Interplay between Spinodal Decomposition and Gelation and Their

C: Surfaces, Interfaces, Porous Materials, and Catalysis

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Interplay between Spinodal Decomposition and Gelation and Their Role in Two- and Three-Dimensional Pattern Formation at Gelatin Gel Surface. Kazuto Sasaki, Masaki Itatani, Daisuke Sato, Kei Unoura, and Hideki Nabika J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b03684 • Publication Date (Web): 14 May 2019 Downloaded from http://pubs.acs.org on May 15, 2019

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The Journal of Physical Chemistry

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Interplay between Spinodal Decomposition and Gelation and their Role in Two- and Threedimensional Pattern Formation at Gelatin Gel Surface Kazuto Sasaki, Masaki Itatani, Daisuke Sato, Kei Unoura, Hideki Nabika* Department of Material and Biological Chemistry, Faculty of Science, Yamagata University, 14-12 Kojirakawa, Yamagata 990-8560, Japan

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ABSTRACT. Understanding the mechanisms underlying the spontaneous formation of Liesegang patterns based on the pre-nucleation and post-nucleation models is of critical importance for understanding pattern formation in nature. In contrast to the rapid experimental and theoretical advances in understanding within the framework of the pre-nucleation model, discussion of the post-nucleation model is mostly limited to numerical analysis. To construct a standard model for a chemical experiment discussed in terms of the post-nucleation model, we have investigated the pattern formation mechanism in a mixed system containing gelatin, starch, and sugar. Fluorescence and differential interference contrast microscopy revealed a process of two-dimensional spinodal decomposition into gelatin-rich and gelatin-poor phases. Since the gelation temperature of the gelatin-rich phase was higher, spatially periodic gelation proceeded selectively in the gelatin-rich phase. As both two-dimensional spinodal decomposition and three-dimensional gelation occurred above the gelation temperature of the initial sol solution, we propose that these patterns form by two-dimensional spinodal decomposition into gelatin-rich and gelatin-poor phases followed by gelation in the gelatin-rich phase, which yields the spatially periodic, three-dimensional patterns of the gelatin gel. Pattern geometry was found to be dependent on sample size or shape. Although three geometries–labyrinth, one-directional, and intermediate patterns–appeared in a circular Petri dish, only a one-directional banded pattern formed in a rectangular cell. We present a good experimental system, in which the correlation of the spacing and other empirical laws with a theoretical basis is possible within the framework of the post-nucleation model.


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INTRODUCTION Nature has a wealth of spatiotemporal patterns that appear under non-equilibrium conditions. One of the most famous and well-investigated spatiotemporal patterns in chemical systems is the Belousov-Zhabotinsky (BZ) reaction, which exhibits both temporal oscillation and a spatial pattern. The spatial pattern appears during the interplay between the reaction and the diffusion of constituents in the reaction medium.1 This type of pattern formation is known as a reactiondiffusion system, which includes not only the BZ reaction, but also the Turing pattern and the Liesegang pattern. Since these reaction-diffusion systems form characteristic patterns by different mechanisms, understanding each system enables deep insight into how nature forms patterns on various temporal and spatial scales. The Liesegang pattern, discovered by the German chemist R. E. Liesegang,2 is characterized by periodic precipitation patterns that obey a simple numerical equation known as the spacing law:3

lim

+1

=1+

,

(1)

where xn is the distance of the nth band from the reaction origin, and p is the spacing coefficient. Exploring on the origin of the spacing and other empirical laws, various experiments have been done using gel, such as gelatin or agarose, as the reaction medium to reduce macroscopic convection of water and the diffusion of precipitates.4-10 In these experiments, gel doped with ion B- is contacted with an aqueous solution containing ion A+, and A+ diffuses from the aqueous phase into the gel phase. A reaction between A+ and B- then forms an insoluble salt by A+ (aq) + B- (aq)

