Freezing the Nonclassical Crystal Growth of a Coordination Polymer Using Controlled Dynamic Gradients

A methodology that can be efficiently used to synthesize, isolate, and study out-of-equilibrium crystal structures employing controlled and diffusion-limited microfluidic environments is demonstrated. Unlike studies conducted with conventional mixing procedures in a flask, it is proven experimentally and with numerical simulations that microfluidic technologies can undoubtedly fine-tune reaction times and reagents concentration profiles; factors that enable out-of-equilibrium crystal forms to be obtained.


DOI: 10.1002/adma.201506462
Crystals are an important type of self-assembled structures, where both long range order and control at the molecular level are central characteristics. [ 12,13 ] In contrast to living systems, where energy dissipating processes allow the appearance of adaptive and emergent functionalities, crystalline ensembles are frequently studied in their thermodynamically stable forms, where fi nal structures are ultimately determined by chemical equilibria, diffusion, and mass transport processes. [ 14 ] Even though crystals, once formed, are static structures that can be investigated at the atomic scale, it has proved diffi cult to establish methods that can precisely "uncover" their self-assembly process into the most thermodynamic stable forms. [ 15,16 ] The most frequent approach employed to understand and control the self-organization of crystalline matter involves varying the functional groups incorporated within their constituent units. [ 17 ] This heuristic approach (based on crystal engineering) has proved to be effi cient in controlling the self-assembly of molecular components into intricate functional structures. [ 18 ] While there is a tremendous interest in rationalizing the crystallization process through the modifi cation of the functional groups present in the molecular building blocks, there is a recognized dearth of methods and processes which allow the isolation and study of out-of-equilibrium species. In this respect, it is important to note that nonequilibrium crystal forms are not only useful in "uncovering" the self-assembly process of crystalline matter, but valuable in rationalizing new artifi cial materials and systems with advanced functionalities.
As crystallization is inherently a kinetic self-assembly process, [ 15,[19][20][21] dynamic processing technologies such as microfl uidics -where molecules can react under diffusion-controlled conditions [22][23][24] -can be used to control and investigate out-ofequilibrium processes. For example, controlled reaction-diffusion systems (such as those encountered in hydrodynamic fl ow focusing mixers) [ 25 ] can be utilized in this respect due to the precise spatial and temporal control over concentration profi les and mass transport. [ 26,27 ] That is, under hydrodynamic fl ow focusing conditions, the average residence time and the width of the reaction zone formed between two-reagent streams (where the diffusive mixing occurs) can be precisely controlled. [ 28,29 ] Herein, we show for the fi rst time that reaction and/or diffusion-limited (microfl uidic) environments can induce concentration gradients that facilitate the formation of novel and exceptionally ordered out-of-equilibrium structures during the crystallization of a coordination polymer (CP). In contrast to macroscopic reaction environments, we prove (both experimentally and through numerical simulations) that dynamic microfl uidic conditions allow the isolation Manually engineered self-assembled structures have for many years been investigated under equilibrium conditions so that their most stable forms are reached, [1][2][3][4][5] until recently. There has been a growing interest in obtaining and studying nonequilibrium self-assembled structures. [6][7][8][9] The primary reason for this is that nonequilibrium structures (which are typically formed transiently under a constant infl ux of energy) [ 10 ] can offer a broad number of intriguing opportunities in the development of novel materials and systems with advanced functionalities. [ 11 ] For example, transient and/or steady-state self-assembled structures generated far from equilibrium are the basis of many sophisticated functions observed in living systems, e.g., DNA replication and/or cell division. [ 10 ] Nonetheless, the controlled synthesis and study of intermediate, self-assembled structures is still a major challenge, which currently limits advancements in materials development and technology.

