Lyotropic Liquid Crystals from Colloidal Suspensions of Graphene Oxide

crystals

Review Lyotropic Liquid Crystals from Colloidal Suspensions of Graphene Oxide

Adam P. Draude and Ingo Dierking * Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK * Correspondence: [email protected]

Received: 20 August 2019; Accepted: 30 August 2019; Published: 31 August 2019

Abstract: Lyotropic liquid crystals from colloidal particles have been known for more than a century, but have attracted a revived interest over the last few years. This is due to the developments in nanoscience and nanotechnology, where the liquid crystal order can be exploited to orient and reorient the anisotropic colloids, thus enabling, increasing and switching the preferential properties of the nanoparticles. In particular, carbon-based colloids like carbon nanotubes and graphene/graphene–oxide have increasingly been studied with respect to their lyotropic liquid crystalline properties over the recent years. We critically review aspects of lyotropic graphene oxide liquid crystal with respect to properties and behavior which seem to be generally established, but also discuss those eﬀects that are largely unfamiliar so far, or as of yet of controversial experimental or theoretical outcome.

Keywords: liquid crystal; graphene oxide; lyotropic; colloid; nematic

1. Introduction Many of the liquid crystal (LC) phases known from applications in displays are based on rod-shaped molecules, so called calamitic mesogens, which exhibit the liquid crystal behaviour as a function of changing temperature and are called thermotropic. Nevertheless, for the formation of liquid crystals only general shape anisotropy of the molecules is necessary, and in 1977, Chandrasekhar et al. [1] reported liquid crystallinity from disk-shaped molecules, called discotic liquid crystals, which are also part of the family of thermotropic LC phases. But liquid crystallinity can also be observed as a function of changing concentration of either amphiphilic molecules, or anisotropic nanoparticles and colloids, in an isotropic host ﬂuid, often water. This leads to a wholly new class of LCs, the lyotropic phases, which are the topic of this paper and indeed of the whole journal volume of this special issue of Crystals. Besides those formed from amphiphilic molecules, several types of lyotropic LCs may be distinguished. Chromonics [2,3] are liquid crystals of dissolved rigid dyes, thus ﬂat molecules, in an isotropic solvent. These stack to form super-molecular structures which then exhibit nematic and columnar phases. Inorganic liquid crystals [4] are lyotropics that can be formed by rod-like colloids, such as vanadium pentoxide, V2O5, and other minerals, but also by disc-shaped colloids, especially clays [5–7]. Such systems have already been observed by Langmuir in 1938 on bentonite clays [8] and form the basis of the Onsager theory, which will be discussed herein. Somewhere in between the molecular size of chromonic dyes and the macroscopic platelets of clays, lies graphene oxide. Since the discovery of graphene in 2004 [9], a stable, two-dimensional hexagonal lattice of carbon with quite surprising and unprecedented physical properties [10], this material has attracted enormous interest (Figure1a). This is on the one side founded by questions of fundamental research, and on the other side by the promise of a large range of possible high volume technological applications. When working with graphene in a liquid crystal environment, one will unfortunately quickly arrive at the conclusion that these composites and mixtures are by no means

Crystals 2019, 9, 455; doi:10.3390/cryst9090455 www.mdpi.com/journal/crystals Crystals 2019 9 Crystals 2019,, 9,, 455x FOR PEER REVIEW 22 of of 20 easy to handle, because graphene is largely insoluble in nearly all liquid solvents. This is very easy to handle, because graphene is largely insoluble in nearly all liquid solvents. This is very different different for graphene–oxide (GO) which exhibits different functional groups at the edges and the for graphene–oxide (GO) which exhibits different functional groups at the edges and the plane of the plane of the graphene oxide sheets, and is readily soluble in many solvents, including water, which graphene oxide sheets, and is readily soluble in many solvents, including water, which is a significant is a significant advantage for environmentally friendly applications (Figure 1b). At certain advantage for environmentally friendly applications (Figure1b). At certain concentrations, roughly concentrations, roughly > 0.1–1 wt%, GO often exhibits very stable lyotropic nematic phases [11–13]. > 0.1–1 wt%, GO often exhibits very stable lyotropic nematic phases [11–13]. One of the interesting One of the interesting aspects of GO liquid crystals is the possibility of self-organized and self- aspects of GO liquid crystals is the possibility of self-organized and self-ordered systems of graphene ordered systems of graphene oxide. This order can then easily be manipulated by application of oxide. This order can then easily be manipulated by application of external stimuli, such as boundary external stimuli, such as boundary conditions, mechanical shear, but possibly also electric and conditions, mechanical shear, but possibly also electric and magnetic fields. After obtaining a certain magnetic fields. After obtaining a certain directional order one could wash away or evaporate the directional order one could wash away or evaporate the solvent, leaving an ordered GO structure, solvent, leaving an ordered GO structure, which may even be reduced chemically or through heat which may even be reduced chemically or through heat application to produce reduced graphene application to produce reduced graphene oxide (rGO), which displays some of the originally oxide (rGO), which displays some of the originally desirable graphene properties. Lyotropic graphene desirable graphene properties. Lyotropic graphene oxide liquid crystals are thus of immense interest oxide liquid crystals are thus of immense interest for nanotechnology and its applications. There have for nanotechnology and its applications. There have been several review articles on the properties of been several review articles on the properties of GO liquid crystals [14–16]. In this paper we want to GO liquid crystals [14–16]. In this paper we want to give a short critical account of what is known, give a short critical account of what is known, what is not yet known, and what are the controversial what is not yet known, and what are the controversial questions with regards to graphene oxide questions with regards to graphene oxide liquid crystals. Effects of flake size and solvent will be liquid crystals. Effects of flake size and solvent will be discussed, alignment, addition of salts and discussed, alignment, addition of salts and polymers, as well as electro-optic properties, and electric polymers, as well as electro-optic properties, and electric and magnetic field effects. and magnetic field effects.

2. Graphene and Graphene Oxide 2 Pristine graphenegraphene isis aa two-dimensionaltwo-dimensional hexagonal hexagonal lattice lattice of of sp sp2 hybridized hybridized carbon carbon with with a basisa basis of two,of two, giving giving rise rise to a honeycombto a honeycomb structure structure [10]. Graphene [10]. Graphene oxide is oxide a very is di aﬀ veryerent different material tomaterial graphene. to Graphenegraphene. isGraphene often obtained is often by obtained mechanical by exfoliation mechanical of exfoliation graphite (the of so-calledgraphite Scotch(the so-called Tape® method) Scotch orTape® grown method) by chemical or grown vapor by deposition. chemical On vapor the otherdepos hand,ition. graphite On the thatother has hand, undergone graphite treatment that has to becomeundergone graphite treatment oxide to readily become exfoliates graphite into oxide monolayers readily exfoliates when dispersed into monolayers in water (Figure when1 dispersed)[ 17]. Thus, in graphenewater (Figure oxide 1) is often[17]. easierThus, tographene produce inoxide large is quantities often easier than to graphene produce and in islarge readily quantities dispersible than in solutiongraphene for and storage is readily or further dispersible processing in solution [18]. There for storage are two or main further processes processing described [18]. in There the literature are two formain producing processes graphite described oxide, in thethe Hummersliterature [for19] producing and Brodie graphite [20] methods. oxide, the Hummers [19] and Brodie [20] methods.

Figure 1. The structures of pristine graphene (a) andand aa modelmodel ofof graphenegraphene oxideoxide ((bb).). TheThe functionalfunctional groups of graphene oxide can vary depending on its method of production and its thermal andand/or/or storage history. The structure of graphene oxide is reminiscent of graphene but the lattice is now distorted and The structure of graphene oxide is reminiscent of graphene but the lattice is now distorted and the covalent bonding of oxygen functional groups such as epoxy, hydroxyl and carboxyl groups [21] the covalent bonding of oxygen functional groups such as epoxy, hydroxyl and carboxyl groups [21] means much more of the carbon is now sp3 hybridized. The disruption to the sp2 bonding network means much more of the carbon is now sp3 hybridized. The disruption to the sp2 bonding network means graphene oxide is not electrically conductive. Typically, graphene oxide is produced by a means graphene oxide is not electrically conductive. Typically, graphene oxide is produced by a modiﬁed Hummers method [22] and the degree of oxidation is characterized by X-ray photoelectron modified Hummers method [22] and the degree of oxidation is characterized by X-ray photoelectron spectroscopy (XPS) measurements. From XPS measurements one can determine the ratio of oxygen spectroscopy (XPS) measurements. From XPS measurements one can determine the ratio of oxygen to carbon atoms in the material, which is often taken as a measure of how oxidized the graphene to carbon atoms in the material, which is often taken as a measure of how oxidized the graphene sheet is. Graphene oxide can be reduced by thermal or chemical means, and the product is known as

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Crystals 2019, 9, x FOR PEER REVIEW 3 of 20 sheet is. Graphene oxide can be reduced by thermal or chemical means, and the product is known as rGO.rGO. When When GO GO is is reduced, reduced, the the first ﬁrst change change to to occur occur is is that that the the C–O C–O peak peak in in XPS XPS decreases decreases in in intensity intensity relativerelative to the C–C and the C–O=O/C=O C–O=O/C=O bonds bonds (Figure (Figure 22))[ [23,24].23,24]. This This can can be be interpreted interpreted as as a a relative relative decreasedecrease in the abundance of epoxy groups (which only include C–O bonds) on the GO surface.

