Final Report Summary - SURFOIDS (Organization and self assembly of colloidal particles trapped on a Isotropic-Fluid/Liquid-Crystal Interface: Effects of particle anisotropy and interface curvature)
Project aims and objectives
The ability to control regular spatial arrangement of particles is one of the central issues of the bottom-up approach to nanotechnology. Self-assemblies of colloidal particles have arisen as a very hopeful alternative. With this approach, the predetermined spatial arrangements such as 3D photonic crystals or metamaterials could be realised spontaneously [1]. Advances in colloidal self-assembly have been limited by the fact that colloidal particles typically interact through potentials with spherical symmetry, which limits the kind of arrangements that they can form to a few types of closed packed lattices. Inducing anisotropy in either the colloidal particles or the medium where the particles interact is expected to lead to novel colloidal architectures with fascinating optical properties. The aim of this project was to explore this experimentally, by taking advantage of the unique properties of liquid crystals.
1. Liquid crystal shells: towards new kinds of anisotropic colloids
Liquid crystals are composed of rod-like molecules that align on average along a particular direction, called the director n, figure 1(a). The energetic ground state is a uniform director field throughout space. However, such alignment is, on many occasions, impossible to achieve everywhere in the system. In these cases, the system is characterised by the presence of singularities or topological defects, which can even exist in the ground state of the system. In particular, this happens when the liquid crystal is confined to a space with curvature. For instance, nematic droplets are typically characterised by two defects located at opposite poles of the droplet, figure 1(b)[2]. These defects break the spherical symmetry of the system and can be exploited to fabricate bipolar colloids. More interesting defect structures appear in nematic shells, where the liquid crystal is confined between two spherical surfaces. In that case, a configuration with four defects arranged in a tetrahedral manner is typically observed, figure 1(c)[3]. These defects could be functionalised to fabricate tetravalent colloids, which are expected to organise in the diamond cubic lattice needed for an efficient optical insulator. Controlling the defect position in a nematic shell would open unprecedented control over the properties of micro-structured materials. In this project, we explored the effect of varying the elastic anisotropy of the liquid crystal, K3/K1, in the defect organisation. We demonstrated the existence of new defect configurations, never observed or predicted before, and provided tools to control the position of the defects on the sphere.
To fabricate the liquid crystal shells, we generated double emulsions in a microfluidic glass capillary device, see figure 2(a)[4]. These double emulsions consisted of an inner aqueous droplet which was encapsulated inside an outer liquid crystal droplet, as schematically shown in figure 2(b), which was in turn dispersed in a continuous aqueous phase. Due to a density mismatch between the inner and middle fluids, our experimental shells are heterogeneous in thickness. The average thickness of the shell, h, is given by the difference between the outer and inner radii, R-a. In our experiments, R was within the 30 - 120 ?m range and h was typically 2 - 3 % of R. The liquid crystal employed was 4-n-octyl-4-cyanobiphenyl (8CB), which undergoes a nematic-smectic phase transition at temperature TNS = 33.5 °C. In the nematic phase, T > TNS, the elastic anisotropy is very slight, K3/K1 1; however, when T approaches TNS, K3/K1 diverges.
We demonstrated that a change in elastic anisotropy can have a dramatic impact in the position of the defects [5]. This is shown in figures 3(a)-(f), which are cross-polarised micrographies of a nematic shell with four defects at different temperatures. For the sake of clarity, we have highlighted the defects with white circles in figure 3(a). When T>>TNS, the four defects appeared grouped together instead of forming a tetrahedron, see figure 3(a). This new configuration results from the thickness heterogeneity of the experimental shells, where bulk elasticity pushes the defects towards the regions where the shell is thinner. This effect becomes secondary when decreasing T toward TNS, where elastic anisotropy plays a dominant role. In this case, the defects arrange themselves in a great circle, see figure 3(f), confirming recent simulation predictions [6]. The transition between the two configurations proceeds through a series of equilibrium states where the position of defects is determined by temperature, as shown in figures 3(b)-(e). During this process, the defects associate in two distinct pairs which behave in an asymmetric way. We performed computer simulations in collaboration with the group of Prof. Zumer of the University of Ljubljana, Slovenia to explain the elastic origin of this behaviour [7].
Below TNS, the translational symmetry of the nematic phase is broken and a smectic shell is formed, see figure 4(a). These results are the first experimental evidence of a smectic shell [8]. For this type of shell, theory predicted a defect structure with four defects, all of which are in the same plane. Our experiments demonstrated that the ground state of the system is much more complex than that, it possesses disclination lines connecting defects, which divide the shell into crescent domains and provoke a wavy modulation of the smectic layers, see figure 4(b). The origin of this unexpected texture observed is currently an open question.
