pysrw.lib.uti_math.get_dist_schultz

pysrw.lib.uti_math.get_dist_schultz(_min, _max, poly_index=0.3)

elect point using a Flory–Schulz distribution

Parameters:

• _min – minimum possible value.

• _max – maximum possible value.

• 0.3 (poly_index =) – particles of varied sizes in the dispersed phase of a disperse system.

The Flory–Schulz distribution is a discrete probability distribution named after Paul Flory and Günter Victor Schulz that describes the relative ratios of polymers of different length that occur in an ideal step-growth polymerization process.

Calculate the Schulz distribution for polydisperse systems. When the polydispersity is small, the Schulz distribution tends to a Gaussian.

Flory–Schulz Distribution:

y = y(0) + Ae^((x(c)-x)/w) * (x/x(c))^(x(c)/w)

Where:

y(0) = minimum (_min). A = amplitude (_max-_min). x(c) = center of distribution (mean of x_range). w = width of distribution ((1 - poly_index^2) / (poly_index^2)).