Figure 2. Figure 2. De-convolvedDe-convolved X-ray X-ray photoelectron photoelectron spectroscopy spectroscopy (XPS) (XPS) spectra spectra in in the the region region of of the the C1s C1s core core electron binding energy. In graphene–oxide (GO) (a), three peaks associated with the bonding of oxygen electron binding energy. In graphene–oxide (GO) (a), three peaks associated with the bonding of to carbon are identiﬁed. In rGO (b), the overall intensity of these peaks is reduced relative to that oxygen to carbon are identified. In rGO (b), the overall intensity of these peaks is reduced relative to originating from C-C bonds. Figure adapted from Chen et al. [23] with permission of Springer Nature. that originating from C-C bonds. Figure adapted from Chen et al. [23] with permission of Springer Nature. Stable dispersions of graphene oxide in appropriate solvents can be described as a colloid—a suspension of one phase (in this case a solid) inside another. Colloids of anisodiametric Stable dispersions of graphene oxide in appropriate solvents can be described as a colloid—a (shape-anisotropic) particles are known to make lyotropic liquid crystal phases, and the same is suspension of one phase (in this case a solid) inside another. Colloids of anisodiametric (shape- true of graphene oxide. anisotropic) particles are known to make lyotropic liquid crystal phases, and the same is true of graphene3. Colloidal oxide. Liquid Crystals of Graphene Oxide

3. ColloidalLiquid crystalsLiquid Crystals are soft condensedof Graphene matter Oxide systems which exhibit orientational ordering of their basic units (and in some cases, a degree of positional order) as a solid phase does, but which can also flow.Liquid As mentioned crystals are above, soft therecondensed are two matter main classessystems of which liquid exhibit crystals—thermotropic orientational ordering and lyotropic of their basic(Figure units3)[ (and25]. Thermotropicin some cases, a liquid degree crystals of position are systemsal order) in as which a solid phases phase does, exhibiting but which liquid can crystal also flow.properties As mentioned can be observed above, to there occur are between two main the cla solidsses and of liquidliquid states.crystals—thermotropic Thus, temperature and and lyotropic pressure (Figure 3) [25]. Thermotropic liquid crystals are systems in which phases exhibiting liquid crystal are the main variables of state which alters their phase. The best known example of thermotropic liquid properties can be observed to occur between the solid and liquid states. Thus, temperature and crystals are the rod-like (calamitic) molecules found in everyday display screens [26]. Lyotropic liquid pressure are the main variables of state which alters their phase. The best known example of crystals are systems of at least two components, and it is their relative concentration that brings about thermotropic liquid crystals are the rod-like (calamitic) molecules found in everyday display screens [26]. orientational ordering of self-assembled structures [27]. Examples include the columnar and lamellar Lyotropic liquid crystals are systems of at least two components, and it is their relative concentration phases of amphiphilic molecules in water [28]. Amphiphilic lyotropic liquid crystals are also the that brings about orientational ordering of self-assembled structures [27]. Examples include the most common type of all liquid crystals, since their lamellae form the basic structure of biological cell columnar and lamellar phases of amphiphilic molecules in water [28]. Amphiphilic lyotropic liquid membranes [27,29]. Colloids of anisodiametric particles in liquid solvents can also possess orientational crystals are also the most common type of all liquid crystals, since their lamellae form the basic ordering at sufficiently high concentrations [30]. Though the structures that are aligning are quite structure of biological cell membranes [27,29]. Colloids of anisodiametric particles in liquid solvents different to the case of amphiphiles, they are nevertheless referred to as lyotropic liquid crystals. can also possess orientational ordering at sufficiently high concentrations [30]. Though the structures that are aligning are quite different to the case of amphiphiles, they are nevertheless referred to as lyotropic liquid crystals.

Crystals 2019, 9, 455 4 of 20 Crystals 2019, 9, x FOR PEER REVIEW 4 of 20

Crystals 2019, 9, x FOR PEER REVIEW 4 of 20 Liquid Crystals

Thermotropics Lyotropics

High Low Molecular Structures Anisodiametric Molecular weight formed from colloid weight amphiphilic particles molecules

e.g. main- and e.g. calamitic, bent- e.g. lamellae in e.g. Tobacco side-chain liquid core and discotic concentrated detergents, mosaic virus, crystal polymers molecules biological cell membranes clays, dyes, graphene oxide

FigureFigure 3. 3. FlowFlow diagram diagram showing showing the the nomenclature nomenclature used used in in the the field ﬁeld of of liquid liquid crystals. crystals. Examples Examples are are given of each type of liquid crystal (LC). givenFigure of each3. Flow type diagram of liquid showing crystal the (LC nomenclature). used in the field of liquid crystals. Examples are given of each type of liquid crystal (LC). In 2010, Behabtu et al. [31] described the observation in polarized optical microscopy (POM) In 2010, Behabtu et al. [31] described the observation in polarized optical microscopy (POM) of of birefringence in suspensions of graphene in chlorosulphonic acid. The authors interpreted these birefringenceIn 2010, inBehabtu suspensions et al. [31] of described graphene the in observation chlorosulphonic in polarized acid. Theoptical authors microscopy interpreted (POM) theseof observations as being due to orientational alignment and hence lyotropic liquid crystallinity of the observationsbirefringence as inbeing suspensions due to orientational of graphene alignmentin chlorosulphonic and hence acid. lyotropic The authors liquid interpreted crystallinity these of the graphene ﬂakes [31]. Just one year later, Kim et al. [11], Dan et al. [13], and Xu and Gao [12,32] reported grapheneobservations flakes as [31]being. Just due one to orientational year later, Kimalignmen et al.t and[11] ,hence Dan lyotropic et al. [13] liquid, and crystallinity Xu and Gao of [12,32] the that graphene oxide dispersed in water behaved in the same way. reportedgraphene that flakes graphene [31]. Justoxide one dispersed year later, in waterKim et behaved al. [11], inDan the et same al. [13], way. and Xu and Gao [12,32] Typical POM images of graphene oxide dispersion in the nematic phase from Xu and Gao [12] reportedTypical that POM graphene images oxide of graphene dispersed oxide in water dispersion behaved in in the the nematicsame way. phase from Xu and Gao [12] are shownTypical in POM Figure images4. These of graphene images show oxide thedispersion evolution in the in thenematic microstructure phase from ofXu graphene and Gao [12] oxide are shown in Figure 4. These images show the evolution in the microstructure of graphene oxide dispersionsare shown asin theFigure concentration 4. These images is increased show the from evolution the isotropic in the phasemicrostructure (image 1) of through graphene the oxide biphase dispersions as the concentration is increased from the isotropic phase (image 1) through the biphase regiondispersions (image as 2) the and concentration into the nematic is increased liquid crystalfrom the phase isotropic (image phase 3). (image 1) through the biphase region (image 2) and into the nematic liquid crystal phase (image 3). region (image 2) and into the nematic liquid crystal phase (image 3).

FigureFigureFigure 4. 4. 4.PPolarized olarizedPolarized optical opticaloptical microscopy microscopy ((POM) (POM)POM) imagesimages images ofof of graphenegraphene graphene oxide oxide oxide dispersions dispersions dispersions increasing increasing increasing in in in 4 concentrationconcentration fromfrom thethe isotropicisotropic phasephase (1(1–55 x 1010−−44 fmf, mwhere, where fm fism theis the mass mass fraction fraction of GO of GO in the in the concentration from the isotropic phase (1–−5 x× 10 − fm, where fm is the mass fraction of GO in the dispersion)dispersion)dispersion) through through through the thethe biphasic biphasicbiphasic regionregion in in which which smsmall smallall clustersclusters clusters of of of birefringent birefringent birefringent domains domains domains can can can be beseen be seen seen 3 −3 3 −3 (2–1(2 – 110 x 10−3fm )fm and) and then then to theto the nematic nematic phase phase (3–3 (3–310 x 10fm− 3).fm The). The scale scale bar bar represents represents 200 200µm. µm. The The arrow (2 – 1× x 10− fm) and then to the nematic phase (3×–3 x− 10 fm). The scale bar represents 200 µm. The arrowinarrow the thirdin in the the image third third indicatesimage image indicates indicates the boundary thethe boundary between betweenbetween two nematic two two nematic domains. nematic domains. domains. This appears This This appears as appears a dark as brush asa a dark brush in polarized microscopy, analogous to the Schlieren textures of thermotropic nematic darkin polarized brush in microscopy, polarized microscopy, analogous to analogous the Schlieren to the textures Schlieren of thermotropic textures of nematic thermotropic liquid nematic crystals. liquid crystals. Reprinted with permission from Xu and Gao [12]. Copyright (2011) American liquidReprinted crystals. with permission Reprinted withfrom Xu permission and Gao [ from12]. Copyright Xu and Gao (2011) [12] American. Copyright Chemical (2011) Society. American Chemical Society. Chemical Society. Theoretically, the lyotropic phase behaviour of anisodiametric nano- and micro-particles is Theoretically, the lyotropic phase behaviour of anisodiametric nano- and micro-particles is describedTheoretically, by the Onsager the lyotropic theory [33 phase]. In his behavio originalur work of anisodiametric of 1949 [33], Onsager nano- and used micro a virial-particles expansion is methoddescribed to describe by the theOnsager orientational theory [33]. ordering In his that original had been work observed of 1949 in [33], suspensions Onsager of used tobacco a virial mosaic describedexpansion by method the Onsager to describe theory the orientational[33]. In his originalordering workthat had of been 1949 observed[33], Onsager in suspensions used a virialof expansion method to describe the orientational ordering that had been observed in suspensions of