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of out-of-equilibrium crystal states through the fi ne-tuning of reaction times and reagent concentration profi les. We focus our studies on the crystallization process of a CP because of the broad number of applications that these materials have brought onto the scene of crystalline matter. [ 30,31 ] From the vast number of CPs that could be employed in our investigations, we demonstrate the above concept by adopting a 2D CP having the formula [Cu(4,4′-bpy)](NO 3 ) 2 (hereafter 1 ; where 4,4′-bpy is 4,4′-bipyridine), which is constructed by connecting µ 2 -oxo-bridged and µ 2 -NO 3 -bridged Cu(II) chains through 4,4′-bpy linkers ( Figure 1 a, Table S1 and Figure S1, Supporting Information). 1 is particularly well-suited to the current investigation since it is easily crystallized (by diffusion of an ethanolic solution of 4,4′-bpy into an aqueous solution of Cu(NO 3 ) 2 ·6H 2 O or by mixing the two solutions with or without stirring), and crystallizes in the form of plate-like crystals (Figure 1 b); a common crystal habit and one whose selfassembly and crystal growth development are unexplored. [ 32 ] Figure 2 a shows the planar microfl uidic device employed in the current investigations. This comprises four input channels and one outlet channel (see the Experimental Section for further details). Two inlet channels are used to inject a pair of sheath fl ows ( Q 1 and Q 4 ) with the two other channels being used to supply the reagent solutions; one containing Cu(NO 3 ) 2 ·6H 2 O ( Q 2 ) and the other containing 4,4′-bpy linker ( Q 3 ). The microfl uidic device was fabricated in polydimethylsiloxane (PDMS) using standard soft-lithographic methods and was covered by a glass cover slide (see Experimental Section for further details). We defi ned the four input channels and corresponding fl ow rates to guarantee rapid crystallization whilst ensuring that microfl uidic channels do not block. In initial studies, we investigated the crystallization of 1 by varying the fl owrate ratio (FRR), whilst keeping the reagent fl ow rates ( Q 2 and Q 3 ) constant. The FRR is defi ned as the ratio of fl ow between the focusing streams and the reagent fl uids (i.e., FRR = (Q 1 +Q 4 )/(Q 2 +Q 3 )). In all cases, crystals of 1 were immediately formed at the interface between the Cu(II) ion and 4,4′-bpy streams after injection. The resulting crystals were collected on transmission electron microscopy grids, fi lter paper and/or diluted on ethanol at the end of the main channel to avoid off-chip reactions. Subsequently, the crystals formed were further characterized by fi eld-emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), polarising optical microscopy (POM), and X-ray powder diffraction (XRPD).
Figures 1 c, 2 c (right), and 3 b (right) show typical TEM and FE-SEM images of crystals of 1 prepared at FRR of 0.1. These crystals that have a square plate-like habit are representative of those synthesized either by conventional diffusion or simple mixing in a macroscopic vessel (Figure 1 b). This is expected since as the FRR decreases at a constant overall fl ow rate, the width of the diffusive mixing zone at the interface between the two reagent streams increases as a function of distance along the channel (i.e., a nonsharp concentration gradient is generated). Accordingly, the reaction zone in which the structures assemble is enlarged, thus mimics to some extent conventional diffusion on the macroscale, and assembly of the most thermodynamic stable structures will be favored. Finite element simulations strongly support the idea that a decrease in the FRR prompts an increase in the reaction-diffusion zone present along the length of the main microfl uidic channel where crystallization takes place ( Figure S2, Supporting Information). Crystals of 1 prepared at an FRR of 0.1 had average dimensions of 2.80 ± 0.52 µm. In addition, both the simulated (derived from the single crystal structure of 1 ) and experimental (resulting from the crystals synthesized at an FRR of 0.1) XRPD patterns are consistent (Figure 2 b; Figure S3, Supporting Information), confi rming that crystals synthesized in the microfl uidic system are structurally identical to crystals prepared through conventional methods. Additionally, it is noted that 1 can be obtained as phase pure; even though the precipitation of a small amount of free 4,4′-bpy ligand is detected.
As shown in Figure 2 c, we then varied the FRR from 0.1 to 5 and observed the formation of numerous and unprecedented nonequilibrium crystal morphologies. In contrast to previous studies, where blocking agents are used to study intermediate states during a crystal growth process, [ 33 ] in the current investigations the ultimate shape of all generated structures solely depends upon the conditions established within the diffusive mixing zone. Increasing the FRR whilst keeping the reagent fl ow rates constant, a rationalized reduction of the diffusive mixing zone can be achieved (i.e., a sharp concentration gradient is generated, see Figure S2, Supporting Information), which leads to diffusion-limited and kinetically controlled environments in which the formation of the most thermodynamic stable crystal forms can be avoided to some extent. [ 34,35 ] That is, at high FRR crystals form at high supersaturation conditions; a result that promotes the formation of out-of-equilibrium crystal forms. [ 36 ] For example, we observed the formation of needles at an FRR of 5; needles that start to orthogonally connect through their edges at an FRR of 4; hollow frames at an FRR of 2; frames partially fi lled with a thinner layer at FRR of 1; and the above-mentioned square plate-like fi lled crystals at FRR of 0.1. Importantly, varying the total fl ow-rate (TFR) without varying the FRR provides a direct way of controlling the average residence (reaction) time for crystallization and thus throughput, but has no signifi cant effect on the habits and structures generated ( Figure S4, Supporting Information). Here, only slight differences on the crystal size were observed. To further understand these experimental results, numerical simulations were performed. Finite element data show that the overall concentration profi les of the reagents do not change drastically when modifying the TFR for a given FRR, but do change remarkably when varying the FRR for a given TFR. In this case, the overall concentration profi les of the reagents become narrower and the maximum concentration is reduced with increasing FRR ( Figure S5, Supporting Information). This observation implies that the concentration of reagents present within the microfl uidic channel (and which are consumed during the formation of crystals) is reduced at higher FRRs for all TFRs considered, and thus provides for precise control of crystallization kinetics and crystal growth.
