Fracto-eutectogels: SDS fractal dendrites via counterion condensation in a deep eutectic solvent.

Glyceline, a deep eutectic solvent comprising glycerol and choline chloride, is a green nonaqueous solvent with potential industrial applications. Molecular mechanisms of surfactant self-assembly in deep eutectic solvents are expected to diﬀer from those in their constituent polar components and are not well understood. Here we report the observation of self-assembled SDS fractal dendrites with dimensions up to B mm in glyceline at SDS concentrations as low as c SDS B 0.1 wt%. The prevalence of these dendritic fractal aggregates led to the formation of a gel phase at SDS concentrations above Z 1.9 wt% (the critical gelation concentration c CGC ). The gel microscopic structure was visualised using polarised light microscopy (PLM); rheology measurements confirmed the formation of a colloidal gel, where the first normal stress diﬀerence was negative and the elastic modulus was dominant. Detailed nano-structural characterisation by small-angle neutron scattering (SANS) further confirmed the presence of fractal aggregates. Such SDS aggregation or gelation has not been observed in water at such low surfactant concentrations, whereas SDS has been reported to form lamellar aggregates in glycerol (a component of glyceline). We attribute the formation of the SDS fractal dendrites to the condensation of counterions ( i.e. the choline ions) around the SDS aggregates – a diffusion-controlled process, leading to the aggregate morphology observed. These unprecedented results shed light on the molecular mechanisms of surfactant self-assembly in deep eutectic solvents, important to their application in industrial formulation.

Surfactant self-assembly has also been investigated in both reline and glyceline (comprising choline chloride and glycerol in a 1 : 2 molar ratio). [23][24][25] It has been found that the interfacial self-assembly behaviour of surfactants in the DES is similar to that in aqueous systems. Using surface tensiometry, Sanchez-Fernandez et al. reported that cationic surfactants dodecyl/ tetradecyl/hexadecyltrimethyl ammonium bromide (C 12 /C 14 / C 16 TAB) displayed a critical micelle concentration (CMC) in glyceline of 22.0, 3.9, and 0.9 mM, respectively. 26 Anionic sodium dodecyl sulfate (SDS) was shown to have a CMC of 2.0 mM in reline 27 and 3.9 mM in glyceline. 28 X-Ray reflectivity (XRR) showed surfactant monolayer formation at the air-reline interface similar to that the air-water interface. 27,28 However, surfactant self-assembly in the bulk DES solution has shown different behaviours compared to in water or in the individual solvents constituting the DES. For instance, Ruiz-Olles et al. observed that 1,3:2,4-dibenzylidene-D-sorbitol (DBS) formed a 'eutectogel' in a range of DES comprising a binary mixture of choline chloride with glycerol, xylitol, sorbitol, or urea. 29 For DBS in reline, SEM and TEM revealed nanofibrillar structures forming an entangled network with a dominant elastic modulus (G 0 ), characteristic of a gel, with a gelation concentration, c = 4 w/v% at 82 1C.
Here, we report gelation of SDS in glyceline at room temperature (RT B 25 1C) at low surfactant concentrations, i.e. c SDS B 1.9 wt%. Surprisingly, the gel phase comprised complex interpenetrating networks of dendritic fractal aggregates of size some hundreds of mm -thus termed a ''fracto-eutectogel''. For comparison, SDS forms globular micelles in water under the same condition, whilst SDS lamellar gels in glycerol (a glyceline constituent hydrogen-bonding rich solvent) have been reported recently. 30 The microscopic structure of this fracto-eutectogel was visualised with polarising light microscopy (PLM) and its nanostructure studied with small-angle neutron scattering (SANS). Rheology measurements provided complementary information on the gel mechanical properties. The unprecedented observation of the microscopic fractal structures as a result of SDS self-organisation in glyceline points to different molecular interactions in DES compared to aqueous systems or single-component hydrogen-bonding rich solvents.

