Pressure Controlled Chemical Gardens - The Journal of Physical

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Pressure Controlled Chemical Gardens Megan Rae Bentley, Bruno Carrera Batista, and Oliver Steinbock J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b03859 • Publication Date (Web): 07 Jun 2016 Downloaded from http://pubs.acs.org on June 11, 2016

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The Journal of Physical Chemistry

Pressure Controlled Chemical Gardens

Megan R. Bentley, Bruno C. Batista, and Oliver Steinbock* Florida State University Department of Chemistry and Biochemistry Tallahassee, FL 32306-4390, USA

ABSTRACT: The dissolution of metal salts in silicate solution can result in the growth of hollow precipitate tubes. These “chemical gardens” are a model of selforganization far from the equilibrium and create permanent macroscopic structures. The reproducibility of the growth process is greatly improved if the solid salt seed is replaced by a salt solution that is steadily injected by a pump; however, this modification of the original experiment eliminates the membrane-based osmotic pump at the base of conventional chemical gardens and does not allow for analyses in terms of the involved pressure. Here we describe a new experimental method that delivers the salt solution according to a controlled hydrostatic pressure. In one form of the experiment, this pressure slowly decreases as zinc sulfate solution flows into the silicate-containing reaction vessel, whereas a second version holds the respective solution heights constant. In addition to three known growth regimes (jetting, popping, budding), we observe single tubes that fill the vessel in a horizontally undulating but vertically layered fashion (crowding). The resulting, dried product has a cylindrical shape, very low density, and one continuous connection from top to bottom. We also present phase diagrams of these growth modes and show that the flow characteristics of our experiments follow a reaction-independent Hagen-Poiseuille equation.

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INTRODUCTION Chemical gardens are one of chemistry’s oldest experimental systems1 but over the past decade they have attracted new interest in the context of selforganization and materials synthesis far from the thermodynamic equilibrium.2-4 Chemical gardens consist of macroscopic and often colorful tubes that can reach lengths of several centimeters within seconds to minutes. The classic experiment is also a well-known classroom demonstration as it simply involves the placement of a metal salt grain into a basic sodium silicate solution. The dissolving salt creates colloidal metal hydroxide that aggregates and surrounds the salt seed with a thin inorganic membrane. The osmotic pressure between the silicate solution and the seed induces the inflow of water, which leads to the breach of the membrane. In the simplest form of the experiment, a buoyant jet of salt solution emerges from the breach site acting as a template for the subsequent tube growth. The growth continues as long as the osmotic pump at the base of the structure is active and ceases once the seed particle is fully dissolved. The resulting tube structures are hollow and their thin walls consist of amorphous silica and metal hydroxides or oxides.5,6 The range of reaction conditions giving rise to this tube growth is not limited to simple metal salts and sodium silicate. For instance, the latter reactant can be replaced by carbonates, phosphates, borates, oxalates, or sulfides7-13 and recently our group demonstrated tube growth solely based on sodium hydroxide and various metal chlorides14. Also polyoxometalates can form hollow tubes15,16 and Cartwright et al.17 discussed naturally occurring ice tubes under sea ice (called brinicles) as a case of inverse chemical gardens. Other examples appear to include hollow microfibers in setting cement2,18,19 as well as tube-like corrosion structures.2,20,21 We also note that the precipitation reactions allow the insitu inclusion of quantum dots, polymer beads, and biological cells, which could allow interesting applications of the tubes as chemical sensors.22,23 The tube wall can also be modified after production resulting in catalytic activity as exemplified by silica-supported ZnO particles and activated aluminosilicates.24,25 Many quantitative studies have eliminated the seed crystals used in the classical experiment and in lieu use a salt solution that is injected into a solution of the second reactant using syringe pumps.26-28 This method removes transients that arise during the dissolution of the salt seed, generates single tubes, and allows the precise knowledge of the salt solution’s concentration and hence its density and viscosity. Using this injection method, distinct growth regimes were identified that depend strongly on the density difference between the outer reservoir solution and the injected metal solution.26 For highly buoyant solutions, one observes the simple template growth mentioned above. At lower buoyancy, this jetting mode gives way to an oscillatory popping growth in which the hollow structure is capped by an expanding, balloon-like membrane. This balloon periodically detaches from the tube and extends the tube length during every cycle. For even smaller density differences, the buoyancy force is not strong enough to exceed the tensile strength of the wall material. Under such conditions, the hardening membrane expands only to a particular size and then breaches to nucleate the bud of a new balloon. Beyond budding, popping, and jetting growth26, some other dynamics and morphologies have been reported which include “fracturing” in which longer, tubular segments detach from the main structure.29 The underlying injection method was also instrumental for measurements of the outer radius of jetting 2


