Pattern formation of drying lyotropic liquid crystalline droplet

Abstract

We present a study of pattern formation in drying sessile droplets of aqueous solutions of cetyltrimethylammonium bromide (CTAB)–water system using polarising optical microscopy (POM) and computer simulation. A 4-fold symmetrical and a 3 dimensional staircase like pattern appear during drying of the droplets of the CTAB–water system. However, when NaBr salt is added to the solution, the pattern changes to a system of concentric rings with a fainter set of hyperbolic fringes superimposed on it. The ring width is found to decrease from the central to the peripheral region. We compared the CTAB–water–NaBr pattern with patterns obtained by simulating a 3-dimensional model with various director configurations using a Jones matrix calculation. A good qualitative agreement of the simulated and experimental patterns is obtained for a model assuming a lenticular shaped droplet with the local directors parallel to each other and aligned horizontally, parallel to the fluid–substrate interface. The circular and hyperbolic fringe patterns as well as variation in width of rings are qualitatively reproduced by the simulation. When the droplet dries out completely dendritic crystals form for the CTAB–water droplet as well as the CTAB–water–NaBr droplet. Our results indicate that as the droplet concentration increases with evaporation, elongated cylindrical micelles form which prefer a mutually parallel, horizontal configuration.

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1 Introduction

The study of evaporating droplets and the patterns they form has recently become a subject of great technological interest.^1,2 Two quite distinct classes of patterns have been observed, (i) the so-called ‘coffee-ring’³ pattern where the solute or suspended particles left after evaporation form a ring at the initial contact line of the drop; the other class are a result of Marangoni flow⁴ which causes the solid residue to form a blob at the center of the drop. When the drying droplet contains a salt and a colloidal gel or a complex fluid an amazing variety of patterns, such as concentric rings, fractals, dendrites, hopper crystals, needle crystals and multifractal aggregates^5–9 are observed. These results are of practical use in medical diagnosis,^10,11 novel technology¹² and show interesting effects such as fractal fingering¹³ etc. Surfactants can play an important role, reducing the surface tension and hence inducing Marangoni flow which alters the deposition pattern significantly.¹⁴ A related field is the study of droplets which form directed and low dimensional ordered aggregates such as liquid crystals.^15,16 Such droplets usually assume spherical shape and are studied while they are dispersed in another fluid.^17,18 The molecular directors of the liquid crystals take up specific arrangements depending on the interactions among themselves and with the spherical interface of the drop. Different geometrical arrangements of the director profile such as radial, bipolar, twisted bipolar, play a vital role in determining the elastic properties of the liquid crystal droplet.^18,20 When viewed between crossed polarisers, the anisotropic arrangements, which may have topological defects show typical patterns, which are useful for identifying the structures formed by the directors. Alignment of nematic liquid crystals at planar fluid–air interfaces have also been studied.¹⁹

Study of sessile drops of such fluids deposited on a solid substrate and allowed to desiccate, adds a new dimension to this problem. The sessile drop usually takes the shape of a section of a sphere, with the contact angle depending on how the fluid wets the substrate. The directors of aggregated molecules may form a pattern which shows up under crossed polarisers.²¹ As the solvent evaporates, the concentration of the fluid changes and the pattern continues to evolve until the drop is completely dried. There are relatively few studies of orientational ordering in sessile droplets, one being the work reported by Smalyukh et al.²² where rod-shaped cells of bacteria are reported to order along the contact line, following the orientation of extended DNA chains.