The isolated needles obtained when performing crystallization at FRR of 5 had an average length of 500 nm and a diameter of 20 nm. At a lower FRR of 4, we detected the coexistence of identical needles with some structures comprising two or three needles perpendicularly connected at their edges. Interestingly, at FRR of 2, hollow frames, with average side dimensions of 2.95 ± 0.71 µm and edge thicknesses of 200 nm, were found to be predominant. Further decreasing the FRR to 1 resulted in a partial fi lling of these hollow frames, fi nally forming the previously described plate-like crystals seen when a FRR of 0.1 was used. Moreover

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by time-lapse scanning electron microscopy (SEM) imaging analysis, [37][38][39][40] in the current investigation all structures generated are crystalline. Accordingly, XRPD studies can provide valuable insights in better understanding and characterizing nanoscale self-organization of the building blocks in their isolated, nonequilibrium forms. XRPD studies were essential to confi rm that all crystals generated under diffusion-limited and kinetically controlled microfl uidic environments corresponded to 1 . Indeed, as shown in Figure 2 b, the XRPD patterns of all crystals obtained at different FRRs perfectly matched that simulated from the crystal structure of 1 . It should be noted that XRPD patterns of the needles obtained at FRRs of 5 and 4 show broad peaks, which are attributed to their lower crystallinity.
To shed light on the growth mechanism that transforms the hollow frames (FRR = 2) to plate-like crystals (FRR = 0.1) (Figure 3 a,b), we further analyzed various nonequilibrium crystal forms of 1 using atomic force microscopy (AFM) and POM. In the early stages of frame formation, we were able to confi rm that the frames are completely hollow, with no evidence of residues inside the frames ( Figure S6, Supporting Information). At the vertices of the frames, the perpendicular needles do not overlap but instead completely interpenetrate ( Figure S7, Supporting Information). Additionally, POM indicates that the optic axis of a crystal is the same in all sides of the frame ( Figure S7, Supporting Information). The progressive fi lling of the internal area of the frames typically occurs by parallel needle growth, as observed in Figure 3 c. For higher degrees of fi lling (Figure 3 d), precise observation of the fi lling fractions shows that needles tend to organize orthogonally in alternative growth levels. Some degree of interweaving occurs in areas where full coverage is yet to be achieved, with the needles at subsequent levels fi lling the gaps. Finally, at some point, needle coalescence occurs and the surface of the area inside the frames becomes uniform, ultimately forming the plate-like crystals.
The detailed mechanism leading to the formation of these ordered out-of-equilibrium structures remains unclear at the current time, however, the process seems to occur so as to lower and/or eliminate high-energy facets in the generated structures; an idea that has previously been suggested by others in regard to the shape-controlled growth of inorganic crystals. [ 15 ] Based on these previous studies with inorganic crystals and consideration of the results presented herein, we propose a dynamic crystal growth process as shown in the idealized sequence of Figure 2 c. It is likely that needles isolated at a high FFR can act as seeds for the assembly of the nonequilibrium trapped intermediate states, which then evolve toward a fi nal thermodynamic stable form: plate-like crystal structures. This proposal is supported by XRPD studies, which prove that all the structures generated have an identical chemical connectivity. Furthermore, the AFM studies support our hypothesis by confi rming that growth of 1 is dynamic and that the agglomeration and progressive fi lling of nonequilibrium forms can occur due to a parallel growth of needle-based structures. The AFM results Adv. Mater. 2016, 28, 8150-8155 www.advmat.de www.MaterialsViews.com therefore suggest that the early stage isolated seeds organize at a single level and in a perpendicular fashion, leading to the fi nal plate-like crystalline morphologies observed in bulk and at an FFR of 0.1 (Figure 1 b,c, respectively).
