Elastic response of colloidal smectics: insights from microscopic theory

• Main Authors: Wensink, H. H, Grelet, E
• Format: Journal Article
• Language: English
• Published: 26-04-2023
• Subjects: Physics - Soft Condensed Matter
• DOI: 10.48550/arxiv.2304.13701

Elongated colloidal rods at sufficient packing conditions are known to form
stable lamellar or smectic phases. Using a simplified volume-exclusion model,
we propose a generic equation-of-state for hard-rod smectics that is robust
against simulation results and is independent of the rod aspect ratio. We then
extend our theory by exploring the elastic properties of a hard-rod smectic,
including the layer compressibility ($B$) and bending modulus ($K_{1}$). By
introducing weak backbone flexibility we are able to compare our predictions
with experimental results on smectics of filamentous virus rods and find
quantitative agreement between the smectic layer spacing, the out-of-plane
fluctuation strength, as well as the smectic penetration length $\lambda =
\sqrt{K_{1}/B}$. We demonstrate that the layer bending modulus is dominated by
director splay and depends sensitively on lamellar out-of-plane fluctuations
that we account for on the single-rod level. We find that the ratio between the
smectic penetration length and the lamellar spacing is about two orders of
magnitude smaller than typical values reported for thermotropic smectics. We
attribute this to the fact that colloidal smectics are considerably softer in
terms of layer compression than their thermotropic counterparts while the cost
of layer bending is of comparable magnitude.