Cetyltrimethylammonium bromide (CTAB) is a cationic surfactant with Br⁻ counterion. It is widely used as an antiseptic, in various synthesis processes as well as in DNA extraction and personal care products. CTAB is known to play a vital role for building nano-structures using evaporation-driven self assembly of nano-materials formed in CTAB matrix.^26–28 Therefore, structural changes in CTAB–water system during evaporation may play an important role in determining the structure and self assembly of nano materials. CTAB in water exhibits a variety of liquid crystalline phases starting from an isotropic solution of spherical micelles at low concentration to a lamellar phase at high concentration. The isotropic phase is in the concentration range 0–25 wt% at 27 °C. In the isotropic phase it forms spherical micelles upto 11 wt% and cylindrical micelles above this concentration. For CTAB concentration 25–60 wt% the cylindrical micelles are known to arrange in a hexagonal phase and in lamellar phases above this concentration range.^23,24 Characteristics of liquid crystalline phases can easily be inferred using a polarising microscope as well as SAXS.²⁴ It is important to emphasize that the phase diagram at different CTAB concentration can be linked with the pattern formation of the CTAB–water system. Interestingly, these structures can be tuned by addition of salts, such as NaBr. In the presence of 0.06 M aqueous solution of NaBr rod like micelles are formed.²⁵ Above 0.5 M of NaBr the micelles become flexible and its molecular weight increases.²⁵ However in the present experiment the situation is slightly different from the conventional single phase at a particular CTAB concentration. Here we encounter a continuous variation of water concentration from the rim of the droplets, which may result in continuous variation of refractive index.

In the present study, we report the observation of pattern formation in drying of a sessile droplet of CTAB solution with sodium-bromide salt. We compare the pattern obtain from experiments with various simulated director configurations. The present study also attempts to understand the role of the director configuration in generating the experimentally observed pattern.

2 Materials and methods

CTAB and NaBr are obtained from Merck, Mumbai, India. We used HPLC grade water to prepare the solutions. We have used the method described in previous literature^23,29 for preparing the samples. Aqueous solutions of CTAB of different concentrations (18, 20, 22.5 and 25) wt% were prepared by dissolving appropriate amounts of CTAB in water with stirring at 60 °C. CTAB is known to form cylindrical micelles²³ in these concentrations in aqueous solution. We also prepare 0.2 M solution of NaBr in water. The previously prepared CTAB and salt solution are mixed at 1 : 1 ratio by volume. This procedure results in the final concentration of CTAB solution to be (9, 10, 11.25 and 12.5) wt%. The samples were kept for one day at room temperature prior to the measurement.

A droplet of either pure CTAB solution or CTAB with NaBr of volume varying from (10–20) μL was deposited using a micro-pipette on a previously cleaned glass slide for microscopic observation. The droplets are allowed to evaporate at relative humidity ≅ (55 ± 10)% and temperature 30 °C. We check the reproducibility of patterns under similar ambient conditions for all observations. The drying process is observed, using polarising microscope (Leica DM 750) through bright field as well as under crossed polarisers. Video and still images are recorded using a camera mounted on the microscope and the images are analysed using ImageJ software. A typical video is shown in the ESI† provided.

3 Results

3.1 Contour of the droplet

The initial appearance of the drop and its time evolution photographed laterally, using Nikon Coolpix l120 camera are shown in Fig. 1. The volume of the droplet was 50 μL and it initially makes an angle of contact of 45° with the glass substrate. Evolution of the drop contour with time is shown in Fig. 1. It is seen that the contact line is pinned and the peripheral region dries faster forming a flatter band or ‘foot’ surrounding a central ‘cap’. Eventually the central region also dries up, the whole process takes about (25–30) minutes.

Fig. 1 Snapshots of the time evolution of the droplet contour containing CTAB and NaBr at time t ≅ (a) 0 (b) 0.26t_evp (c) 0.51t_evp (d) 0.68t_evp (e) 0.82t_evp (f) 0.9t_evp where t_evp ≅ 25 min, where t_evp = total evaporation time. The cap and foot regions as discussed in text are marked with arrows.

