Anisotropic viscoelastic phase separation in polydisperse hard rods leads to nonsticky gelation
- aSchool of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom;
- bCentre for Nanoscience and Quantum Information, University of Bristol, Bristol BS8 1FD, United Kingdom;
- cUniversité Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France;
- dH. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
See allHide authors and affiliations
Edited by Noel A. Clark, University of Colorado, Boulder, CO, and approved January 2, 2020 (received for review May 30, 2019)

Significance
Networks of mesoscopic colloidal particles, gels, are everyday materials. Yet, our understanding of colloidal gels lags far behind their utility: Gels are out of equilibrium, so their properties change over time, often with significant consequences, such as failure of the material. However, until now, we were confident of one thing: To aggregate into a network, the colloidal particles need to attract one another. Here, we show that, in fact, colloids can form a network without significant attractions. This is surprising because particles without an attraction usually distribute themselves throughout space, rather than forming a network of particle-rich and -poor regions. Our work opens the way to “nonsticky gels” and a deeper understanding of this perplexing state of matter.
Abstract
Spinodal demixing into two phases having very different viscosities leads to viscoelastic networks—i.e., gels—usually as a result of attractive particle interactions. Here, however, we demonstrate demixing in a colloidal system of polydisperse, rod-like clay particles that is driven by particle repulsions instead. One of the phases is a nematic liquid crystal with a highly anisotropic viscosity, allowing flow along the director, but suppressing it in other directions. This phase coexists with a dilute isotropic phase. Real-space analysis and molecular-dynamics simulations both reveal a long-lived network structure that is locally anisotropic, yet macroscopically isotropic. We show that our system exhibits the characteristics of colloidal gelation, leading to nonsticky gels.
Gelation, the emergence of a network of arrested material, is among the most striking everyday features of soft condensed matter (1) and is an example of viscoelastic phase separation, where a contrast in viscosity between the demixed phases leads to the formation of a long-lived network (2). Gels can be soft (and biological) materials such as proteins (3), clays (4), foods (5), hydrogels (6), and tissues (7). In addition, a more diverse range of materials, including granular matter (8), phase-demixing oxides (9), and metallic glass formers (10), also exhibit gelation.
Despite its widespread occurrence, a complete understanding of gelation remains a challenge (1). Two properties unify particulate gels produced to date. Firstly, the constituent particles experience a significant attraction to one another [which may be effective, induced, for example, by depletion effects from added polymer (11)], resulting in phase separation that arrests before completion. Secondly, with some exceptions, such as local crystallization (12), both phases are isotropic. The interparticle attraction is closely related to the phase behavior. In gelation, spinodal decomposition (immediate demixing) leads to a “colloidal liquid” phase which is of sufficient volume fraction that its high viscosity results in a long-lived network in which full demixing is suppressed (1, 2, 13, 14). Thus, colloidal gels exhibit dynamical contrast between the phases formed through spinodal decomposition (15).
Here, we depart from this paradigm of gelation driven by attraction between particles: We consider a system of polydisperse colloidal rods without significant attractions. Nevertheless, in such a system, spinodal decomposition occurs from a thermodynamically unstable isotropic fluid to an isotropic fluid in coexistence with a nematic liquid crystal (16⇓–18).
While the phase behavior and spinodal mechanism of demixing suggests that gelation may be found, it is important to consider the dynamics: Why should the phase separation in our system arrest such that a gel forms? Now the nematic phase exhibits an anisotropic viscosity. Although the viscosity along the director is comparable to that in the isotropic phase, perpendicular to the director, the viscosity is much higher for our polydisperse system. For suitable compositions, we furthermore expect percolation of the nematic phase. We shall show that the rods align parallel to the “arms” of the gel, and, thus, while there may be flow along the arms, perpendicular flow is very strongly suppressed. We thus argue that polydisperse rods in which attraction is not important feature many of the properties required for spinodal gelation. This concept of gels formed by nematic–isotropic spinodal decomposition is shown in Fig. 1.
