Dynamic Light Scattering

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Dynamic Light Scattering

• ZetaPALS w/ 90Plus particle size analyzer

Also equipped w/ BI-FOQELS Otsuka DLS-700 (Rm
CCR230)
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• Dynamic Light Scattering (DLS)
• Photon Correlation Spectroscopy (PCS)
• Quasi-Elastic Light Scattering (QELS)
• Measure Brownian motion by
• Collect scattered light from suspended particles
  to
• Obtain diffusion rate to
• Calculate particle size

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Brownian motion

• Velocity of the Brownian motion is defined by the
  Translational Diffusion Coefficient (D)
• Brownian motion is indirectly proportional to
  size
• Larger particles diffuse slower than smaller
  particles
• Temperature and viscosity must be known
• Temperature stability is necessary
• Convection currents induce particle movement that
  interferes with size determination
• Temperature is proportional to diffusion rate
• Increasing temperature increases Brownian motion

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Brownian motion

• Random movement of particles due to bombardment
  of solvent molecules

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Stokes-Einstein Equation

• dH hydrodynamic diameter (m)
• k Boltzmann constant (J/Kkgm2/s2K)
• T temperature (K)
• ? solvent viscosity (kg/ms)
• D diffusion coefficient (m2/s)

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Hydrodynamic diameter
Particle diameter

• The diameter measured by DLS correlates to the
  effective particle movement within a liquid
• Particle diameter electrical double layer
• Affected by surface bound species which slows
  diffusion

Hydrodynamic diameter
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Nonspherical particles

Rapid
Equivalent sphere
Slow
Hydrodynamic diameter is calculated based on the
equivalent sphere with the same diffusion
coefficient
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Experimental DLS

• Measure the Brownian motion of particles and
  calculate size
• DLS measures the intensity fluctuations of
  scattered light arising from Brownian motion
• How do these fluctuations in scattered light
  intensity arise?

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What causes light scattering from (small)
particles?

• Explained by JW Strutt (Lord Rayleigh)
• Electromagnetic wave (light) induces oscillations
  of electrons in a particle
• This interaction causes a deviation in the light
  path through an angle calculated using vector
  analysis
• Scattering coefficient varies inversely with the
  fourth power of the wavelength

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Interaction of light with matterRayleigh
approximation

• For small particles (d ?/10), scattering is
  isotropic
• Rayleigh approximation tells us that
• I a d6
• I a 1/?4
• where I intensity of scattered light
• d particle diameter
• ? laser wavelength

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Mie scattering from large particles

• Used for particles where d ?0
• Complete analytical solution of Maxwells
  equations for scattering of electromagnetic
  radiation from spherical particles
• Assumes homogeneous, isotropic and optically
  linear material

Stratton, A. Electromagnetic theory, McGraw-Hill,
New York (1941) www.lightscattering.de/MieCalc
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Brownian motion and scattering
Constructive interference
Destructive interference
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Brownian motion and scattering Multiple particles
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Instrument layout
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Intensity fluctuations

• Apply the autocorrelation function to determine
  diffusion coefficient
• Large particles smooth curve
• Small particles noisy curve

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Determining particle size

• Determine autocorrelation function
• Fit measured function to G(t) to calculate G
• Calculate D, given n, ?, and G
• Calculate dH, given T and ?

User defined values.
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How a correlator works

• Random motion of small particles in a liquid
  gives rise to fluctuations in the time intensity
  of the scattered light
• Fluctuating signal is processed by forming the
  autocorrelation function
• Calculates diffusion

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How a correlator works

• Large particles the signal will be changing
  slowly and the correlation will persist for a
  long time
• Small, rapidly moving particles the correlation
  will disappear quickly

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The correlation function

• For monodisperse particles the correlation
  function is
• Where
• A baseline of the correlation function
• Bintercept of the correlation function
• G Dq2
• Dtranslational diffusion coefficient
• q(4pn/?0)sin(?/2)
• nrefractive index of solution
• ?0wavelength of laser
• ?scattering angle

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The correlation function

• For polydisperse particles the correlation
  function becomes
• where g1(t) is the sum of all exponential decays
  contained in the correlation function