3.2 Desiccation as observed through crossed polarisers

3.2.1 Droplet containing CTAB–NaBr. Several snapshots extracted from the recorded video (ESI†) of the drying process are shown in Fig. 2. The initiation of solvent evaporation starts 7 minutes after deposition. As the evaporation continues concentric circular patterns of dark and bright rings appear at a distance ≅ 100 μm from the droplet boundary and proceed towards the centre while the central region remains dark. This pattern is observed in the droplets for all concentrations of CTAB solutions. The appearance of the rings at the periphery is faster for higher concentration than that in lower concentration of CTAB. Careful observation shows another set of hyperbolic bands, facing outward, which intersect the circular fringes as shown in Fig. 3. As the droplet dries the surface of the drop develops wrinkles, as observed in similar experiments on collagen samples.²¹ At the last stage of drying the onset of crystallization is clearly visible at the peripheral band as shown in Fig. 2f–i. Branched dendrites grow towards the central cap, gradually obliterating the circular ring patterns as the aligned liquid crystal arrangement is disrupted. Bluish and reddish colors appear in the crystalline pattern, similar to earlier observations.³⁰ Finally the crystal dendrites grow into the circular cap region and the system dries up completely.

Fig. 2 Different stages of the evaporating droplets of CTAB–NaBr at time t ≅ (a) 0.15t_evp (b) 0.25t_evp (c) 0.3t_evp (d) 0.4t_evp (e) 0.47t_evp (f) 0.71t_evp (g) 0.75t_evp (h) 0.92t_evp (i) 0.99t_evp, where t_evp ≅ 20 min. Concentration of CTAB is 10 wt%. The concentric ring pattern appear in the boundary region before complete drying as shown in (c–e). Dendritic crystal growth is shown in subsequent stages (f–i).

Fig. 3 Formation of hyperbolic bands (shown by the white arrows) superposed on concentric rings in the drying droplets of CTAB–NaBr. Concentration of CTAB is 10 wt% and NaBr is 0.1 M.

3.2.2 Droplet without NaBr. The drop patterns for aqueous CTAB with no NaBr are much more complex. Adding salt facilitates the cylindrical micelles to grow and develop pronounced birefringence, their arrangement finally leads to the ring like patterns seen as long as enough water is present in the sample.^25,31 Without salt the structures are smaller, possibly the birefringence is shear induced and may not persist in absence of flow.³² The patterns observed in this case are peculiar structures which look like curving three-dimensional staircases. These form immediately after deposition and persist upto complete spreading of the droplet Fig. 4. The pattern is observed for concentrations above 22.5 wt%.

Fig. 4 Droplets without NaBr. Droplets without crossed polariser for (a) CTAB concentration 22.5 wt%. Droplets under crossed polariser for CTAB concentration (b) 20 wt% (c) and (d) 22.5 wt% (e) and (f) 25 wt%. The scale bar in the image has length equal to 100 μm.

The transition from concentric ring pattern to the dendritic crystalline growth in the final stages of drying is observed without salt as well.

The ring widths are seen to vary with the size of the deposited drop but varying the CTAB concentration does not make a noticeable difference. To quantify and compare the pattern characteristics as function of the drop size, we measure variation in the widths of the successive rings. The resolution of the patterns is not good enough for very precise measurement. Widths are measured at several different positions for each ring and averaged. There is some fluctuation and the standard deviation of these measurements is about 0.35 but the trend in the results is quite clear. Fig. 5a shows the average widths W(N) of the rings for drop volume 10, 15 and 20 μL, counting their position N from the centre of the pattern towards the periphery.

Fig. 5 Ring width W(N) as a function of ring number N for the drying droplet of CTAB–NaBr. Ring number is counted from the central ring towards the periphery of the drop, (a) widths measured from the experiment for different volumes of the droplet. Results for 10, 15 and 20 μL are represented by circle (red), triangle-up (green) and triangle-down (blue) symbols. (b) Width calculated using simulations, the ring widths are scaled with respect to the width of the 1st experimental ring. Square (black) symbols represent Sim I calculation and circular (red) symbols Sim II calculation respectively.

