Dynamic light scattering (DLS) determines particle size by measuring the rate of fluctuation in scattered light intensity caused by particles undergoing Brownian motion. DLS analyzes these intensity fluctuations using a correlation function to determine the diffusion coefficient and hydrodynamic radius of particles based on the Stokes-Einstein equation. The technique works by measuring the speed at which particles diffuse under Brownian motion using a laser light source, detector, and digital signal processor to construct a correlation function from the scattered light intensity data and extract size information.

1. Dynamic light
scattering for size
determination
By,
Pooja Mehta
Centre for Nanotechnology
Central University Of Jharkhand

2. Outline
What is DLS
Application
Brownian motion
Stoke’s Einstein equation : Relating particle size to particle
motion
How DLS works
The correlation function
How correlator work
limitation of DLS

3. What is Dynamic light Scattering
• Particle size can be determined by measuring the random
change in intensity of light scattered from suspension.
• It measure and interpolate the light scattering up to
microsecond
• So it measure real time intensity, thus measuring the dynamic
properties
Size distribution
Hydrodynamic radius
Diffusion coefficient

4. Application Of DLS
• We measure Hydrodynamic Size of nanoparticle ,protein and
biomaterial
• We can also study stability of nanoparticles as function of time
• Good for detecting the aggregation of the particles
Other Then these
• Required small volume of sample
• Complete recovery of sample after measurement
• Sample preparation is not required for the measurement

5. Brownian motion
• Brownian motion is the fundamental of this instrument
• Brownian motion of the particle is random motion due to the
bombardment by the solvent molecule surround them.
• Brownian motion of the particles are related to size.
• It describes the way in which very small particles move in fluid
suspension

6. Stoke’s Einstein Equation: Relating
particle size to particle motion
• This random motion is modeled by the Stokes-Einstein
equation.
d=
𝒌𝑻
𝟑Пŋ 𝑻 𝑫
• d is the hydrodynamic radius of the particle ,the diameter of
the sphere that has same diffusion coefficient as the particle.
• Temperature of the measurement must be stable ,as the
viscosity of the liquid.

7. Hydrodynamic radius
• “The size of a hypothetical hard sphere that diffuses in the
same fashion as that of the particle being measured”

8. How DLS Works
• In DLS we measured the speed at which the particles are
diffusing due to Brownian motion.
• Speed of diffusion is measured by measuring the rate at which
the intensity of the scattered light fluctuates.
• Small particles causes the intensity to more fluctuate than
larger.
• It measure the diffusion coefficient by using correlation
function.

9. How these fluctuation in scattered
light arises ?
Speckle Pattern for a
sample containing
Stationary Particle
For the particle in Brownian
motion a speckle pattern
is observed where the
position of each speckle is
seen to be in constant
motion Because the phase
addition from moving
particle is constantly
evolving and forming new
pattern.

10. Experimental setup of the DLS
LASER
Attenuator
Sample
cell
Detector
Detector
173°
90°
Digital
signal
Processer,
Correlator
Software for
data analyzerScattered light

11. DLS signal
Obtained optical signal shows random change due to random change
in the position of the particle.
The “ noise “ is actually the particle motion and will be used to measure the particle
size.

12. Correlation function
• A correlation function is statistical correlation between
random variables at two different points in space or time,
usually as a function of the spatial or temporal distance
between the points.
• Within the correlation curve all of the information regarding
the diffusion of particles within the sample being measured.
• Correlator construct correlation function G(τ), of the scattered
intensity
G(τ)=<I(t).I(t+τ) ,τ is delay time

13. Cont.
 If the intensity at time t is
compared with the intensity at
time t+δt, there will be a strong
correlation between two signal.
 Correlation of a signal arriving
from random source will decrease
with time.
 If the particle will large the signal
will changes slowly and correlation
will sustain for long time.

14. Correlogram
Typical intensity fluctuations
for large and small particles and
Corresponding Correlogram

15. How the correlator works
• It is a signal comparator. It is design to measure the similarity
between two signals or one signals with itself with varying
time.
• The correlogram give many information the time at which the
correlation starts significantly decay is an indication of
mean size of the sample
• The steeper the curve the more mono disperse the sample is.
More extended the decay becomes the greater the
polydispesity.

16. Correlation function for
monodispresed Particle
For monodispersed particle in Brownian motion , the
correlation [G] function is an exponential decaying function
of decay time τ
G(τ) =A[1+Bexp(-2Г τ)]
Delay constant (Г) is related to the diffusion coefficient of
the particle ,D
Г=𝑫𝒒 𝟐
q is the scattering vector which is given by
and q=
𝟒П𝒏𝒔𝒊𝒏(Ɵ/𝟐)
𝝀

17. The correlation function for
polydisperse particle
• G(τ) =A[1+Bexp(2(-Г’ τ+ẚ/2+----)]
Г’ is delay constant
Г’=𝑫′𝒒 𝟐
D’ is the diffusion coefficent of the And by
Polydispersity Index =
ẚ
𝟐
Г’
• measure the distribution of size in our sample.
• for monodisperse it is about 0.01-0.05 but the value
greater than 0.7 indicate that sample has a very broad
size distribution.

18. Limitation of DLS
• We measure the hydrodynamic radius of the particle, not able
to measure the actual size of the particle
• The particles having size greater than 1000nm are not
measured by this method
• Size of Solid particles are not measured by DLS

19. Reference
• DLS technical note www.malvern.co.uk
• http://www.wyatt.eu/
• Dynamic Light Scattering for Nanoparticle Size Analysis -
HORIBA

20. Thank you for your attention