The cloud points of aqueous solutions containing polyoxyethylene surfactant molecules with a distribution
of chain lengths were studied for several nonionic surfactants. Experimentally, the cloud points
increased as the oxyethylene chain lengths increased with a linear or logarithmic relation of the number
of oxyethylates, as proposed by Schott. An experimental scale, the p Po scale, was previously developed
to correspond to the cloud points, where p is the average number of oxyethylene units per molecule and
Po is the shortest chain length reference. However, no previous prediction methods of cloud point
addressed systems containing a range of chain lengths. In this work, we propose a rescaling of the
representative chain length as s Po, where s is the cloud point-weighted mean ethylene oxide chain
below p, and approximated as (p Po)/PDI where PDI is the polydispersity index. Using the rescaled
length, the experimental data for C12Es (lauryl alcohol ethoxylate, LAE), NPE-10 (nonyl phenol ethoxylate)
and TDE-10 (tridecyl alcohol ethoxylate) were successfully predicted with no additional parameters, such
as {(p Po)/(PDI)}/CP = a + b{(p Po)/(PDI)}, where PDI indicates the Broadness of the chain length
distribution.