4 Analysis of the pattern observed under polarising microscope

Pattern formation in liquid crystalline droplets, especially thermotropic droplets has been reported in several earlier works.¹⁵ Arrangement of the director profile may show singularities or topological defects and these leave their signature in the symmetry of the pattern observed in the intensity of the transmitted light. The arrangement of the anisotropic units in a confined liquid crystal droplet depends crucially on the interactions at the interfaces. In the case of a sessile droplet, there are two interfaces – (a) a planar interface between the fluid and the solid substrate and (b) a curved interface at the fluid–air boundary. The directors of the units may prefer to align normal or parallel to the interface. The sessile drop has axial symmetry. This fact in conjunction with the anchoring preference of the director at the boundary may lead to twisted configurations along certain directions.³³ The usual method of analysis is to simulate a droplet of a desired shape and symmetry arising from various director alignment configurations and look for the best match between the simulated and experimental patterns. Therefore, this pattern recognition is considered as a feasible identification method for the arrangement of the directors in the real droplet.

One such technique to simulate the patterns formed by the droplet is the Jones matrix calculation as described by Shurcliff et al.³⁴ The Jones matrix represents the phase change and rotation of the plane of polarization, when polarised light passes through an anisotropic sample which may have birefringence and/or optical activity due to chirality. In this technique the intensity of the polarised light transmitted through an optical retarder is obtained by calculating the absolute value of the product of the Jones matrix and the Jones vector. Here the optical retarder is represented by the Jones matrix and the polarisation of the light which enters represents the Jones vector. For a liquid crystal droplet the directors are considered as an optical retarder and each of the local directors has its respective Jones matrix. Then the incident Jones vector and the Jones matrices of the directors along the beam path and the analyser are multiplied sequentially to obtain the exit Jones vector or final Jones vector. The absolute value of the exit Jones vector gives the transmitted intensity.¹⁸ Once a model is visualized which has the correct symmetry and is feasible from physical and chemical considerations, a simulation of the pattern observed under crossed polarisers can be carried out. Let us assume that light polarised along X-axis enters the system along the vertical Z-axis from below and forms a pattern in the X–Y plane after exiting the analyser which allows the Y-polarised light to pass through.

Two convenient techniques have been used to implement this scenario; (I) by integrating along the direction of light propagation over vertical columns of the model system at (x,y) with the director configuration being a function of (x,y,z).³⁵ The final intensity distribution consists of 2 terms – one represents the chirality and involves the number of topological defects m (ref. 36) in the model configuration, the other represents the linear birefringence involving the phase difference between ordinary and extraordinary rays. In the second method (II) the system is discretized or ‘gridded’ into convenient units. Each unit is assigned a local director according to the chosen model, the phase shift and rotation of the incident polarised beam due to each unit is multiplied iteratively to get the Jones matrix for the whole system, whence the final intensity distribution is calculated. In this procedure the topological defects, if any, are taken into account automatically. We have employed both these methods in our analysis to validate our conclusion. The methods are described in some detail below.

4.1 Simulation algorithm (I)

We first describe the method used by Son et al.,³⁶ with necessary changes corresponding to our experimental system. The present system is the sessile drop which is bounded by a plano-convex lens shaped boundary as shown in Fig. 6. The plane surface being the fluid–solid interface and the convex surface the air–fluid interface. Let R be the radius of curvature of the lens and f is the ratio of thickness at the centre to the radius of curvature. The thickness at the centre is then fR. The system height at (x,y), is given by h(x,y). Here, the refractive indices for the birefringent material for ordinary and extraordinary rays are designated n_o and n_e respectively, and the effective refractive index n_eff is given bywhere θ(x,y,z) is the angle between the director at (x,y,z) and the Z-axis. The phase retardation ΔΦ when polarised light traverses the height h(x,y) through the system is calculated as

Fig. 6 Schematic diagram of the droplet. In the present case the shape of the droplet is considered as a section of a sphere. The height of the section at the centre is taken as 0.16R, where R is the radius of the sphere, in accordance with experimental observation.