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Broad particle size distribution

• Correlation function becomes nontrivial
• Measurement noise, baseline drifts, and dust make
  the function difficult to solve accurately
• Cumulants analysis
• Convert exponential to Taylor series
• First two cumulants are used to describe data
• G Dq2
• µ2 (D2-D2)q4
• Polydispersity µ2/ G2

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Cumulants analysis

• The decay in the correlation function is
  exponential
• Simplest way to obtain size is to use cumulants
  analysis1
• A 3rd order fit to a semi-log plot of the
  correlation function
• If the distribution is polydisperse, the semi-log
  plot will be curved
• Fit error of less than 0.005 is good.

1ISO 133211996 Particle size analysis -- Photon
correlation spectroscopy
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Cumulants analysis

• Third order fit to correlation function
• b z-average diffusion coefficient
• 2c/b2 polydispersity index
• This method only calculates a mean and width
• Intensity mean size
• Only good for narrow, monomodal samples
• Use NNLS for multimodal samples

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Cumulants analysis
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Polydispersity index

• 0 to 0.05 only normally encountered w/ latex
  standards or particles made to be monodisperse
• 0.05 to 0.08 nearly monodisperse sample
• 0.08 to 0.7 This is a mid-range polydispersity
• gt0.7 Very polydisperse. Care should be taken in
  interpreting results as the sample may not be
  suitable for the technique (e.g., a sedimenting
  high size tail may be present)

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Non-Negatively constrained Least Squares (NNLS)
algorithm

• Used for Multimodal size distribution (MSD)
• Only positive contributions to the
  intensity-weighted distribution are allowed
• Ratio between any two successive diameters is
  constant
• Least squares criterion for judging each
  criterion is used
• Iteration terminates on its own

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Correlation functionCorrelograms

• Correlograms show the correlation data providing
  information about the sample
• The shape of the curve provides clues related to
  sample quality
• Decay is a function of the particle diffusion
  coefficient (D)
• Stokes-Einstein relates D to dH
• z-average diameter is obtained from an
  exponential fit
• Distributions are obtained from
  multi-exponential fitting algorithms
• Noisy data can result from
• Low count rate
• Sample instability
• Vibration or interference from external source

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Correlation functionCorrelograms
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Data interpretationCorrelograms

• Very small particles
• Medium range polydispersity
• No large particles/aggregrates present (flat
  baseline)

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Data interpretationCorrelograms

• Large particles
• Medium range polydispersity
• Presence of large particles/agglomerates (noisy
  baseline)

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Data interpretationCorrelograms

• Very large particles
• High polydispersity
• Presence of large particles/agglomerates (noisy
  baseline)

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Upper size limit of DLS

• DLS will have an upper limit wrt size and density
• When particle motion is not random (sedimentation
  or creaming), DLS is not the correct technique to
  use
• Upper limit is set by the onset of sedimentation
• Upper size limit is therefore sample dependent
• No advantage in suspending particles in a more
  viscous medium to prevent sedimentation because
  Brownian motion will be slowed down to the same
  extent making measurement time longer

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Upper size limit of DLS

• Need to consider the number of particles in the
  detection volume
• Amount of scattered light from large particles is
  sufficient to make successful measurements, but
• Number of particles in scattering volume may be
  too low
• Number fluctuations severe fluctuations of the
  number of particles in a time step can lead to
  problems defining the baseline of the correlation
  function
• Increase particle concentration, but not too high
  or multiple scattering events might arise

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Detection volume
Detector
Laser
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Lower particle size limit of DLS

• Lower size limit depends on
• Sample concentration
• Refractive index of sample compared to diluent
• Laser power and wavelength
• Detector sensitivity
• Optical configuration of instrument
• Lower limit is typically 2 nm

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Sample preparation

• Measurements can be made on any sample in which
  the particles are mobile
• Each sample material has an optimal concentration
  for DLS analysis
• Low concentration ? not enough scattering
• High concentration ? multiple scattering events
  affect particle size

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Sample preparation

• Upper limit governed by onset of
  particle/particle interactions
• Affects diffusion speed
• Affects apparent size
• Multiple scattering events and particle/particle
  interactions must be considered
• Determining the correct particle concentration
  may require several measurements at different
  concentrations