2. Oganisation of hard spheres in liquid crystal shells
The organisation of colloidal particles in a liquid crystal, often referred to as nematic colloids, has been intensively studied in flat geometries. However, the organisation of colloids in spherical liquid crystal shells is completely unexplored experimentally. In the latter case, curvature and topological defects are expected to play a key role in particle organisation. In this part of the project, we studied the organisation of small silica beads in nematic shells with different geometries.
Surfaces generally impose a preferred alignment direction for the nematic director relative to their local normals. Commonly, this alignment is tangential or normal to the particle surface. Respecting surface anchoring entails important orientational distortions in the liquid crystal, which typically extend over several particle diameters. The coupling of these distortions with the orientational distortions provoked by the defects results in long-range attractive forces. In our experiments, we employed silica beads that induce strong normal anchoring at their surfaces. These particles were included in the nematic phase before the formation of the double emulsions. Since the employed beads were larger than the average shell thickness, the beads got trapped at the nematic/water interface, see inset in figure 5(a). In these configurations, we observed new distributions of particles and defects, resulting from an interesting interplay between surface tension and nematic elasticity [9]. Elastic forces led to the association of particles and defects, which appeared arranged in a plane that was normal to the gravity axis. The high of this plane with respect to the shell equator was controlled by surface tension: the defect-particle pairs locate where the thickness of the shell provides the contact angles necessary to fulfil the Young equation. However, the position of defect-particle pairs in the plane was determined by nematic elasticity, which forces the defects to maximise their separations, see figure 5(a). Increasing the number of silica beads in the shell led to colloidal aggregation and forced the formation of defects with high topological charge, which had not ever been observed in nematic shells. An example of this is shown in figure 5(b), where two silica form a dimer with topological charge s = +2; this kind of defect is energetically forbidden in the absence of beads.
3. Conclusions and impact of the project
The usual absence of directionality to the interaction between colloids has limited the complexity of the structures they can spontaneously form. One way to address this is to coat spherical colloid particles with a thin layer of nematic liquid crystal and functionalise the unavoidable defects or bold spots that arise when nematic order is established on the surface of a sphere. The number and arrangement of these defects can vary, providing flexibility for tuning directional interactions that are more difficult to achieve through other methods. When this project was started, many theoretically predicted structures were not observed yet and control over defect location remained elusive. During this project, we have developed tools for the experimental realisation of nematic and smectic shells. We have experimentally reproduced some theoretically predicted structures and demonstrated the existence of new configurations that were not predicted before. Even more interestingly, we have shown that varying the elastic anisotropy of a nematic liquid crystal shell through temperature enables us to systematically control the number and orientation of defects formed. Such control opens up the possibility of engineering particles with tunable-valence and directional-binding capabilities, which can lead by self-assembling to micro-structured materials such as photonic crystals or metamaterials. Additionally, we have shown that the functionalisation of defects to induce self-assembly can be potentially achieved by including small hard-spheres in the liquid crystal phase. The results mentioned above have led to five publications (two of them have already been published in top-class scientific journals, and three of them are under consideration or in preparation), five communications in international conferences and three invitations to seminars. The impact of our results has been recognised by the scientific committees of prestigious journals and conferences and highlighted in the Soft Matter World Newsletters (January, 2012).
References
1. Lavrentovich, O.D. Liquid crystals, photonic crystals, metamaterials, and transformation optics. Proceedings of the National Academy of Sciences of the United States of America, 2011. 108(13): p. 5143-5144.
2. Lopez-Leon, T. and A. Fernandez-Nieves, Drops and shells of liquid crystal. Colloid and Polymer Science. 289(4): p. 345-359.
3. Lopez-Leon, T., et al., Frustrated nematic order in spherical geometries. Nature Physics. 7(5): p. 391-394.
4. Utada, A.S. et al., Monodisperse double emulsions generated from a microcapillary device. Science, 2005. 308(5721): p. 537-541.
5. Lopez-Leon, T., et al., Nematic-Smectic Transition in Spherical Shells. Physical Review Letters. 106(24): p. 4.
6. Shin, H., M.J. Bowick, and X.J. Xing, Topological defects in spherical nematics. Physical Review Letters, 2008. 101(3): p. 4.
7. Sec, D., et al., Ground states of topological defects in nematic shells with elastic anisotropy. Physical Review Letters, 2012(submitted).