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tobacco mosaic viruses. The underlying principle of the theory is that some volume a particle would otherwise be able to move into is excluded by the presence of a further particle i.e., the particles cannot interpenetrate one another. As the volume concentration of particles increases, this means there is less and less space available to a particular particle and for anisodiametric particles orientational ordering spontaneously emerges at a critical concentration. The transition is known as an entropy-driven transition [34]. Thus far, all known theories about entropy driven phase transitions in colloidal lyotropics have used the approximation that the particles are inflexible. Forsyth et al. [35] extended the Onsager model to the hard-disk fluid in 1977. Their findings showed that the phase behaviour of disks was distinctly different from rods. When the aspect ratio (diameter/thickness) of the discs increases, transitions to the biphase and the nematic phase occur at lower volume concentrations. The reverse happens for rods; as their aspect ratio (length/diameter) Crystalsincreases2019 so, 9 ,does 455 the minimum volume concentration required for the onset of orientational ordering.5 of 20 Bates and Frenkel [36], almost two decades later, have argued that the extension of Onsager’s viruses.theory from The underlying rods to discs principle is invalid. of the theory Furthe is thatrmore, some they volume argued a particle that wouldsince real otherwise systems be ableare topolydisperse, move into ismodel excluded systems by the should presence be as of well. a further Their particleapproach i.e., was the to particles use Monte–Carlo cannot interpenetrate simulations oneof infinitely another. thin As the disks volume with concentrationvarying polydispersity of particles (σ increases, = 〈D〉/√(〈D this2 〉 means– 〈D〉2), there where is less〈D〉 andis the less average space availablediameter toof athe particular disk). Their particle results and forare anisodiametric summarized in particles Figure orientational 5. For ease orderingof interpretation, spontaneously these emergesresults have at a been critical converted concentration. into units The typically transition used is in known experimental as an entropy-driven graphene oxide transition research (i.e., [34]. Thusmicrometers, far, all known vol %) theories using the about method entropy of Shen driven et al. phase [37]. transitionsIt can be seen in colloidalthat the width lyotropics of the have biphasic used theregion approximation increases with that increasing the particles polydispersity, are inflexible. but the range of polydispersity investigated in the simulationsForsyth does et al. not [35 stretch] extended to that the typically Onsager encountered model to the for hard-disk graphene fluidoxide in dispersions 1977. Their [37]. findings showedWhen that the the concentration phase behaviour of graphene of disks oxide was distinctly is further di increased,fferent from other rods. phases When can the be aspect observed. ratio (diameterThe first phase/thickness) to appear of the with discs increasing increases, concentrat transitionsion to is the the biphase lamellar and phase. the nematic In the lamellar phase occur phase, at lowerthe graphene volume oxide concentrations. sheets form The layers reverse which happens lead to forBragg rods; reflection as their in aspect small-angle ratio (length X-ray/ scatteringdiameter) increases(SAXS) [12]. so does On the minimumbasis of ellipsometry volume concentration measurements required and for freeze-fracture the onset of orientational cryo-SEM (scanning ordering. electronBates microscopy), and Frenkel Xu [36 and], almost Gao have two also decades proposed later, havethat this argued lamellar that phase the extension is in fact of chiral. Onsager’s They theorypropose from the rods structure to discs of is this invalid. phase Furthermore, to be an an theyalogue argued of thatthe sincetwist real grain systems boundary are polydisperse, phases of modelthermotropic systems liquid should crystals, be as well.with Theirlamellar approach blocks wasof GO to usetwisted Monte–Carlo relative to simulations one another of forming infinitely a thinhelical disks superstructure. with varying polydispersityThis observation (σ =is Drema/√(rkable,D2 – sinceD 2), neither where Dtheis graphene the average oxide diameter nor the of h i h i h i h i thesolvent disk). is Theirchiral, results so it is are not summarized clear from where in Figure th5e. chirality For ease of of the interpretation, system arises. these When results the have graphene been convertedoxide is covalently into units functionalized typically used inwith experimental polyacrylonitrile, graphene there oxide is also research evidence (i.e., micrometers,of a chiral nematic vol %) usingphase, the in which method the of GO Shen sheets et al. form [37]. Ita helical can be seenstruct thature thebut widthare not of yet the in biphasic lamellae. region These increases results were with increasingestablished polydispersity, using ellipsometry but theand range SAXS of [38]. polydispersity When the sheet-to-sheet investigated interaction in the simulations is modified does with not stretchsalt, the to phase that typically diagram encountered becomes more for graphene complex, oxide and dispersionsthis will be [37discussed]. later in this review. Meanwhile in the next section, the nematic phase is discussed in more detail.

Figure 5. The phase diagram for a hard-disk fluid ﬂuid with 25% polydispersity from simulations by Bates and Frenkel. The isotropic (Iso) and nematic (N) ph phasesases are labelled and the shaded part corresponds to the biphasic region.region. Inset: the the effect eﬀect of polydispersity on the width of the biphase.

When the concentration of graphene oxide is further increased, other phases can be observed. The first phase to appear with increasing concentration is the lamellar phase. In the lamellar phase, the graphene oxide sheets form layers which lead to Bragg reflection in small-angle X-ray scattering (SAXS) [12]. On the basis of ellipsometry measurements and freeze-fracture cryo-SEM (scanning electron microscopy), Xu and Gao have also proposed that this lamellar phase is in fact chiral. They propose the structure of this phase to be an analogue of the twist grain boundary phases of thermotropic liquid crystals, with lamellar blocks of GO twisted relative to one another forming a helical superstructure. This observation is remarkable, since neither the graphene oxide nor the solvent is chiral, so it is not clear from where the chirality of the system arises. When the graphene oxide is covalently functionalized with polyacrylonitrile, there is also evidence of a chiral nematic Crystals 2019, 9, 455 6 of 20 phase, in which the GO sheets form a helical structure but are not yet in lamellae. These results were established using ellipsometry and SAXS [38]. When the sheet-to-sheet interaction is modified with salt, the phase diagram becomes more complex, and this will be discussed later in this review. Meanwhile inCrystals the next 2019, section,9, x FOR PEER the nematic REVIEW phase is discussed in more detail. 6 of 20

4.4. EEffectsffects ofof FlakeFlake SizeSize andand SolventSolvent Recently,Recently, AhmadAhmad etet al.al. [[39]39] havehave investigatedinvestigated thethe dependencedependence ofof thethe electro-opticalelectro-optical propertiesproperties ofof GOGO dispersionsdispersions on on the the graphene graphene oxide oxide flake flake size. size. We We will will return return to electro-optic to electro-optic effects effects later later but we but note we herenote thathere the that authors’ the authors’ experimentally experimentally determined determined phase diagram phase diagram is quite diisff erentquite todifferent that produced to that fromproduced the simulations from the simulations of Bates and of Frenkel Bates [and36] (FigureFrenkel6 ).[36] There (Figure are various 6). There explanations are various as explanations to why this couldas to why be the this case. could Firstly, be the GO case. sheets Firstly, are not GO rigid sheets but inare fact not are rigid highly but flexiblein fact are [40]. highly Secondly, flexible they [40]. are notSecondly, infinitely they thin are but not have infinitely a finite thin thickness but have of around a finite 1 nmthickness as determined of around by atomic1 nm as force determined microscopy by (AFM)atomic [24force,41]. microscopy Furthermore, (AFM) the polydispersity [24,41]. Furtherm of GOore, systems the polydispersity cannot usually of be GO approximated systems cannot by a normalusually distributionbe approximated (as the by simulations a normal distribution do), and is (as usually the simulations asymmetric do), with and a is tail usually to higher asymmetric particle sizeswith (skeweda tail to distribution,higher particle Pearson sizes distribution). (skewed dist Ahmadribution, et Pearson al. [39] determined distribution). the Ahmad phase boundaries et al. [39] throughdetermined polarized the phase photography boundaries of graphenethrough polarize oxide dispersionsd photography contained of graphe withinne oxide a Pasteur dispersions pipette. Undercontained such within conditions, a Pasteur the isotropic pipette. phase Under appears such black.conditions, However, the itisotropic is possible phase to observe appears transient black. birefringenceHowever, it is caused possible by flow to observe driven alignmenttransient birefringence in the isotropic caused phase [by37 ]flow (see thedriven next alignment section for in more the detail),isotropic which phase could [37] be(see misinterpreted the next section as for the more onset detail), of the biphasic which could region. be Furthermore,misinterpreted the as transition the onset fromof the the biphasic two-phase region. region Furthermore, to the nematic the phasetransition is eff fromectively the continuous, two-phase makingregion to the the boundary nematic diphasefficult is toeffectively determine continuous, by either photography making the of boundary macroscopic diff samplesicult to ordetermine microscopy. by either photography of macroscopic samples or microscopy.