AB (aq) near the interface between the aqueous and gel phases. With a continuous


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supply of A+ from the aqueous phase to the gel phase, the concentration of the molecular-state salt AB (aq) in the gel is continuously increased via the salt formation reaction. When the concentration of AB (aq) exceeds the solubility product of salt AB, solid AB (s) precipitates via the formation of nuclei AB (nucl). Under certain chemical and physical conditions, which include concentration, temperature, and gel density, the solid particles form precipitates with spatial periodicity according to the spacing law. The process involving nucleation, known as the pre-nucleation model, is one of two well-known proposed mechanisms of Liesegang pattern formation.11-17 The other proposed mechanism is known as the post-nucleation model, which is based on a phase separation.18,19 Although various complex patterns have been explained numerically in the framework of the post-nucleation model, few experimental systems undergo Liesegang pattern formation by phase separation. For a comprehensive understanding of the Liesegang pattern formation mechanism, it is essential to correlate the pre-nucleation and postnucleation models with experimental evidence in addition to numerical simulations. It is thus necessary to design an experimental system that forms Liesegang patterns based on phase separation, which can be considered within the framework of the post-nucleation model. It is especially important to devise chemical and physical conditions that are similar to those of a conventional experimental system based on the pre-nucleation model, which employs a chemical process in a gel medium. To ensure that (i) the pattern appears by phase separation and (ii) appears in the gel medium, phase separations in mixtures of gelatin and starch,20-23 gelatin and dextrin/dextran,24-30 gelatin and amylopectin,31 and gelatin with artificial polymers32-36 are promising systems that can be used for model experiments to study the Liesegang pattern formation mechanism according to the post-nucleation model. It is well-known that in a binary system consisting of two different


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polymers, a change in a chemical and/or physical parameter can lead to various thermodynamic states (Figure 1). When a homogeneous sol of the mixture denoted as “A” in Figure 1 is cooled to “B”, which is below the coexisting line in the phase diagram, it transitions from a stable to a metastable thermodynamic state. Under this condition, the system still undergoes precipitate formation via the nucleation process described by the pre-nucleation model. However, when the initial state “A” is cooled to “C”, which is below the spinodal line, the system enters an unstable state. Here, a rapid phase separation known as spinodal decomposition proceeds without the nucleation process.37 Mixed solutions of gelatin and other polymers with the potential to produce spatially periodic patterns via phase separation can serve as model systems to provide experimental evidence of pattern formation according to the proposed post-nucleation model. To elucidate the pattern formation mechanism in a gelatin mixture to be used as model systems, we investigated in the present study the relationship between phase separation and the gelation process and its influence on two- and three-dimensional pattern formation. This was carried out through microscopic observations using a typical mixed system of gelatin, sugar, and starch.20-23 By comparing fluorescence and differential interference contrast (DIC) microscopy results, a two-dimensional phase separation into gelatin-rich and gelatin-poor phases was identified. Furthermore, a three-dimensional morphological change observed with laser microscopy revealed the process of gelation, although this change occurred at a temperature above the gelation temperature of the mixed solution. By comparing two- and three-dimensional observations, we examined the pattern formation mechanism of the system in the context of spinodal decomposition followed by gelation. Initial spinodal decomposition formed the gelatinrich and gelatin-poor phases, and the gelation temperature in the gelatin-rich phase increased. Gelation thus proceeded in the gelation-rich phase above the gelation temperature of the initial


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mixed solution, which formed the two- and three-dimensional periodic patterns. Based on the mechanism proposed in the present study, it will be possible to construct an experimental system for the post-nucleation model in which periodic patterns are formed via phase separation.

MATERIALS AND METHODS All chemicals and solvents were commercially available and used as received without further treatment. Gelatin and sucrose were purchased from Nacalai Tesque Inc. (Kyoto, Japan). Starch, glucose, and 2-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxy-D-glucose (2-NBDG) were purchased from Wako Pure Chemical Industries (Tokyo, Japan). Fluorescein 5isothiocyanate (FITC) was purchased from TCI (Tokyo, Japan). Two stock solutions (i) a mixture of gelatin and FITC and (ii) a mixture of starch, sucrose, and glucose, were prepared by mixing their respective constituents in water at 75 °C for 25 min with continuous stirring. The two solutions were then combined and mixed with continuous stirring at 75 °C for 25 min. The final solution contained 6.99 wt.% gelatin, 4.00 wt.% starch, 21.5 wt.% sucrose, 27.5 wt.% glucose, 0.01 wt.% FITC, and 40 wt.% water. Samples with depths of 500 Jm were prepared individually by pouring 1.5 mL of the mixed solution into a Petri dish (6.2 cm i.d.). The samples were gelled and stored at 3 °C until use. To control the temperature of the samples during microscopic observation, the Petri dishes were placed on a thermoplate (Tokai Hit, Shizuoka, Japan). The structures of the samples at various temperatures were examined with a BX-53 fluorescence microscope (Olympus, Tokyo, Japan) equipped with a differential interference contrast (DIC) attachment and an OPTELICS laser microscope (Lasertec, Kanagawa, Japan). Viscosity of the mixed solution was measured with a SV-10 viscometer (A & D Company, Tokyo, Japan).


