[Paper Review] Liquid Crystal Foams: Formation and Coarsening

Mark Buchanan|arXiv (Cornell University)|Jun 25, 2002

Pickering emulsions and particle stabilization3 citations

TL;DR

This study investigates coarsening in pure liquid crystal foams made from 8CB, where bubble growth follows a power law ⟨R⟩∼t^λ with λ≈0.20, significantly slower than the classical t^1/3 behavior in wet foams. The reduced growth rate is attributed to defect-mediated surface tension effects in the nematic and smectic phases, suggesting a novel t^1/5 scaling due to elastic distortions at bubble surfaces.

ABSTRACT

Coarsening in foams made from the pure liquid crystal, 8CB, has been studied. The foam was made in the nematic phase ($ extrm{T} = 35 ^{\circ} extrm{C}$) by bubbling nitrogen through the pure liquid crystal. The coarsening behavior was investigated at three temperatures; at $ extrm{T} = 22 ^{\circ} extrm{C}$ and $33^{\circ} extrm{C}$ in the smectic phase and at $ extrm{T} = 34^{\circ} extrm{C}$ in the nematic phase. In smectic and nematic phases the mean bubble radius $$ has been measured as a function of time $ \sim t^λ$. In classical wet soap foams the growth exponent is typically $λ\approx 0.33$ where coarsening is by gas diffusion from bubbles with high curvature to bubbles with low curvature. In liquid crystal foams a growth exponent, $λ= 0.20 \pm 0.05$ is observed. This may be explained by the presence of defects at the surface of the bubbles which slow down the coarsening behaviour. This growth exponent can be observed in both nematic and smectic phases. At higher temperatures typically $>35^{\circ} extrm{C}$ coalescence dominates the coarsening behaviour. In the isotropic state, $>41.5^{\circ} extrm{C}$, the foam is rapidly unstable.

Motivation & Objective

• To investigate coarsening dynamics in foams composed solely of a thermotropic liquid crystal, without surfactants or solvents.
• To determine whether the absence of surfactants and the presence of liquid crystal elasticity alter the classical coarsening exponent λ observed in wet soap foams.
• To explore the role of topological defects and elastic distortions at bubble surfaces in modifying surface energy and slowing coarsening.
• To compare coarsening behavior across the nematic and smectic phases of 8CB, and to examine the transition to rapid coalescence in the isotropic phase.

Proposed method

• Foams were generated by bubbling nitrogen through pure 8CB liquid crystal in a glass cell at 35 °C (nematic phase), followed by temperature equilibration to 22 °C, 33 °C (smectic), and 34 °C (nematic) for measurements.
• Time-lapse video microscopy was used to track bubble size evolution at the glass cell surface, with 2D bubble size distributions corrected to estimate 3D mean radius ⟨R⟩.
• The mean bubble radius ⟨R⟩ was calculated using the harmonic mean formula ⟨R⟩ = N / (∑ r_i⁻¹), where r_i is the radius of the i-th bubble.
• Growth exponents λ were determined from log-log plots of ⟨R⟩ versus time t, fitting ⟨R⟩ ∼ t^λ.
• Liquid volume fraction φ_l was estimated via rapid heating and recovery, yielding φ_l ≈ 0.40 immediately after foam formation and φ_l ≈ 0.34 at the end of experiments.
• Theoretical modeling considered gas diffusion via Fick’s law and modified surface tension σ ∝ 1/R² due to defect-surface interactions, leading to a predicted t^1/5 scaling.

Experimental results

Research questions

• RQ1 What is the coarsening exponent λ in pure liquid crystal foams, and how does it compare to classical wet foam behavior?
• RQ2 How do topological defects at the bubble surface influence the surface energy and coarsening kinetics in liquid crystal foams?
• RQ3 Does the coarsening behavior differ between the nematic and smectic phases of 8CB?
• RQ4 Why does coalescence dominate over diffusion-driven coarsening at temperatures above 35 °C?
• RQ5 Can the observed λ ≈ 0.20 be explained by a defect-mediated, R-dependent surface tension leading to a t^1/5 scaling law?

Key findings

• The coarsening exponent λ was measured as 0.20 ± 0.05 in both the smectic (22 °C and 33 °C) and nematic (34 °C) phases, significantly slower than the classical t^1/3 scaling of wet foams.
• The observed λ ≈ 0.20 is consistent with a t^1/5 scaling law, suggesting that defect-induced surface tension variations (σ ∝ 1/R²) slow down coarsening.
• In the isotropic phase (>41.5 °C), foam instability and rapid coalescence dominate, with λ ≈ 1, indicating a transition from diffusion-controlled to coalescence-dominated dynamics.
• The liquid volume fraction decreased from φ_l ≈ 0.40 to 0.34 during coarsening, indicating drainage, but film thickness remained approximately constant.
• Defects such as edge dislocations or focal-conic defects at the bubble surface are proposed as the source of R-dependent surface tension, explaining the anomalous coarsening exponent.
• This is the first experimental observation of a t^1/5 coarsening law in foams, attributed to elastic distortions from surface defects in liquid crystal systems.