Emergence of different crystal morphologies using the coffee ring effect

Macroscopic patterns in nature formed during crystal growth e.g. snow crystals have a significant influence on many material properties, such as macroscopic heat conduction, electrical conduction, and mechanical properties, even with the same microscopic crystal structure. Although crystal morphology has been extensively studied in bulk, the formation of patterns induced by re-crystallization during evaporation is still unclear. Here, we find a way to obtain concentric circles, a dendritic pattern, and a lattice pattern by pinning the edge of droplets using the coffee ring effect; only aggregates of crystallites are seen in the absence of pinning. Our systematic study shows that the macroscopic patterns depend both on initial concentration and evaporation rate. In addition, our qualitative analysis suggests that the local concentration of solute at the center of the pattern is related to the macroscopic patterns.

. Time evolution of (a) the normalized height h(t) and (b) the normalized diameter L(t) before the crystallization starts. Circles correspond to droplets with the particles, while squares correspond to droplets without particles. When the solution is mixed with particles, L(t) remains constant due to pinning at the edge due to the coffee ring effect, and h decreases linearly before the crystallization starts. Here, we investigate the morphology of the crystal formed during evaporation of a sessile droplet of sodium bicarbonate (NaHCO 3 ) solution with pinning at the edge. We mix the solution with latex particles in order to pin the edge and stop the droplet shrinking. This method has particular advantages for investigating crystallization by evaporation. For example, the evaporation rate β(t) becomes constant before the crystallization occurs, as we will describe in detail in the Results section. We perform a series of evaporation experiments while varying the initial concentration and evaporation rate, and find either a concentric circular pattern or a dendritic pattern in the same solution, depending on how these variables are set.

