Methods of Measuring Colloidal Sizes

  ◦ ◦ ◦ 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

Solvent Molecules oppose motion Colloidal particle undergoing settling

 A terminal velocity is reached mg  1     f dx dt Where m – mass of particle   - specific volume of colloidal particle - solvent density f – particle frictional factor

 The frictional factor in a given medium is obtained from Stokes Law f  6  a  – solvent viscosity a - particle radius

 ◦ ◦ ◦ In the limit of Slow particle motion Dilute colloidal suspensions Solvent is considered as a continuum of viscosity  dx dt  2 a 2 g   9  2   1 

   Frictional factors depend on the particle shape f increases as ◦ Particle asymmetry increases ◦ Degree of interaction with solvent increases ◦ Define the frictional ratio, f/f o .

Ratio of the f value of the particle to that of an unsolvated sphere.

 Recall Kinetic Theory of motion KE  3 2 RT

 Brownian motion is dependent on the translational diffusion coefficient of the particle x    1 2 ◦  D – particle diffusion coefficient Transport property relating the displacement of the particle to its concentration gradient

 The diffusion coefficient of a suspended particle is related to f via the Einstein Equation Df  k B T For spherical particles D  6 k B T  a

 Fick’s first and second laws relate the diffusion coefficients to the concentrations gradients J   D   c z  c  t   J  x   D  2 c  z 2

 At constant T,P – investigate the non expansion work done when substance is transported along gradient     d  dw  d        x   T , P dx

 Work is done pushing the molecules down the gradient dw   dx

where

       x   T , P

 ◦ ◦ 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.

  ◦ ◦ Taylor Dispersion methods NMR Techniques Pulsed gradient spin echo experiments (PGSE) Diffusion oriented spectroscopy (DOSY)

 ◦ ◦ Under gravity Balance method – cumulative mass of settling particles is obtained as a function of time Practical lower limit is about 1 micron W  m p    dm d p ln t   W m = weight fraction of settled particles with Stokes diameter >a 1 p (t) = mass of settled particles with time

 ◦ ◦ Under centrifugal force High Field – up to 4 x 10 5 g is applied.

Displacement of boundary is monitored with time M  RT  2 D  t 2 ln   t x 1 2  1 x 1   

 ◦ Under low field Measure concentration profile in the tube as a function of position. M   2  2 RT x 2 2  ln  x 1 2 c 2   1 c 1   

  ◦ 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

  Osmosis Pressure in dilute non macromolecule solutions  = MRT In macromolecular solutions   RT M  1  B 1 c  B 2 c 2  ...



 Plot the osmotic pressure as a function of concentration c lim  0  c  RT M Plot  /c vs. c and extrapolate to 0 concentration. The intercept will yield the molar mass of the sample.

     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

   ◦ 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.

Semi permeable membrane Start [NaX (aq)] L [NaP (aq)]=[P] [NaX (aq)] R Equil.

[NaX (aq)] L + x [NaP (aq)]=[P] [NaX (aq)] L - x 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.

  ◦ Shine a beam of light at colloidal systems ◦ ◦ ◦ Absorption Transmission Scattering Tyndall Effect Intensity of transmitted radiation related to solution turbidity (  ) I I o t  e  

  Size and shapes of colloidal systems can be obtained from scattering measurements ◦ ◦ ◦ ◦ Advantages of Light Scattering Absolute No perturbations of system Polydispersed systems Fast

  ◦ ◦ ◦ 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

 ◦ ◦ ◦ 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

 Intensity of scattered radiation as a function of angle I  I r o 2  8  4  4  2  1  cos 2    R   1  cos 2   Rayleigh Ratio R   1  cos 2  

 Obtain the Rayleigh ratio at 90  K    1 M 16  3  R Kc R 90  90  2 N  A 2 n  4 o o 2    dn dc    2

   ◦ 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

   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.

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  1 2  D   4  n c o  o sin  2   2  1/2 0.5

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Frequency