## Distribution Calculations

### Quick Start

A supplier can legitimately give you four different values for the size of your nanoparticles. As a customer, you had better understand what the values mean and which one is most important to you.

So create your own distribution by varying the position, height and width of two components in your product, and see how they affect the different measures of particle size.

### Distribution

_{1}nm

_{1}

_{1}

_{2}nm

_{2}

_{2}

A nanoparticle supplier can honestly tell you that their product contains 99% particles <10nm, but you can find that the product comprises 99% of 1000nm particles: why? This can arise if the supplier quotes "number distribution" (which suppliers like to do because it makes their dispersions look very good) and you measure "mass distribution" which focuses on where most of the mass of your particles is to be found.

This doesn't make much sense unless you can simulate some particle distributions and look at the cumulative number, area and mass distributions. In this app you can create two different particle distributions with different peak positions, r, heights, h, and widths, w, then look at the cumulative number, area and mass distributions (Cum.N, Cum.A and Cum.M). The peaks are "gamma distribution functions" to give a characteristic tail shape. The effect of w is rather obscure on such functions - just play with w values to get something that looks OK. Once you start to play you will find why suppliers like number distributions and users like mass distributions.

Finally the app calculates the different diameters that are often quoted. D[1,0] is the
*number* average (or mean), D[3,2] is the *volume/surface* or
*Sauter* average and D[4,3] is the *mean diameter over volume* or
*DeBroukere* mean. Note that these are sometimes shown as D̅10, D̅32 and D̅43, where the ̅ symbol means "average". Unfortunately these short-hands with the bar can be confused with common symbols such as D50 which is also calculated. D50 means the diameter where half the particles have a volume less and half have a volume more.