For the lenticular system with thickness fR (f = 1 for a hemisphere) the height at (x,y) is given by

The final intensity pattern I(x,y) after the light exits the analyzer is obtained from the Jones matrix for a director configuration with topological charge m given by

with ϕ = arctan(y/x) ashere is represented as the column vector of the incident polarised light. I(x,y) is the transmitted light intensity which is the product of the Jones matrix of the optically anisotropic medium and the column vector of the incident polarised light. Incident polarised light is represented by the light passing through the polariser.

4.2 Simulation algorithm (II)

An alternative method is to discretize the system by placing it in a cubic grid. We follow here, the method described by Ding and Yang, 1992 (ref. 20) for spherical drops, introducing required modifications appropriate to the system. We superpose a square grid on the system, dividing it into unit cubes of thickness t, with positions defined by (x,y,z). A local director is assigned to each unit cube. When light of wavelength λ, passes through a thickness t of a birefringent medium with refractive indices n_o and n_e, the ordinary and extraordinary rays develop a phase difference, given bywhere γ is the angle between the direction of the incident light and director and the effective refractive index n_e(γ) is

The amplitude of the light incident on the polarizer is

E_in = E₀ e^iωt (8)

If θ₁ is the angle between the polarizing direction and optic axis, in the first unit, relative amplitudes of e-ray and o-ray can be written as

A₁ = E₀ cos θ₁ e^iωt (9)

B₁ = E₀ sin θ₁ e^iωt (10)

After passing through the first grid unit, there is a phase difference δ₁ between e-ray and o-ray, so amplitudes are now

A′₁ = E₀ cos θ₁ e^iωt−δ₁ (11)

B′₁ = E₀ sin θ₁ e^iωt (12)

In the second grid where θ = θ₂

A₂ = A′₁ cos(θ₂ − θ₁) − B′₁ sin(θ₂ − θ₁) (13)

B₂ = A′₁ sin(θ₂ − θ₁) + B′₁ cos(θ₂ − θ₁) (14)

Phase difference created in the second unit is δ₂. A set of recurrence relations for transit through n units can thus be written and the final amplitude at the analyser, assumed normal to the polariser will be

E = A′_n sin θ_n − B′_n cos θ_n (15)

here θ is defined as the angle between the polariser and the projection of the local director (optic axis) on the normal plane of the incident light. The intensity distribution of light emerging after the nth step is given by

I = EE* = |E|² (16)

4.3 Calculating the CTAB–NaBr intensity distribution

According to the appearance of the sessile droplet shown in Fig. 1, we model the system as a section of a sphere of radius R with maximum height h_max ∼ 0.16R. The schematic diagram of the droplet is shown in Fig. 6. Light polarised along the X-direction by a polariser and propagating along the Z-direction is assumed to be incident on the drop. The light emerging through the drop passes through an analyser allowing Y-polarised light to pass. The calculation of the final intensity distribution using the two alternative methods is described below. We first apply algorithm I to this system as follows. We look for a pattern of local directors in the lens shaped sample which produces the intensity distribution observed experimentally. As shown in the initial droplet configuration Fig. 1, our system can be represented by a thin section of a sphere, with the thickness at the center approximately equal to 0.16 × R, R being the radius of curvature. We take the wavelength of light as λ ∼ 550 nm and the height of the droplet as 0.1 mm (=100 units), so 1 length unit = 1000 nm. Refractive index data for this material not being available, we use the values for smectic liquid crystals used by Son et al.,³⁶ where n_o and n_e have been taken as 1.67 and 1.53 respectively. All micelles are assumed to align in the X–Y plane, pointing in one direction so that we consider 2θ(x,y,z) = π/2. Then the effective refractive index and the phase retardation is written as

n_eff(x,y,z) = n_e (17)

where Δn is a parameter representing the difference between refractive index of e-ray and o-ray. The value here is Δn = n_e − n_o = 0.14. In this case, we see that there are no topological defects for this distribution, since, with all directors aligned in the same direction, there is no discontinuity or point of singularity. Thus the term containing the topological charge m in equation³⁶ is omitted and the intensity distribution becomes simply

