The Moment-Ratio Notation

In this system of notation, mean size values are expressed as the ratio between two moments of the number density distribution of parameter x. Here, x is a characteristic parameter, most commonly the diameter d (or x) but it can also be some other parameter. The term Dp,q is used to designate a mean value obtained from summing discrete individual x values to the power of p (x ), which represents the relationship between the measured signal and the particle parameter x. The value of the x summation is then normalized by a summation of X values to the power of q, which represents the relation between the weighting of each particle to its parameter x in the measurement [54]  

We can see from the above table that the mean sizes can be quite different if one uses an electron microscope ( D, o= 4.00), or a laser diffraction instrument ( D4,3 = 9.74) to measure this four-particle system. The difference between a number-averaged mean (q = 0) and a mass-averaged mean (q = 3) resides in the fact that in the number average the mean value represents values from particles with the largest population while in the mass average the mean value represents more from particles with the largest size. The same is true for a real distribution. A number distribution may be completely different from its corresponding mass 

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Dielectric constant Rotational diffusion coefficient Translational diffusion coefficient Mean value in the moment-ratio notation Electric field of light Electric field Geometric term in OPC Conductivity... 

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