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RESULTS AND DISCUSSION A sample containing gelatin, starch, and sugar in a Petri dish was first confirmed to be a homogeneous sol solution without any patterns at 60 °C by observation with fluorescence microscopy (Figure 2a), indicating these molecules were mixed homogeneously in the aqueous phase. When the temperature of the thermoplate was reduced to 38 °C, distinctive patterns with various morphologies appeared in the same sample. The observed patterns were categorized into the following three groups: labyrinth (Figure 2b), one-directional (Figure 2c), and an intermediate between the two (Figure 2d). We have confirmed that these patterns were not appeared by an evaporation of water during the experiments, because the same patterns were also observed when the Petri dish was covered by film. One-directional pattern formation was further supported by the appearance of a distinctive peak in the fast Fourier transform (FFT) pattern, whereas no such peak appeared in the patterns of the labyrinth and intermediate structures (Figure 2f). There was no relationship between temperature and the morphology of the patterns. Morphological selectivity was instead affected by the size or shape of the sample cell, which was later investigated with a rectangular cell. This result indicated that morphological selectivity was not determined by the thermodynamic nature of the mixture, but rather by shape-dependent directional propagation of the pattern formation reaction. Although further cooling did not change the pattern morphology that appeared at 30 °C, heating a sample to the initial temperature of 60 °C returned it to its original homogeneous state without any patterns (Figure 2e). It was possible that the patterns were formed by the gelation of gelatin molecules in the mixed solution. To characterize the contribution of gelation to pattern formation, the gelation temperature was measured from the change in the viscosity of the sample solution (Figure 2g). As the sample


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solution was cooled from 60 °C to 28 °C, viscosity remained nearly zero down to 38 °C, which was the temperature at which the patterns appeared. When the sample temperature fell below ~30 °C, viscosity rapidly increased. This confirmed that the mixed solution underwent gelation at approximately 30 °C. Based on this finding, it could be concluded that the pattern formation observed at 38 °C was not associated with the gelation of the bulk solution. However, it should be noted that the viscosity measurement was performed with the bulk solution in a glass beaker using a sensor with a constant sine-wave vibration. This vibration caused local mixing of the sample solution near the viscosity sensor. Because the solution was being mixed, the change in its viscosity was detected as a macroscopic feature, not a local one. In contrast, each microscopic observation was made with a 500-µm thick sample in a Petri dish, so the effects of stirring and convection were absent. This meant the possibility of a transient state, in which local gelation occurred at the molecular scale without affecting the macroscopic viscosity of the whole sample, could not be excluded. The formation of such transient structure at molecular scale that proceeds before macroscopic gelation appears has been reported by tracing the structural changes in gelatin solution by comparing the rheological gel point with the time evolution of the probe diffusion rate [38]. It was thus unreasonable to assume that microscopic gelation was not involved in pattern formation, because the patterns formed at a higher temperature than the macroscopic gelation temperature. We used FITC dye to visualize the phase separation in the gelatin mixture by fluorescence microscopy.21 Fluorescein dye was also used as a probe for fluorescence recovery after photobleaching (FRAP) to investigate the process of gelation in solution.38 Since fluorescein diffusion was detected even after gelation, the dye exhibited little or no preference for either the gelatin gel or the sol state. It was therefore difficult to distinguish between gel and sol in the


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bright and dark regions of the fluorescence microscope images shown in Figure 2. We decided to use 2-NBDG instead of FITC for imaging, because 2-NBDG would selectively partition into the phase in which glucose, sugars, and polysaccharides were the predominant components, because the chemical backbone of 2-NBD-G is glucose. Actually, 2-NBD-G can be used as a probe for the uptake and presence of glucose in Escherichia coli cells.39 Under the same fluorescence microscopy conditions with 2-NBDG at 38 °C, we observed the formation of the labyrinth, onedirectional, and intermediate patterns similar to those in the system with FITC (Figure 3). Both FITC and 2-NBDG were seen in bright and broad areas that were separated by dark, narrow lines. Since 2-NBDG partitioned into the sugar-rich phase, the bright regions corresponded to the sugar-rich and gelatin-poor phase. The dark regions corresponded to the sugar-poor and gelatinrich phase. Thus, the patterns appearing above the gelation temperature of the bulk solution could be the phase-separated patterns of the gelatin-rich (sugar-poor) and gelatin-poor (sugarrich) phases. This result indicated that phase separation proceeded at a higher temperature than did gelation of the mixed gelatin. The relationship between phase separation and gelation temperatures has been investigated in a gelatin/maltodextrin system.24,25 It was clearly shown that, depending on the sample composition, the temperature of phase separation in this system could exceed the gelation temperature. Our assumption that phase separation was first triggered at a higher temperature than the gelation temperature was thus reasonable. Additional experiments and observations provided further confirmation that phase separation occurred in the mixed solution. A DIC image of the area shown in the fluorescence microscope image had a pattern of dark and light regions with nearly identical geometry (Figure 4). This indicated that the dark and bright phases observed with fluorescence microscopy differed in either their thickness, refractive index, or both. Since these differences strongly confirmed that