Results
Firstly, we examine the evaporation of a solution droplet mixed with latex particles with a diameter of 0.052 μm. We measure the height h(t) at the top and the diameter L(t) of the sessile droplet using top and side views acquired with a video camera. In our experiment, h(0) = 1.3 mm and L(0) = 5.1 mm for 20 mm 3 droplets. Figure 1 shows the time evolution of h(t) and L(t) of a 4.7 wt% NaHCO 3 solution droplet at 20 °C and a relative humidity (Rh) of 50%. The filled circles correspond to the time evolution of h(t) and L(t) normalized by h(0) and L(0). We also show h(t) and L(t) without the latex particles for reference (squares). We find that L(t) is unchanged with time until crystallization occurs (t x = 66 min). This means that the edge of the droplet is pinned by the coffee ring effect. We also find that h(t) decreases linearly with time. Since L(t) is constant, the evaporation rate β(t) is also constant since β(t)∝ − ∂h(t)/∂t. It is known that β(t) is proportional to the perimeter of the droplet edge before a critical time 15,16 , while β(t) drastically increases beyond the critical time 19 ; our result is consistent with β(t) ∝ L(t). We note that this relation can be observed in all cases which we examined. We also note that the effect of humidity fluctuation (Rh ~ ± 4.0%) is negligible during evaporation. Meanwhile, when the droplet does not contain latex particles, h(t) suddenly increases and L(t) spontaneously decreases at t = 56 min, before crystallization occurs (t x = 62 min). From in-situ observation of the sessile droplet, we see that the edge of the droplet detaches from the glass and that the droplet is re-shaped at t = 56 min. After the crystallization occurs ( > t t x ), several additional effects should occur e.g. local temperature change 27 , local density change due to crystallization, local change of surface tension 26 etc. Thus, the evaporation rate is not expected to be constant after crystallization starts. In our experiments, we were unable to measure the local evaporation rate after > t t x . Next, we look at crystallization dynamics in a sessile droplet with a pinned edge [See Supplementary video Smovie. 1]. Figure 2(a-d) shows the crystallization dynamics in a 0.47 wt% droplet without the latex particles (right droplet in Fig. 2). We find that the crystallization occurs at the edge first, and that macroscopic dewetting occurs. Finally, the solution is absorbed by the crystal at the edge and the center becomes empty shown as in Fig. 2(e). This is similar to crystallization seen in evaporation from droplets of CaSO 4 solution 25 . In contrast, a left droplet in Fig. 2(a-d) contains the latex particles. Although the crystallization occurs at the edge first, just like in the droplet without the latex particles, the solution remains at the center due to the strong pinning at the edge. Subsequently, we observe a concentric circular (CC) pattern at the center of the droplet shown as in Fig. 2(f). The experiment is performed with the same sample at the same time; thus experimental conditions such as concentration, temperature, and humidity are the same. Note that the patterns are locally different. At the edge, we observe clusters of crystals, much like in Fig. 2(e), while we observe a needle-like pattern nearby. In the following, we focus on pattern formation at the center of the initial droplet using solutions containing latex particles.
We investigate the dependence of β on macroscopic crystal patterns with changing humidity. Figure 3(a-c) shows how the crystal patterns vary with initial concentration φ 0 = 2.8 wt% at different humidities; (a) 67%, (b) 50% and (c) 20%. It is clear that β becomes larger with decreasing humidity. Interestingly, we observe a dendritic (DD) pattern at β = 0.0018 mm 3 /s and 0.0035 mm 3 /s as shown in Fig. 3(a) and (b), while a CC pattern is formed when β = 0.0056 mm 3 /s, as shown in Fig. 3(c). Here we classify a pattern as CC if the pattern has a periodic structure in the radial direction, and is laterally isotropic or periodic. On the other hand, the DD pattern is radially connected and random in the lateral direction. We also find that the size of the core in dendritic patterns is larger for smaller β. This points to the central role played by β in pattern formation.
We also investigate the dependence of pattern formation on φ 0 at fixed β. We performed evaporation experiments with different φ 0 at the same time. Figure 4 shows the pattern formed for β = 0.0035 mm 3 /s with different φ 0 ; (a) 8.4 wt%, (b) 2.8 wt%, and (c) 0.47wt%. At φ 0 = 8.4 wt% and 2.8 wt%, a DD pattern is formed [ Fig. 4(a) and (b)], while a CC pattern is observed for φ 0 = 0.47 wt% [ Fig. 4(c)]. This reveals that the initial concentration is also important for macroscopic pattern formation, not just the evaporation rate.
We go on to investigate the dynamics of crystal pattern formation. Figures 5 and 6 show the time evolution of the CC pattern and the DD pattern, respectively. We find that crystal nucleation occurs around the center of the droplet; the pattern then spreads radially from the nucleated crystal. This is quite different from CC pattern formation by stick-slip evaporation dynamics 20 . We measure the front of the pattern as a function of time and find that the pattern spreads linearly. We find that the velocity of the spread of the CC pattern is 0.015 mm/s, while that of the DD pattern is 0.0078 mm/s i.e. the CC pattern spreads approximately 2 times faster even though β is almost same.
We obtain a diagram of CC and DD patterns as functions of β and φ 0 as shown in Fig. 7. Circles and crosses correspond to CC and DD patterns, respectively. We perform the same experiment for each point at least 3 times. We find that the CC pattern is observed for larger β and smaller φ 0 , while a DD pattern is observed for smaller β and larger φ 0 . Near the boundary, we observe both, or an intermediate pattern which is radially periodic but laterally random. Here we note that we changed temperature in the range between 20 °C and 60 °C. Since the temperature strongly depends on the dynamics of the crystallization, we cannot rule out the temperature effects. However, the results shown as in Figs 3 and 4 suggest that the transition between the two patterns can occur even though the temperature is same.
In order to investigate the effect of φ 0 and β, we estimate a supersaturation φ φ = S / x s when the crystallization occurs. φ x and φ s are the concentration at t = t x and the saturation concentration, respectively. φ x is simply calculated as where V x is the volume at t = t x . S is the mean value over the droplet. Here, we find that S dramatically increases with smaller β and larger φ 0 shown as in Fig. 8. Comparing with the morphology diagram,     each ion. We obtain ∼ Pe 160 for β = 10 −1 mm 3 /s and 1.6 for β = 10 −3 mm 3 /s. This means that the concentration becomes high near the edge due to advection when β is large. Thus, S is less than 1 for smaller φ 0 even though crystallization occurs. In addition, φ s should depend on the concentration of the impurity i.e. latex particles. Near the edge, the concentration of latex particles is expected to be high; this may affect S. Thus, the relation between S and the pattern should be considered to vary over space.
We then measure the height when crystallization starts, h(t x ), in order to investigate the φ 0 dependence of S. Figure 9 shows h(t x ) as a function of φ 0 and different β. We find that h(t x ) weakly depends on φ 0 . Interestingly, this suggests that crystallization occurs for similar droplet shape rather than the concentration at t x . It is consistent that S is larger with the larger φ 0 . Considering both Peclet number and h(t x ), the concentration in the droplet should be high and less inhomogeneous for smaller β and larger φ 0 , when the DD pattern is formed. That is, the concentration at the center at t = t x should be high for the smaller β and the larger φ 0 , while it should be low for large β and small φ 0 .
Next, we go on to investigate the period ξ of the concentric circles in the radial direction by analyzing the images. As an example of image analysis, we show the intensity I over the cross section (yellow line) in the inset [ Fig. 10]. Note that I changes periodically; we obtain ξ as the average distance between the main neighboring peaks. ξ is averaged over 4 different lines for each set of concentric circles. We show ξ as a function of φ 0 in Fig. 11(a) and ξ as a function of β at fixed φ 0 in Fig. 11(b). It is found that ξ increases with increasing φ 0 or with decreasing β. This suggests that ξ increases as we approach the region preferring DD patterns. From the point of view of morphology, concentric circles are distinct from radial patterns like the dendritic. However, we could not find a discontinuous transition between the two patterns in our experiment.
We also examine the crystal pattern using other solutions with pinning at the edge of the droplet. Figure 12 shows the crystal pattern of a NaCl solution with φ 0 = 0.1 wt% at (a) 24 °C and Rh = 60% and (b) 18 °C and Rh = 40%. We observe DD and CC patterns in NaCl as well as in NaHCO 3 . We note that NaCl forms a monocrystal at the center of the droplet when the edge is not pinned by latex particles 25 . A lattice pattern is obtained in aluminium potassium sulfate dodecahydrate solution with φ 0 = 0.3 wt% at 18 °C and Rh = 40%. We thus note that various macroscopic patterns can be obtained by pinning the edge of the droplet.
Finally, we discuss the effect of dewetting from the substrate. As we showed above in Fig. 2, CC or DD patterns are formed at the center when the solution macroscopically wets the substrate. It was reported that a DD pattern is formed by dewetting in a colloidal suspension 29 . Although the crystallization is different in nature from the aggregation of the colloidal particles, the effect of dewetting seems crucial for pattern formation. Thus, we need to investigate the relationship between local concentration and the local dewetting; a challenge for the near future might be to perform an evaporation experiment with changing substrate affinity.

