Confinement effects on lyotropic nematic liquid crystal phases of graphene oxide dispersions

Graphene oxide (GO) forms well ordered liquid crystal (LC) phases in polar solvents. Here, we map the lyotropic phase diagram of GO as a function of the lateral dimensions of the GO flakes, their concentration, geometrical confinement configuration and solvent polarity. GO flakes were prepared in water and transferred into other polar solvents. Polarising optical microscopy (POM) was used to determine the phase evolution through the isotropic-biphasic-nematic transitions of the GO LC. We report that the confinement volume and geometry relative to the particle size is critical for the observation of the lyotropic phase, specifically, this determines the low-end concentration limit for the detection of the GO LC. Additionally, a solvent with higher polarisability stabilises the LC phases at lower concentrations and smaller flake sizes. GO LCs have been proposed for a range of applications from display technologies to conductive fibres, and the behaviour of LC phase formation under confinement imposes a limit on miniaturisation of the dimensions of such GO LC systems which could significantly impact on their potential applications.


Introduction
Graphene oxide (GO) has garnered significant attention in recent years as a derivative of graphene which shows significant mechanical strength and chemical versatility while being produced and processed in large quantities, specifically for mechanical reinforcement in nano-composites, as a source of reduced GO for electrical and thermal applications, and as an optical material [1,2]. GO is known to form highly stable colloidal liquid crystalline phases in aqueous and a variety of organic polar solvents, which is essential for some of GO's most promising applications such as wet-spun fibres and GO liquid crystal displays [3][4][5][6][7][8][9][10][11][12][13][14].
Liquid crystals (LC), in general, are characterised by their fluidity combined with ordering that results in directional and anisotropic properties common to crystalline systems [15][16][17]. The LC phase may be formed when the material is made up of shapeaniso tropic (rod or disc-like) molecules or anisotropic (non-spherical) particles. When the liquid crystalline state is achieved purely by temperature variation, then the phase is called thermotropic. When colloids of aniso tropic particles form LC phases within a particular concentration and temperature range, they are said to be lyotropic [18]. In general, the colloidal suspensions of geometrically anisotropic particles can produce a LC phase above a critical concentration. The critical volume fraction V crit depends on the aspect ratio, A R = W/L, of the particle as V crit ≈ 4/A R = 4 L/W [19], where for 2D particles, L and W represent the thickness and the lateral width.
The liquid crystalline behaviour of anisotropic colloids was first observed in the tobacco and tomato mosaic virus (TMV) [20] and vanadium pentoxide (V 2 O 5 ) [21] in the early 20th century. A few decades later Mourchid et al studied colloidal plate-like charged particles and clay particles to report liquid crystalline behaviour [22]. They found that the concentration and the ionic properties of the particles are crucial for controlling the stability of the suspension. The first theoretical work was reported by Onsager [19]. The theory of Onsager was based on the fact that when the concentration of particles reaches a certain level, the freedom of the particles is constrained. As a result, the entropy of the colloid decreases due to overlapping excluded volumes of the particles.
Confinement effects on lyotropic nematic liquid crystal phases of graphene oxide dispersions 2 To compensate the entropy decrease, the particles start to acquire orientational order. Thus, above a critical concentration orientation order is achieved and a nematic LC phase is formed. Similarly colloidal suspensions of 1 dimensional (1D) carbon nanotubes (CNTs) have shown a phase transition to the nematic LC phase [23][24][25]. In CNT LCs, the order parameter, which is a measure of the degree of order of the LC phase, can be modified by controlling their length and entanglement [26].
The corresponding 2 dimensional (2D) nanoparticle is graphene, and it's derivative GO which is decorated with a variety of oxygen-containing functional groups such as carboxyl, hydroxyl and epoxide on its basal plane and edges [8,27]. GO retains a significant fraction of the mechanical strength of pristine graphene, is chemically versatile to a wide range of organic chemistry reactions due to the abundance of reactive functional groups, and can be exfoliated from graphite into monolayer particles that possess a large aspect ratio greater than 10 4 . The oxygen-containing functional groups distinguish GO from graphene in allowing for a high dispersibility in water and other polar solvents.
GO dispersions in polar solvents, especially water, are known to exhibit highly stable lyotropic nematic phases at fairly low concentrations, especially for particles of high aspect ratio. Such dispersions have been employed as a starting point for wet-spinning of GO fibres which display extraordinary strength and flexibility, and when converted to reduced (r)GO, also display high electrical conductivity [28]. GO LCs have also been demonstrated for LC display and other optical applications [4,5], and to produce conductive transparent electrodes to replace indium tin oxide in the display industry [29,30]. In all such applications, there is either a processing step or application design wherein the GO LC is subjected to a high degree of confinement, such as in a spinning nozzle or between the transparent electrodes of a display pixel. Simultaneously, there is a drive to produce and adopt GO particles of increasing size (and aspect ratio) as this confers improved mechanical, optical and electronic properties on the resulting material. It is therefore incumbent to study the effect of confinement on the formation, stability and observability of the GO LC phase as function of other parameters such a particle size and concentration.
In this study, GO LC samples with mean particle sizes from 0.5 to 20 µm and concentration from 0.5 to 4 mg ml −l were studied within geometries of 50 to 500 µm thickness. In addition, the dependence of the lyotropic nematic phase on the GO-concentration in different solvents is examined, specifically deionised water (DIW), dimethylformamide (DMF) and dimethylsufoxide (DMSO). The interplay between cell thickness, flake concentration, flake size, isotropic solvent and temperature on LC phase stability was investigated and the regions of stable LC phase, biphasic and isotropic or pseodo-isotropic phases was mapped.