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tubes as a function of the employed pump rate30 and studies of the slower (and strictly inward directed) thickening dynamics of the tube wall.31 Solution injection was also used for the production of chemical gardens at air-fluid interfaces32 as well as the investigation of constrained chemical gardens in quasi-two dimensional Hele-Shaw cells33,34 and microfluidic channels35. The advantages of experiments with injection-grown precipitate tubes typically relate to the solution delivery at constant or otherwise predetermined volume rates36; however, the pressure situation in the tube is less well defined and hence hinders further quantitative analyses. It is also difficult to make direct comparisons to the conventional seed-controlled system in which osmotic pressure is the main engine of the growth process. We have therefore developed a novel method that combines elements of both experiments by implementing a gravity-driven solution delivery. In this article, we describe and characterize this method. We show that hydrostatically controlled pressure differences between the two reactant solutions can induce jetting, popping, and budding growth and report a novel behavior that we term crowding growth.

Experimental Although syringe pumps appear to be straightforward devices for the delivery of solutions at controlled flow rates, they suffer from several shortcomings and limitations.37 These include surprisingly long response times that depend on fluidic resistance and compliance, limited volumes, pulses especially if stepper motors are used, build-up of very high pressures if the fluidic system is clogged, and possible backflow. In addition, knowledge of the pressure in the injection nozzle requires direct measurements with a pressure gauge and the result can be expected to change during a given growth experiment and possibly even between seemingly identical experiments. To overcome some of these problems and to establish a closer connection with the classic seed-based experiment, we devised the set-up shown in Fig. 1a. The large cylindrical reservoir with a diameter of 19 cm holds a 0.5 M ZnSO4 solution (J. T. Baker). The density and dynamic viscosity of this solution are ρZn = 1.076 g/mL and η = 1.37 mPa s, respectively.38 Plastic tubing (inner diameter 5 mm, length 40 cm) connects this reservoir to the bottom of a second glass cylinder (inner radius R = 1.75 cm), which is typically filled with 150 mL of Na2SiO3·5H2O (Fisher Scientific) at various concentrations. The pressure difference induced by a mismatch in the levels of the two solutions drives the flow of zinc solution into the silicate-containing reaction chamber. The zinc sulfate solution enters the silicate solution through a 4 cm long glass capillary. The capillary’s inner radius is r = 0.6 mm and was determined by visual measurement and from the weight difference between the empty and the water-filled capillary. The set-up also includes a valve coupled to the tubing that grants control over the onset and the termination of an experiment. We use two different reaction vessels. The first one is a simple glass cylinder. During the injection of zinc sulfate, the volume contained in this cylinder gradually increases and, accordingly, there is a change in the pressure difference (Δp) between both reservoirs. The second vessel has a sidearm 3



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spout that allows excess liquid to flow out of the vessel (Fig. 1b), thus maintaining a constant Δh and hence an approximately constant ∆p. The remaining very small changes in ∆p are due to the inflow of ZnSO4 solution that slowly alters the average density in the small vessel. Notice that the cross-section of the ZnSO4 reservoir is 23 times larger than that of the reaction vessel and we can hence assume that the solution level h1 is constant during the entire experiment. All experiments are carried out at room temperature. Most of our measurements are based on the video signal of a monochrome charged-coupled device camera (COHU 2122). These include the tube morphologies, tube growth dynamics, and the volume change (πR2∆h) in the reaction vessel. The acquisition of the video frames is controlled by HL Image ++97 software and the resulting image sequences are analyzed using in-house Matlab and Mathematica scripts. The composition of the dried product was analyzed using powder x-ray diffraction (PANanalytical X’Pert PRO) operating at the Cu Kα emission line.

Figure 1. (a) Schematics of our experimental setup. Tube growth is driven by the hydrostatic pressure difference between a wide reservoir containing a large volume of ZnSO4 solution (0.5 M) and a small glass cylinder with Na2SiO3 solution. The height difference ∆h = h1-h2 between the two solution levels is controlled by a laboratory scissor jack. The parameters ρSi and ρZn denote the densities of the silicate and zinc solution, respectively and g is the gravitational acceleration. (b) In some experiments, the small cylindrical reaction vessel is replaced by a glass cylinder with a sidearm that allows excess solution to flow out of the vessel, which ensures that ∆h is constant even during repeated or longer measurements.

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Results In our experiments, we vary the concentration of sodium silicate and the height difference ∆h between the two reactant solutions while keeping the zinc sulfate concentration constant. We observe four distinct growth regimes (Fig. 2) of which the most frequently observed are budding (a,b) and jetting (c). The latter structures are similar to those observed earlier in injection experiments for which the flow rate was held constant by a syringe pump.26 In our experiments, however, we notice large variations in thickness of the budding tubes as exemplified by the structures in Figs. 1a,b that have average widths of about 3 and 15 mm, respectively. Popping tubes are observed occasionally but are, compared to earlier studies, less prominent and usually occur as a transient growth mode. All structures formed in our experiments are slightly translucent.