Materials
Protonated sodium dodecyl sulfate (h-SDS) (Sigma-Aldrich, 498.0%) was recrystallised three times from ethanol, and its purity was checked with 1 H NMR. h-Glycerol (Fisher Scientific, 498.0%) and d-glycerol (Sigma-Aldrich, 498.0% and 498.0 atom%D) were used as received. h-Choline chloride (Sigma-Aldrich, 498.0%) and d 9 -trimethyl-choline chloride (Sigma-Aldrich, 498.0% and 498.0 atom%D) were used as received. h-/d-glyceline was prepared by mixing h-/d-choline chloride and h-/d-glycerol in a 1 : 2 molar ratio in a shaker incubator (Stuart SI505) at 550 rpm at 60 1C for two hours (2 h). The gel-like phase was prepared by adding a designated amount of h-SDS to h-or d-glyceline, then incubating the mixture in the shaker incubator at 550 rpm at 60 1C for 2 h before equilibrating at room temperature overnight. All the samples were kept sealed from moisture before measurements, due to hygroscopicity of both choline chloride and glycerol. In a further study, we have examined the effect of water addition systematically (manuscript in preparation).

Surface tensiometry
Equilibrium surface tension measurements were carried out in ambient conditions with the Wilhelmy plate method using a Krüss K100 tensiometer, with the platinum plate cleaned by flaming between measurements. Due to the relatively high viscosity of h-glyceline (B380 cP), the samples were left to equilibrate for 30 minutes to allow for diffusion of surfactants to the air-liquid interface.

Viscometry and oscillation rheology
All rheological measurements were performed using a rotational rheometer (Malvern Panalytical Kinexus Pro) in a cone-plate geometry (CP 4/20) to minimise the wall-depletion effect observed in oscillation measurements. 31 Viscometry measurements were carried out with the shear rate, _ g, decreasing from 100 s À1 to 0.001 s À1 and each measurement was run for 3 minutes or until it reached a steady state equilibrium. Oscillation rheology measurements involved first characterising the linear viscoelastic region while changing the deformation, g, (or the strain rate) applied, at a constant frequency o = 1 Hz. A strain value was then selected from this linear region, typically g = 0.012%, for frequency sweep measurements.

Polarised light microscopy (PLM)
PLM was carried out using an Olympus BX53-P microscope, where the polarisers were crossed at 901 with respect to each other and images were captured using Stream software. PLM measurements were carried out under ambient conditions, using 10, 20, and 40Â magnifications. A 530 nm first order waveplate was placed in the optical patch to improve the contrast in some cases.

Small-angle neutron scattering (SANS)
SANS measurements were made using quartz cells with a 2 mm path length with a 0.5 h integration time on the Loq 32 smallangle diffractometer at the ISIS Pulsed Neutron Source (STFC Rutherford Appleton Laboratory, Didcot, UK). Loq utilizes neutrons with wavelengths l = 2-10 Å and the data were collected in the q range of 0.008-1.6 Å À1 , corrected for the detector efficiency, sample transmission, and background scattering and converted to scattering cross-section data (qS/qO vs. q) using MantidPlot. 33 The data were then converted to an absolute scale (cm À1 ) using the scattering intensity from a standard sample (a solid blend of hydrogenous and perdeuterated polystyrene). 34

SANS data analysis
The SANS data at 25 1C were fitted using two different models. The first was a lamellar paracrystal stack model (Fig. 8b), in which individual SDS lamellae stacks in solution were treated as being independent of each other, with the lamellae considered as a whole rather than separate headgroup and tail layers. The general scattering intensity for the lamellar systems is described as [35][36][37][38] IðqÞ ¼ 2pVPðqÞSðqÞ The second model used to fit data at 25 1C was a mass fractal model (Fig. 8c) describing the scattering from fractal-like aggregates in solution 39 where the form factor is where r = D/2 is the radius of the building block or particle. The structure factor is where is the gamma function, x the correlation length, and D m the mass fractal dimension.