Sample preparation
GO was prepared from graphite flakes in DI water by a modified Hummers' method [31,32] and then redispersed into two other solvents, DMF and DMSO. Briefly, graphite (10 g, 80 mesh, 94% C) was first treated with NaNO 3 (9 g, Sigma-Aldrich) and concentrated H 2 SO 4 (338 ml, Sigma-Aldrich) at room temperature (RT) for 3 h to obtain intercalated graphite. The mixture was cooled in an ice bath and 45 g of KMnO 4 (Sigma-Aldrich) were gradually added. After addition of the oxidizing agent, the reaction mixture was stirred at RT for 1 week to complete the oxidation. The oxidised graphitic slurry was then diluted with a solution of 5% H 2 SO 4 , followed by the slow addition of 5 g of H 2 O 2 (Sigma-Aldrich) as solution. The resulting graphite oxide was purified by repeated centrifugation and redispersion in DI water until the pH of the supernatant was neutral. Appropriate amounts of GO were dried, weighed and redispersed in DI water, DMF and DMSO to obtain a concentration of 4 mg ml −1 . To avoid the flake damage, the dispersions were made by stirring the GO powder for 1 week with the magnetic stirrer, followed by 10 min of high shear mixing at 6000 RPM with a Silverson Model L4M shear mixer. This process ensures that the GO concentration is solely determined by the initial mass of dry GO and the solvent volume; there is no loss of GO material during redispersion or other factors that might affect concentration. The other concentrations were made by diluting the stock dispersion. GO dispersions of different size distributions were prepared by starting with a dispersion of large mean flake size and subjecting it to different durations of shear or ultrasonic mixing, namely shear mixing for 1, 2, 5 h respectively using 8000 rpm for the first 3 sizes, and ultrasonication (100% power, 37 kHz) for 2 h for the smaller size.
For the sake of convenience, we can approximate the density of GO to that of the parent material graphite at 2266 mg cm −3 , which allows for an interconversion of 1.0 mg ml −1 to 0.102 wt.% to 0.044 vol.% of GO in aqueous suspension.
Microscopy slide glasses of 2.5 cm × 2.5 cm were cut and washed in acetone and methanol in a sonication bath for 30 min. To study the LC properties by means of POM, sandwich cells were assembled with different gaps of 50, 100, 150, etc up to 500 µm controlled by spacers and glued using a UV curable glue (Norland N68) as shown in figure 3(a). The cells were filled by capillary action with the dispersions of different GO concentrations.