I(x,y) = cos²(ΔΦ/2) (20)

This is equivalent to assuming that for this system the micelles formed are linearly birefringent, i.e. due to asymmetry, ordinary and extraordinary rays having different refractive indices are produced. There is, however, no evidence of chirality in the structure, which would rotate the plane of polarization. The intensity pattern consists of concentric bright and dark rings as shown in Fig. 7a, which is in agreement with our experimental pattern. The thickness of the rings decreases as we move away from the center, which is also a characteristic of the experimental pattern. The system of hyperbolic fringes is present too. These are seen more clearly if the system size is increased. We show that other typical configurations where m ≠ 0, such as one with radial directors lead to completely different patterns under crossed polarizers as shown in Fig. 7b. This, further, validates our proposed model. Next we repeat the simulation using algorithm II, where the system is discretized and show that a similar result is obtained, which matches the experimental observation. Here, the system is discretized into cubes of height t (=1). The difference n_e − n_o is taken as 0.27. Directors in all the units are assumed to lie in the X–Y plane making an angle 45° with the X-axis. Plane polarised light entering the unit at (x,y,0) passes through the vertical column, exiting at (x,y,z_max). The iterative procedure, described in Section 4.2, is applied until the top of the vertical column (x,y,z_max) is reached. Finally multiplying the matrix for the analyser gives the transmitted intensity of the light at (x,y). The intensity pattern obtained is again the system of concentric circles as shown in Fig. 7c. The pattern depends on the ratio t/λ and we show a pattern with a value 1.818 for t/λ. As for algorithm I, we show the intensity patterns for some other director configurations to demonstrate that these are quite different from the observed pattern in the present experiment Fig. 7d.

Fig. 7 Simulated intensity pattern of CTAB–NaBr droplet assuming lenticular drop with all directors parallel to each other and to the substrate calculated from simulation-I and simulation-II is shown in (a) and (c). A hypothetical hemispherical droplet with directors radially distributed from the centre calculated from simulation-I is shown in (b) and spherical drop with radial directors from simulation-II is shown in (d).

5 Discussion

CTAB is a much studied prototype surfactant.³⁷ Such materials are known to be optically active under shear.^38,39 The shear dependent birefringence of such materials usually disappears as soon as the flow stops, but examples of materials where the birefringence persists are also reported.³² CTAB forms micelles at concentrations above 0.008 wt% and in presence of a salt, such as sodium halide the micelles can join up becoming very long, as the repulsion between the head groups is reduced by the salt. The viscosity of this fluid becomes very high due to entanglement of the long micelles. The present study on drying droplets of CTAB with NaBr shows several different stages of drying. Initially when there is plenty of water, concentric circular rings appear under crossed polarisers, while the bright-field image is featureless. The widths of the rings decreases from the centre to the periphery of the drying drop as shown in Fig. 5a. Widths vary to some extent on increasing the droplet size. For all 3 curves W(N) falls with N, steeply at first and at a slower rate for larger N. The graphs for 15 and 20 μL are nearly coincident for small N but for larger N, there is an increase in W(N) with drop volume. The plot for 10 μL is well separated. For larger volumes the graphs are considerably flatter. The change in the nature of the W(N) versus N curve may be due to the fact that the larger drop no longer approximates a section of a sphere, but is flatter and ‘pancake’ shaped. It is seen that on varying the CTAB concentration ring widths are more or less unaffected, this indicates that the local director orientation is independent of the size and shape of the micelles. The variation in width calculated from both simulation methods is shown Fig. 5b. The width falls off faster with ring number for the simulation but possibly the central region in the experiment cannot be seen as it is obliterated by the cap region. Our simulations identify this pattern to be a result of the directors lying parallel to the solid substrate, and all pointing in the same direction. One may argue that the particular common direction taken by the directors affects the view under cross-polarisers. When the drop is placed, it is very unlikely that this direction will be exactly in alignment with the polariser or the analyser and hence look completely dark. Any other direction will show the concentric ring pattern with varying brightness. We have attempted to rotate the sample slowly on the microscope stage within crossed polarisers, this does cause a change in brightness of the pattern and the field appears dark at two mutually perpendicular radial directions. These correspond the positions where the directors are oriented along the polariser or analyser. Since the drop is still in fluid state, motion disturbs it and it is difficult to reach complete extinction. When water evaporates from the droplet, the concentration of the CTAB may reach to the point in the phase diagram of CTAB–water phases where CTAB forms hexagonal cylindrical micelles. Addition of NaBr may leads to worm like micelles which results from the transition of cylindrical micelles to rod like micelles. These rods are likely to be orientated parallel to the interface. Concerning the orientation of the rods relative to the director, the average direction of the long axis of the rods in a small volume is most likely to coincide with the local director, similar to the director orientation in nematic liquid crystals. Photographs of the drop in elevation Fig. 1, shows that the angle of contact is small and the outer periphery dries first, leaving a cap-like region at the center. Starting of crystal growth with drying is clearly seen under crossed polarisers Fig. 2. Dendritic crystal growth continues along the periphery, while a central circular region still looks uniformly dark. Finally, in the last stage Fig. 2 the dendritic crystal aggregates intrude into the circular cap and the whole drop dries up. The whole process can be clearly seen in the video (ESI†).

