electroconvection overview - modulation experiments - domain growth

with additional support from Research Corporation and the Sloan Foundation.

Electroconvection: The study of patterns in nematic liquid crystals that are driven by AC electric fields.

Nematic liquid crystals are long rod-like molecules that tend to align with each other. The direction of the average alignment is referred to as the director. For the study of electroconvection, the nematic liquid crystal is confined between two glass plates with a thickness of 25 - 100 microns. The glass is treated so the that the director is aligned in a uniform directions parallel to the plates. The glass also is coated with transparent conductors, and an ac voltage is applied perpendicular to the plates. Above a critical value of the voltage, a periodic distortion of the director and an associated flow in the form of convection rolls develops. This is referred to as a pattern. The pattern is imaged from above using a microscope (see photograph on the left) and generally consists of a single set of stripes or a superposition of a small number of stripe with different orientations. In electroconvection, the director selects out a direction, so it is possible to have oblique rolls. These are patterns where the wavevector of the pattern forms a nonzero angle with respect to the director. An example of such a pattern is show in the image on the right.

Electronconvection is useful for studying a number of interesting nonlinear and pattern forming problems.
These include (but are not limited to):

Spatiotemporal chaos refers to deterministic patterns with unpredictable, non-periodic spatial and temporal variations (the image at the right is a single snapshot in time that highlights the non-periodic spatial behavior of the amplitude of a set of convection rolls). Spatio-temporal chaos occurs in a wide variety of systems where spatial degrees of freedom contribute to the dynamics, such as population dynamics, traffic flow, chemical reaction/diffusion systems, and arrays of Josephson junctions. Some aspects of spatio-temporal chaos that we study using electroconvection include:
  • the dynamics as a function of system size in order to elucidate the role of the spatial degrees of freedom.
  • resonace effects and regularization of spatiotemporal chaos using temporal and spatial modulations of the driving force.

  • Our recent work has focused on using modulations of the control parameter to stabilize regular dynamics. Movies of the
    impact of resonant modulation can be found at the picture page. These movies illustrate the establishment of regular
    standing wave patterns from irregular traveling waves. This work has been published in
    Temporal Modulation of the Control Parameter in Electroconvection in the Nematic Liquid Crystal I52, M. Dennin, Phys. Rev. E 62, 7842 (2000).

    We have also used modulation to study the dynamics of localized states, known as worms. This work has been submitted
    to Phys. Rev. E.

    Domain growth deals with the study of systems after a sudden change in an external parameter. In the case of electronvection,
    one can make a sudden change in the driving voltage from below the critical voltage to above the critical voltage. If the steady
    state consists of oblique rolls, a pattern of small domains of zig and zag rolls forms. As a function of time, these domains
    grow in size, that is the pattern "coarsens". We study the scaling behavior of the growth of these domains. Currently, we
    find that the size of the domains grows as t1/4. There is currently no theoretical explanation for this behavior. We can
    study the domain coarsening in two systems: I52 and N4. I52 is the system used for the modulation experiments. For domain
    coarsening, we make sudden changes in the modulation strength to generate standing waves of zig and zag domains that
    coarsen. In N4, the patterns are stationary zig and zag rolls, and we make sudden changes in the applied voltage. The
    coarsening behavior in both systems appears to be similar. However, one difference is the structure of the domain walls.
    For an examples of the coarsening, see the movie page.