(A) Schematic illustration of anisotropic viscoelastic phase separation. Spinodal decomposition leads to a bicontinuous network of isotropic (I) and nematic (N). A, Inset shows that rods align parallel to the director, indicated as
We identify four criteria of spinodal gelation (2). 1) The system must undergo spinodal decomposition; 2) there must be dynamic asymmetry between the phases (that is to say, one phase is substantially more viscous that the other); 3) the more viscous phase must percolate (19); and 4) the nonequilibrium nature of the gel leads to aging, in particular, coarsening.
To realize such materials, we combine real-space analysis of a colloidal model system of polydisperse hard rods with computer simulation to demonstrate the character of nonsticky gelation. Our sepiolite colloidal rods exhibit two features which are important here. Firstly, any attractions are small, as the phase diagram is consistent with that of polydisperse hard rods (20), and, as we shall show, computer simulations without any attractions exhibit the same behavior. This means that any gelation behavior we find is not attributed to attractions or even effective attractions such as those found in colloid–polymer mixtures (11). Secondly, the rods are rather polydisperse (with an effective aspect ratio
Gelation via isotropic–nematic spinodal decomposition in polydisperse hard rods. (A) The fraction of the nematic phase
The fact that the rods undergo spinodal decomposition satisfies criterion 1, and the large gap in volume fraction between isotropic and nematic phases at coexistence suggests that the latter may exhibit slow dynamics, satisfying criterion 2. Criterion 3, of percolation, also follows from spinodal decomposition; likewise, criterion 4, of aging. It is thus possible that the criteria identified for spinodal gelation are met by this system of rods, and this we go on to show.
Experimental and Simulation Methodology
Experimental System.
The isotropic–nematic phase separation of colloidal suspensions of fluorescently labeled sepiolite clay particles was studied by using confocal imaging of samples with concentrations in the coexistence range. The phase diagram of our system was determined before confocal analysis, and, from this, we extracted the range of concentrations of interest. Here, we used the effective bulk rod volume fraction ϕ as a measure of the concentration, which was determined from the number density of rods and the mean rod volume. Rods were taken to be cylinders of length equal to that measured with transmission electron microscopy (TEM) plus 2δ, and diameter equal to the width measured plus 2δ. Here,
Confocal images of the system were obtained with a Leica SP5 confocal microscope using a white-light laser emitting at 500 nm. Borosilicate glass capillaries with cross-sections of
Computer Simulation.
We modeled the experimental system using rods with a steep repulsive interaction. We used molecular dynamics (MD) and neglected the effect of solvent-mediated hydrodynamic interactions. Significant though these are (22), here, we chose to focus our computational resources on simulating as large a system size as possible, so that the length scales and timescales may be comparable to the experiments. Our systems consisted of up to 180,000 rods with polydispersity only in length. The length distribution of our model rods is described by a Gaussian with an average rod length of
Nonsticky Gels of Polydisperse Rods
Our presentation of results is as follows. Firstly, we considered the phase behavior. While the isotropic–nematic transition of long rod-shaped particles has been known since the pioneering work of Onsager (23), our results show the importance of polydispersity in broadening the coexistence gap of the isotropic–nematic transition, with a nematic phase whose density is around nine times that of the isotropic phase (20). Note that the viscosity of the nematic phase varied markedly with respect to the mean rod orientation (24, 25), which has significant consequences for the behavior of the networks we obtain.
Secondly, we considered spinodal decomposition, which we demonstrate leads to a percolating network of nematic phase. We then determined the dynamical asymmetry between the isotropic and nematic phases and found the latter to be very much more viscous than the former, for flow perpendicular to the director. Finally, we considered coarsening of the network. We found behavior broadly similar to that known for spinodal gels formed of spheres (13, 15, 26), but we emphasize that the gels we obtained should exhibit flow along channels comprising the nematic phase, but that perpendicular flow should be suppressed, as our simulations showed that rods aligned parallel to the nematic domains (Fig. 1).
Phase Behavior.
We present the phase diagram of our system in Fig. 2. Here, we considered the fraction of nematic phase
This quantitative agreement with the theoretical phase behavior for hard rods suggests that attractions are not important, but residual attractions cannot be ruled out. However, significant attractions along the length of the rods cause bundling (29, 30), while “patchy” attractions lead to the formation of a random network of rods (30). While it is hard to be certain of the absence of attractions, since either bundling or a random network would suppress the isotropic–nematic transition, the occurrence of the transition suggests that, for our system, neither effect is dominant. We therefore conclude that any attractions are weak. This is quite different from conventional gelation in spheres, where attractions drive gelation (1, 14).