Surface tensiometry measurements of SDS in glyceline
The surface tension, g, vs. ln(c SDS ) plots in water, glycerol, and glyceline at room temperature (RT B 25 1C) are shown in Fig. 1, with the data for glycerol from ref. 30 included for comparison. The critical micelle concentration, CMC, pure solvent surface tension, g 0 , minimum surface tension, g min , and the headgroup area, A HG , at BCMC determined from the surface excess are summarised in Table 1. All three curves show SDS adsorption at the air-liquid interface and an apparent CMC at RT, indicative of SDS surface activity and self-assembly in these solvents. The cohesive energy and the related Gordon parameter, G = g 0 /V m 1/3 where V m is the molecular volume, of a solvent has previously been used to gauge the solvophobic effect in driving self-assembly, 40,41 with a higher G value indicative of a more pronounced solvophobic effect and hence promoting amphiphile self-assembly more strongly. 40,42 Glyceline has a lowest surface tension value compared to water and glycerol (Table 1). This would point to the lowest cohesive energy density of glyceline among the three solvents, as measured by the Gordon parameter. 40,42 The calculated G values for the three solvents are listed in Table 2. However, the CMC of SDS in glyceline is the lowest of the three solvents at 5.4 mM (vs. 8.1 and 11.7 mM in water and glycerol, respectively), also with the lowest g min ( Table 1). The Hildebrand solubility parameter, d H B (CED) 1/2 where CED is the cohesive energy density, is another measure of cohesion. The d H values for the three solvents are compared in Table 2, and it shows a different trend to G and cannot be reconciled with the observed CMC (Table 1). This suggests that the self-assembly behaviour of SDS in DES glyceline cannot be readily predicted by the Gordon parameter or the Hildebrand solubility parameter, which have been widely used to gauge the cohesive energy and the solvophobic effect in pure solvents.  ln(c SDS ) for SDS at the air-water (red circles), air-glycerol (blue circles), and air-glyceline (green circles) interfaces at room temperature (RT). The surface tensions of the pure solvents, g 0 , are indicated by the horizontal dashed lines. The curve corresponding to SDS at the air-glycerol interface is taken from ref. 30. Table 1 A summary of the parameters determined from surface tensiometry measurements of SDS in water, glycerol, and glyceline: the surface tension of the pure solvent (g 0 ), the minimum surface tension after addition of SDS (g min ), the critical micelle concentration (CMC), the surface excess (G), and the surfactant headgroup area (A HG ). The data corresponding to SDS at the air-glycerol interface are taken from Ref. 30  (i.e. 5-220 mM; 0.9-37.0 CMC; cf. Table 3). At 60 1C, all the samples were transparent and fluid (Fig. 2a); however, when cooled to RT B 25 1C, an opaque phase formed. At c SDS Z1.9 wt%, the sample could hold its weight upon inversion (Fig. 2b). In contrast, SDS in aqueous solutions formed transparent fluid phases consistent with globular micellar solutions. [43][44][45] For comparison, opaque SDS gel phases have been observed in glycerol, 30 with a critical gelation SDS concentration of c CGC B 2 wt% (or 110 mM) below a critical gelation temperature of T GC B 45 1C. 30 The observation of SDS gelation in glyceline suggests interpenetrated networks of aggregates at RT, which would break up at elevated temperatures. Such an SDS-inglyceline gel (or in other DES), at low SDS concentrations, has not been previously reported in the literature to our knowledge.