FigureFigure 6.6. Experimentally determined lyotropic phase diagramdiagram for graphene oxide dispersed in water. TheThe insetinset figuresfigures showshow photographsphotographs ofof samplesample heldheld inin aa PasteurPasteur pipettepipette betweenbetween crossedcrossed polarizers.polarizers. ItIt isis byby suchsuch photographsphotographs thethe authorsauthors interpretedinterpreted thethe locationlocation ofof thethe phasephase boundaries.boundaries. AdaptedAdapted withwith permissionpermission fromfrom refref [[39],39], TheThe OpticalOptical Society.Society. The overall trend of the phase diagram is at odds with the theoretical model of Bates and The overall trend of the phase diagram is at odds with the theoretical model of Bates and Frenkel Frenkel [36] with the phase boundaries shifting to higher concentration with decreasing mean particle [36] with the phase boundaries shifting to higher concentration with decreasing mean particle size – size – the inverse of the theoretical prediction. The reasons for this are not currently well understood. the inverse of the theoretical prediction. The reasons for this are not currently well understood. What What is known is that current theoretical models are too restrictive and do not accurately represent an is known is that current theoretical models are too restrictive and do not accurately represent an experimental system. GO sheets are not, for example, infinitely thin, ridged and of approximately equal experimental system. GO sheets are not, for example, infinitely thin, ridged and of approximately size. Although it still appears that the primary driver for the onset of liquid crystallinity is excluded equal size. Although it still appears that the primary driver for the onset of liquid crystallinity is volume effects, there are other ways flakes can interact with each other, as will be discussed herein. excluded volume effects, there are other ways flakes can interact with each other, as will be discussed Since, in principle, the phase behaviour of colloidal systems of graphene oxide is only dependent on herein. concentration, the isotropic liquid which acts as the solvent should not play any part, and all solvents that Since, in principle, the phase behaviour of colloidal systems of graphene oxide is only dependent on concentration, the isotropic liquid which acts as the solvent should not play any part, and all solvents that can disperse graphene oxide without aggregation, flocculation or sedimentation should be equal. It has been widely reported [21,41,42] that water, dimethylformamide (DMF) and N-methyl- 2-pyrrolidone (NMP) are the best of the common laboratory solvents for dispersing graphene oxide. Accordingly, lyotropic liquid crystalline behavior was found in all three of these in another paper by Ahmad et al [42] (Figure 7).

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can disperse graphene oxide without aggregation, ﬂocculation or sedimentation should be equal. It has been widely reported [21,41,42] that water, dimethylformamide (DMF) and N-methyl-2-pyrrolidone (NMP) are the best of the common laboratory solvents for dispersing graphene oxide. Accordingly, lyotropic liquid crystalline behavior was found in all three of these in another paper by Ahmad et al. [42] Crystals(Figure 20197)., 9, x FOR PEER REVIEW 7 of 20

FigureFigure 7. 7. PolarizingPolarizing optical optical photographs photographs of of dispersions dispersions of of graphene graphene oxide oxide in in different different solvents solvents and and at at differentdifferent concentrations concentrations are are shown shown ( (bb).). In In tetrahydrofuran tetrahydrofuran (THF), (THF), GO GO tends tends to to flocculate, flocculate, meaning meaning spontaneousspontaneous orientational orientational order order does does not not occur. occur. The The apparatus apparatus used used to contain to contain the dispersions the dispersions for observationfor observation is shown is shown in part in part(a). Reprinted (a). Reprinted from fromAhmad Ahmad et al. et[42], al. with [42], withthe permission the permission of AIP of AIP Publishing. Publishing. Ionization of the polar oxygen functional groups on the GO surface in solvents leads to GO Ionization of the polar oxygen functional groups on the GO surface in solvents leads to GO being being negatively charged, and thus electrostatic interactions play a role in the dispersion of graphene negatively charged, and thus electrostatic interactions play a role in the dispersion of graphene oxide oxide and the pair-wise interaction. By measuring the conductivity of GO dispersions in the three and the pair-wise interaction. By measuring the conductivity of GO dispersions in the three different different solvents Ahmad et al. [42] showed that the surface ionization of GO varies depending on solvents Ahmad et al. [42] showed that the surface ionization of GO varies depending on the solvent, the solvent, with water having the highest conductivity and hence aqueous GO having the highest with water having the highest conductivity and hence aqueous GO having the highest surface surface ionization. ionization. 5. Alignment of GO Liquid Crystals 5. Alignment of GO Liquid Crystals The alignment of conventional thermotropic liquid crystals can be achieved using surface treatment of theThe glass alignment used to confineof conventional them for study.thermotropic Examples liquid include crystals rubbed can polyimide be achieved for planar using alignment surface treatmentand the use of the of surfactantsglass used to such confine as C-TAB them orforDMOAP study. Examples for homeotropic include rubbed alignment. polyimide Graphene for planar oxide alignment and the use of surfactants such as C-TAB or DMOAP for homeotropic alignment. liquid crystals are a very different system however, with flakes being tens of thousands of times larger Graphene oxide liquid crystals are a very different system however, with flakes being tens of than thermotropic liquid crystal molecules. In 2011, Dan et al. [13] reported that nematic GO confined thousands of times larger than thermotropic liquid crystal molecules. In 2011, Dan et al. [13] reported in a rectangular capillary aligned spontaneously with the average GO sheet normal (the optical axis in that nematic GO confined in a rectangular capillary aligned spontaneously with the average GO sheet this case) being parallel to the capillary axis. However, they suspected this was a metastable state [13]. normal (the optical axis in this case) being parallel to the capillary axis. However, they suspected this Recently Al-Zangana et al. [43] have shown that graphene oxide sheets in solution tend to prefer was a metastable state [13]. Recently Al-Zangana et al. [43] have shown that graphene oxide sheets to lie parallel to glass. Thus, the director aligns perpendicularly to a glass surface. This has been in solution tend to prefer to lie parallel to glass. Thus, the director aligns perpendicularly to a glass demonstrated by the construction of both covered and uncovered glass channels constructed from surface. This has been demonstrated by the construction of both covered and uncovered glass microscope slides and coverslips (Figure8). In polarized optical microscopy, the channel appears channels constructed from microscope slides and coverslips (Figure 8). In polarized optical bright when its axis is placed at 45◦ to each of the polarizers, indicating uniform alignment of the microscopy, the channel appears bright when its axis is placed at 45° to each of the polarizers, director field perpendicular to the axis of the channel, along its length. When a glass plate is placed on indicating uniform alignment of the director field perpendicular to the axis of the channel, along its top of this channel, the middle section becomes dark, irrespective of the position of the channel relative length. When a glass plate is placed on top of this channel, the middle section becomes dark, to the polarizers. This indicates local homeotropic alignment of the director field i.e. the graphene irrespective of the position of the channel relative to the polarizers. This indicates local homeotropic oxide is parallel to the glass plate. alignment of the director field i.e. the graphene oxide is parallel to the glass plate. Shear flows can also cause GO liquid crystals in the isotropic phase to be birefringent. This has been demonstrated by Shen et al. [37] by using magnetic stirring and manual shaking of samples between crossed polarizers (Figure 9). The birefringence observed can be explained by the graphene oxide flakes feeling a torque caused by the velocity field of the solvent. This causes local alignment of the graphene oxide flakes, and hence birefringence, where the change in velocity of the solvent is greatest.

Crystals 2019, 9, 455 8 of 20 Crystals 2019, 9, x FOR PEER REVIEW 8 of 20

Crystals 2019, 9, x FOR PEER REVIEW 8 of 20

FigureFigure 8. ( a8.) ( Schematica) Schematic diagram diagram showingshowing the the orientation orientation of ofGO GO flakes flakes with with respect respect to the to director, the director, n. n. (b(b)) The The confiningconfining geometry geometry used used to to photog photographraph GO GO dispersions dispersions (POM) (POM) in parts in parts(c,d). In (c ,(dc)). the In top (c) the top glassglass plate plate is is present present and and the theLC LCbecomes becomes homeotropic homeotropic in the centre in the of centre the channel. of the In channel. part (d) Inthe part top (d) the topplate plate is removed is removed and the and boundary the boundary conditions conditions are set by the are vertical set by walls. the The vertical director walls. configurations The director in each case are also shown below the POM pictures. (b–d) reproduced and adapted from Al-Zangana configurations in each case are also shown below the POM pictures. (b–d) reproduced and adapted et al. [43] under the terms of the Creative Commons Attribution 3.0 licence. fromFigure Al-Zangana 8. (a) Schematic et al. [43 ]diagram under theshowing terms the of orientation the Creative of GO Commons flakes with Attribution respect to 3.0the licence.director, n. (b) The confining geometry used to photograph GO dispersions (POM) in parts (c,d). In (c) the top Tkacz et al. [44] have also shown that dispersions of reduced graphene oxide can be used to Shearglass flows plate can is present also cause and the GO LC becomes liquidcrystals homeotropic inthe in the isotropic centre of the phase channel. to be In birefringent.part (d) the top This has produce highly aligned films on glass substrates. The authors proposed that diffusion of sheets in the been demonstratedplate is removed by and Shen the etboundary al. [37 conditions] by using are magneticset by the vertical stirring walls. and The manualdirector configurations shaking of samples fluid, assisted by capillary forces, causes the self-assembly of the sheets on the substrate. between crossedin each case polarizers are also shown (Figure below9). the The POM birefringence pictures. (b–d) observedreproduced canand adapted be explained from Al-Zangana by the graphene et al. [43] under the terms of the Creative Commons Attribution 3.0 licence. oxide flakes feeling a torque caused by the velocity field of the solvent. This causes local alignment of the graphene oxide flakes, and hence birefringence, where the change in velocity of the solvent produceTkacz highly et al. aligned [44] have films also on shownglass substrates. that disper Thsionse authors of reduced proposed graphene that diff oxideusion canof sheets be used in the to is greatest.fluid, assisted by capillary forces, causes the self-assembly of the sheets on the substrate.