Characterisation
Scanning electron microscopy (SEM) was performed on a Zeiss Ultra SEM. UV-vis spectroscopy was carried out in a Genesys 10S spectrophotometer. Texture image acquisition was performed by means of a Leica DMLP polarising microscope and a uEye digital camera at resolution 2048 × 1088 pixels. The sample temperature was controlled by a Linkam TMS94 hot-stage and temperature controller, with relative accuracy of ±0.1 K. The zeta-potential measurements were carried out by using a Malvern Zetasizer Nano Z apparatus. The mass loss upon heating and reducing the GO to rGO was examined via thermogravimetric analysis (TGA, Q5000 from TA Instruments). Phase transition studies were carried out using differential scanning calorimetry (DSC, Perkin Elmer Diamond).

Optical absorption and dispersion colour
As shown in figure 1(a), the samples are named as GO-DIW, GO-DMSO, and GO-DMF respectively. We note that the GO-DIW solutions appear lighter than those of the other samples, when in fact the concentrations are identical. The fact that different GO dispersions of the same concentration in different solvents have different colour has been previously reported [33][34][35]. This colour variation was correlated to UV-vis absorption spectroscopy on the three GO dispersions at concentration of 0.02 mg ml −1 ( figure 1(b)), which indicates that GO dispersed in DMF and DMSO have higher absorption intensities compared to the GO in DIW, whereas the shape of the spectra in the visible region is similar, so more accurately, there is a difference in colour intensity rather than colour itself, between the three dispersions. The mechanism behind this colour difference is still under investigation. Pendolino et al attributed a difference in the colour of GO dispersions in water and methanol to structural modifications when dispersed in different polar solvents [36]. Results of UV-vis spectra and visual inspection could be interpreted as chemical modification of GO dispersed in DMF and DMSO, considering the fact that an increased absorption intensity is an indication of the extension of pi-pi * conjugated domains which occurs during the reduction/deoxygenation of GO. In that case a red shift of pi-pi * (230 nm) transition peak will occur. Unfortunately, from our measurements we cannot observe the 230 nm peaks of GO in DMF and DMSO because the residual solvents absorption peaks in the same region. On the other hand, we consider the significant structural differences regarding the water and DMF/DMSO as solvents; water is polar protic while DMF and DMSO are aprotic respectively, they exhibit different relative static permittivities (often referred to as dielectric constant), and different hydrogen bonding abilities. We speculate that the mechanism of stabilisation between GO-DIW and GO-DMF/DMSO is different. Whereas in water the GO is stabilised by hydrogen bonds formed with the water molecules (protic solvent) and electrostatic repulsion between GO flakes because of the negatively charged carboxylate groups, in DMF and DMSO (aprotic solvents) the mechanism of stabilisation can be rather attributed to a layer of confined solvent near the surface which prevent aggregation via sterics. This results in a different solvent molcule density at the viscinity of the GO flakes compared to the bulk solvent volume, resulting in a change in the local refractive index (RI), even though the bulk RI of the three solvents are similar. This in turn would result in higher absoption intensities, and consqeuently darker colour. A detailed study of this phenomenon is beyond the scope of this paper but it suffices to note here that the dispersion concentrations are accurate and different interaction mechanisms between the GO flakes and solvents are responsible for the observed colour variations.

Size distribution of GO dispersions
The size distribution of all GO dispersions were characterised using SEM (figure 2). The sizes of 200 flakes from multiple SEM images for each suspension was measured manually using ImageJ ® , always in the horizontal direction through the centre of the flake in order that shape anisotropies do not skew the distribution results; it is assumed that the drying process does not introduce any orientation anisotropy. A typical feature of the exfoliation process, and also due to the irregularity and various polygonal shapes of the GO flakes, the size distributions are relatively broad for all four GO samples as shown in the inset of figure 2. The size distribution is affected by the particle and grain size in the starting graphite material, the intercalation, oxidation and exfoliation conditions in the preparation of GO, and the subsequent redispersion and size reduction efforts that involve shear or ultrasonic mixing. All these processes tend to yield broad size distributions. Nonetheless, the dispersions we have selected have statistically significant differences in their size distributions.

