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D LS T h e o r y
Obtaining particle size from the diffusion coefficient
The goal of the DLS technique is to determine the diffusion coefficient D of the particles
(assumed uniform here) from the "raw" data -- i.e. the fluctuating light scattering signal, as
represented in Figure 4a,b,c. From D we can easily calculate the particle radius R. using the
well-known Stokes-Einstein relation,
D= kT/6πηR
(2)
where k is Boltzmann's constant (1.38 X 10-16 erg K-1), T the temperature (oK, = oC + 273) and η
the shear viscosity of the solvent (e.g. η = 1.002 X 10-2 poise for water at 20oC). Thus, we see
that the rate at which the particles jitter about in the suspension, as measured by D, is inversely
related to the particle radius R.
From Equation 2 we see that, in general, the diffusion coefficient D of particles of a given size
increases with increasing temperature T. This is due primarily to the T-dependence of the
solvent viscosity η. (The fact that T is the numerator in Equation 2 is less small, in percentage,
when expressed in deg. Kelvin.) For example, η for pure water falls to 0.890 X 10-2 poise at
25oC -- i.e. more than a 10% change from the value at 20oC. Clearly, the less viscous the
solvent, the more rapid will be the random-walk diffusion of the particles and the faster the
resulting intensity fluctuations. Hence, changes in T are completely indistinguishable from
changes in particle radius R. as they affect D. For this reason, the sample temperature MUST
be constant (and accurately known) in order to obtain a meaningful measurement of D and,
hence, of R using Equation 2.
A cursory examination of the three fluctuating scattering signals in Figure 4a,b,c suggests that
extraction of the diffusion coefficient from the "noise" is not a straightforward matter. Signal (b)
clearly fluctuates faster than does (c), but is slower than (a); hence, its particle size must lie
between the values associated with (a) and (c). However, obtaining quantitative information
from these kinds of scattering signals is another matter altogether. What comes to our rescue is
the mathematical operation known as autocorrelation.
Nicomp 380 Manual
PSS-380Nicomp-030806
06/06
Page 2 -7