Figure 9. Time series of polarized photographs showing the temporary flow-induced alignment of graphene oxide flakes in the isotropic phase by (a) magnetic stirring and (b) manual shaking. Reprinted by permission from Springer Nature: Nature Materials, Shen et al. [37] © 2014.

6. Ions and Polymers in GO Liquid Crystals FigureFigure 9. Time 9. Time series series of polarizedof polarized photographs photographs showingshowing the the temporary temporary flow-induced ﬂow-induced alignment alignment of of Xu and Gao [12] have demonstrated that electrostatic interactions also play a role in the lyotropic graphenegraphene oxide oxide ﬂakes flakes in the in isotropic the isotropic phase phase by (a )by magnetic (a) magnetic stirring stirring and ( band) manual (b) manual shaking. shaking. Reprinted behaviour of graphene oxide to some degree. To reveal this, they measured the phase behaviour by by permissionReprinted by from permission Springer from Nature: Springer Nature Nature: Materials, Nature Materials, Shen et al. Shen [37 ]et© al.2014. [37] © 2014.

6. Ions and Polymers in GO Liquid Crystals Xu and Gao [12] have demonstrated that electrostatic interactions also play a role in the lyotropic behaviour of graphene oxide to some degree. To reveal this, they measured the phase behaviour by Crystals 2019, 9, 455 9 of 20

Tkacz et al. [44] have also shown that dispersions of reduced graphene oxide can be used to produce highly aligned films on glass substrates. The authors proposed that diffusion of sheets in the fluid, assisted by capillary forces, causes the self-assembly of the sheets on the substrate.

6. Ions and Polymers in GO Liquid Crystals

CrystalsXu 2019 and, 9, Gaox FOR [12 PEER] have REVIEW demonstrated that electrostatic interactions also play a role in the lyotropic9 of 20 observingbehaviour POM of graphene images oxideas a function to some of degree. salt (NaCl) To reveal concentration. this, they measuredIf the NaCl the concentration phase behaviour was too by high,observing the repulsive POM images force as between a function the of sheets salt (NaCl) was concentration.reduced such Ifthat the floccu NaCllation concentration occurred. was Small too amountshigh, the repulsiveof NaCl did force however between influence the sheets the was width reduced of the such two-phase that flocculation region significantly occurred. Small (Figure amounts 10). Theof NaCl authors did howeveralso measured influence the the zeta-potential width of the two-phaseof the dispersion region significantlyfor each concentration (Figure 10). studied The authors and foundalso measured the absolute the zeta-potentialvalue decreased of with thedispersion increasing forNaCl each content. concentration These results studied indicate and foundthat both the electrostaticabsolute value and decreased excluded with volume increasing effects NaClplay a content. role in Thesethe lyotropic results indicatebehaviour that of bothgraphene electrostatic oxide, and that excluded the overall volume stability effects of play the nematic a role in phase the lyotropic is reduced behaviour in an electrolyte of graphene environment. oxide, and However, that the Zhaooverall et stability al. [45] ofhave the nematicshown that phase by is coating reduced the in anGO electrolyte flakes with environment. polyelectrolytes, However, the Zhaonematic et al.phase[45] canhave remain shown stable that by even coating in NaCl the GO concentrations flakes with polyelectrolytes, of up to 6.2 M, the depending nematic phase on the can polyelectrolyte remain stable employed.even in NaCl concentrations of up to 6.2 M, depending on the polyelectrolyte employed.

Figure 10. TheThe dependence dependence of of (a ()a the) the phase phase diagram diagram of ofa GO-LC a GO-LC (where (where fm isf mtheis mass the mass fraction fraction of GO) of andGO) ( andb) the (b) zeta the zetapotential potential of the of theGO GO dispersion dispersion on onthe the concentration concentration of of NaCl NaCl salt salt in in the the solution. solution. Reprinted with permission from Xu and Gao. [[12]12] Copyright (2011) AmericanAmerican ChemicalChemical Society.Society. Konkena and Vasudevan [46] have also demonstrated that by varying the GO and NaCl salt Konkena and Vasudevan[46] have also demonstrated that by varying the GO and NaCl salt concentrations, a number of different phases or arrested states can be formed (Figure 11). By arrested concentrations, a number of different phases or arrested states can be formed (Figure 11). By arrested states, the authors refer to structures which are not at global minima of the thermodynamic potential, states, the authors refer to structures which are not at global minima of the thermodynamic potential, thus metastable [46]. At high GO concentrations, but low salt concentrations where electrostatic thus metastable [46]. At high GO concentrations, but low salt concentrations where electrostatic repulsion dominates the interactions, a glass is observed. This is attributed as a Wigner glass, which is repulsion dominates the interactions, a glass is observed. This is attributed as a Wigner glass, which analogous to the Wigner crystals of electrons in solids [47,48]. Wigner glasses have also been observed is analogous to the Wigner crystals of electrons in solids [47,48]. Wigner glasses have also been in dispersions of other plate-like materials such as laptonite [49]. GO glasses and gels do not flow, observed in dispersions of other plate-like materials such as laptonite [49]. GO glasses and gels do unlike nematic liquid crystals, and so can be easily identified by inverting the container of the GO not flow, unlike nematic liquid crystals, and so can be easily identified by inverting the container of dispersion. To further demonstrate a glass experimentally, the authors performed dilution experiments. the GO dispersion. To further demonstrate a glass experimentally, the authors performed dilution The glass, in which GO interactions are predominantly repulsive, melts upon the addition of further experiments. The glass, in which GO interactions are predominantly repulsive, melts upon the solvent whereas the states observed at higher salt concentrations do not [46] Konkena and Vasudevan addition of further solvent whereas the states observed at higher salt concentrations do not [46] further suggest that at higher salt concentrations, the dominant GO interaction is an attractive one Konkena and Vasudevan further suggest that at higher salt concentrations, the dominant GO which leads to a phase which appears dark between crossed polarizers but turns bright when sheared. interaction is an attractive one which leads to a phase which appears dark between crossed polarizers These observations point towards homeotropic alignment of the graphene oxide sheets i.e. collectively but turns bright when sheared. These observations point towards homeotropic alignment of the the sheets are in the same plane as the substrate and perpendicular to the light path. This behaviour graphene oxide sheets i.e. collectively the sheets are in the same plane as the substrate and is attributed to the onset of a columnar phase by the authors, based on the appearance of the POM perpendicular to the light path. This behaviour is attributed to the onset of a columnar phase by the textures [46] though recent X-ray scattering experiments by Rubim et al. suggest that this observation authors, based on the appearance of the POM textures [46] though recent X-ray scattering could be a lamellar phase [50]. experiments by Rubim et al. suggest that this observation could be a lamellar phase [50]. Crystals 2019, 9, 455 10 of 20 Crystals 2019, 9, x FOR PEER REVIEW 10 of 20 Crystals 2019, 9, x FOR PEER REVIEW 10 of 20

