2000). This cup dates from the Roman times. The glass appears green in daylight (reflected light), but looks red when light is transmitted from the inside of the Joint Initiative of IITs and IISc Funded by MHRD 14/18

15 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 vessel. The red color of gold-ruby glass is caused by small particles of metallic gold, which form when the gold-containing colorless glass is annealed. Modern gold-ruby glass is usually made by adding gold to the raw materials as a solution of tetrachloroauric acid or potassium dicyanoaurate. At about 1400 C, the gold disperses in the melt, and the glass remains colorless after rapid cooling to ambient temperature. Upon annealing between about C, the red color appears as a result of the nucleation and growth of small metallic gold particles. The optimum size for yielding a strong ruby color is 5 60 nm. Colloidal dispersions sometimes appear turbid due to the scattering of light. Solutions of some macromolecular materials may appear to be clear, but actually they are slightly turbid due to weak scattering of light. When light is incident on a perfectly homogeneous system, there is no scattering. Pure liquids, dust-free gases and true solutions can approach this limit of no-scattering. The turbidity of a material is defined by the expression, I I0 exp l (1.3.13) where I 0 is the intensity of the incident light beam, I is the intensity of the transmitted light beam, l is the length of the sample and is the turbidity. Equation (1.3.13) is valid for a non-absorbing system. The LambertBeer law describes the intensity of the transmitted light when only absorption takes place, but no scattering. I I0 exp al (1.3.14) where a is the absorbance of the material. In a system where both absorption and scattering are important, the following composite formula applies. I I0 exp a l (1.3.15) The experimental value of extinction is the sum of a and. Joint Initiative of IITs and IISc Funded by MHRD 15/18

16 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 Exercise Exercise 1.3.1: The variation of osmotic pressure of a polystyrene solution in toluene with its concentration at 298 K is given below. c (kg/m 3 ) o (cm of toluene) Determine the molecular weight of the polymer from these data. Given: density of toluene at 298 K = 860 kg/m 3. Exercise 1.3.2: Calculate the diffusion coefficient of a colloid particle of 5 nm diameter in benzene at 300 K. What would be its mean square displacement based on Brownian movement after 60 s? Estimate the diffusion coefficient of the particle at 310 K. Given: viscosity of benzene at 300 K is 0.6 mpa s, and the same at 310 K is 0.5 mpa s. Exercise 1.3.3: Answer the following questions. a. What is Brownian movement? What type of particles exhibit such movement? b. Explain EinsteinSmoluchowski equation. c. How does the diffusion coefficient of a colloid particle depend upon the viscosity of the liquid according to StokesEinstein equation? d. Explain how you would determine Avogadro s number from Brownian motion. e. What is the origin of osmotic pressure? What is reverse osmosis? f. Explain how you will determine the molecular weight of a macromolecular colloid from osmotic pressure measurements. g. What is number-average molecular weight? h. Explain Donnan equilibrium. i. What is the difference between Rayleigh scattering and Mie scattering? j. What type of light scattering would you expect in pure liquid or air? k. What is Tyndall effect? Joint Initiative of IITs and IISc Funded by MHRD 16/18

17 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 l. Explain the main features of ultramicroscope. m. Explain why the blue light is more scattered than the red light. n. Explain how the molecular weight of a macromolecule is related to the turbidity of its solution. Joint Initiative of IITs and IISc Funded by MHRD 17/18

18 NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 3 Suggested reading Textbooks D. J. Shaw, Introduction to Colloid and Surface Chemistry, Butterworth- Heinemann, Oxford, 1992, Chapter 2. P. C. Hiemenz and R. Rajagopalan, Principles of Colloid and Surface Chemistry, Marcel Dekker, New York, 1997, Chapters 2, 3 & 5. P. Ghosh, Colloid and Interface Science, PHI Learning, New Delhi, 2009, Chapter 2. Reference books D. F. Evans and H. Wennerström, The Colloidal Domain: Where Physics, Chemistry, Biology, and Technology Meet, Wiley-VCH, New York, 1994, Chapter 1. G. J. M. Koper, An Introduction to Interfacial Engineering, VSSD, Delft, 2009, Chapter 1. R. J. Hunter, Foundations of Colloid Science, Oxford University Press, New York, 2005, Chapter 1. Journal articles F. E. Wagner, S. Haslbeck, L. Stievano, S. Calogero, Q. A. Pankhurst, and K. -P. Martinek, Nature, 407, 691 (2000). F. G. Donnan, J. Membr. Sci., 100, 45 (1995). Joint Initiative of IITs and IISc Funded by MHRD 18/18