Figure 2. Four distinct tube growth regimes observed for different combinations of [SiO32-] and ∆h: (a) budding (1 M, 1.5 cm); (b) budding (bulky) (0.75 M, 2 cm); (c) jetting (1 M, 4 cm); (d) crowding (0.5 M, 4 cm). The field of view is approximately 3.5 cm × 13 cm but the horizontal axis is slightly deformed due to the cylindrical shape of the reaction vessel (here no sidearm spout).

At low silicate densities, ranging from 0.5 M to 0.63 M, the tube structures are not erect like the samples shown in Figs. 2a-c but rather fill the cylindrical reaction vessel from the bottom up (Fig. 2d and SI movie). This process occurs in a horizontally undulating but vertically layered fashion and will be referred to as “crowding”. Visual inspection strongly suggests that the main growth characteristics of budding, namely the production of a nodular chain by rhythmic breaching and expansion of new solution-filled nodules, are still present. Accordingly, crowding can be considered a non-buoyant form of budding but the resulting structures are sufficiently different to warrant a clear distinction by name.

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Figure 3. (a) Photo of the dried product structure obtained during crowding growth. The approximate diameter is 3.5 cm. (b) The corresponding x-ray diffraction pattern is assigned to Zn4O3(SO4)⋅7H2O and amorphous silica.

Figure 3a shows a photo of a crowding structure after extraction from the reaction vessel and drying at ambient conditions. The product shape matches the cylindrical geometry of our reaction vessel and the shrinkage during drying is negligible. The sample has an extremely small density and is also very fragile. Weight measurements yield an average value of about 20 g/L, which is about 15 times the density of air. We emphasize that these samples consist of one continuous channel connecting the base of the sample with its top surface. The average width of this channel is in the range of millimeters but varies with some spatial rhythm according to the characteristics of budding growth. The channel is bound by a thin wall that—based on earlier reports6,31—can be expected to have a width of about 10 µm. Furthermore, our optical micrographs show the presence of structure-free pockets (e.g. Fig. 2d and also the SI movie) which, prior to drying, are filled with sodium silicate solution and form due to imperfect layering of the non-buoyant, budding-like tube. It seems likely that these pockets remain as empty voids after drying. X-ray diffraction measurements of the dried product yield a diffraction pattern that we assign to Zn4O3(SO4)⋅7H2O and amorphous silica (see Fig. 3b).

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Figure 4. (a) Growth regimes observed for distinct silicate concentrations c and height differences Δh, in experiments without sidearm. The markers indicate crowding (square), thin and thick budding (open and solid triangle, respectively), jetting (circle), popping (cross), backflow (arrow) observed in device. (b) Calculated driving pressures ∆p and density differences ∆ρ for the experiments in (a). Small, black and larger, red markers correspond to the pressure at the beginning and the end of tube growth, respectively. Backflow can occur for ∆p < 0.

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Figure 4a shows a phase diagram of the different growth morphologies based on experiments that employed a reaction vessel without sidearm spout. Crowding (square markers) is observed for low silicate concentrations which correspond to negative or low buoyancy of the injected zinc solution. The related budding growth (triangles) is found at higher silicate concentrations, but gives way to jetting (circles) at larger values of ∆h. In addition, there is a triangular region in the upper, left area of the phase diagram, in which no precipitate structures form in the reaction vessel due to a backflow of the heavy silicate solution into the reservoir-connecting tubing (downward arrow). Open and solid triangles distinguish qualitatively between the thin and thick budding structures that we discussed in the context of Figs. 2a,b. Indications for the presence of popping growth (crosses) are found for high silicate concentrations and intermediate values of ∆h. We also compiled a comparable phase diagram from experiments in which the solution level of the reaction vessel h2 (and hence also ∆h) was kept constant by allowing outflow of excess volume though a sidearm spout (Fig. 1b). The main structure of this phase diagram (Fig. S1) is very similar to the one shown in Fig. 4a but the border between the budding and the jetting regime is shifted slightly in the direction of larger ∆h values. The overall similarity between the two phase diagrams can be understood if we consider the solution volume transferred during the growth of a single tube. If we estimate the latter as about 1-5 mL, the corresponding change in ∆h is only 0.1-0.5 cm. Since this change slightly decreases the hydrostatic pressure during the growth experiment, it favors budding over jetting, which again is in qualitative agreement with our observations. We emphasize that the use of a controlled outflow is nonetheless useful for repeated growth experiments as they reduce undesired variations in density and concentration. For the tube growth near the injection nozzle, the driving pressure ∆p and the resulting flow rate Q can be understood in terms of elementary equations. With respect to the variables and parameters introduced in Fig. 1a, we find that