A further interesting observation concerns the shape of the nematic regions, as shown in the confocal image in Fig. 2B. Here, the contrast is due to the much higher concentration of rods in the nematic compared to the isotropic phase, and the brightness levels were set such that isotropic appeared dark. Nucleating nematic droplets were expected to be elongated in shape, approximately elliptical, but with sharp ends (i.e., tactoids) (31), as has been observed in experiments on more monodisperse systems than those we consider here (32, 33). Indeed, the morphology of the bicontinuous network was consistent with tactoid-like objects having fused together. Thus, we cannot rule out the formation of tactoids and their subsequent coalescence prior to imaging. Note also that since the rod width was subresolution, we did not obtain the local director field in our experimental data.
Spinodal Decomposition.
Allied with the observation of morphology distinct from that of (isolated) tactoids anticipated in the case of nucleation and growth, we found that the isotropic–nematic phase separation occurs in a spinodal-like fashion. Even at the shortest observation time accessible to our experiments (45 s from stopping vortex mixing) and at the weakest supersaturation (ϕ = 0.021), we never observed nucleation and growth. That is to say, we did not find nucleation of nematic regions; these had always formed prior to our shortest observation time.
Gels often exhibit a bicontinuous texture. In Fig. 3A, we show a three-dimensional (3D) rendering of regions identified as nematic. We have confirmed that the regions identified as the nematic phase indeed percolate in all three dimensions and thus concluded that the percolation requirement for gelation is met. Close inspection of data such as that rendered in Fig. 3A suggests some alignment of the nematic domains. We believe this to be related to the capillary into which the sample is flowed for imaging. Such alignment may present an opportunity to produce networks whose orientation may be controlled.
Polydisperse hard rods exhibit the properties required for spinodal gelation: a percolating network and dynamic asymmetry. (A) A 3D rendering of nematic domains identified from a confocal microscopy image of a sample with a bulk effective volume fraction
Dynamics.
We now turn to the dynamical asymmetry between the phases, which is a necessary ingredient for viscoelastic phase separation, i.e., spinodal gelation (2). We shall see that our system exhibits a rather unusual form of dynamic asymmetry, due to the anisotropic dynamics of the nematic phase. In both our experiments and simulations, we measured the dynamics in a system of either isotropic or nematic phase. In this way, we probed the dynamics of the bulk phase, rather than domains in the gel network. To measure the dynamical behavior in our experiments, we used a time-correlation function
In Fig. 3B, we fit the time-correlation function according to a stretched exponential form
Further insight was gained from simulation data shown in Fig. 3C, which suggest that the situation is profoundly different from the case of spheres, in which the dynamics have no preferred direction. Here, we compared the intermediate scattering function
Not all volume fractions in the simulations mapped to those in the corresponding experiments. In particular, we found the isotropic phase at somewhat higher volume fraction than in the experiments. We note that determining effective volume fractions in experiments is a challenging task (35), not to mention that the gels formed were, of course, out of equilibrium, so we would not necessarily expect a perfect mapping. We leave the accurate determination of the equilibrium phase diagram of this system to the future, noting that the network which forms is out of equilibrium and that the experiments and simulations do follow different dynamics, which can influence the network formation (36).
Coarsening.
A further key feature of gels formed by spinodal decomposition is that they coarsen over time, and this is governed by the dynamics of the more viscous phase (2, 15, 26). Our system was no exception, and in Fig. 4, we present the coarsening behavior at different volume fractions in the coexistence region (Materials and Methods). The confocal images and 3D renderings in Fig. 4 A and B reveal structural evolution of the nematic network for
Time evolution of the system. (A and B) Confocal images for a bulk volume fraction of, i.e., prior to demixing
Conclusion and Discussion
We have argued that the properties of particulate gels, which have until now been associated with systems of attractive particles, can in fact be realized with polydisperse colloidal rods without significant attractions. By conceptual arguments, based on the dynamical contrast between the isotropic and nematic phases and spinodal demixing, we have made the case that such gels may be found in systems of rods with sufficient polydispersity, with the feature that the viscosity of the nematic network is anisotropic: Material can flow along the interior of the “arms” of the network.