Rheological properties of the fracto-eutectogel
A representative plot of shear stress, s, as a function of shear rate, _ g, of the SDS-in-glyceline gel (5.3 wt%, B53 CMC) is shown in Fig. 3a, displaying shear thinning behaviour with a nonlinear stress-rate (s-_ g) relationship. The magnitude of s (o100 Pa) is consistent with a weak physical gel that can be disturbed by the applied shear, indicated by the presence of an inflection point at _ g B 5 s À1 in the s-_ g plot. This behaviour is similar to previously reported gel phases consisting of fibrillar aggregates. [46][47][48][49][50][51] Fig. 3b shows the variation of the shear viscosity, Z, with c SDS at two different shear rates (taken from linear fits before and after the inflection point). At the lower shear rate (0-5 s À1 ; LSR), Z LSR increased linearly with c SDS , in contrast to the constant Z HSR at the higher shear rate (5-100 s À1 ;HSR). This suggests that the 3D structure in the gel phase was broken up at the HSR into smaller aggregates, manifesting in a constant viscosity value over the c SDS range.
The behaviour of the first normal stress difference, N 1 , (Fig. 3a, inset) is different from that expected of fibrillar dispersions, for which N 1 would typically increase with _ g due to fibrous aggregates becoming elongated in the direction of the applied shear. [52][53][54] Here, N 1 decreased with _ g (for _ g 4 B0.05 s À1 ), indicating that the aggregates became shorter in the direction of the applied shear. The decreasing N 1 with _ g can be attributed to hydrodynamic friction between individual aggregates, 55,56 implying the presence of globular aggregates. Unlike the shear thickening behaviour often observed in colloidal dispersions due to shear-induced aggregation, 57,58 the shear thinning and N 1 behaviour observed in this study suggest that, while the aggregates showed hydrodynamic friction, there was no flocculation-induced shear thickening, a behaviour observed in some colloidal gels. 59,60 The elastic and viscous moduli (G 0 and G 00 , respectively) are shown as a function of the deformation (or strain, g, Fig. 4a) to demonstrate the viscoelastic behaviour of the 5.3 wt% SDS-inglyceline gel in response to an applied deformation. The presence of a linear viscoelastic region (LVER) at small deformations (g B 0.001-0.1%) shows that the structure of the gel was unaffected by small strains.
A previous report showed that the magnitude of G 0 (g) and G 00 (g) of an SDS-in-glycerol gel was an order of magnitude higher than that observed here. 30 The MacKintosh model, assuming the system consisting of a semiflexible network, 61 relates the bending modulus, k, of the constituent fibres to the gel elastic modulus, G 0 LVER g ð Þ $ k 2 . The estimated k values using this model are plotted against c SDS in Fig. 5, showing a Table 3 SDS concentrations (in wt%) for the samples in Fig. 2, and the sample numbers are applicable to both Fig. 2a   linear relationship, with a maximum k value of B50 Pa, which was lower than that observed for the SDS-in-glycerol gel (k B 140 Pa).
The behaviour of G 0 (g) and G 00 (g) beyond the LVER shows the sensitivity of the gel network to the applied deformation, as both moduli decreased by two orders of magnitude, possibly due to the breakup of the larger aggregates into smaller ones. The gel appeared elastic at low deformations (g o 0.2%), with G 0 (g) 4 G 00 (g); however, a crossover point is observed at g* B 0.3%, above which G 00 (g) 4 G 0 (g), indicating a transition to a more liquid-like phase.
The values of the LVER elastic and viscous moduli as a function of c SDS are shown in Fig. 4b. As c SDS increased, a transition from a liquid-like to a solid-like material can be observed at c SDS B 1.2 wt% (the slopes of the G 0 /G 00 vs. c SDS plots before and after the transiton are listed in Table 4). This concentration can be deemed (as similarly defined in ref. 30) a critical gelation concentration, c CGC , consistent with the macroscopic observations in the inverted vial test (Fig. 2).
The gel structure appeared to be more sensitive to the magnitude of deformation than the speed at which it was applied. Fig. 4c shows the variation of G 0 and G 00 at low strain (g o 0.2%) as a function of the shear frequency, o, for the 5.3 wt% SDS-in-glyceline gel. Over the o range measured, the elastic modulus remained dominant (i.e. G 0 4 G 00 ) with no crossover, indicating a solid-like behaviour. Whilst the gel showed sensitivity to strains, g, the moduli were less sensitive to the frequency, o. The absence of the G 0 (o)-G 00 (o) crossover would suggest that the system was not comprised of fibrillar aggregates 62 -and instead more likely of globular aggregates. The magnitudes of the two moduli (G 0 B 12.5 kPa and G 00 B 4 kPa) are quite high compared to surfactant-based gels of elongated wormlike micelles [63][64][65][66] (in the range of 10-100 Pa). However, these values are comparable to those of the SDS-in-glycerol gel (G 0 B 27 kPa and G 00 B 11 kPa). 30 The dependence of G 0 and G 00 (at a high frequency o = 10 Hz) on c SDS is shown in Fig. 4d, with a similar transition (cf. Table 4) observed compared to the amplitude sweep data (Fig. 4b).
Whilst the G 0 (o) and G 00 (o) magnitude increased with c SDS , there was no crossover and the elastic modulus remained dominant (G 0 (o) 4 G 00 (o)) even in the liquid regime. The lack of a crossover arises from the lower sensitivity of globular aggregates to the speed at which the deformation is applied, without structural changes observed in the globular aggregates. This again suggests that the structure of the gel consisted of particulates, akin to a colloidal gel. 67