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Sample preparation

• An important factor determining the maximum
  concentration for accurate measurements is the
  particle size

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Sample concentrationSmall particles

• For particle sizes lt10 nm, one must determine the
  minimum concentration to generate enough
  scattered light
• Particles should generate 10 kcps (count rate)
  in excess of the scattering from the solvent
• Maximum concentration determined by the physical
  properties of the particles
• Avoid particle/particle interactions
• Should be at least 1000 particles in the
  scattering volume

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Sample preparation

• When possible, perform DLS on as prepared sample
• Dilute aqueous or organic suspensions
• Alcohol and aggressive solvents require a
  glass/quartz cell
• 0.0001 to 1(v/v)
• Dilution media (1) should be the same (or as
  close as possible) as the synthesis media, (2)
  HPLC grade and (3) filtered before use
• Chemical equilibrium will be established if
  diluent is taken from the original sample
• Suspension should be sonicated prior to analysis

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Checking instrument operation

• DLS instruments are not calibrated
• Measurement based on first principles
• Verification of accuracy can be checked using
  standards
• Duke Scientific (based on TEM)
• Polysciences

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Count rate and z-average diameter Repeatability

• Perform at least 3 repeat measurements on the
  same sample
• Count rates should fall within a few percent of
  one another
• z-average diameter should also be with 1-2 of
  one another

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Count rateRepeatability problems

• Count rate DECREASES with successive measurements
• Particle sedimentation
• Particle creaming
• Particle dissolution or breaking up
• Resolution
• Prepare a better, stabilized dispersion
• Get rid of large particles
• Coulter

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Count rateRepeatability problems

• Count rate is RANDOM with successive measurements
• Dispersion instability
• Sample contains large particles
• Bubbles
• Resolution
• Prepare a better, stabilized dispersion
• Remove large particles
• De-gas sample

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Z-average diameterRepeatability problems

• Size DECREASES with successive measurements
• Temperature not stable
• Sample unstable
• Resolution
• Allow plenty of time for temperature
  equilibration
• Prepare a better, stabilized dispersion

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Repeatability of size distributions

• The sized distributions are derived from a NNLS
  analysis and should be checked for repeatability
  as well
• If distributions are not repeatable, repeat
  measurements with longer measurement duration

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References

• http//www.bic.com/90Plus.html
• http//www.brainshark.com/brainshark/vu/view.asp?t
  extM913802pi62212
• http//www.malvern.co.uk/malvern/ondemand.nsf/frmo
  ndemandview
• http//www.brainshark.com/brainshark/vu/view.asp?t
  extM913802pi96389
• http//www.brainshark.com/brainshark/vu/view.asp?t
  extM913802pi73504
• http//physics.ucsd.edu/neurophysics/courses/physi
  cs_173_273/dynamic_light_scattering_03.pdf
• http//www.brookhaven.co.uk/dynamic-light-scatteri
  ng.html
• Dynamic Light Scattering With Applications to
  Chemistry, Biology, and Physics, Bruce J. Berne
  and Robert Pecora, DOVER PUBLICATIONS, INC.
  Mineola. New York
• Scattering of Light Other Electromagnetic
  Radiation, Milton Kerker, Academic Press (1969)

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Evaluating the correlation function

• If the intensity distribution is a fairly smooth
  peak, there is little point in conversion to a
  volume distribution using Mie theory
• However, if the intensity plot shows a
  substantial tail or more than one peak, then a
  volume distribution will give a more realistic
  view of the importance of the tail or second peak
• Number distributions are of little use because
  small error in data acquisition can lead to huge
  error in the distribution by number and are not
  displayed

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Correlogram from a sample of small particles
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Correlogram from a sample of large particles
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Extra

• Time-dependent fluctuations in the scattered
  intensity due to Brownian motion
• Constructive and destructive interference of
  light
• Decay times of fluctuations related to the
  diffusion constants --- particle size
• Fluctuations determined in the time domain by a
  correlator
• Correlation average of products of two
  quantities
• Delay times chosen to be much smaller than the
  time required for a particle to relax back to
  average scattering