[Paper Review] Rotational averaging-out gravitational sedimentation of colloidal dispersions and phenomena

Djamel El Masri, Teun Vissers+8 more|arXiv (Cornell University)|Nov 18, 2011

Material Dynamics and PropertiesMaterials Science82 references18 citations

TL;DR

This study demonstrates that rotational averaging using a home-built rotating stage effectively suppresses gravitational sedimentation in colloidal dispersions, enabling observation of intrinsic self-assembly behavior free from gravity-induced stratification. Key results show that gravity induces phase separation and inhomogeneous structuring—such as sequential fluid/crystal phases in charged colloids and collapsed gels in oppositely charged systems—while rotation yields homogeneous crystallization and uniform structures.

ABSTRACT

We report on the differences between colloidal systems left to evolve in the earth's gravitational field and the same systems for which a slow continuous rotation averaged out the effects of particle sedimentation on a distance scale small compared to the particle size. Several systems of micron-sized colloidal particles were studied: a hard sphere fluid, colloids interacting via long-range electrostatic repulsions above the freezing volume fraction, an oppositely charged colloidal system close to either gelation and/or crystallization, colloids with a competing short-range depletion attraction and a long-range electrostatic repulsion, colloidal dipolar chains, and colloidal gold platelets under conditions where they formed stacks. Important differences in the structure formation were observed between the experiments where the particles were allowed to sediment and those where sedimentation was averaged out. For instance, in the case of colloids interacting via long-range electrostatic repulsions, an unusual sequence of dilute-Fluid/dilute-Crystal/dense-Fluid/dense-Crystal phases was observed throughout the suspension under the effect of gravity, related to the volume fraction dependence of the colloidal interactions, whereas the system stayed homogeneously crystallized with rotation. For the oppositely charged colloids, a gel-like structure was found to collapse under the influence of gravity with a few crystalline layers grown on top of the sediment, whereas when the colloidal sedimentation was averaged out, the gel completely transformed into crystallites that were oriented randomly throughout the sample. Rotational averaging out gravitational sedimentation is an effective and cheap way to estimate the importance of gravity for colloidal self-assembly processes.

Motivation & Objective

• To investigate how gravitational sedimentation distorts the self-assembly of colloidal systems in ground-based experiments.
• To develop and validate a simple, low-cost method to average out gravitational effects using slow continuous rotation.
• To compare structural evolution in identical colloidal systems under gravity versus rotation to isolate gravity's influence.
• To assess the effectiveness of rotational averaging in achieving homogeneous colloidal structures comparable to microgravity conditions.
• To extend the method’s applicability to systems with external fields, such as MHz-frequency electric fields.

Proposed method

• A home-built rotating stage was used to apply slow, continuous rotation to capillary samples, averaging out gravitational sedimentation over time.
• The rotation rate was chosen to ensure that sedimentation timescales were much longer than the rotational period, minimizing net particle displacement.
• Structural evolution was monitored using real-space optical and confocal microscopy to track particle arrangements and phase behavior.
• The Péclet number (Pe = σ⁴Δρg / 12kBT) was used to quantify the relative importance of sedimentation versus diffusion, with Pe ≪ 1 indicating negligible gravity effects.
• Comparative experiments were conducted with identical samples kept stationary (gravity-on) and rotating (gravity-averaged) for the same duration.
• The method was extended to systems under MHz-frequency electric fields, demonstrating compatibility with external field-driven assembly.

Experimental results

Research questions

• RQ1 How does gravitational sedimentation alter the phase behavior and self-assembly pathways in charged colloidal dispersions?
• RQ2 To what extent does rotational averaging suppress sedimentation-induced inhomogeneities in colloidal gels and crystals?
• RQ3 Can rotational averaging produce structurally homogeneous samples comparable to microgravity conditions in ground-based experiments?
• RQ4 How does gravity influence the formation of anisotropic structures such as gold platelet stacks and dipolar chains?
• RQ5 What are the limits of rotational averaging in systems with competing interactions (e.g., depletion attraction and electrostatic repulsion)?

Key findings

• In charged colloids above the freezing volume fraction, gravity induced a transient sequence of dilute-fluid/dilute-crystal/dense-fluid/dense-crystal phases due to volume fraction-dependent interactions, while rotation yielded homogeneous crystallization.
• For oppositely charged colloids, gravity caused gel collapse with only a few crystalline layers forming on the sediment, whereas rotation transformed the entire gel into randomly oriented crystallites.
• In gold platelet dispersions, rotation prevented sedimentation-induced column growth; after 72 hours on the rotating stage, only short columns formed, in contrast to long columns after 24 hours of horizontal storage.
• The column size distribution evolved significantly under gravity: long columns formed after 24 hours of horizontal storage, while rotation maintained a distribution of short columns throughout the volume.
• The gravitational length (lg = kBT/G) and Péclet number (Pe ∝ σ⁴Δρg) confirmed that sedimentation dominates for micron-sized particles with high density mismatch, especially when Pe ≫ 1.
• Rotational averaging proved effective across diverse systems, including hard-sphere fluids, dipolar chains, and competing interaction systems, demonstrating broad applicability for suppressing gravity artifacts.