Microscopic structure of the ordered surfactant mesophase
Polarised light microscopy (PLM) revealed an anisotropic mesophase at room temperature at SDS concentrations (c SDS 4 1.9 wt%) (Fig. 6), consisting of dendritic feather-like aggregates of some mm in length scale with no particular alignment. The dendritic fractal 68,69 morphology (seen in detail in Fig. 6c, d) exhibits a central fibre that supports secondary fibres, which in turn support tertiary fibres, and so on. A fibre order parameter, n f , can be defined as the fibre position away from the parent or central fibre, where the parent fibre n f = 1. As n f increases, both the fibre length and the diameter generally decrease (Fig. 7b). It is conceivable that the fibres grew sequentially: first the growth of the parent fibres, then the secondary fibres and the tertiary fibres. The detailed mechanism -whether the parent and child  Table 4 Values for the slopes in the liquid and gel regimes of the plots of the elastic (G 0 ) and viscous (G 00 ) moduli vs. c SDS for the amplitude (g from the LVER) and frequency (o = 10 Hz) sweep measurements in Fig. 4b and   fibres grow simultaneously, or the parent grows first and then stops to allow the children to grow -is unclear. Fig. 8 shows the SANS scattering profiles at different c SDS , with the data fitted to a mass fractal model (Fig. 8c) and, for c SDS = 1.2, 2.7, and 5.3 wt%, also a lamellar paracrystal model (Fig. 8b).

Gel nanostructure from SANS
The appearance of a Bragg peak at q B 0.30 Å À1 at the higher SDS concentrations (c SDS = 1.2, 2.7 and 5.3 wt%), corresponding to d B 2p/q B 20.9 Å, suggests the formation of an ordered mesophase. There was no plateau observed in the low-q region of the SANS scattering profiles at any c SDS , indicating the presence of a large structure or mesophase in the gel whose size was not accessible in the q-range of the SANS measurement. The coherence length, L c , which is indicative of the disorder of the meso-structure, can be obtained from analysing the broadening of the Bragg peaks using the Scherrer equation [70][71][72][73][74][75][76] where K is a shape factor (here K B 1), and Dq is the full width at half maximum of the Bragg peak.
The L c vs. c SDS behaviour (Fig. 9) appears different at low c SDS (1.2 wt%) compared to the two higher c SDS samples (2.7 and 5.3 wt%), implying different structural orders. The L c value at the two higher c SDS converged to L c B 140 Å at T = 40 1C.
As only one Bragg peak is present in the scattering profile, it cannot ascertain the exact mesophase type; this peak could also arise from the presence of solid SDS crystallites. Complementary X-ray reflectivity (XRR) measurements at the air-glyceline interface (Fig. S1, ESI †) showed the presence of a second Bragg peak at q B 0.6 Å À1 , consistent with the n a = 1, 2 peaks of a lamellar phase or surfactant crystal. A recent study has similarly shown the presence of aggregates with a lamellar structure in SDS-inglycerol gel, 30 and thus the obtained SANS profile was fitted to a lamellar paracrystal stack model (Fig. 8b). The fits to 5.3, 2.7, and 1.2 wt% h-SDS in d-glyceline are shown in Fig. 8 with the fitting parameter values in Table 5. The reduced intensity and number of Bragg peaks observed in this study -as compared in glycerol in the previous study 30 -could be attributed to the presence of choline chloride in glyceline, which could disrupt the structural order of the SDS lamellar phase.
The thickness, t L , and the d-spacing of the lamellar phase show a close agreement, t L B d B 20 Å (cf. Fig. 8b), indicating   that the lamellar sheets consisted solely of SDS bilayers. A full SDS bilayer of thickness of two SDS lengths would give t L B 35-45 Å; however, smaller SDS lamellar spacing has been reported, t L B 25-28 Å 77,78 in the presence of additives, such as a cosolvent. The smaller value reported here, t L B 20 Å, could arise from a tilted SDS bilayer or interpenetration of the tails. The high polydispersity of the lamellar thickness implies polymorphisms with different SDS packing and conformations, leading to different d-spacing. We acknowledge that, along with the large thickness polydispersity, the presence of a single Bragg peak and the relatively small fitted t L value could mean the paracrystal lamellar model might not best describe data.
Fractal models were also trialled to fit the SANS data -to capture the structural features at larger length scales. Of these, the mass fractal model 39 was found to best fit the SANS profiles at 25 1C (Fig. 8a, c and Table 6). The fitted radii, r, of the aggregates decreased with increasing c SDS , a feature also evident from PLM (Fig. S2, ESI †), where larger aggregates were more noticeable at lower c SDS . This could be due to the growth of the aggregates being stunted by the number of aggregates forming, suggesting that the growth mechanism is that all fibre orders (n f = 1, 2, and 3) grow simultaneously. 79 The fractal dimension, D m , is related to the Hausdorff dimension, 80,81 which is a mathematical description of scale invariances that appear identical when viewed over a range of scales. Mass fractals typically have D m B 2-3; for instance broccoli has a D m B 1.8 and cauliflower a D m B 1.9. 82 D m B 2 is indicative of smoother aggregates and D m B 3 is from rougher aggregates, with D m 4 2 implying three dimensional fractals. 83,84 Table 5 shows D m B 2.8-3 across the c SDS studied, indicating very rough mass fractal aggregates of similar D m to that reported of human lungs. 85 The fractal dimension can also be estimated directly from a power law fit to the low-q data of the scattering profile, 39 i.e. B q DÀ6 (Table 7). This yielded lower D m values (1.5-2.8) compared to those obtained through the fitting to the SANS profiles of the higher c SDS . This difference could be due to the sensitivity of the mass fractal model regarding the dimensionality of the interfacial region between the cluster and solvent bulk, as opposed to the cluster itself, as noted by Mildner and Hall.39

