Nonlinear shear response and anomalous pressure dependence of viscosity in a Langmuir monolayer

We have studied the strain response of heneicosanoic acid monolayers to an applied sinusoidal shear stress. We have measured the complex shear modulus (G = G' + iG'') as a function of strain amplitude and frequency, monolayer pressure, and temperature. We find that G' and G'' are independent; of the strain only at very small strain amplitudes; beyond an 'elastic limit', both G' and G'' decrease with increasing strain amplitude. G' and G'' are discontinuous at the L-2-L-2' and L-2'-S phase transitions. In the low-pressure L-2 phase, G' and G'' first increase with increasing pressure and then anomalously decrease. Compared to existing X-ray data, we find an unexpected correlation: over a range of temperatures, the pressure at which G'' is a maximum is also the one at which the monolayer lattice is hexagonal (undistorted).