Colloidal stability and choice of solvents
The zeta (ζ)-potential is a widely accepted significant indicator of the stability and sedimentation behavior of colloidal dispersions. The magnitude of the ζpotential demonstrates the level of electrostatic repulsion between charged particles in the dispersant medium. When the ζ-potential is small, attractive forces may overcome the repulsive forces, the dispersion will destabilise and the particles aggregate. However, high ζ potential (negative or positive) confirms the stability of colloidal suspensions and their resistance to aggregation [37,38]. The stability of diluted GO-DIW were examined by the ζ-potential technique, yielding ζ-potential of −46 mV at a concentration of 0.02 mg ml −1 , which is more negative than that of standard stable colloids. The values are an indication of the excellent dispersion of GO in water [4].
The choice of other solvents for this work was based on a set of criteria specific to lyotropic phase formation and study. The solvents should be capable of dispersing GO stably at high concentration, without aggregation, and without the need for ultrasonication which will affect the flake size. Furthermore, the solvent should be high-boiling to prevent evapouration and variation of concentration over the course of the experiment. This rules out solvents like N-methylpyrrolidone (NMP) and N-cyclohexyl-2-pyrrolidone (CHP) which requires ultrasonication for complete dispersion, and  low-boiling solvents such as acetone and tetrahydrofuran (THF). DMF and DMSO adhere to the criteria outlined here, while providing significant variation in relative static permittivity to water, and were therefore slected for this study.

