Perturbation-response relationship in liquid interfacial systems: non-linearity assessment by frequency-domain analysis

Fourier series analysis is utilised to quantitatively evaluate the linearity limits and characterise the non-linearity of the perturbation-response relationship, in the frequency domain, for dynamic surface properties of 2 % (w/w) aqueous solutions of poly(sodium 4-styrenesulfonate). Under condition of periodic oscillations with different amplitudes at the same frequency (i.e., at single-line spectrum), the total harmonic distortion (THD) parameter shows the existence of a linearity range in the relationship between an imposed change of interfacial area and the ensuing surface tension response. Experiments at two-line spectrum, both with harmonic and with non-harmonic tones, also convey information about the linearity of the response. Under linearity approximation, results reveal that the magnitude of the surface dilational modulus can be determined even under periodic oscillations with a non-monochromatic spectrum, by taking just the proper components of the Fourier series.