In our flow experiments, the concentration of the inflowing zinc sulfate solution is not varied and hence the corresponding density ρZn is constant. The density of the silicate ρSi is well described by the linear , where ρ0 is the density of pure water. In independent concentration dependence experiments, we measured the value of ξ as 130 g/mol (Fig. S2). Accordingly, we obtain

as the critical silicate concentration, above which ∆p < 0 and backflow occurs. The corresponding curve has been superposed on the phase diagram (diagonal line in Fig. 4a) and is in good agreement with our observations. Furthermore, the two solutions are of equal density if . We hence expect crowding for c ≤ c’crit and otherwise jetting popping, and budding dynamics. In Fig. 4a, the 8


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constant c’crit = 0.69 mol/L is represented as the horizontal line and indeed serves as a good approximation for the boundary between crowding and the other growth morphologies. Notice that for consistency, we use the fitted value of ρ0 = 986 g/L which is about 1% lower than the actual value of 998 g/L. The driving pressure in Eq. 1 describes the conditions during the initial stages of the precipitate growth. This pressure changes slightly as the structure grows in the upward direction. Assuming that the fluid in the interior of the structure has the density of the injected zinc solution, we find that the pressure difference depends on the tube height l according to

For l = 0, this equation yields Eq. (1) and at the end of the upward directed growth processes (i.e. at the air-solution interface), we find . The latter state is not the mechanical equilibrium as the flow of zinc solution continues generating the floating precipitate structures that can be discerned in upper portions of Figs. 2a,c. In Fig. 4b, we replot the original phase diagram in terms of the driving pressure and the density difference ∆ρ = ρSi − ρZn. The small circular markers (black) represent the initial pressure ∆p from Eq. 1 (or equivalently ∆p(0) from Eq. (3)) and the end point (large circles, red) of the connected line is the corresponding end pressure ∆pf. The individual lines have the same order as the markers in Fig. 4a (e.g. the upper right line corresponds to the upper right marker in (a)). Notice that the driving pressure ∆p(l) increases in most cases because the silicate solution is heavier than the inflowing zinc solution; for crowding, however, this situation is reversed although the pressure drop is very small. The simple analysis presented above allows us to interpret the transition between the different growth regimes in terms of the driving pressure and the density difference. The open tube growth in the jetting regime occurs for strong driving pressure and is in addition favored by a strongly buoyant jet. At lower pressure values (∆p < 0.3 kPa), we observe budding and the growing structure remains closed during its entire formation. Lastly, we find crowding in experiments with negative density differences (ρSi − ρZn < 0). In addition, we can compare our experimental conditions to those in conventional chemical gardens where tube growth is related to the osmotic pressure between the silicate solution and the dissolving seed crystal which is compartmentalized by a thin, semi-permeable membrane of metal hydroxide and gel-like silica. Notice that the metal salt concentration in the latter compartment has never been measured directly. Pantaleone et al., however, performed pressure measurements during budding-like growth of closed tubes in a silicate-CaCl2 system and detected pressure changes of up to 0.3 kPa between rupture events.39,40 The surprisingly small magnitude of this pressure has been discussed in ref. 41.

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Figure 5. (a) Evolution of the solution level h2 (∆h2 = h2 - const) in the reaction chamber during early stages of the gravity-driven injection experiments. The curves represent injection of water into water (blue circles), solutions of ZnSO4 (0.5 M) into ZnSO4 (0.36 M) (green squares), and ZnSO4 (0.5 M) into Na2SiO3 (0.5 M) (red triangles). The continuous curves are exponential fits based on Eq. (6). (b) Average flow rate during the growth of budding tubes. In these experiments, ZnSO4 (0.5 M) was delivered into Na2SiO3 (0.75 M) solution using the reaction cylinder with sidearm (i.e. h2 = const). The continuous and dashed lines are the graph of Eq. (6) without free parameters and the best linear fit, respectively.

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As mentioned earlier, many recent studies on chemical gardens utilize syringe pumps for the injection of the metal salt solution and hence tightly control the volume flow rate. The flow rate can be derived for our experiments analytically and—as we will show in the following—is widely independent from changes in the flow resistance of the self-extending precipitate tube. The Hagen-Poiseuille equation

describes the laminar flow of fluid of viscosity η through a pipe of length L and radius r.42 This volume flow rate also determines the speed v=dh2/dt with which the solution level in the small vessel of radius R increases. With l denoting the time-dependent height of the precipitate structure and under the assumption that the tube is filled with a fluid of density ρZn, Eqs. (3,4) yield