In summary, we have shown that diffusion-limited and kinetically controlled growth regimes occurring in microfl uidic devices can provide valuable insights into crystallization processes. In contrast to other methods where trapping of the structures generated during a polymerization process is achieved by taking aliquots in a controlled solvent-induced precipitation regime, [ 41 ] we show, for fi rst time, that hydrodynamic fl ow-focusing condition provided by the adoption of a continuous-fl ow microfl uidic scheme can be a powerful experimental tool for the generation and isolation of nonequilibrium forms. We believe that the microfl uidic-based approach presented here circumvents limitations generally ascribed to the isolation and study of transient forms during crystallization processes. We have demonstrated that microfl uidic dynamic processing provides an accessible range of nonequilibrium structures present during crystal growth. These results are exciting since the control and prediction of chemical and physical properties in crystalline matter can only be achieved when methods that can precisely uncover the self-assembly process can be established. The technology presented constitutes a potential route toward a wealth of new and improved materials, where the rationalization of controlled chemical and physical properties may become reality.

Experimental Section
Materials and Methods : The reagents Cu(NO 3 ) 2 •6H 2 O and 4,4′-bipyridine (4,4′-bpy) were obtained from Sigma-Aldrich Co. High purity EtOH was purchased from Teknokroma. Deionised Milipore Mili-Q water was used in all experiments. SEM images were collected on a scanning electron microscope (ZEISS EI MERLIN FE-SEM) at acceleration voltages of 0.2-30 kV. Aluminium was used as support. TEM images were obtained with a JEOL JEM 1400 electron microscope. X-ray EDX microanalysis was performed using an Oxford Instruments INCA energy SEM system. All measurements were performed at room temperature and at a voltage of 120 kV. XRPD measurements were performed using an X'Pert PRO MPD diffractometer (Panalytical) especially confi gured for in-plane diffraction.
Microfl uidic Device Fabrication : The microfl uidic channels employed in this study were structured in PDMS (SYLGARD 184 Silicone Elastomer Kit) using an SU-8 (2015, Microchem) master form fabricated by standard photolithographic techniques. Before attaching the cured and structured PDMS mould to a glass coverslip through plasma activation, inlet holes connecting the microfl uidic channels were punched with a Biopsy puncher. The cross-sectional dimensions of the microchannels were 50 µm × 50 µm for the four input microchannels, and 250 µm × 50 µm for the main reactor channel. The total length of the main reactor channel was 9 mm. Synthesis of 1 Using Laminar Flow : The syntheses of different crystal morphologies of 1 were carried out in a planar microfl uidic device that consists of four input channels and one outlet channel, imprinted in PDMS and was covered by a glass plate. Reactant solutions were injected via a syringe pump system at given fl ow rates. The fl ow rates were defi ned (all in µL/min) using the following abbreviations: fl ow (1), Q 1 ; fl ow (2), Q 2 ; fl ow (3), Q 3 ; and fl ow (4), Q 4 . In a typical synthetic procedure, crystals of 1 were initially prepared by injecting an aqueous solution of Cu(NO 3 ) 2 •6H 2 O (100 × 10 −3 M ) in Q 2 and an ethanolic solution of 4,4′-bpy (100 × 10 −3 M ) in Q 3 . Both were accomplished by an auxiliary fl ow with the corresponding solvents, Q 1 and Q 4 .
X-Ray Crystallography : X-ray single-crystal diffraction data for 1 were collected on the BM16 Spanish line of the ESRF synchrotron in Grenoble ( λ = 0.7901 Å). Data were indexed, integrated, and scaled using HKL2000 software. [ 1 ] The H atoms were included in theoretical positions but not refi ned. The low max value was due to the data collection process, which was performed in the BM16 line with only a phi scan. The structure was solved by direct methods using the program SHELXS-97. [ 2 ] Refi nement and all further calculations were carried out using SHELXL-97. Empirical absorption corrections were applied in both cases using SCALEPACK. [ 1 ] AFM Measurements : Atomic force microscopy images were taken in amplitude modulation dynamic AFM mode, in pure noncontact conditions with an Asylum MFP3D system, using Pt-coated tips (Nanosensors PPP-EFM) and a resonance frequency around 70 kHz. Images were obtained using a scanning rate of 1 Hz and keeping the amplitude of oscillation constant at about 50 nm. For Kelvin probe force microscopy images, an AC voltage of 1 V amplitude was applied to the tip at a distance of 50 nm to the surface, and the surface potential function difference between the tip and the sample was obtained.
Numerical Simulations : The 2D steady-state fl uid fl ow and mass transport across the microfl uidic device was simulated using a Finite Element approach, considering geometries and boundary-conditions as described in the manuscript. Diffusion coeffi cients of both reagents were assumed to be 10 −9 m 2 s −1 , in line with literature data for ethanolwater mixtures. [ 3 ] Density and dynamic viscosity of reagents and sheathed currents were assumed to be those of the corresponding pure solvents, i.e., 103 kg m −3 and 8.9 × 10 −4 Pa•s for water-based currents and 789 kg m −3 and 1.1 × 10 −3 Pa•s for ethanol-based currents, respectively.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.