In contrast the CTAB solution with no salt shows quite different patterns, which are yet to be understood fully. A cavitation in the dried droplets of CTAB solutions is observed by Jadav et al.²⁸ The cavity is formed due to pinning of the droplet to the substrate and subsequently nucleation of the micelles at the periphery forming a skin layer. The size of the cavity is found to decrease as the concentration increases in the droplets. In the present case the 3 dimensional staircase like pattern in the CTAB solutions may persist as long as the size of the cavity remains very small. Aqueous CTAB shows a structural transition from spherical to cylindrical micelles at concentration of 11 wt% (ref. 23). For low concentration (20 wt%) a pattern with 4-fold symmetry appears, but it is not very well resolved and changes with time. For a higher concentration of 22.5 wt%, initially a pattern with two series of folds, which appear to interlock at the boundary are seen Fig. 4. Such features have been reported in collagen.²¹ Later on the pattern changes to a vortex like appearance. For the highest concentration studied, which is 25 wt% the initial appearance is even more striking, resembling curved step-like interlocking aggregates. Somewhat similar patterns have been reported in drying drops of DNA.³⁰ This pattern also disintegrates to a distorted vortex-like figure having a roughly 4-fold symmetry. It seems that for these compositions micelles are small and the fluid is less viscous, so the birefringence we observe is shear induced. It may be possible to explain the 20% patterns with a hemispherical (i.e. half) bipolar drop shown in²⁰ Fig. 4.

6 Conclusions

We have observed drying of sessile droplets of aqueous CTAB solutions with and without added NaBr salt. Characteristic patterns are observed under crossed polarisers, which are a signature of the organisation of anisotropic micelles formed. Simulations of several possible arrangements have been done by standard methods to identify the organisation of the directors, with respect to the substrate and to each other. We find that an array with directors arranged in planes parallel to the fluid–substrate interface and parallel to each other, reproduces the experimentally observed pattern for the droplets of CTAB–NaBr solutions. The director orientation is likely to coincide with the average direction of the long axis of the anisotropic micelles. Droplets without salt show more complicated three-dimensional stair-case like arrangements, which are yet to be understood.

Acknowledgements

We acknowledge DST, Govt. of India for funding this research (project No. SR/S2/CMP-127/2012). We thank Prof. S. P. Moulik for academic discussions. B. Roy thanks DST PURSE, Govt. of India for providing a Junior Research Fellowship.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra22579a

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