8. Lopez-Leon, T., et al., Smectic shells. Journal of Physics: Condensed Matter, 2012. 24.
9. Gharbi, M.A. et al., Colloids trapped on nematic shells: textures and dynamics. 2012 (in preparation).
The ability to control regular spatial arrangement of particles is one of the central issues of the bottom-up approach to nanotechnology. Self-assemblies of colloidal particles have arisen as a very hopeful alternative. With this approach, the predetermined spatial arrangements such as 3D photonic crystals or metamaterials could be realised spontaneously [1]. Advances in colloidal self-assembly have been limited by the fact that colloidal particles typically interact through potentials with spherical symmetry, which limits the kind of arrangements that they can form to a few types of closed packed lattices. Inducing anisotropy in either the colloidal particles or the medium where the particles interact is expected to lead to novel colloidal architectures with fascinating optical properties. The aim of this project was to explore this experimentally, by taking advantage of the unique properties of liquid crystals.
1. Liquid crystal shells: towards new kinds of anisotropic colloids
Liquid crystals are composed of rod-like molecules that align on average along a particular direction, called the director n, figure 1(a). The energetic ground state is a uniform director field throughout space. However, such alignment is, on many occasions, impossible to achieve everywhere in the system. In these cases, the system is characterised by the presence of singularities or topological defects, which can even exist in the ground state of the system. In particular, this happens when the liquid crystal is confined to a space with curvature. For instance, nematic droplets are typically characterised by two defects located at opposite poles of the droplet, figure 1(b)[2]. These defects break the spherical symmetry of the system and can be exploited to fabricate bipolar colloids. More interesting defect structures appear in nematic shells, where the liquid crystal is confined between two spherical surfaces. In that case, a configuration with four defects arranged in a tetrahedral manner is typically observed, figure 1(c)[3]. These defects could be functionalised to fabricate tetravalent colloids, which are expected to organise in the diamond cubic lattice needed for an efficient optical insulator. Controlling the defect position in a nematic shell would open unprecedented control over the properties of micro-structured materials. In this project, we explored the effect of varying the elastic anisotropy of the liquid crystal, K3/K1, in the defect organisation. We demonstrated the existence of new defect configurations, never observed or predicted before, and provided tools to control the position of the defects on the sphere.
To fabricate the liquid crystal shells, we generated double emulsions in a microfluidic glass capillary device, see figure 2(a)[4]. These double emulsions consisted of an inner aqueous droplet which was encapsulated inside an outer liquid crystal droplet, as schematically shown in figure 2(b), which was in turn dispersed in a continuous aqueous phase. Due to a density mismatch between the inner and middle fluids, our experimental shells are heterogeneous in thickness. The average thickness of the shell, h, is given by the difference between the outer and inner radii, R-a. In our experiments, R was within the 30 - 120 ?m range and h was typically 2 - 3 % of R. The liquid crystal employed was 4-n-octyl-4-cyanobiphenyl (8CB), which undergoes a nematic-smectic phase transition at temperature TNS = 33.5 °C. In the nematic phase, T > TNS, the elastic anisotropy is very slight, K3/K1 1; however, when T approaches TNS, K3/K1 diverges.
We demonstrated that a change in elastic anisotropy can have a dramatic impact in the position of the defects [5]. This is shown in figures 3(a)-(f), which are cross-polarised micrographies of a nematic shell with four defects at different temperatures. For the sake of clarity, we have highlighted the defects with white circles in figure 3(a). When T>>TNS, the four defects appeared grouped together instead of forming a tetrahedron, see figure 3(a). This new configuration results from the thickness heterogeneity of the experimental shells, where bulk elasticity pushes the defects towards the regions where the shell is thinner. This effect becomes secondary when decreasing T toward TNS, where elastic anisotropy plays a dominant role. In this case, the defects arrange themselves in a great circle, see figure 3(f), confirming recent simulation predictions [6]. The transition between the two configurations proceeds through a series of equilibrium states where the position of defects is determined by temperature, as shown in figures 3(b)-(e). During this process, the defects associate in two distinct pairs which behave in an asymmetric way. We performed computer simulations in collaboration with the group of Prof. Zumer of the University of Ljubljana, Slovenia to explain the elastic origin of this behaviour [7].
Below TNS, the translational symmetry of the nematic phase is broken and a smectic shell is formed, see figure 4(a). These results are the first experimental evidence of a smectic shell [8]. For this type of shell, theory predicted a defect structure with four defects, all of which are in the same plane. Our experiments demonstrated that the ground state of the system is much more complex than that, it possesses disclination lines connecting defects, which divide the shell into crescent domains and provoke a wavy modulation of the smectic layers, see figure 4(b). The origin of this unexpected texture observed is currently an open question.