Especially during the early growth stage, the term l(ρSi–ρZn) is much smaller than ρSih2 and can hence be neglected. The resulting simple inhomogeneous differential equation has the solution

where C* and c0 are positive constants. For experiments with external outflow (Figs. 1b, S1), the exponential height change does obviously not hold and the flow rate is essentially constant. We now compare Eq. (6) to three different experiments that involve the flow of water into water, ZnSO4 solution into ZnSO4 solution, and lastly ZnSO4 into Na2SiO3 solution, all for experiments without sidearm (Fig. 5a). Notice that the latter conditions produce tube growth in the crowding regime. In all three cases, the measured values of ∆h2 = h2-C*+c0 are in good agreement with the expected exponential function (Eq. 6). Least-square fitting yields the following k values for the experiments shown in Fig. 5: 0.0097 s-1 (water into water), 0.0082 s-1 (zinc into zinc solution), and 0.0074 s-1 (zinc into silicate solution). Notice that the small difference between the latter two values and the excellent fit quality suggest that the tube structure does not affect the flow dynamics significantly. We also confirmed that r4/L in Eq. (6) is in reasonable agreement with the value of 0.0033 mm3 expected from independent measurements of the inner radius and length of the injection capillary. Considering the appropriate densities and viscosities, the fitted k values yield r4/L = 0.0024, 0.0027, and 0.0024 mm3 which are consistent and close to the geometry-derived number. Considering that the crowding experiment in Fig. 5a involves a self-extending tube and rhythmic bursting of the precipitate structure, it is surprising that Eq. (6) is sufficient to describe the observed changes in the solution level h2. To further investigate the applicability of our hydrodynamic description 11



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(specifically Eq. (4)) to tube-forming experimental conditions, we have measured the volume flow rate Q for a range of ∆h values using our set-up with a continuous outflow (i.e. h2 = const, see Fig. 1b). The reactant concentrations are selected to yield budding growth and the average flow rate is measured volumetrically from the outflow of solution during the initial phase of the experiment. As shown in Fig. 5b, we find a linear relation between Q and ∆h. Using least square fitting, we obtain the empirical equation Q = φ ∆h + q0 with φ = 286 cm2/h and q0 = -37 cm3/h (dashed line). This result can be compared to the theoretical expression for Q(∆h) that is readily obtained from the earlier equations. The continuous line in Fig. 5b graphs this linear dependence for a constant h2 and the parameters from our independent data (specifically r4/L = 0.0024 mm3). The result is in good agreement with our measurements and yield a slope of 261 cm2/h which is only 9 % smaller than the fitted value for φ. The theoretical intercept q0 is -64 cm3/h and similar to the measured value. We hence conclude that, at least for early crowding and budding, the flow rate can indeed be described by simple fluid dynamics that ignore the presence and growth of the precipitate tube.

Figure 6. (a) Image sequence of crowding growth at very low pressure. The height difference between the ZnSO4 (0.5 M) and the Na2SiO3 (0.5 M) solutions is kept constant at ∆h = 0.5 cm. Time between frames: 9 min. Image height: 13 cm. (b) Cumulative volume transferred from the ZnSO4(aq) reservoir into the reaction vessel for the experiment shown in (a). Arrows indicate bursting events. (c) Distribution of flow rates measured after bursting events similar to those highlighted in (b). The data are compiled from 19 bursting events observed in different experiments at nearly identical conditions (see (a)).

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The latter finding suggests that pressure variations due to bursting events of the budding structure are small compared to the known driving pressure and also smaller than the burst-related pressure variations observed in experiments by Pantaleone et al.39,40 In this context, we note that our experiments occasionally show the intermittent cessation of crowding growth. This phenomenon occurs only for very small, positive values of ∆h and hence weak driving pressures that were not systematically studied in the context of the experiments above. Figures 6(a,b) show a representative image sequence and the corresponding evolution of the cumulative volume transferred from the large reservoir into the reaction vessel. The transferred volume V(t) is measured by collecting the excess liquid that flows through the sidearm into a graduated cylinder. Figure 6b reveals repeated plateaus that individually can last for up to 10 min, although the average is closer 5 min. During these phases, the precipitate structure does not extend in length and, within our experimental resolution, no zinc solution is transferred into the reaction vessel. The existence of the plateaus implies that the average flow rate is not described by our simple analysis. Their end points correspond to bursting events in which the tube membrane yields spontaneously to trigger new growth during which V(t) increases nearly linearly. From the slopes of V(t), we directly obtain the distribution of post-burst flow rates (Fig. 6c). The maximum of this distribution occurs close to 1.3 mL/min which corresponds to about 80 mL/h. If we use Eq. (4) to describe this intermittent flow, we obtain a pressure of 30 Pa which estimates the critical pressure needed to rupture the tube wall. Notice that this value is small compared to the pressure ranges studied in the context of Fig. 3. We interpret the observed variations of the critical pressure (i.e. the distribution in Fig. 6c) as a result of the poorly understood variations in the precipitate wall. These variations are rather complex because they involve temporal changes as well as local defects that might be of great importance for the occurrence of the reported bursting events. In addition, there is some osmotically driven pressure change that results from the contrast between the total concentrations of dissolved ions within the structure and the surrounding silicate solution. Such a flow is the main driving force in the conventional chemical garden experiment which seeds a small salt grain into a large volume of silicate solution. Due to the consumption of reactants during the structure growth, these values can only be estimated based on the initial ion concentrations, which serve as upper limits. The latter are 2×0.5 mol/L for the interior solution and 3×0.5×α mol/L for the exterior solution, where α is the degree of sodium silicate dissociation which at this total concentration is about 0.6-0.7.43 Accordingly, the resulting ratio is about 1:1. Since the wall material consists predominantly of zinc hydroxide and the zinc solution is spatially confined, we conclude that osmotic flow is weak and most likely outward directed. The resulting small pressure drop cannot be the cause of the observed bursting events as they would stabilize the precipitate structure. While more systematic studies of this dependence might be required, we suggest that this semi-quantitative analysis supports our original interpretation of the bursting events in the light of materials variations. In this context, future studies could also investigate a possible dependence between the average interburst period and the applied hydrostatic pressure, which might reveal possible connections to results in ref. 41.