Figure 11.11. TheThe phase phase diagram diagram of graphene oxide dispersionsdispersions as determined by KonkenaKonkena andand VasudevanFigureVasudevan 11. [The[46]46] displayingdisplayingphase diagram isotropic,isotropic, of graphene nematic,nematic, columnar coluoxidemnar disp andandersions glassglass phases.phases.as determined Reprinted by with Konkena permission and Vasudevanfromfrom ref.ref. [[46],46 [46]], CopyrightCopyright displaying (2014)(2014) isotropic, AmericanAmerican nematic, ChemicalChemical columnar Society.Society. and glass phases. Reprinted with permission from ref. [46], Copyright (2014) American Chemical Society. Graphene oxide liquid crystals are often observed with water as the solvent. Typically, the water Graphene oxide liquid crystals are often observed with water as the solvent. Typically, the water is deionizedGraphene and oxide at pH liquid ~7 for crystals a fresh ar dispersion.e often observed However, with thewater LC as behaviour the solvent. can Typically, also be observed the water at is deionized and at pH ~7 for a fresh dispersion. However, the LC behaviour can also be observed ispH deionized 2, 6 and 9 and as reported at pH ~7 by for Tkacz a fresh et al.dispersion. [51] As the Ho pHwever, increases, the LC the behaviour fraction of can dissociated also be observed carboxylic at pHat pH 2, 6 2,and 6 and9 as reported 9 as reported by Tkacz by Tkaczet al. [51] et al.As [the51] pH As increases, the pH increases, the fraction the of fraction dissociated of dissociated carboxylic groups changes (the pKa value is ~4 for these groups [52]) and so too does the width of the biphasic carboxylic groups changes (the pKa value is ~4 for these groups [52]) and so too does the width of the groupsregion changesbetween (thethe pKisotropica value isand ~4 fornematic these phases.groups [52])This andwork so furthertoo does suggests the width that of theelectrostatic biphasic biphasic region between the isotropic and nematic phases. This work further suggests that electrostatic regioninteractions between between the isotropicGO sheets and are nematic important phases. for th Thise onset work of lyotropicfurther suggestsbehavior. that Furthermore, electrostatic at interactions between GO sheets are important for the onset of lyotropic behavior. Furthermore, interactionsbiphasic concentrations, between GO highly sheets ordered are important phase-separated for the onset nematic of lyotropic droplets behavior. were observed Furthermore, [51]. at at biphasic concentrations, highly ordered phase-separated nematic droplets were observed [51]. biphasicThe concentrations,addition of polymers highly to ordered a colloidal phase-separated liquid crystal nematicsystem is droplets often performed were observed to better [51]. stabilize The addition of polymers to a colloidal liquid crystal system is often performed to better stabilize the dispersionThe addition via of steric polymers hindrance to a colloidal or to cause liquid gelati crystalon. Recently, system is Shimoften etperformed al. [53] have to better reported stabilize that the dispersion via steric hindrance or to cause gelation. Recently, Shim et al. [53] have reported that thethe dispersionaddition of via polyethylene steric hindrance glycol or (PEG) to cause to GO gelati LCson. causes Recently, the onset Shim of et the al. [53]nematic have phase reported to occur that the addition of polyethylene glycol (PEG) to GO LCs causes the onset of the nematic phase to occur theat lower addition concentrations of polyethylene of GO glycol in the (PEG) total to volume GO LCs. Furthermore, causes the onset they of report the nematic that the phase Wigner to occur glass at lower concentrations of GO in the total volume. Furthermore, they report that the Wigner glass attransition lower concentrations of the GO dispersion of GO inis pushedthe total up volume to higher. Furthermore, GO concentrations. they report [53] that Therefore the Wigner the overall glass transition of the GO dispersion is pushed up to higher GO concentrations. [53] Therefore the overall transitioneffect of the of theaddition GO dispersion of PEG widensis pushed the up nematic to higher phase. GO concentrations. The concentrations [53] Therefore of PEG required the overall to eﬀect of the addition of PEG widens the nematic phase. The concentrations of PEG required to observe effectobserve of thesethe addition effects are of raPEGther widenshigh (Figure the nematic 12). phase. The concentrations of PEG required to observethese eﬀ ectsthese are effects rather are high rather (Figure high 12 (Figure). 12).

Figure 12. (a) The phase diagram of a graphene oxide liquid crystal with added polyethylene glycol Figure 12. (a) The phase diagram of a graphene oxide liquid crystal with added polyethylene glycol Figure(PEG) as12. determined (a) The phase by Shim diagram et al. of [53]. a graphene (b) Typical oxide POM liqu imagesid crystal for different with added GO/waterPEG polyethylene mixtures. glycol (PEG) as determined by Shim et al. [53]. (b) Typical POM images for diﬀerent GO/waterPEG mixtures. (PEG)Weak asbirefringence determined canby Shim be seen et al. as [53]. the ( bPEG) Typical concentration POM images is increase for differentd in anGO/waterPEG initially isotropic mixtures. GO Weak birefringence can be seen as the PEG concentration is increased in an initially isotropic GO Weakdispersion. birefringence Republished can bewith seen permission as the PEG of concentrationthe Royal Society is increase of Chemistry,d in an initiallyfrom Shim isotropic et al. [53];GO dispersion. Republished with permission of the Royal Society of Chemistry, from Shim et al. [53]; dispersion.permission Republishedconveyed through with permissionCopyright Clearance of the Roya Center,l Society Inc. of Chemistry, from Shim et al. [53]; permission conveyed through CopyrightCopyright Clearance Center,Center, Inc.Inc. Crystals 2019, 9, 455 11 of 20

The addition of PEG to a concentration of 20 wt% in the mixture causes the macroscopic viscosity of the whole dispersion to decrease by a factor of 20–30 relative to that of GO in pure water, for the same concentration of GO. This, the authors rightly suggest, points to a need for a greater understanding of the micro-structure of the polymer-solvent-GO system at the GO surface. In a follow-up work by the same group [54], a selection of molecular weights of PEG were used. It was shown that PEG with a 1 larger average molecular weight (10,000 gmol− ) reduced electrostatic repulsion between the sheets, which is the origin of the glass transition in GO. Reduction of this repulsive energy was oﬀered as explanation for a decrease in the macro-viscosity of the LC. If PEG with a lower molecular weight 1 (400 gmol− ) was added, the viscosity did not decrease by the same amount.

7. Electro-Optic Effects Birefringence induced by electric fields can be observed in a variety of otherwise optically isotropic materials. These effects are commonly grouped into one of two categories, the Pockels effect or the Kerr effect, depending on whether the induced birefringence is proportional to the magnitude of the applied electric field or its square, respectively [55]. The Pockels effect only occurs in crystals which lack inversion symmetry. Dispersions of graphene oxide in the isotropic, biphasic and nematic phases have displayed electric field-induced birefringence [37,39,42,56]. In the case of the nematic phase, this corresponds most likely to a reorientation of the director field as a whole, as is the case with thermotropic nematics. In the less concentrated phases, a Kerr effect is observed where each flake, from whichever orientation it was in, aligns itself to the electric field. This behavior of a GO flake in an electric field can be described by the Maxwell–Wagner–O’Konski model [57,58]. The key parameters of the GO in this framework are the aspect ratio and the ionic conductivity at the surface. It is known that in aqueous dispersions GO is negatively charged with an ionic double layer at its surface [12]. Shen et al. [37] measured the Kerr coefficient of aqueous dispersions of graphene oxide and found 5 2 values of the order 10− mV− . This value is very high in comparison to other materials known to 9 2 have high Kerr coefficients such as thermotropic liquid crystal blue phases (~10− mV− )[59–61] or 12 2 nitrobenzene (10− mV− )[62]. In a qualitatively similar system consisting of suspended platelets of clay the Kerr coefficient was four orders of magnitude lower than that of graphene oxide [62]. Shen et al. [37] also observed that the electric field-induced birefringence decreased as the concentration was increased through the biphasic region and that in the concentrated nematic phase there was barely 1 any effect of the electric field at up to 20 Vmm− . By analogy, thermotropic nematic liquid crystals 1 require much higher field strengths to switch the director (~0.7 Vµm− ). In contrast, Ahmad et al. [42] 1 measured a significant field-induced birefringence in the nematic phase with field strengths of 10 Vmm− or lower (Figure 13). Interestingly, they also found that the maximum field-induced birefringence of a given flake size distribution depended on what solvent it was dispersed in [42]. Water was found to outperform both DMF and NMP at high frequency (10 kHz), but electrophoretic drift of the GO particles was observed at lower frequencies (100 Hz). Both of these results were attributed to the higher ionic content of the aqueous dispersion [42] which occurs because the surface functional groups of graphene oxide are easily ionized in aqueous dispersions. The maximum field-induced birefringence has been shown to be affected by the flake size and distribution [63] (Figure 13) but interestingly also the number of cleaning steps taken in the production of the graphene oxide [64]. Crystals 2019, 9, x FOR PEER REVIEW 11 of 20 The addition of PEG to a concentration of 20 wt% in the mixture causes the macroscopic viscosity of the whole dispersion to decrease by a factor of 20–30 relative to that of GO in pure water, for the same concentration of GO. This, the authors rightly suggest, points to a need for a greater understanding of the micro-structure of the polymer-solvent-GO system at the GO surface. In a follow-up work by the same group [54], a selection of molecular weights of PEG were used. It was shown that PEG with a larger average molecular weight (10,000 gmol−1) reduced electrostatic repulsion between the sheets, which is the origin of the glass transition in GO. Reduction of this repulsive energy was offered as explanation for a decrease in the macro-viscosity of the LC. If PEG with a lower molecular weight (400 gmol−1) was added, the viscosity did not decrease by the same amount.

