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What are Z-average and polydispersity index (PDI)?


Z-average is the intensity-weighted mean hydrodynamic size of the ensemble collection of particles measured by DLS. 


The Z-average is a hydrodynamic size that is determined by an ISO method, i.e., the cumulants method. For the cumulants method, the correlation function is solved by the following expression:


the correlation function of  the cumulants method


where A is the intercept of the correlation function, which represents the signal-noise ratio and Γ  is the average decay rate, which can be substituted into the equation Γ =q2D  to calculate the average diffusion coefficient  D of all particles.  D  is then put into the Stokes-Einstein equation to produce the average particle size DH  , namely the Z-average mean hydrodynamic diameter.


Stokes-Einstein equation


For dynamic light scattering, the Z-average is used to present the average particle size, which is the intensity-weighted average size. PDI (Polydispersity Index), defined by PDI=µ2/Γ  , which indicates the width of the distribution. 


As a rule of thumb, the following PDIs are shown for different samples.


Sample Type PDI
Mono-dispersed Sample 0 - 0.05
Narrow-dispersed Sample 0.05 – 0.08
Moderate-dispersed Sample 0.08 – 0.7
Wide-dispersed Sample > 0.7


DLS is a technique suitable for samples whose particle size distributions are relatively narrow. For samples with PDI greater than 0.7, DLS measurement might not be applicable.





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