Summary
In summary, we investigate macroscopic crystal patterns formed by evaporation of solution droplets. We put latex particles in the solution such that the edge of the droplet is pinned by the coffee ring effect. Firstly, we show that the concentric circles (CC) and the dendritic (DD) pattern are observed when the edge is pinned. Our systematic study shows that the CC pattern is formed for larger evaporation rate and lower initial concentration, while Figure 11. (a) ξ as a function of φ 0 . (b) ξ as a function of β at fixed φ 0 . Circles and squares correspond to ξ at φ 0 = 1.9 wt% and 0.47 wt%, respectively. It is found that ξ increases with increasing φ 0 or with decreasing β.
the DD pattern is formed for lower evaporation rate and larger initial concentration. We also suggest that a CC pattern is favored when the local concentration is low at the center; on the other hand, a DD pattern is formed if the local concentration is large. We firmly believe that this investigation will stimulate further studies to control macroscopic crystal patterns and understand crystallization mechanisms.

Materials and Methods
We used sodium bicarbonate (NaHCO 3 ) with 99% purity purchased from Wako Chemical Industries, Ltd. The saturation concentration of NaHCO 3 solution is 8.7 wt%. We put a 20 mm 3 droplet of the solution on a cover glass; recrystallization occurs on evaporation. For looking at macroscopic patterns with a combined coffee ring effect, polystyrene latex particles (Magsphere Co.) with 0.052 μm diameter was mixed into the solution with a volume fraction 0.01%. The sample temperature was controlled with a transparent hot stage (Blast Co.) and the humidity was measured for every experiment. We observed the macroscopic crystal patterns using an optical microscope (Nikon ECSROPSE-TS100). The time evolution of the droplet size is observed with a digital camera (Panasonic, HC-W570M). We also performed similar experiments with sodium chloride (NaCl) and aluminum potassium sulfate dodecahydrate with 99% purity purchased from Wako Chemical Industries, Ltd.