Separating viscoelastic and compressibility contributions in pressure-area isotherm measurements

Monolayers of surface active molecules or particles play an important role in biological systems as well as in consumer products. Their properties are controlled by thermodynamics as well as the mechanical properties of the interface itself. For insoluble species forming Langmuir monolayers, surface pressure-area isotherms are typically used to characterize the thermodynamic state. A Langmuir trough equipped with a Wilhelmy plate is often used for such measurements. However, when Langmuir interfaces are compressed and become more structured, the elastic response of these interfaces can interfere with the measurement of the surface pressure-area isotherm, even when the compression speed is slow. Recent reports of compression data for highly elastic interfaces revealed a dependence of the apparent surface pressures on the geometry of the measurement trough. In the present work, this dependence is investigated by considering adequate constitutive models. Since deformations in such compression experiments can be large, linearized versions of the Kelvin-Voigt model do not suffice. We develop a framework for quasi-linear constitutive models by choosing suitable non-linear strain tensors, adequately separating the shear and dilatational effects in a frame invariant manner. The proposed constitutive models can be used as building blocks to describe viscoelastic behavior as well. The geometry dependence in isotherm measurements is then shown to be a consequence of varying contributions of the isotropic surface pressure and extra shear and dilatational elastic stresses. Using these insights, an approach is proposed to obtain the intrinsic surface pressure-area isotherms for elastic interfaces. As a case study, experimental data on graphene oxidesheets at the air-water interface is investigated to evaluate the proposed model.