7. Electro-Optic Effects Birefringence induced by electric fields can be observed in a variety of otherwise optically isotropic materials. These effects are commonly grouped into one of two categories, the Pockels effect or the Kerr effect, depending on whether the induced birefringence is proportional to the magnitude of the applied electric field or its square, respectively [55]. The Pockels effect only occurs in crystals which lack inversion symmetry. Dispersions of graphene oxide in the isotropic, biphasic and nematic phases have displayed electric field-induced birefringence [37,39,42,56]. In the case of the nematic phase, this corresponds most likely to a reorientation of the director field as a whole, as is the case with thermotropic nematics. In the less concentrated phases, a Kerr effect is observed where each flake, from whichever orientation it was in, aligns itself to the electric field. This behavior of a GO flake in an electric field can be described by the Maxwell–Wagner–O'Konski model [57,58]. The key parameters of the GO in this framework are the aspect ratio and the ionic conductivity at the surface. It is known that in aqueous dispersions GO is negatively charged with an ionic double layer at its surface [12]. Shen et al. [37] measured the Kerr coefficient of aqueous dispersions of graphene oxide and found values of the order 10−5 mV−2. This value is very high in comparison to other materials known to have high Kerr coefficients such as thermotropic liquid crystal blue phases (~10−9 mV−2)[59–61] or nitrobenzene (10−12 mV−2) [62]. In a qualitatively similar system consisting of suspended platelets of clay the Kerr coefficient was four orders of magnitude lower than that of graphene oxide [62]. Shen et al. [37] also observed that the electric field-induced birefringence decreased as the concentration was increased through the biphasic region and that in the concentrated nematic phase there was barely any effect of the electric field at up to 20 Vmm-1. By analogy, thermotropic nematic liquid crystals require much higher field strengths to switch the director (~0.7 Vµm−1). In contrast, Ahmad et al. [42] measured a significant field-induced birefringence in the nematic phase with field strengths of 10 Vmm-1 or lower (Figure 13). Interestingly, they also found that the maximum field-induced birefringence of a given flake size distribution depended on what solvent it was dispersed in [42]. Water was found to outperform both DMF and NMP at high frequency (10 kHz), but electrophoretic drift of the GO particles was observed at lower frequencies (100 Hz). Both of these results were attributed to the higher ionic content of the aqueous dispersion [42] which occurs because the surface functional groups of graphene oxide are easily ionized in aqueous dispersions. The maximum field- induced birefringence has been shown to be affected by the flake size and distribution [63] (Figure Crystals13) but2019 interestingly, 9, 455 also the number of cleaning steps taken in the production of the graphene oxide12 of 20 [64].

Crystals 2019, 9, x FOR PEER REVIEW 12 of 20

FigureFigure 13. 13. TheThe induced induced birefringence birefringence of of GO GO dispersions dispersions as as a a function function of of voltage voltage for for three three different different solvents:solvents: water water ( (aa),), DMF DMF ( (bb)) and and NMP NMP ( (cc).). Reprinted Reprinted from from Ahmad Ahmad et et al. al. [42], [42], with with the the permission permission of of AIPAIP Publishing. Publishing. (d (d) )The The field field induced induced birefringence birefringence of of diff differenterent dispersions dispersions with with different different average average flakeflake sizes sizes and and concentrations concentrations as as a a function function of of electr electricic field. field. Reprinted Reprinted with with permission permission from from ref. ref. [39], [39], TheThe Optical Optical Society. Society. The time taken for the graphene oxide dispersions to become fully aligned to the electric field The time taken for the graphene oxide dispersions to become fully aligned to the electric field is is known as the response time. The relaxation time is defined as the time taken for the system to known as the response time. The relaxation time is defined as the time taken for the system to relax relax once the electric field is removed. Both the response and relaxation times for graphene oxide once the electric field is removed. Both the response and relaxation times for graphene oxide dispersions have been found to be just under half a second, depending on the flake size distribution dispersions have been found to be just under half a second, depending on the flake size distribution and concentration (Figure 14)[39,63]. This has been shown to be affected by flake size and in particular and concentration (Figure 14) [39,63]. This has been shown to be affected by flake size and in the flake size distribution [39,63]. The higher the fraction of large flakes (>1 µm) in a mixture which particular the flake size distribution [39,63]. The higher the fraction of large flakes (>1 µm) in a otherwise contains mainly small flakes (<1 µm) the slower the response to electric fields and the slower mixture which otherwise contains mainly small flakes (<1 µm) the slower the response to electric the relaxation time when the field is removed. This has been attributed to increased inter-particle fields and the slower the relaxation time when the field is removed. This has been attributed to friction when larger flakes are present [63]. increased inter-particle friction when larger flakes are present [63].

Figure 14. Response times of the aqueous dispersions shown in Fig.11d. (a) on-time (b) off-time. Figure 14. Response times of the aqueous dispersions shown in Fig.11d. (a) on-time (b) off-time. Adapted with permission from ref. [39], The Optical Society. Adapted with permission from ref. [39], The Optical Society. Graphene oxide in aqueous dispersions ages with time. This is due to C–C bond cleavage and the formationGraphene ofoxide vinylogous in aqueous carboxylic dispersions acids ages [65]. with This time. reaction This also is due releases to C–C protons bond andcleavage decreases and thethe formation pH of the of dispersion. vinylogous Consequently, carboxylic acids the electro-optic[65]. This reaction performance also releases has been protons shown and to decreases decrease thewith pH time of the [66 ].dispersion. Over the courseConsequently, of one week the electro-optic of storage at performance room temperature, has been Shen shown et al. to [66 decrease] found withthat thetime field-induced [66]. Over the birefringence course of one fell week by approximately of storage at room 25% astemperature, compared toShen fresh et GO.al. [66] However, found thatthey the did field-induced find that re-cleaning birefringence the material fell by withapproximately fresh water 25% in aas centrifuge compared restores to fresh the GO. performance However, theycompletely did find [66 that]. re-cleaning the material with fresh water in a centrifuge restores the performance completely [66]. 8. Effect of Magnetic Fields 7. Effect of Magnetic Fields Early in the story of graphene oxide lyotropic liquid crystals, Kim et al. [11] reported that over a longEarly time in (5the h) story a magnetic of graphene field (0.25T)oxide lyotropic could cause liqui ad nematiccrystals, graphene Kim et al. oxide[11] reported dispersion that to over align a long(Figure time 15 ).(5 h) a magnetic field (0.25T) could cause a nematic graphene oxide dispersion to align (Figure 15).

Crystals 2019, 9, 455 13 of 20 Crystals 2019, 9, x FOR PEER REVIEW 13 of 20

Figure 15. Alignment of aqueous graphene oxide sheets using a magnetic field as reported by Figure 15. Alignment of aqueous graphene oxide sheets using a magnetic field as reported by Kim et Kim et al. [11]. (a) POM texture of the nematic GO LC immediately after preparation. (b) The texture al. [11]. (a) POM texture of the nematic GO LC immediately after preparation. (b) The texture after 3h after 3h with no external field present. (c) Schematic diagram showing the magnetic field set-up and with no external field present. (c) Schematic diagram showing the magnetic field set-up and POM POM textures of the aligned GO LC. Reproduced from ref. [11] with permission from John Wiley textures of the aligned GO LC. Reproduced from ref. [11] with permission from John Wiley and Sons. and Sons.

SinceSince thatthat time,time, itit appearsappears thatthat thisthis eeffectffect hashas notnot beenbeen independentlyindependently demonstrated.demonstrated. Recently, wewe havehave performedperformed smallsmall angleangle X-rayX-ray scatteringscattering measurementsmeasurements ofof thethe nematicnematic phasephase ofof graphenegraphene oxideoxide withwith anan inin situsitu magneticmagnetic fieldfield ofof approximatelyapproximately 0.90.9 T,T, appliedapplied perpendicularlyperpendicularly toto thethe X-rayX-ray beam.beam. The experiments used a SAXSLABSAXSLAB GaneshaGanesha 300XL300XL machine.machine. This uses a coppercopper KKαα X-rayX-ray sourcesource andand aa 2D2D PilatusPilatus 300K300K detectordetector whichwhich isis movablemovable alongalong thethe beambeam axisaxis soso thethe sample-detectorsample-detector distancedistance can be adjusted. adjusted. The The experimental experimental set-up set-up is iswell well described described by byFigure Figure 1 in1 Simsin Sims et al. et [67]. al. [ The67]. Thediffraction diffraction pattern pattern was was initially initially anisotropic, anisotropic, presumably presumably due due to an to anaverage average preferred preferred orientation orientation in inthe the diffraction diffraction capillary capillary used used to contain to contain the dispersi the dispersion,on, or from or from shear shear alignment alignment as it entered. as it entered. After Afterapproximately approximately 19 hours 19 hours in the inmagnetic the magnetic field, ther field,e was there no was change no change in the inalignment the alignment of the ofGO the sheets GO sheetsand they and remained they remained out of outalignment of alignment with the with direct theion direction of the offield the (Figure field (Figure 16c). The16c). graphene The graphene oxide oxideused had used the had XPS the spectrum XPS spectrum shown shown in Figure in Figure 16(a) 16 anad and the the size size distribution distribution shown shown in inFigure Figure 16(b). 16b. The stark difference in behaviour we observe compared to that of Kim et al. [11] could be due to the The stark difference in behaviour we observe compared to that of Kim et al. [11] could be due to degree of oxidation of the GO. Recently Diamantopoulou et al. [68] have demonstrated that the the degree of oxidation of the GO. Recently Diamantopoulou et al. [68] have demonstrated that the magnetic response of GO and rGO is very different. This suggests that the precise conditions during magnetic response of GO and rGO is very different. This suggests that the precise conditions during the fabrication and storage of the graphene oxide, which affect the degree of reduction, could have the fabrication and storage of the graphene oxide, which affect the degree of reduction, could have an an effect on its magneto-optic response. effect on its magneto-optic response.