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Conclusions We have described a simple experimental set-up that allows the study of precipitate tubes in terms of pressure differences between the interior and exterior reactant solutions. While this driving pressure is not perfectly constant during the growth process, we can control it accurately during the initial growth phase. We specifically found that for pressure differences larger than about 0.3 kPa, the dynamics switch from budding to jetting growth. This transition is particularly important because jetting involves permanently open tubes whereas budding structures are essentially closed. As the tubes grow in the upward direction, the driving pressure changes according to the height of the structure and the involved densities. Under the assumption that the density of the interior solution does not change, this−usually small−pressure variation can be described by simple equations. It is also noteworthy that the change is typically positive meaning that the driving pressure increases during most of our experiments. An increase in the driving force of a system approaching equilibrium is perhaps unusual; however, most of the volume transfer needed to reach mechanical equilibrium occurs after the tube reaches the airsolution interface. This main stage of the equilibration process causes the formation of large precipitate plugs and was not further studied. The volume flow rates in our experiments are not externally controlled but selected by the system according to the given pressure conditions, the geometric parameters of the set-up, and in particular the dimensions of the injection nozzle. Our experiments have shown that the flow rate is not significantly affected by the precipitate structure. Accordingly, we could neglect the l term in Eq. 5. The only exception is the intermittent growth at very low driving pressures (Fig. 6). Accordingly, the flow rates in most experiments can be predicted from the Hagen-Poiseuille equation and the ∆h-dependent pressure, which is an added advantage of our method. Perhaps surprisingly, the radius and length of the injection nozzle is an important parameter that affects various aspects of the growth dynamics. Future studies could evaluate very large or very small values of the relevant r4/L term. For instance, values much smaller than the one studied here will cause smaller flow rates yielding overall “older” and hence thicker precipitate walls that are less likely to show the peculiar reaction-induced self-healing characteristics of these structures. Also jetting could be less likely at these small flow rates as diffusion processes have more time to induce a capping of the tube structure. For large values of r4/L, one might observe flow-rate changes induced by the precipitate tube and related differences in the growth dynamics. At conditions for which the density of the injected solution is either very similar or higher than the density of the sodium silicate solution, we observe crowding growth that eventually fills the entire reaction vessel. The resulting macroscopic material is unusual because it has one continuous connection from the base to the top of the structure, a very low density, and a third “phase” consisting of pockets that were excluded during the layering of the structure. We note that crowding is not characteristic for our pressure-controlled growth experiments and similar structures should be observable in flow-ratecontrolled injection studies. More work is needed to further characterize the interesting features of this low-density material and the likely dependence of these features on the density mismatch of the reactant solutions. Such experiments could include the use of fluorescent probes in the silicate solution 14


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that should allow the localization of the excluded pockets. Our method also opens possibilities for studies such as perturbation experiments in which the driving pressure is varied periodically by simple repeated submergence of an inert object into the large solution reservoir.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Phase diagram for experiments with outflow; concentration-dependent density measurements; details regarding the SI movies (PDF) Movie showing crowding growth and the outflow from the container with spout (AVI)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Phone: +1 850-644-4824. Notes The authors declare no financial interest.

ACKNOWLEDGMENTS We acknowledge financial support from the National Science Foundation (DMR-1005861). B.C.B. acknowledges the National Council for Scientific and Technological Development (CNPq, Brazil) for a postdoctoral fellowship.