2. Oganisation of hard spheres in liquid crystal shells
The organisation of colloidal particles in a liquid crystal, often referred to as nematic colloids, has been intensively studied in flat geometries. However, the organisation of colloids in spherical liquid crystal shells is completely unexplored experimentally. In the latter case, curvature and topological defects are expected to play a key role in particle organisation. In this part of the project, we studied the organisation of small silica beads in nematic shells with different geometries.
Surfaces generally impose a preferred alignment direction for the nematic director relative to their local normals. Commonly, this alignment is tangential or normal to the particle surface. Respecting surface anchoring entails important orientational distortions in the liquid crystal, which typically extend over several particle diameters. The coupling of these distortions with the orientational distortions provoked by the defects results in long-range attractive forces. In our experiments, we employed silica beads that induce strong normal anchoring at their surfaces. These particles were included in the nematic phase before the formation of the double emulsions. Since the employed beads were larger than the average shell thickness, the beads got trapped at the nematic/water interface, see inset in figure 5(a). In these configurations, we observed new distributions of particles and defects, resulting from an interesting interplay between surface tension and nematic elasticity [9]. Elastic forces led to the association of particles and defects, which appeared arranged in a plane that was normal to the gravity axis. The high of this plane with respect to the shell equator was controlled by surface tension: the defect-particle pairs locate where the thickness of the shell provides the contact angles necessary to fulfil the Young equation. However, the position of defect-particle pairs in the plane was determined by nematic elasticity, which forces the defects to maximise their separations, see figure 5(a). Increasing the number of silica beads in the shell led to colloidal aggregation and forced the formation of defects with high topological charge, which had not ever been observed in nematic shells. An example of this is shown in figure 5(b), where two silica form a dimer with topological charge s = +2; this kind of defect is energetically forbidden in the absence of beads.
3. Conclusions and impact of the project
The usual absence of directionality to the interaction between colloids has limited the complexity of the structures they can spontaneously form. One way to address this is to coat spherical colloid particles with a thin layer of nematic liquid crystal and functionalise the unavoidable defects or bold spots that arise when nematic order is established on the surface of a sphere. The number and arrangement of these defects can vary, providing flexibility for tuning directional interactions that are more difficult to achieve through other methods. When this project was started, many theoretically predicted structures were not observed yet and control over defect location remained elusive. During this project, we have developed tools for the experimental realisation of nematic and smectic shells. We have experimentally reproduced some theoretically predicted structures and demonstrated the existence of new configurations that were not predicted before. Even more interestingly, we have shown that varying the elastic anisotropy of a nematic liquid crystal shell through temperature enables us to systematically control the number and orientation of defects formed. Such control opens up the possibility of engineering particles with tunable-valence and directional-binding capabilities, which can lead by self-assembling to micro-structured materials such as photonic crystals or metamaterials. Additionally, we have shown that the functionalisation of defects to induce self-assembly can be potentially achieved by including small hard-spheres in the liquid crystal phase. The results mentioned above have led to five publications (two of them have already been published in top-class scientific journals, and three of them are under consideration or in preparation), five communications in international conferences and three invitations to seminars. The impact of our results has been recognised by the scientific committees of prestigious journals and conferences and highlighted in the Soft Matter World Newsletters (January, 2012).
References
1. Lavrentovich, O.D. Liquid crystals, photonic crystals, metamaterials, and transformation optics. Proceedings of the National Academy of Sciences of the United States of America, 2011. 108(13): p. 5143-5144.
2. Lopez-Leon, T. and A. Fernandez-Nieves, Drops and shells of liquid crystal. Colloid and Polymer Science. 289(4): p. 345-359.
3. Lopez-Leon, T., et al., Frustrated nematic order in spherical geometries. Nature Physics. 7(5): p. 391-394.
4. Utada, A.S. et al., Monodisperse double emulsions generated from a microcapillary device. Science, 2005. 308(5721): p. 537-541.
5. Lopez-Leon, T., et al., Nematic-Smectic Transition in Spherical Shells. Physical Review Letters. 106(24): p. 4.
6. Shin, H., M.J. Bowick, and X.J. Xing, Topological defects in spherical nematics. Physical Review Letters, 2008. 101(3): p. 4.
7. Sec, D., et al., Ground states of topological defects in nematic shells with elastic anisotropy. Physical Review Letters, 2012(submitted).
8. Lopez-Leon, T., et al., Smectic shells. Journal of Physics: Condensed Matter, 2012. 24.
9. Gharbi, M.A. et al., Colloids trapped on nematic shells: textures and dynamics. 2012 (in preparation).
