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 L2−L2‘ and
L2‘−S phase transitions. In the low-pressure L2 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).
Isotherms and x-ray diffraction studies of eicosanoic acid Langmuir monolayers show a phase in which the molecular tilt is intermediate between nearest-neighbor (NN) and next-nearest-neighbor (NNN) directions. The transition from this “I” phase to an NN-tilted structure is first order, with a ∼60° change in the tilt direction, while the transition to an NNN-tilted structure is apparently continuous. These results can be explained using a Landau-type theory for uniaxially distorted lattices, which is a modification of an existing theory for hexagonal lattices [J. V. Selinger and D. R. Nelson, Phys. Rev. Lett. 61, 416 (1988)].
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We have developed an apparatus that is capable of simultaneously measuring the viscosity of Langmuir monolayers and visualizing their flow. It consists of a circular trough with a nearly circular elastic barrier that can be rotated to generate two-dimensional Couette flow. The “inner cylinder” is a Teflon knife-edge disk that is hung by a thin wire. The torque on the inner cylinder is determined by measuring the angular displacement of the disk. A stepper motor controls the barrier rotation. Viscosity can be measured in two different ways: by oscillating the torsion pendulum and by generating Couette flow. The dynamic viscosity range of the apparatus is 10−4<η<103 g/s. Typical shear rates range from 10−4 to 101 s−1. A Brewster angle microscope is mounted on the apparatus. This is used to study various properties of the monolayer such as: velocity profiles, domain shape during shear, domain relaxation after shear, and size distribution of domains.
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