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the components or compositions of the dark and bright phases were distinct, we concluded the observed patterns were the structures formed by phase separation. Both the fluorescence and DIC observations indicated a structural change with twodimensional information. Although detailed analysis by DIC would also yield three-dimensional information, three-dimensional morphological changes were analyzed directly by observation with a laser microscope (Figure 5). Before the pattern appeared under the fluorescence microscope, the surface was homogeneous without micrometer-scale roughness (Figure 5a,c). In contrast, three-dimensional roughness as large as 50 Jm was observed after pattern formation by phase separation (Figure 5b,d). As confirmed by the viscosity measurement, the sample in which phase separation occurred at 38 °C was a sol state with almost zero viscosity. If both the bright and dark phases seen under the fluorescence microscope were in the sol state, the sample would be unlikely to exhibit and fix three-dimensional roughness. Thus, a gelation process that increased viscosity was considered along with phase separation to describe the pattern formation mechanism in the present system. To propose the mechanism underlying the spontaneous pattern formation in the present system, we have carried out the same experiments with changing the composition of the initial sol solution (Table 1). In the experiment conducted so far used the sol solution containing gelatin, starch and sugars (sample 1). Even if starch was removed, if one of sugars was contained, the pattern appeared (sample 2 to 4). Contrary, the pattern did not appear without the sugar (sample 5, 6). From these experiments, gelatin and sugar were suggested to play an important role in the pattern formation of the present system. Although our experiments were conducted for sample 1 according to the previous researches,20-23 further experiments could be done without starch for simplicity. However, it is still noticed that the addition of starch would modulate the viscosity


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and bulk modulus that contribute to the temperature and kinetics of the phase separation and the pattern formation. Given the importance of gelatin and sugar, Figure 6 illustrates our proposed mechanism, which is based on successive phase separation of gelatin and sugar, and gelation. Analysis with fluorescence microscopy, viscosity measurement, and laser microscopy confirmed that the initial state was a homogeneous sol mixture at 60 °C. The mixture was thermodynamically stable when the sample temperature was kept above the temperatures of phase separation (Tps) and gelation (Tgel). The sol state underwent spinodal decomposition below Tps, and phase separation into spatially periodic gelatin-rich (sugar-poor) and gelatin-poor (sugarrich) phases proceeded spontaneously, as observed with fluorescence and DIC microscopy. Since the gelatin-rich phase had a higher gelatin concentration, Tgel in this phase (TgelR) was higher than Tgel in the initial mixture and the gelatin-poor phase with lower gelatin concentrations.40 When the sample temperature was decreased further to below TgelR but above Tgel of the initial mixture, gelation proceeded only in the periodic gelatin-rich phase that formed by spinodal decomposition. Gelation rapidly increased the viscosity and generated three-dimensional roughness as the volume changed. This process was identified as a three-dimensional morphological change with the laser microscope. Thus, we concluded the mechanism of pattern formation observed in the present study was phase separation, the two-dimensional pattern of which was fixed by subsequent spatio-selective gelation of the gelatin-rich phase. Since some perturbation, noise and fluctuation are required to initiate phase separation, molecular scale inhomogeneity of constituent molecules would drive a phase separation to increase the concentration difference between gelatin-rich and gelatin-poor regions. This system can serve as a good model for pattern formation according to the post-nucleation model, which is based on pattern formation triggered by phase separation.


