Periodic Patterns at the Neighborhoods of the Frèedericksz Threshold

Abstract

The theory that describes the arising twist-bend periodic walls at the neighborhoods of the Frèedericksz critical point affirms that the mode with the fastest initial grown will fix the observed properties of these patterns. From this principle it follows that just above the Freèdericksz threshold there is a region where this leading mode becomes null and, therefore, a homogeneous bending of the director would be detected. This prediction was not confirmed by the experiment and walls with very well defined wavelength were found. We will shown here that around the Frèedericksz threshold the fastest growing mode can not be defined and a new way to compute the observed structures will be proposed.

Key Words:

• patterns
• patterns formation
• Frèedericksz threshold