Effect of boundary conditions
LCs in general are strongly influenced by the boundary conditions of the substrates, confinement and anchoring as a result of the interaction between the LC molecules and the bounding surfaces [39]. A variety of polymer layers, spin coated and rubbed are employed to promote alignment of thermotropic LC phases [39,40]. However, for the systems investigated here, none of these procedures have provided any particular alignment as commonly observed for thermotropic LCs. As can be seen in figure 3, polarizing microscopy reveals that alignment of the GO lyotropic nematic can also be obtained without any surface modification to the glass surfaces, as the substrates used were only cleaned, but not treated for any particular alignment. Uniform birefringence indicates a homogeneous alignment of the director n throughout the cell and over large length scales, i.e. the GO plane is parallel to the bounding glass plates. Here the suspensions were examined in two geometries; (i) the cell bounded on the sides by spacers with a glass coverslip covering the top and bottom of the cell, producing a 'closed channel' and (ii) a similar cell but without a top glass coverslip, producing an 'open channel' geometry respectively. The texture of cell (i) is shown in figure 3(b), along with the schematic side-view diagram of the cell including the GO flake orientation, figure 3(c). In the case of GO flakes, the director N, i.e. the most common axis of orientation, is defined as the normal to the flake, thus perpendicular to the plane of the flake, and indicated by arrows in the figure. The central part of the cell shows a dark phase appearance with zero birefringence (light propagation parallel to the optic axis), known as the homeotropic or pseudo-isotropic orientation as it mimics the lack of birefringence observed in the isotropic phase. The birefrengence becomes pronounced towards the edges of the cell. A splay of the GO flakes, thus a bend of the director, is observed as we move from the bounding glass plate towards the middle of the cell, changing the transmitted light intensity from bright to dark. The opposite scenario is observed moving further to the opposite bounding plate, exhibiting a symmetric pattern from dark to bright. This suggests that when GO is bound by parallel surfaces, owing partly to the strong interaction between the hydrophillic GO and glas surfaces, the flakes align parallel to the bounding surfaces.
However, in cell (ii) without the glass cover, figures 3(d) and (e), the birefringent area is visible throughout the whole cell, the transmitted intensity only slightly reduced in the middle of the cell, due to the slight splay of the GO flakes caused by the curva-ture of the LC-air interface. In this configuration the director N follows the curvature of the free top surface. The POM texture can be attributed to the GO alignments schematically depicted in figure 3(e). The direction of the flakes with respect to glass has been investigated previously [10], where it was proposed that the observed alignment relative to the top and bottom sides of the cell is likely to be metastable since it is partially triggered by the assembling kinetics during the cell preparation by capillary action, and also by the elasticity of the LC phase. In contrast, we found that the homogeneous, well aligned texture can be retained for days as long as the cell is completely sealed and no solvent evaporates. Both geometries point to the strong, planar anchoring between GO flakes and the glass surface.
The direction of the alignment has been further investigated by rotating the sample in the channel geometry between crossed polarizers. As shown in figure 4, by rotating the cell along the viewing axis perpend icular to the viewing direction, the bright and the dark states are reached with a periodicity of 90°. This indicates a well-aligned director of the liquid crystalline phase of GO colloids, with lowest transmission at 0° and 90° and maximum transmission at 45°. Figures 5(a)-(c) show GO textures of the lyotropic nematic phase in GO suspensions for different solvents as a function of concentration and sample thickness. Since the birefringence of the lyotropic nematic LC phase is of the order of 10 −3 [18], the thickness of the samples has to be markedly larger compared to the samples prepared for thermotropic LC phases [41,42]. Here the range of the thickness of the sandwich cells is d = 50-500 µm, and the range of the LC concentrations is c = 0.5-4.0 mg ml −1 for all solvents (DIW, DMSO and DMF). For all three solvents it is seen that the nematic lyotropic phase can not be observed for low GO concentrations or narrow cell gaps. This could be due to two reasons: (i) the birefringence is suppressed by homeotropic or pseudo-isotropic alignment, or (ii) the LC phase is altogether suppressed by thin cell gaps, leading to the formation of an isotropic phase, at small cells gaps and low concentrations. The macroscopic appearance of the two scenarios is nearly indstinguisgable.
However, the total suppresion of the nematic phase due to narrow cells gaps is counterintuitive, rather, one would expect the opposite behaviour based on the strong anchoring and planar alignment of GO flakes at the glass surface as seen in figure 3.
On the other hand, it should be noted that for thermotropic LCs, the application of mechanical shear or a magntic field can generally be used to at least temporarily reorient the director from pseudo-isotropic, homeotropic orientation to a birefrengent, planar one. This leads to a temporary tilt of the molecules and thus to birefringence, which can be observed as a bright flash in polarizing microscopy. A respective effect will not be observable for a true isotropic phase. For GO LCs, the application of mechanical shear caused no birefringence which would be detected as flash of transmitted light. Secondly, the application of a magnetic field [43,44] at a strength of 0.2 T at an angle of ~80° to the director (in situ under the microscoe) does not induce reorientation and planar alignment either.
The uncharacteristic lack of response to shear and magnetic fields could also be attributed to the strong anchroing of the GO flakes by the bounding glass surfaces, and the consequently imposed ordering that propogates the whole cell, the effect of which is particularly stronger for thinner cell gaps. We therefore favour the first interpretation, that the confinement imposed here results in the formation of homeotropic alignment and pseodo-isotropic behaviour, reinforced by the strong anchoring of the GO flakes between parallel glass surfaces.
It should further be pointed out that the observed behaviour is independent of solvent. The pseudoisotropic phase, observed at low concentration or small gaps, transforms into a biphasic region characterised by partial birefringence at moderate conentrations or gaps, after which the lyotropic nematic phase eventually fully develops and is observable even for small cell gaps at high-enough concentrations, or at low concentraitons for large-enough gaps. From the texture grids it can clearly be seen that the phase formation is most easily achieved for DIW, as compared to DMSO and  While for the other solvents, the transmitted intensity fluctuates somewhat with respect to sample thicknesses, most likely due to director misalignment. The measurements indicate that the onset of liquid crystalline phase observation for GO-DIW is occurring at lower sample thicknesses for equal concentrations as compared to GO-DMSO and GO-DMF. Or from a different perspective, at a comparable sam-ple thickness the nematic phase of GO-DIW is better developed than for the other two solvents. Again, we believe that this is due to better phase formation either due to the protic nature or higher relative static permittivity of water.

Effect of GO flake size
The size or the aspect ratio of the GO flakes plays an essential role in the formation of the lyotropic phase [11]. There is a limit for the particle size of the sample to yield an observable lyotropic nematic phase. It is known that below GO flakes of very small size do not order to produce a LC phase and are instead isotropically oriented. Figure 6 shows the dependence of the lyotropic nematic phase on the size of the GO flakes as a function of gap size. When confinement is  imposed, the isotropic appearance, in the form of the pseudo-isotropic phase, extends even to higher GO flake sizes for the smaller gap sizes. The transitions between the pseudo-isotropic to biphasic to nematic states are clearly seen for all flake sizes larger than 0.27 µm. In another view, the lyotropic liquid crystalline phase formation in favour of pseudoisotropic behaviour is enhanced for increasing GO flake size for any given gap.