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To be a good system for the post-nucleation Liesegang model, one-directional patterns must be formed, such as stripes or bands. These patterns are frequently used in the Liesegang experiment, because analysis is easy and straightforward for studying the spacing law (eq. 1) and other empirical laws. For this purpose, we investigated sample shape by switching from the circular reaction medium (6.2 cm i.d.) to a 1 cm × 5 cm rectangular cell (Figure 7a). This shape is used quite commonly for one-directional band formation in Liesegang patterns. As was seen in the Petri dish, phase separation occurred when the sample temperature was reduced from 60 °C to 38 °C (Figure 7b,c). Unlike what we observed in the Petri dish, only a one-directional pattern formed in the rectangular cell, in which dark bands aligned parallel to the short axis of the cell. The band pattern was observed throughout the rectangular cell (Figure 7d). Although the origin of the size or shape effect on pattern selectivity is unclear, the band pattern is quite convenient for analysis and discussion concerning the empirical rules of the Liesegang phenomenon. Furthermore, the pattern generated in the rectangular sample was formed by phase separation and can be discussed in the framework of the post-nucleation model. Our next challenge is clearly to characterize the pattern geometry by introducing chemical or physical gradients along the long axis of the rectangular cell. This will enable evaluation of the spacing law and other empirical rules in the framework of the post-nucleation model.

CONCLUSION Pattern formation in a sol solution containing gelatin, starch, and sugar was investigated. Fluorescence and DIC microscopy revealed that pattern formation proceeded by twodimensional spinodal decomposition into gelatin-rich (sugar-poor) and gelatin-poor (sugar-rich) phases above the gelation temperature of the initial sol solution. Because the gelatin-rich phase


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had a higher gelation temperature, gelation proceeded selectively in this phase. The formation of spatially periodic patterns was confirmed by a three-dimensional morphological change under laser microscope observation. Because this process occurs above the gelation temperature of the initial sol solution, we propose these patterns form by two-dimensional spinodal decomposition into gelatin-rich and gelatin-poor phases, followed by gelation only in the gelatin-rich phase. Labyrinth, one-directional, and intermediate patterns formed under the same conditions in a Petri dish, whereas only a one-directional banded pattern more common in conventional Liesegang experiments formed in a rectangular cell. This indicates that patterns with different geometries are thermodynamically equivalent. Propagation of the reaction fronts of phase separation and gelation would affect the pattern geometry. Our findings provide a good experimental system that makes possible the correlation of the spacing and other empirical laws with theoretical understanding within the framework of the post-nucleation model. This will be carried out in future work by applying chemical and/or physical gradients in a rectangular sample. This will lead to a more general model that unifies the essences of the pre- and post-nucleation models, which can be a standard model for a comprehensive understanding of the formation mechanism of similar patterns in nature.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] ACKNOWLEDGMENT This work was supported by JSPS KAKENHI Grant Number 18K19051.


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A Coexisting line B (metastable) Spinodal line C (unstable)

Figure 1. Phase diagram showing the transition to metastable and unstable states by crossing the coexisting and spinodal lines, respectively.


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(a)

(e)

cooling (b) labyrinth

(f)

heating (c) one-directional

(d) intermediate

(g)

Figure 2. (a) – (e) Fluorescence microscope images collected during the temperature change from (a) 60 °C to (b) – (d) 38 °C and back to (e) 60 °C. (f) FFT patterns from the fluorescence microscope images of labyrinth-type (red), one-directional (green), and intermediate (blue) geometries. (g) Change in the viscosity of the mixed solution as a function of temperature. Scale bar = 200 µm.


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(a)

(b)

(c)

Figure 3. Fluorescence microscope images collected at 38 °C with the sample doped with NBDG. Three different geometries, (a) labyrinth-type, (b) one-directional, and (c) intermediate, were also confirmed. Scale bar = 200 µm.


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(a)

(b)

Figure 4. (a) A fluorescence microscope image and (b) DIC image taken in the same area showing phase separation at 38 °C. Scale bar = 100 µm.


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(a)

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(b)

(c)

(d) 20 m

1 m

20 m

Figure 5. Laser microscope images collected (a) before and (b) after phase separation, which was confirmed with fluorescence microscopy. (c) and (d) are height line profiles of red lines depicted in (a) and (b), respectively. Scale bar = 50 µm.


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Table 1. Dependence of a Composition of the Initial Sol Solution on a Pattern Formation sample 1 2 3 4 5 6

gelatin

starch

× × × ×

sucrose

glucose

pattern

× × × ×

× ×

× ×


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glass substrate silicon rubber sample solution

(b)

(c)

short axis

(a)

long axis

(d) short axis

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1000 µm long axis

Figure 7. (a) Configuration of the rectangular cell. Fluorescence microscope images of the sample in the rectangular cell at (b) 60 °C and (c) 38 °C. Scale bar = 200 µm. (d) Whole-area image of the sample in the rectangular cell at 38 °C. The images were linked using the PowerPoint software package. Scale bar = 1000 µm.


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TOC GRAPHIC

labyrinth

one-directional

200 µm

intermediate

200 µm

200 µm

1000 µm


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Interplay between Spinodal Decomposition and Gelation and Their

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