When adsorbed polymer overlays the spheres the scattering function of the system is given by (28)

It is important to note in Eq 28 that the scattering function of the adsorbed polymer has the same rapidly oscillating trigonometric functions as the sphere themselves, and thus require the same averaging process in modeling the scattering experiment.

s](Q) = Scattering function of homogeneous spheres, equal to [3[V.

Finally, we compare our nonlinear large-signal S-parameters to another form of nonlinear mapping, known as nonlinear scattering functions [6-7].

Here, we compare the nonlinear large-signal S-parameters, introduced in this paper, to another form of nonlinear mapping, known as nonlinear scattering functions, introduced by Verspecht [6-7].

For a two-port nonlinear device, excited by a single-tone signal, and assuming all harmonic signals are relatively small compared to the fundamental signals, Verspecht defines nonlinear scattering functions as

Thus, equating the nonlinear large-signal S-parameters with the nonlinear scattering functions is generally valid only in the small-signal, linear case.

Since this is not generally true, the formulations for nonlinear large-signal S-parameters and nonlinear scattering functions are not equivalent.