This prediction we have realized using a colloidal model system of polydisperse rods of sepiolite clay. We have presented four key pieces of evidence in support of our claim, which we have supported with molecular-dynamics simulations. Firstly, the system undergoes spinodal decomposition. Secondly, the phase coexistence in these polydisperse hard rods is broad enough that the density of the nematic phase (around nine times higher than the coexisting isotropic phase) is sufficient that significant dynamic contrast between the phases is expected. We determined the dynamic contrast, with the nematic phase being much more viscous than the isotropic phase in our experiments, while our simulation data revealed strong anisotropy in the dynamics of the nematic phase. In particular, we found that the rods can readily diffuse along the director, but exhibit significant dynamic slowing perpendicular to the director. Thirdly, we have shown that the nematic phase percolates. Finally, we found coarsening behavior of the nematic domains, which is characteristic of domain coarsening in spinodal gels. We thus demonstrate a class of nonsticky gels.
We note a feature of our system distinct from gels formed of spheres. In the case of spheres, as indicated in the phase diagram of Fig. 2C, the density of the colloid-rich phase is a strong function of attraction strength, and, at high density, the dynamics of spheres is a strong function of density (15). Thus, in addition to the effects of changing the interactions between the particles, the attraction strength provides a parameter by which the density of the colloid-rich network may be controlled. In particular, one finds that moving deeper in the gel region of the phase diagram upon increasing the attraction that the rate of coarsening slows drastically, owing to the slower dynamics of the increasingly dense colloid-rich phase of spheres (2, 15).
In the case of our rods, the situation was profoundly different. In this athermal system, the rod volume fraction of the nematic phase at phase coexistence was fixed at
It is possible to add attraction between the particles to this system by adding polymers (29). Upon adding polymer, we expect a broadening of the isotropic–nematic phase coexistence (38). Under these conditions, we expect that the gelation we observed here would be even more marked because the dynamic contrast between the phases would be even larger. This further leads to the question as to whether a more polydisperse system than those we have considered would, in fact, lead to a nematic phase with even slower dynamics than that we observed here.
A natural extension of this work is to inquire whether such behavior is restricted to rod-like particles. We expect that this nonsticky gelation may be exhibited by a variety of anisotropic particles, which exhibit a phase coexistence gap such that the viscosity of the coexisting phases is sufficiently different. The dynamic anisotropy, of course, depends on the shape of the particles, but we expect that plate-like particles may exhibit comparable behavior, if the coexistence gap between their isotropic and nematic phases is large enough. More generally, the phase behavior of a large variety of anisotropic hard particles has recently been calculated (39, 40). Determination of coexistence gaps, and particularly dynamic contrast between their coexisting phases, likely in the case of polydispersity, may show that a wide range of particle shapes exhibit nonsticky gelation.
Materials and Methods
Sample Preparation.
Colloidal rod suspensions were made by using sepiolite mineral clay particles. The zeolitic water was displaced by the fluorescent dye acridine orange (41). The dye-doped particles were treated with surfactant cetyltrimethylammonium bromide solution in deionized water and centrifuged. The clay particles were dispersed in toluene and stabilized by using a polymer coating of SAP230 (Infineum). Further details can be found in SI Appendix.
Time-Correlation Functions.
The dynamics of the system were characterized by using time sequences of
To obtain fully demixed isotropic and nematic phases, a suspension in the coexistence regime was allowed to phase separate in a capillary for 48 h. This compares to the timescale of the gel, which is several hours. Each phase was imaged far from the interface and the walls of the capillary. Two different time steps τ were chosen: 0.020 s for the isotropic phase and 1.0 s for the nematic phase. The data in Fig. 3B have been corrected to account for noise in the intensity measured with the confocal microscope. This was made by normalizing the
Computer Simulations.