Crystals 2019, 9, 455 14 of 20 Crystals 2019, 9, x FOR PEER REVIEW 14 of 20

Figure 16. XPS and size distribution of the graphene oxide used in our magnetic field experiment (a,b). TheFigure inset 16. shows XPS and a typical size distribution POM texture of of the the graphene GO (scale oxide of 500 usedµm). in ( cour) Small-angle magnetic X-rayfield experiment scattering (SAXS)(a,b). The patterns inset producedshows a typi bycal this POM GO at texture a 0.5 wt% of the dispersion GO (scale in DMF.of 500 Theµm). magnetic (c) Small-angle field is inX-ray the horizontalscattering direction.(SAXS) patterns After leaving produced the sampleby this GO overnight at a 0.5 in wt% the field,dispersion no alignment in DMF. e ffTheect wasmagnetic observed. field is in the horizontal direction. After leaving the sample overnight in the field, no alignment effect was observed.

8. Applications of Graphene Oxide Colloids Lyotropic Behaviour Graphene oxide dispersions are an ideal example of stable dispersions of high aspect ratio plate- like particles. The stability of such dispersions opens up a variety of solution-based processing routes. The spontaneous self-assembly into nematic and lamellar phases with increasing concentration has been shown to assist in the manufacture of novel three-dimensional architectures. An example of this is in the production of graphene oxide membranes [69]. Such membranes have received increased interest over recent years due to their potential use in the desalination of water [69,70]. The technology has arisen from the observation that water permeates the membranes rapidly, faster even than helium [71]. Membranes have been fabricated by vacuum filtration of a GO dispersion [71] or by evaporation of the solvent [72]. However, in 2016, Akbari et al. [69] showed that the shear alignment of a concentrated dispersion in the nematic state on a substrate can produce membranes with very even topography over a large area (Figure 17b). A further example of nematic behavior leading to ordered three-dimensional architectures is the observation of photonic behavior in GO

Crystals 2019, 9, 455 15 of 20

9. Applications of Graphene Oxide Colloids Lyotropic Behaviour Graphene oxide dispersions are an ideal example of stable dispersions of high aspect ratio plate-like particles. The stability of such dispersions opens up a variety of solution-based processing routes. The spontaneous self-assembly into nematic and lamellar phases with increasing concentration has been shown to assist in the manufacture of novel three-dimensional architectures. An example of this is in the production of graphene oxide membranes [69]. Such membranes have received increased interest over recent years due to their potential use in the desalination of water [69,70]. The technology has arisen from the observation that water permeates the membranes rapidly, faster even than helium [71]. Membranes have been fabricated by vacuum filtration of a GO dispersion [71] or by evaporation of the solvent [72]. However, in 2016, Akbari et al. [69] showed that the shear alignment of a concentrated dispersion in the nematic state on a substrate can produce membranes with very even topography over a large area (Figure 17b). A further example of nematic behavior leading to ordered three-dimensional architectures is the observation of photonic behavior in GO dispersions. Li et al. [73] found that for a dispersion of high aspect-ratio sheets with low polydispersity, Bragg reflections could be observed in natural light at nematic concentrations (Figure 17c). The exact mechanism for this is not fully understood, but the authors noted that a sensitive balance of forces and flake sizes was key to the appearance of reflections, since the addition of NaCl or sonication (to reduce the flake size) both removed Bragg reflections [73]. Nevertheless, appropriately designed, such photonic crystals could be used in novel inks, or since their colour is based on concentration, humidity sensors. Li et al. also propose that if such structures could be controlled by external fields, GO-based photonic crystals could also be used for energy-efficient colour display applications [73]. Since the liquid crystallinity of graphene oxide dispersions was first discovered [11], the anisotropic ordering and self-assembly properties have been exploited in the production of fibrous materials. Kim et al. have shown that fibres drawn from concentrated GO dispersions with added poly(acrylic acid) have highly ordered microstructures and display birefringence (Figure 17d) [11]. The rheological properties of nematic graphene oxide dispersions make them favourable for wet-spinning of fibres [14] which was first demonstrated by Xu and Gao in 2011 [32]. A topic at the forefront of graphene applications is that of smart clothing and wearable electronics. GO can be reduced to restore some of graphene’s conductivity, and conductive fibres using liquid crystal-assisted assembly, followed by reduction, are already at a mature stage of research [14,16,74]. As well as the potential for display technology based on the Kerr effect of GO dispersions in the isotropic phase (as discussed earlier in this review) He et al. have reported on a re-writable reflective display using nematic-phase GO dispersions [75]. When the concentrated dispersion is sheared in the plane of the surface, the surface becomes more reflective due to the larger amount of GO-surface area interacting with the light. Then, using a stick-like implement, the GO director field can be disturbed, and one is able to create writing on the surface (Figure 17a). Crystals 2019, 9, 455 16 of 20 Crystals 2019, 9, x FOR PEER REVIEW 16 of 20

FigureFigure 17. 17.( a(a)) A A rewritable rewritable reflective reflective display display based based on on a a graphene graphene oxide oxide nematic nematic liquid liquid crystals. crystals. ThroughThrough application application of aof rod, a rod, writing writing can can be achieved be achieved by reorientation by reorientation of the of director the director without without the need the forneed polarizers. for polarizers. Republished Republished with permission with permission of the of Royal the Royal Society Society of Chemistry of Chemistry from Hefrom et al.He [75et ];al. permission[75]; permission conveyed conveyed through through Copyright Copyright Clearance Clearance Center, Inc.Center, (b) Shear-alignment Inc. (b) Shear-alignment of nematic of GO nematic can beGO exploited can be inexploited the fabrication in the offabrication large-area, of highly large-area, uniform highly membranes uniform for membranes desalination for applications. desalination Reproducedapplications. under Reproduced a Creative under Commons a Creative Attribution Commo 4.0ns International Attribution License4.0 International from Akbari License et al. [from69] (cAkbari) For a sensitiveet al. [69] range (c) For of flakea sensitive size and range concentrations, of flake size Li and et al. concentrations, [73] observed selectiveLi et al. [73] reflection observed of visibleselective light reflection in a gel-like of GOvisible LC, light with thein a wavelength gel-like GO of reflectiveLC, with lightthe increasingwavelength with of timereflective as water light evaporatedincreasing andwith concentration time as water of GO evaporated increased. and Reprinted concentration with permission of GO increased. from ref. [73Reprinted]. Copyright with (2014)permission American from Chemical ref. [73]. Society. Copyright (d) This polarized(2014) American photograph Chemical represents Society. the first (d demonstration) This polarized of aphotograph hand-drawn represents firer composed the first of a demonstration graphene oxide of liquid a hand-drawn crystal and firer poly(acrylic composed acid). of a graphene Orientation oxide of theliquid flakes crystal along and the lengthpoly(acrylic of the acid). fibre leads Orientation to a high of levelthe flakes of birefringence. along the length Reproduced of the fibre from leads ref. [11 to] a withhigh permission level of birefringence. from John Wiley Reproduced and Sons. from ref. [11] with permission from John Wiley and Sons. 10. Conclusions 9. Conclusions In the present paper we have reviewed the general properties of lyotropic graphene oxide In the present paper we have reviewed the general properties of lyotropic graphene oxide liquid liquid crystals. We especially discussed some characterization methods of the employed graphene crystals. We especially discussed some characterization methods of the employed graphene oxide oxide sheets or flakes, the occurrence of liquid crystallinity with respect to flake size and solvent, sheets or flakes, the occurrence of liquid crystallinity with respect to flake size and solvent, including including a comparison to a simple theoretical description, which was found to only poorly describe a comparison to a simple theoretical description, which was found to only poorly describe the experimental observations. Alignment properties of GO liquid crystals were discussed, as were the effects of added salt and polymers. Only few investigations have been carried out so far concerning

Crystals 2019, 9, 455 17 of 20 the experimental observations. Alignment properties of GO liquid crystals were discussed, as were the effects of added salt and polymers. Only few investigations have been carried out so far concerning the effect of applied electric and magnetic fields. Some of the reported results indicate a controversial and even opposing behaviour, whose underlying possible reasons were considered. Graphene oxide liquid crystals are certainly a very interesting, timely and worthwhile field of investigation, with a potential for the development of fundamental liquid crystal and soft matter understanding, as well as for future applications in the areas of nanotechnology, templating, electro-optic devices, all the way to possibilities in fibre composites or the desalination of sea water.

Author Contributions: A.P.D. and I.D. together conceived of the subject matter and structure for this review. A.P.D. wrote the main text created the figures and sought copyright permissions where reproductions were necessary. I.D. supervised the project and contributed to the writing of the manuscript. A.P.D. prepared and characterized the graphene oxide samples and analysed the data from the experiments. Funding: This research was funded by The Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom, grant number EP/L01548X/1. Acknowledgments: The authors would like to acknowledge Maria Iliut and Aravind Vijayaraghavan for kind provision of the GO used in the original experiments described in Section7. Furthermore we would like to thank Robert M. Richardson and Andrew Thomas for assistance with the SAXS and XPS experiments, respectively. Conflicts of Interest: The authors declare no conflict of interest.

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