Summary, further discussions and proposed gelation mechanism
We have observed the formation of a gel in glyceline, a deep eutectic solvent (DES), at an SDS critical gelation concentration as low as c CGC B 1.9 wt% (i.e. 12.7 CMC). PLM revealed that the gel phase comprised fractal dendritic aggregates of Bmm in size, consistent with the SANS data fitted using a mass fractal model. At comparable c SDS , SDS would form spherical micellar aggregates in water as expected from its packing parameter of B 0.25. 86,87 At much higher concentrations and at higher T (4 80 1C), SDS would form lamellar or hexagonal phases (c SDS B 75 and 45 wt%, respectively). 43,44 The formation of dendritic fractal aggregates has not been reported, and we term it a fracto-eutectogel.
The dendritic aggregates oriented anisotropically and their hierarchical structures might be considered as comprising parent and child fibres. The fibre length and diameters of the fibres decreased with increasing fibre order, n f , implying that the growth of the parent fibre preceded the child fibres. Rheology measurements confirmed relatively weak interactions of the network entanglement, akin to a physical colloidal gel. The negative first normal stress difference, N 1 , and elastic properties of the gel phase were consistent with a colloidal gel comprising globular aggregates in solution.
Dendrites are fern-like or tree-like fractals common in nature, such as hoarfrost, 88 and have been widely studied. The driving force for dendrite formation is related to the Mullins-Sekerka instability. [89][90][91][92] It describes the progression of a solid front, or the dendrite tip, in a liquid medium, where the cooled solid advances into a warm, or undercooled, medium. 93,94 For growth to occur, the interface must be warmed to the Table 5 Fitting parameters for the paracrystalline lamellar stack model for c SDS = 1.2, 2.7 and 5.3 wt% h-SDS in d-glyceline at RT B 25 1C (cf. Fig. 1a): SDS bilayer thickness t L , number of layers in the stack n Layers , d-spacing, polydispersity of the d-spacing s d , scattering length density of SDS r SDS , scattering length density of glyceline r Gly , polydispersity of the SDS bilayer thickness s t , and chi squared value w 2 (as a measure of the goodness of the fit)  temperature of the liquid, typically as a result of latent heat released by kinks along an otherwise smooth surface. 95,96 The growth of fractals, and dendritic patterns in particular, is driven by surface tension anisotropy as proposed by Gruber and Mullins,97 where the surface tension of perturbed surfaces deviates from that of unperturbed planar surfaces. 98,99 SANS measurements showed the formation of a bulk mesophase at all c SDS studied, well described by a mass fractal model with a fractal dimension D m = 2.8-3.0 in the gel phase (or a smaller value using the power law fit to the low q SANS data), confirming the PLM visualization. This contrasts with SDS selfassembly in aqueous systems, 43,44,78 forming globular aggregates at comparable c SDS .
The morphological details of the fracto-eutectogel are also quite unusual for non-aqueous systems. For example, an SDSin-glycerol gel 30 has been recently reported at comparable c SDS at RT, comprising fibrous networks of lamellar building blocks.