Nematic to isotropic phase transition
So far, it has been shown that the transition from an pseudo-isotropic to a lyotropic nematic phase state T N-I depends on the size of the GO flakes, their concentration, thickness of the sample and the polarity of the solvent. Addionally, both temperature and concentration dependence can be incorporated into the phase diagram for describing the lyotropic nematic of GO suspensions. Figure 7(a) shows the temperature stability of the LC phases by POM while the sample was being heated. This did not reveal any trans ition to an isotropic phase in the temperature region starting from RT to the vicinity of the boiling point of the solvent or maximum accessible temperature with the LC test cells before destruction. The TGA scan, figure 7(b), of GO clearly shows that there is a mass loss upon heating. Some of the mass-loss in the temper ature range of 25-165 °C can be attributed to the water loss, CO and CO 2 [45], despite having dried the GO previously. The chemical transition of GO to rGO occurs at approximately T = 165 °C (see figure 7(b)), a temperature which was also observed by Cui et al [45] for this process. Above 165 °C, the hydrophobic nature of rGO dominates dispersion stability and results in flocculation or aggregation, and consequently rGO does not form LC phases in aqueous media [26]. Thus TGA has revealed that the GO employed in our invest igations is chemically stable from RT up to approximately 165 °C.
Secondly, DSC was used to possibly reveal any thermodynamic changes. As shown in figure 7(c), two samples (GO-DIW) with concentrations 1.1 and 0.55 mg ml −1 were investigated. The results of DSC, similar to POM, did not show any phase transition up to 60 °C. To avoid contaminating the DSC system, the maximum temperature of 60 °C was chosen, because of the solvent, the sample pans have to be heated with a hole in the lid, allowing evaporation at increased temper atures. Similarly, Kim et al have reported that the nematic phase was maintained up to the boiling point of the solvent [11]. It can thus be concluded that once the lyotropic phase has been formed, it is very stable. In contrast to common lyotropic phases [18], the mesogenic units of GO LC are solid flakes with a 2D carbon backbone with functional groups and not produced by weak bonding of small amphiphilic molecules for instance, energies of the order of kT are not likely to break bonds easily upon heating to a temperature T, where k is the Boltzmann constant.
It has been demonstrated that graphene LCs can be used in displays based on Kerr effect [4] which would have the advantage of fast switching and no viewing angle compensation considerations. Additionally, GO LCs is the starting material for wet-spun graphene fibres [46] which have potential applications in smart textiles and sensors. Lastly, GO and its derivatives encounter a number of confinement and flow conditions during their production, processing and applications such as ink-jet printing [47], which will all be impacted by the confinement effects reported here.

Conclusions
Stable dispersions of GO in DI water and other solvents were prepared at a range of particle sizes and concentrations. The GO suspensions exhibited a lyotropic nematic LC phase that is dependent on a variety of parameters. Firstly, liquid crystalline behaviour is more pronounced for increasing concentration and especially also for increasing size of the GO flakes. Our investigations indicate that for small cell gaps the birefringence is suppressed and can thus not be observed by polarising microscopy. This is attributed to the formation of a strongly anchored homeotropic alignment of the GO flakes leading to a pseudo-isotropic behaviour in favour of the birefringent lyotropic nematic phase. It is also observed that the solvent medium plays an important role in the formation of the lyotropic nematic phase; in water which is a protic solvent with higher relative static permittivity, the nematic phase forms at lower GO concentrations and at smaller flake sizes. Confinement conditions and GO-substrate interactions have a pronounced effect on the orientation of the lyotropic nematic director even for untreated substrates. The confinement effect we report is valid across different solvents with different degrees of lyotropic phase stability. These confinement effects should be taken into consideration when designing processes and products that employ GO LC phases. Employing several methods, such as POM and DSC, we could not detect any phase changes to an isotropic phase simply on heating the samples up to the boiling point of the solvent.