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Kinetic/Optical Properties

Kinetic/Optical Properties. Methods of Measuring Colloidal Sizes. Motion. Thermal motion Brownian Motion on the microscopic scale Diffusion and translation on the macroscopic scale Techniques for measuring colloidal sizes Sedimentation (under gravitational or applied field)

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Kinetic/Optical Properties

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  1. Kinetic/Optical Properties Methods of Measuring Colloidal Sizes

  2. Motion • Thermal motion • Brownian Motion on the microscopic scale • Diffusion and translation on the macroscopic scale • Techniques for measuring colloidal sizes • Sedimentation (under gravitational or applied field) • Colligative Properties • Scattering techniques

  3. Sedimentation Colloidal particle undergoing settling Solvent Molecules oppose motion

  4. A terminal velocity is reached • Where m – mass of particle • - specific volume of colloidal particle • - solvent density • f – particle frictional factor

  5. The Frictional Factor • The frictional factor in a given medium is obtained from Stokes Law  – solvent viscosity a - particle radius

  6. Stokes Law • In the limit of • Slow particle motion • Dilute colloidal suspensions • Solvent is considered as a continuum of viscosity 

  7. Frictional Factors • Frictional factors depend on the particle shape • f increases as • Particle asymmetry increases • Degree of interaction with solvent increases • Define the frictional ratio, f/fo. • Ratio of the f value of the particle to that of an unsolvated sphere.

  8. Diffusion • Recall Kinetic Theory of motion

  9. Brownian Motion • Brownian motion is dependent on the translational diffusion coefficient of the particle • D – particle diffusion coefficient • Transport property relating the displacement of the particle to its concentration gradient

  10. Diffusion and Frictional Factors • The diffusion coefficient of a suspended particle is related to f via the Einstein Equation For spherical particles

  11. Fick’s Laws of Diffusion • Fick’s first and second laws relate the diffusion coefficients to the concentrations gradients

  12. The Thermodynamic Force • At constant T,P – investigate the non-expansion work done when substance is transported along gradient

  13. Thermodynamics Force (II) • Work is done pushing the molecules down the gradient where

  14. Measurement of Diffusion Coefficients • Free boundary methods • a boundary between two solutions of different concentrations is formed in a cylindrical cell • Determine the evolution of the concentration distribution with time.

  15. Measurement of Diffusion Coefficients (II) • Taylor Dispersion methods • NMR Techniques • Pulsed gradient spin echo experiments (PGSE) • Diffusion oriented spectroscopy (DOSY)

  16. Sedimentation • Under gravity • Balance method – cumulative mass of settling particles is obtained as a function of time • Practical lower limit is about 1 micron W = weight fraction of settled particles with Stokes diameter >a1 mp(t) = mass of settled particles with time

  17. Sedimentation (II) • Under centrifugal force • High Field – up to 4 x 105g is applied. • Displacement of boundary is monitored with time

  18. Sedimentation (III) • Under low field • Measure concentration profile in the tube as a function of position.

  19. Osmosis

  20. Osmosis • The movement of water through a semi-permeable membrane from dilute side to concentrated side • the movement is such that the two sides might end up with the same activity • Osmotic pressure: the pressure required to prevent this movement

  21. Osmosis • Osmosis Pressure in dilute non macromolecule solutions  = MRT • In macromolecular solutions

  22. Molar Mass Determination • Plot the osmotic pressure as a function of concentration Plot /c vs. c and extrapolate to 0 concentration. The intercept will yield the molar mass of the sample.

  23. Terminology • Isotonic: having the same osmotic pressure • Hypertonic: having a higher osmotic pressure • Hypotonic: having a lower osmotic pressure • Hemolysis: the process that ruptures a cell placed in a solution that is hypotonic to the cell’s fluid • Crenation: the opposite effect

  24. Donnan Equilibrium • Named after Frederick G. Donnan • refers to the distribution of ionic species between two solutions separated by a semipermeable membrane • Small molecule and ionis can pass through the membrane. • Polymers are retained by the membrane.

  25. Donnan Equilibrium Semi permeable membrane [NaX (aq)]L [NaX (aq)]R Start [NaP (aq)]=[P] [NaX (aq)]L + x [NaX (aq)]L - x Equil. [NaP (aq)]=[P] The condition for equilibrium is that the Gibbs Energy of the NaX in solution is the same across the Membrane. A flow of ions across membrane results to equalize the chemical potentials.

  26. Light Scattering • Shine a beam of light at colloidal systems • Absorption • Transmission • Scattering • Tyndall Effect • Intensity of transmitted radiation related to solution turbidity ()

  27. Light Scattering and Colloidal Sizes • Size and shapes of colloidal systems can be obtained from scattering measurements • Advantages of Light Scattering • Absolute • No perturbations of system • Polydispersed systems • Fast

  28. Scattering Theory • Debye Scattering • Larger particles, difference between particle refractive index and medium refractive index is small • Mie Scattering above approximately 250nm diameter • Scattered intensity is angle dependent • Significant difference between the particle refractive index and the refractive index of the dispersing medium

  29. Scattering Theory • Rayleigh Scattering • Consider colloidal systems as point sources of scattered light • Particles size is small compared with the wavelength of the light • The intensity of the scattered light is uniform in all directions for larger particles

  30. Scattering Theory • Intensity of scattered radiation as a function of angle Rayleigh Ratio

  31. Molar Masses from Scattering • Obtain the Rayleigh ratio at 90

  32. Dynamic Light Scattering • Incident light is coherent and monochromatic (e.g., a laser) • observe time-dependent fluctuations in the scattered intensity using a suitable detector • Fluctuations arise from the fact that the particles are small enough to undergo Brownian motion • Analysis of the time dependence of the intensity fluctuation can therefore yield the diffusion coefficient of the particles

  33. DLS/PCS • Light scattered by a moving particle will experience a Doppler shift • For a collection of particles undergoing Brownian Motion, a Doppler frequency broadening will result. • The width of the Doppler broadened peak at half-height will yield the particle diffusion coefficient.

  34. Doppler Broadening 1.0 1/2 0.5 0.0 Frequency

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