Particle Size Determinations: Dynamic Light Scattering: page 161 text

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1 Particle Size Determinations: Dynamic Light Scattering: page 161 text Dynamic light scattering (also known as Photon Correlation Spectroscopy or Quasi- Elastic Light Scattering) is a technique which can be used to determine the size distribution profile of small particles in solution Why is the light from the sky blue? The sky changes colour because of scattering Scattering is a complicated process but is dependent on The wavelength of the radiation 10-1

2 Sunsets When the air is clear the sunset will appear yellow, because the light from the sun has passed a long distance through air and some of the blue light has been scattered away. 10-2

3 DYNAMIC LIGHT SCATTERING When a beam of light passes through a colloidal dispersion, the particles or droplets scatter some of the light in all directions. When the particles are very small compared with the wavelength of the light, the intensity of the scattered light is uniform in all directions (Rayleigh scattering); for larger particles (above approximately 250nm diameter), the intensity is angle dependent (Mie scattering). If the light is coherent and monochromatic, as from a laser for example, it is possible to observe time-dependent fluctuations in the scattered intensity using suitable detector Commercial instrument Jobin Yvon The LB-550 measures particle size from 1nm to 6µm and a concentration range from ppm up to 40% solids, all in as little as 30 seconds, making it ideally suited to a wide range of applications. 10-3

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5 Brownian Motion DLS measures Brownian motion and relates this to the size of the particles. Brownian motion is the random movement of particles due to the bombardment by the solvent molecules that surround them. The velocity of the Brownian motion is defined by a property known as the translational diffusion coefficient (usually given the symbol, D). The size of a particle is calculated from the translational diffusion coefficient r = kt/6d0b 0: viscosity D: diffusion coefficient r: Van der Waals radius: see your CHEM 2060 lecture notes 10-5

6 The observed signal depends on the phase addition of the scattered light falling on the detector. In example A, two beams interfere and cancel each other out resulting in a decreased intensity detected. In example B, two beams interfere and enhance each other resulting in an increased intensity detected. See lab experiment 10-6

7 Surface Area and Porosity BET Method BET theory covers adsorption molecules on a surface. It is the basis for an important analysis technique for the measurement of the specific surface area of a material. In 1938, Stephen Brunauer, Paul Hugh Emmett, and Edward Teller published an article about their theory in a BET consists of the first initials of their family names. Physisorption : weak 10 to 50 kj/mol adsorption Chemisorption: strong over 100kJ/mol Fraction of surface coated with molecules is called coverage --ranges from 0 to If you know how many molecules are adsorbed then you know (available) surface area

8 Surface Area is important in characterizing nanostructures BET theory came from the Langmuir Isotherm recall Langmuir Langmuir, J. Amer. Chem. Soc., 40, 1361 (1918); J. Amer. Chem. Soc.,54, 2798 (1932); I. Langmuir, Nobel Lecture, 1932]. Nobel Prize Chemistry Consider the equilibrium A: adsorbate S: surface 10-8

9 The rate of adsorption will be proportional to the pressure of the gas and the number of vacant sites for adsorption. If the total number of sites on the surface is N, then the rate of change of the surface coverage due to adsorption is: The rate of change of the coverage due to the adsorbate leaving the surface (desorption) is proportional to the number of adsorbed species: 10-9

10 In these equations, k a and k d are the rate constants for adsorption and desorption respectively and p is the pressure of the adsorbate gas. At equilibrium, the coverage is independent of time and thus the adsorption and desorption rates are equal. The solution to this condition gives us a relation for 2 So: = where K = ka / kd. See CHEM 1050 K = kf/kb 10-10

11 Note that because K is an equilibrium constant, the value of K at various temperatures determined from the Langmuir isotherm allows for the evaluation of the enthalpy of adsorption, Keq and T the equilibrium constant can be measured at various temps. this gives us a way to get )G 0. also if we plot lnk vs 1/T we can get )H 0 and )S 0 lnk Background for the lab experiment )G 0 = -RT lnkeq = ) H 0 -T ) S 0 Divide by -RT lnkeq = - ) H 0 /RT + T ) S 0 /RT lnkeq = - ) H 0 /RT + )S 0 /R y = m (x) + c i.e. a plot of lnk vs 1/T will give a straight line of slope - )H 0 /R. at two temperatures T 1 and T 2 we obtain lnk 2 = - )H 0 /RT 2 + )S 0 /R lnk 1 = - )H 0 /RT 1 + )S 0 /R Subtract: - ln(k 2 /K 1 ) = (- )H 0 /R)[1/T 2-1/T 1 ] ln(k 2 /K 1 ) = ()H 0 /R)[(T 2 -T 1 )/T 1 T 2 ] CHEM 1050!!! /T 10-11

12 This done by the Vant Hoff Eqn (see CHEM 2820: Thermodynamics And Kinetics Langmuir Isotherm 10-12

13 The Langmuir isotherm gives us a wonderfully simple picture of adsorption at low coverage and is applicable in some situations. At high adsorbate pressures and thus high coverage, this simple isotherm fails to predict experimental results and thus cannot provide a correct explanation of adsorption in these conditions. What is missing in the Langmuir treatment is the possibility of the initial overlayer of adsorbate acting as a substrate surface itself, allowing for more adsorption beyond a saturated (monolayer) coverage. This possibility has been treated by Brunauer, Emmett, and Teller [J. Amer. Chem. Soc., 60, 309 (1938)] and the result is named the BET isotherm. This isotherm is useful in cases where multilayer adsorption must be considered. It takes the form 10-13

14 where n/n mono is the ratio of the moles adsorbed to the moles adsorbed in a single monolayer, and z = p/p0, where p0 is the vapor pressure of the pure condensed adsorbate. The n/nmono ratio represents a generalized coverage' because its value can exceed unity. The constant c represents the relative strengths of adsorption to the surface and condensation of the pure adsorbate. Simple theory predicts an approximate value of this constant as: 10-14

15 The BET isotherm predicts that the amount of adsorption increases indefinitely as the pressure is increased since there is no limit to the amount of condensation of the adsorbate. In the limit that adsorption to the surface is much 'stronger' than the condensation to a liquid (such as for the adsorption of unreactive gases onto polar substrates) the BET isotherm simplifies to the form (c=4): 10-15

16 The Langmuir isotherm is found to be useful only at very small coverages (sub-monolayer) but is generally applied to all cases involving chemisorption. This would correspond to the limiting case of c approaching infinity in the BET formalism, and no insight is provided by BET below one monolayer in this limit. The BET isotherm is found to describe adequately the physisorption at intermediate coverage ( 2 = ) but fails to represent observations at low or high coverage. The BET isotherm is reasonably valid around 2 =1.0, however, and this is useful in characterizing the area of the absorbent. If one can determine experimentally the number of moles of adsorbate required to give 2 = 1.0 (i.e. a monolayer), one can determine the specific area of the absorbent: More next time 10-16