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REFERENCES (1) Glauber, J. R. Furni Novi Philosophici; Amsterdam, 1646; English translation by Christopher Packe, London, 1689. (2) Cartwright, J. H. E.; Garcia-Ruiz, J. M.; Novella, M. L.; Otalora, F. Formation of Chemical Gardens. J. Colloid Interf. Sci. 2002, 256, 351-359. (3) Barge, L. M.; Cardoso, S. S. S.; Cartwright, J. H. E.; Cooper, G. J. T.; Cronin, L.; De Wit, A.; Doloboff, I. J.; Escribano, B.; Goldstein, R. E.; Haudin, F.; et al. From Chemical Gardens to Chemobrionics. Chem. Rev. 2015, 115, 8652−8703. (4) Steinbock, O.; Cartwright, J. H. E.; Barge, L. M. The Fertile Physics of Chemical Gardens. Phys. Today 2016, 69, 44-51. (5) Balköse, D.; Özkan, F.; Köktürk, U.; Ulutan, S.; Ülkü, S.; Nişli, G. Characterization of Hollow Chemical Garden Fibers from Metal Salts and Water Glass. J. Sol-Gel Sci. Technol. 2002, 23, 253-263. (6) Pagano, J. J.; Thouvenel-Romans, S.; Steinbock, O. Compositional Analysis of Copper-silica Precipitation Tubes. Phys. Chem. Chem. Phys. 2007, 9, 110-118. (7) Toth, A.; Horvath. D; Smith, R.; McMahan, J. R.; Maselko, J. Phase Diagram of Precipitation Morphologies in the Cu2+-PO43- System. J. Phys. Chem. C. 2007, 111, 14762-14767. (8) Ibsen, C. J. S.; Mikladal, B. F.; Jensen, U. B.; Birkedal, H. Hierarchical Tubular Structures Grown from the Gel/Liquid Interface. Chem. Eur. J. 2014, 20, 16112−16120. (9) Batista, B. C.; Cruz, P.; Steinbock, O. From Hydrodynamic Plumes to Chemical Gardens: the Concentration-Dependent Onset of Tube Formation. Langmuir 2014, 30, 9123-9129. (10) Barge, L. M.; Doloboff, I. J.; White, L. M.; Stucky, G. D.; Russell, M. J.; Kanik, I. Characterization of Iron-Phosphate-Silicate Chemical Garden Structures. Langmuir 2012, 28, 3714-3721. (11) Cartwright, J. H. E.; Escribano, B.; Khokhlov, S.; Sainz-Díaz, C. I. Chemical Gardens from Silicates and Cations of Group 2: A Comparative Study of Composition, Morphology and Microstructure. Phys. Chem. Chem. Phys. 2011, 13, 1030−1036. (12) Cartwright, J. H. E.; Escribano, B.; Sainz-Díaz, C. I. Chemical Garden Formation, Morphology, and Composition. I. Effect of the Nature of the Cations. Langmuir 2011, 27, 3286−3293. (13) Satoh, H.; Tsukamoto, K.; Garcia-Ruiz, J. M. Formation of Chemical Gardens on Granitic Rock: A New Type of Alteration for Alkaline Systems. Eur. J. Mineral. 2014, 26, 415−426. (14) Batista, B. C.; Steinbock, O. Chemical Gardens without Silica: The Formation of Pure Metal Hydroxide Tubes. Chem. Comm. 2015, 51, 12962-12965. 16


Page 16 of 19

Page 17 of 19

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


(15) Ritchie, C.; Cooper, G. J. T.; Song, Y.-F.; Streb, C.; Yin, H.; Parenty, A. D. C.; MacLaren, D. A.; Cronin, L. Spontaneous Assembly and Real-time Growth of Micrometre-scale Tubular Structures from Polyoxometalate-based Inorganic Solids. Nature Chem. 2009, 1, 47-52. (16) Cooper, G. J. T.; Bowman, R. W.; Magennis, E. P.; Fernandez-Trillo, F.; Alexander, C.; Padgett, M. J.; Cronin, L. Directed Assembly of Inorganic Polyoxometalate-based Micrometer-Scale Tubular Architectures by Using Optical Control. Angew. Chem. Int. Ed. 2012, 51, 12754-12758. (17) Cartwright, J. H. E.; Escribano, B.; Gonzalez, D. L.; Sainz-Diaz, C. I.; Tuval, I. Brinicles as a Case of Inverse Chemical Gardens. Langmuir 2013, 29, 7655-7660. (18)

Double, D. D.; Hellawell, A. The Hydration of Portland Cement. Nature 1976, 261, 486-488.

