Hai, all. Can anyone tell me how to calculate the hydrodynamic particle size in DLS? Is it possible to do it from Zavg and if so how? Or is Zavg itself is the particle size?
I might sound stupid but I cannot get an idea how to calculate the particle size from the DLS data we obtain. I saw many equations and theory but how to calculate it practically,this is what I want to know. Also, is apparent particle size is same as that of hydrodynamic size?
Thank you
Aruni
Provided that your sample is relatively mono-disperse (one peak in the distribution with narrow standard deviation) the z-average will correspond to the hydrodynamic particle diameter in nm.
http://www.malvern.com/en/support/resource-center/technical-notes/TN101104DynamicLightScatteringIntroduction.aspx
Thank you, Mr. Sokolov. In this case, I would like to add another question. Is the apparent particle size is same as that of hydrodynamic size or Zavg?
In solution each particle a charged particle will be surrounded by a double layer of ions and hence will be larger than the actual size of the particle itself. Z-average is a measure of the size of particle+ this double layer. In order to get the actual size of particle electron microscopy is a better technique.
DLS produces data in the form of a correlation function, from which decay rates can be determined.
Size is determined from decay rate by the Stokes Einstein equation.
Assuming that your sample is mono-disperse, the decay rate can be determined from a simple exponential fit.
Z Average size is the result of a Cumulants analysis of the correlation function, where the decay is described by an exponential raised by a polynomial.
Cumulant analysis can therefore be simply applied by taking the natural log of the correlation function and then fitting a quadratic.
An advantage of this approach is that the analysis can cope with sample polydispersity, which will be revealed by the size of the t^2 coefficient in the Cumulants fit.
If your sample is multimodal, the Z Ave size becomes meaningless and distribution analyses such as Contin need to be used to determine the distribution of decay rates that describe your correlation function.
As mentioned, the physical size of a particle can be determined through other methods including SEM, AFM etc
Any size determined from DLS is the hydrodynamic size, as the results are determined by quantifying how the sample particles move through solution (note that this may vary with dispersant given the interaction between the charged double layer around the particles and the dispersant).
Thank you all.
In this case, I would like to add one more question how can we calculate the diffusion coefficient. I know it is automatically calculated by the software. I tried to find out the equation and I ended up in the general definition of ' Diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion)' but the practical way of solving it, I am not able to understand. If someone can help me with this it would be really great.
Thank you..
The diffusion coefficient is what is directly calculated from the measured autocorrelation function (g1), and the size is then calculated from the diffusion coefficient (D) for known values of the sample temperature and viscosity.
For a monomodal sample, the autocorrelation function is described as:
g1(t)=exp(-Gamma*t)
Where Gamma is a decay rate which is a function of diffusion coefficient and q vector (angle and wavelength of the scattering light)
Gamma=q^2D
where q = 4*pi*n / lambda *sin (theta/2)
The size is then calculated from the Diffusion coefficient by the Stokes Einstein equation
D = kT/6*pi*eta*R
where eta is the sample viscosity.
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