Here, a lamellar model could well capture the Bragg peaks in the SANS data (Fig. 8), suggesting lamellar packing of SDS in the dendritic fractal aggregates as observed in hydrated crystalline systems. 100 Surfactants are known to form hydrated crystals below the Krafft point 101 and crystallisation of inorganic ions in DES has also been reported. 102,103 Gelation and crystallisation are often viewed as two competing processes. 104,105 However, the crystal engineering approach to forming supramolecular gels has been reported. 106,107 For instance, anthracenyl groups of cholesteryl 4-(2anthryloxy)butanoate (CAB) forms a stacked helical arrangement, leading to a thermally reversible gel network; 107,108 inulin gels comprise networks of small crystallites. 109 The contrast between the observation in glyceline (choline chloride : glycerol in 1 : 2 ratio) here and in glycerol 30 points to the pivotal role of choline chloride in facilitating the formation of fractal aggregates. We note that a critical gelation temperature, T GC , exists, above which SDS forms cylindrical aggregates.
The role of choline chloride in the self-assembly of such aggregates may be explained by the counterion condensation theory, 110 commonly used to describe polyelectrolyte systems but also extended to other systems. [111][112][113] In our system, the parent fibre grows in one dimension into a rod-like shape and simultaneously choline ions are diffusing to the fibre surface through counterion condensation (Fig. 10). The condensed choline ions lead to certain points along the fibre that radiate heat more effectively, causing kinking along the otherwise flat rod surface as a result of Mullins-Sekerka instability. [89][90][91][92] Due to the bridging effect of the condensed choline ions, this leads to increased growth at the kink sites, resulting in branching and dendritic growth 95,96 (Fig. 10f). Such a counterion condensation effect is more favourable in glyceline due to its lower dielectric constant (e Glyceline B 10 114 vs. 78.3 115 and 42.5 116 for water and glycerol, respectively), due to stronger attractions between opposite ions and, in turn, a stronger bridging effect. Such cation-bridging has been observed; 117-119 for instance, SDS and caesium dodecyl sulfate formed hemicylinders bridged with Na + /Cs + counterions at the water-graphite interface. 119 At c SDS 4 1.9 wt%, jamming of the fractal aggregates -rather than their interpenetration -would lead to a colloidal gel, consistent with the rheological observations, which indicate a structure closer to a colloidal gel rather than an entangled fibrillar network.
Fractal aggregates exist already at low SDS concentration (c SDS B 0.1 wt%) evident from PLM observations (Fig. S3 in ESI †) with the constituent fibres appearing thicker possibly due to a smaller number of nucleation sites at the lower SDS concentration.
The SDS Krafft point in glycerol, a component of glyceline, is T k 4 30 1C, 120 below which crystallisation of surfactants is favoured over self-assembly. 121 Surface tensiometry measurements ( Fig. 1) however points to SDS surface activity and thus self-assembly tendency at RT. Addition of salt has been shown to alter the Krafft point of ionic surfactants, [122][123][124] and the presence of choline chloride could thus suppress the Krafft point, giving rise to the self-assembly tendency of SDS observed at RT.
Further experimental work would be required to fully validate the proposed formation mechanism for the fracto-eutectogel of SDS in glyceline. For instance, use of cationic, zwitterionic, and a nonionic surfactants (e.g. DTAB, cocobetaine, and C 5 E 12 respectively) would inform whether the cationic choline ion would stabilise the different types of headgroup. Our results have fundamental implications to gelation and self-assembly important in application of DES as green solvents.

Conflicts of interest
The authors declare no conflict of interest.