Colloids and Surfaces A: Physicochemical and Engineering Aspects
Dynamic particle packing in freezing colloidal suspensions
Graphical abstract
(np is number density in close-packed state. V is pulling speed).
In the field of freezing colloidal suspensions, it is important to understand the particle-scale behavior of particle packing. Here, we reveal the dynamics of particle packing by identifying the behavior of each single particle in situ. The typical pattern consists of locally ordered clusters and amorphous defects. The microscopic mechanism of pattern formation is ascribed to the non-equilibrium particle-packing process on the particle scale, described with the dimensionless Péclet number. The macroscopic migration of a particle layer is also revealed by an analytical model involving parameters of freezing speed and initial volume fraction of particles.
Introduction
Freezing of colloidal suspensions is ubiquitous in nature and technology [1]. It is an important factor in many research areas, such as ice templating of porous ceramics [2], polymers and composites [3], bone tissue engineering [4], science of soft matter [5], [6], geophysical science [7], thermal energy storage [8], crystal growth [9], cryobiology [10], etc. In all of these cases, the segregation of particles from the growing ice and the consequent increase of particle concentration in the fluid regions are vital. In particular, the arrangement of segregated particles on the scale of single particles is important, because the particle-scale structure is the key to understanding the rejection of particles and hence predicting the large-scale structure [11].
During freezing of a suspension, particles are expelled from ice [12], [13], forming a close-packed layer in front of the freezing interface. This process can cause self-assembly of the particles [14] similar to that caused by drying [15], [16] or sedimentation [17] of colloidal suspensions. Similarities between these patterns suggest that the physics underlying the colloidal behavior may be similar, though the driving forces in each case differ. Therefore, knowledge gained from studying particle packing in freezing colloidal suspensions may be applicable to colloidal suspensions in diverse circumstances, such as drying or sedimentation of colloidal suspensions.
Researchers have tried to reveal dynamic particle packing during freezing colloidal suspensions through theoretical models [18], experiments [11], [14], [19], [20], [21], [22], [23], [24], [25], [26], [27] and simulations [28], but are still far from a complete understanding of the phenomenon [26], [27]. Presently, there is no theory that can fully predict the morphology or detailed characteristics of particle packing. Previous theories assume that the particles in the condensed layer form a random close packing [18], and the condensed layer is considered uniform with an average particle density. However, the detailed structure and dynamics of the condensed layer has not previously been identified by experiments on the scale of individual particles. Most studies involve a posteriori analysis of samples after fixing the particle structure [22], [23], [24], [25]. They provided only static information about the final arrangement of particles. Some experiments have tried to resolve the dynamic behavior of particle layers by using X-ray radiography and tomography [19], [20], [21], [26], [27] as well as small-angle X-ray scattering [11]. X-ray techniques can probe inside visibly opaque materials. X-ray tomography can even provide a full three-dimensional reconstruction of the samples. However, none of these techniques provided information about the dynamic packing status on the scale of individual particles due to limited spatial resolution (˃ 1 μm) in fast X-ray tomography (temporal resolution < 1 s) [29]. Molecular dynamics simulations [28] have been also used to investigate dynamic particle packing during freezing suspensions, which stimulates us to conduct laboratory experiments to gain information about how real systems behave.
In this Letter, we present in-situ observation of dynamic particle packing on the scale of individual particles made during directional freezing in carefully controlled experiments. A uniform thermal gradient and a constant pulling speed are controlled independently [30]. The typical pattern in the close-packed particle layer consists of locally ordered clusters and amorphous defects. The microscopic mechanism of pattern formation is investigated by particle packing process on the particle scale. Finally, the mechanisms of macroscopic particle layer migration are quantified by an analytical model involving parameters of freezing speed and initial volume fraction of particles.
Section snippets
Experiments
In our experiments, a narrow-gapped sample cell was designed to obtain quasi-two-dimensional, mono-layer suspensions of micron-sized spherical particles in which the packing behavior of individual particles could be identified. The manufacturing and operation of the colloidal-monolayer sample cells is identical to Ref [31]. The glass surfaces were rigorously cleaned by chromic acid and deionized water for three times, so that particles did not stick to the walls. The colloidal suspensions were
Results and Discussions
Fig. 1 shows the dynamic process of creating a close-packed particle layer during directional freezing. The continuous dynamic process is shown in the Supplementary Movie S2. In Fig. 1, the left side of the sample is the cooling zone (−3 °C), while the right side is the heating zone (+2 °C), which builds a linear thermal gradient G = 9.24 K/cm. Directional freezing is provided by sample translation from right to left [30]. When the pulling speed, V = 0.4 μm/s, is applied, the freezing interface starts
Conclusions
In the present work, the dynamic establishing of a close-packed particle layer in freezing of colloidal suspensions is in-situ observed. The pattern of the close-packed particle layer is identified as locally ordered clusters and amorphous inter-defects. The formation mechanism of amorphous defects is mainly from the competition between the particles’ Brownian motion and the dynamic particle attachment on the particle layer interface, and the dimensionless Péclet number is used to describe the
Acknowledgements
J.Y. thanks M. Grae Worster for his revising the manuscript and numerous discussions. This research has been supported by Nature Science Foundation of China (Grant Nos. 51371151 and 51571165), Free Research Fund of State Key Laboratory of Solidification Processing (100-QP-2014 and 158-QP-2016), the Fund of State Key Laboratory of Solidification Processing in NWPU (13-BZ-2014) and Innovation Foundation for Doctor Dissertation in NWPU (CX201703).
References (40)
- et al.
Biomass-based particles for the formulation of Pickering type emulsions in food and topical applications
Coll. Surf. A: Physicochem. Eng. Aspects
(2014) - et al.
Fabrication and characterization of biomimetic collagen–apatite scaffolds with tunable structures for bone tissue engineering
Acta Biomater.
(2013) - et al.
One-dimensional Stefan problem formulation for solidification of nanostructure-enhanced phase change materials (NePCM)
Int. J. Heat Mass Transfer
(2013) - et al.
The interaction between a particle and an advancing solidification front
J. Cryst. Growth
(1999) - et al.
Structure–property-processing correlations in freeze-cast composite scaffolds
Acta Biomater.
(2013) - et al.
Time-lapse, three-dimensional in situ imaging of ice crystal growth in a colloidal silica suspension
Acta Mater.
(2013) - et al.
Particle redistribution and structural defect development during ice templating
Acta Mater.
(2012) - et al.
Structural properties of materials created through freeze casting
Acta Mater.
(2010) - et al.
Atomic-size effect and solid solubility of multicomponent alloys
Scr. Mater.
(2015) - et al.
Phase field crystal modeling of grain rotation with small initial misorientations in nanocrystalline materials
Comput. Mater. Sci
(2014)