We modeled our colloidal rods as linear rigid bodies composed of a number of spheres of mass m that interact only with the spheres of neighboring rods via a Weeks–Chandler–Andersen potential,
For our simulations, we used the open-source MD simulation package LAMMPS (42), which has a dynamical integrator for rigid bodies (43, 44). To simulate our experimental conditions, we first equilibrated a system of polydisperse rods at a low volume fraction (
Acknowledgments
We thank Bob Evans and Hajime Tanaka for helpful discussions; Mike Allen and Jens Eggers for a critical reading of the manuscript; Francesco Turci for help with the dynamical analysis; Richard Stenner, Jacek Wasik, and Azaima Razali for help with some experiments; and M. Perez (Tolsa) for donating the sepiolite clay. C.F.-C. acknowledges Consejo Nacional de Ciencia y Tecnología and the Mexican Government for a student scholarship. C.P.R. acknowledges the Royal Society and European Research Council Consolidator Grant NANOPRS, Project 617266. Engineering and Physical Sciences Research Council (EPSRC) Grant EP/ H022333/1 provided support for provision of the confocal microscope used in this work. TEM studies were carried out in the Chemistry Imaging Facility at the University of Bristol (UoB) with equipment funded by UoB and EPSRC Grants EP/K035746/1 and EP/M028216/1. This work was carried out using the computational facilities of the Advanced Computing Research Center, UoB (http://www.bris.ac.uk/acrc/).
Footnotes
- ↵1To whom correspondence should be addressed. Email: paddy.royall{at}bristol.ac.uk.
Author contributions: C.F.-C., C.P.R., and J.S.v.D. designed research; C.F.-C. performed research; C.F.-C., C.P.R., and J.S.v.D. analyzed data; and C.F.-C., C.P.R., and J.S.v.D. wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
Data deposition: Data are available at the University of Bristol data repository, https://data.bris.ac.uk/data/ (https://doi.org/10.5523/bris.1gfhyy3l2qipg2t8wg6t6f1c0k).
This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1909357117/-/DCSupplemental.
Published under the PNAS license.
References
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- D. Bouttes,
- E. Gouillart,
- E. Boller,
- D. Dalmas,
- D. Vandembroucq
- ↵
- R. E. Baumer,
- M. J. Demkowicz
- ↵
- ↵
- T. H. Zhang,
- J. Klok,
- R. H. Tromp,
- J. Groenewold,
- W. K. Kegel
- ↵
- ↵
- C. P. Royall,
- S. R. Williams,
- H. Tanaka
- ↵
- I. Zhang,
- C. P. Royall,
- M. A. Faers,
- P. Bartlett
- ↵
- M. P. B. van Bruggen,
- J. K. G. Dhont,
- H. N. W. Lekkerkerker
- ↵
- ↵
- M. P. Lettinga et al.
- ↵
- M. E. Cates,
- M. Fuchs,
- K. Kroy,
- W. C. K. Poon,
- A. M. Puertas
- ↵
- P. Woolston,
- J. S. van Duijneveldt
- ↵
- ↵
- M. P. Lettinga,
- J. K. G. Dhont,
- Z. Zhang,
- S. Messlinger,
- G. Gompper
- ↵
- ↵
- ↵
- M. P. B. van Bruggen,
- H. N. W. Lekkerkerker,
- G. Maret,
- J. K. G. Dhont
- ↵
- V. Testard,
- L. Bethier,
- W. Kob
- ↵
- H. H. Wensink,
- G. J. Vroege
- ↵
- ↵
- ↵
- N. Kazem,
- M. Carmel,
- C. E. Maloney
- ↵
- P. Prinsen,
- P. van der Schoot
- ↵
- P. W. Oakes,
- J. Viamontes,
- J. X. Tang
- ↵
- N. Puech,
- E. Grelet,
- P. Poulin,
- C. Blanc,
- P. van der Schoot
- ↵
- S. Buzzaccaro,
- M. D. Alaimo,
- E. Secchi,
- R. Piazza
- ↵
- ↵
- C. P. Royall,
- J. Eggers,
- A. Furukawa,
- H. Tanaka
- ↵
- ↵
- R. Tuinier,
- T. Taniguchi,
- H. Wensink
- ↵
- P. F. Damasceno,
- M. Engel,
- S. C. Glotzer
- ↵
- M. Dijkstra
- ↵
- N. Yasarawan,
- J. S. van Duijneveldt
- ↵
- S. Plimpton
- ↵
- ↵
- ↵
- ↵
- C. Ferreiro-Cordova,
- C. P. Royall,
- J. S. van Duijneveldt
Citation Manager Formats
Article Classifications
- Physical Sciences
- Chemistry