(19) Double, D. D.; Hellawell, A.; Perry, S. J. The Hydration of Portland Cement. Proc. R. Soc. London A 1978, 359, 435-451. (20) Riggs, O. L.; Sudbury, J. D.; Hutchinson, M. Effect of pH on Oxygen Corrosion at Elevated Pressures. Corrosion 1960, 16, 94−98. (21) Stone, D. A.; Goldstein ,R. E. Tubular Precipitation and Redox Gradients on a Bubbling Template. Proc. Natl. Acad. Sci. USA 2004, 101, 11537-11541. (22) Makki, R.; Ji, X.; Mattoussi, H.; Steinbock, O. Self-Organized Tubular Structures as Platforms for Quantum Dots. J. Am. Chem. Soc. 2014, 136, 6463-6469. (23) Batista, B. C.; Cruz, P.; Steinbock, O. Self-Alignment of Beads and Cell Trapping in Precipitate Tubes. ChemPhysChem 2015, 16, 2299–2303. (24) Collins, C.; Mokaya, R.; Klinowski, J. The “Silica Garden” as a Brønsted Acid Catalyst. Phys. Chem. Chem. Phys. 1999, 1, 4669−4672. (25) Pagano, J. J.; Bánsági Jr., T.; Steinbock, O. Bubble-templated and Flow-controlled Synthesis of Macroscopic Silica Tubes Supporting Zinc Oxide Nanostructures. Angew. Chem. Int. Ed. 2008, 47, 99009903. (26) Thouvenel-Romans, S.; Steinbock, O. Oscillatory Growth of Silica Tubes in Chemical Gardens, J. Am. Chem. Soc. 2003, 125, 4338-4341. (27) Makki, R.; Roszol, L.; Pagano, J. J.; Steinbock, O. Tubular Precipitation Structures: Materials Synthesis under Nonequilibrium Conditions. Phil. Trans. R. Soc. A 2012, 370, 2848-2865. (28) Pratama, F. S.; Robinson, H. F.; Pagano, J. J. Spatially Resolved Analysis of Calcium-silica Tubes in Reverse Chemical Gardens. Colloids Surfaces A 2011, 389, 127-133. (29) Pagano, J. J.; Bánsági Jr., T.; Steinbock, O. Tube Formation in Reverse in Silica Gardens. J. Phys. Chem. C 2007, 111, 9324-9329. 17



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(30) Thouvenel-Romans, S.; van Saarloos, W.; Steinbock, O. Silica Tubes in Chemical Gardens: Radius Selection and its Hydrodynamic Origin. Europhys. Lett. 2004, 67, 42-48. (31) Roszol, L.; Steinbock, O. Controlling the Wall Thickness and Composition of Hollow Precipitation Tubes. Phys. Chem. Chem. Phys. 2011, 13, 20100-20103. (32) Hussein, S. Maselko, J.; Pantaleone, J. T. Growing a Chemical Garden at the Air–Fluid Interface. Langmuir 2016, 32, 706-711. (33) Haudin, F.; Cartwright, J. H. E.; Brau, F.; De Wit, A. Spiral Precipitation Patterns in Confined Chemical Gardens. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 17363−17367. (34) Haudin, F.; Cartwright, J. H. E.; De Wit, A. Direct and Reverse Chemical Garden Patterns Grown upon Injection in Confined Geometries. J. Phys. Chem. C 2015, 119, 15067−15076. (35) Batista, B. C.; Steinbock, O. Growing Inorganic Membranes in Microfluidic Devices: Chemical Gardens Reduced to Linear Walls. J. Phys. Chem. C 2015, 119, 27045–27052. (36) Makki, R.; Steinbock, O. Synthesis of Inorganic Tubes under Actively Controlled Growth Velocities and Injection Rates. J. Phys. Chem. C 2011, 115, 17046-17053. (37) See e.g., Ferry, M. S.; Razinkov, I. A.; Hasty, J. Microfluidics for Synthetic Biology: From Design to Execution. Methods Enzymol. 2011, 497, 295–372. (38) Lide, D. R. (ed.) CRC Handbook of Chemistry and Physics 84th edition, CRC Press, Boca Raton, 2003, p. 8-85. (39) Pantaleone, J. T.; Toth, A.; Horvath, D.; RoseFigura, L.; Morgan, W.; Maselko, J. Pressure Oscillations in a Chemical Garden. Phys. Rev. E 2009, 79, 056221, 1-8. (40) Kaminker, V.; Maselko, J.; Pantaleone, J. The Dynamics of Open Precipitation Tubes. J. Chem. Phys. 2014, 140, 244901. (41) Pantaleone, J. T.; Toth, A.; Horvath, D.; Rother McMahan, J.; Smith, R.; Butki, D.; Braden, J.; Mathews, E.; Geri, H.; Maselko, J. Oscillations of a Chemical Garden. Phys. Rev. E 2008, 77, 046207. (42)

Sutera, S. P.; Skalal, R. The History of Poiseuille’s Law. Ann. Rev. Fluid Mech. 1993, 25, 1-19.

(43) Halasz, I.; Li, R.; Agarwal, M.; Miller, I. Dissociation, Molweight, and Vibrational Spectra of Aqueous Sodium Silicate Solutions. Studies in Surface Science and Catalysis, 2007, 170, 800-805. doi:10.1016/S0167-2991(07)80924-4

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Pressure Controlled Chemical Gardens - The Journal of Physical

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