Electron transparent nanotubes reveal crystallization pathways in confinement

The cylindrical pores of track-etched membranes offer excellent environments for studying the effects of confinement on crystallization as the pore diameter is readily varied and the anisotropic morphologies can direct crystal orientation. However, the inability to image individual crystals in situ within the pores in this system has prevented many of the underlying mechanisms from being characterized. Here, we study the crystallization of calcium sulfate within track-etched membranes and reveal that oriented gypsum forms in 200 nm diameter pores, bassanite in 25–100 nm pores and anhydrite in 10 nm pores. The crystallization pathways are then studied by coating the membranes with an amorphous titania layer prior to mineralization to create electron transparent nanotubes that protect fragile precursor materials. By visualizing the evolutionary pathways of the crystals within the pores we show that the product single crystals derive from multiple nucleation events and that orientation is determined at early reaction times. Finally, the transformation of bassanite to gypsum within the membrane pores is studied using experiment and potential mean force calculations and is shown to proceed by localized dissolution/reprecipitation. This work provides insight into the effects of confinement on crystallization processes, which is relevant to mineral formation in many real-world environments.


TiO 2 Deposition on TE Membranes
Titania coatings were deposited in a Cambridge Nanotech Fiji F200 Atomic Layer Deposition (ALD) System in a class 100 cleanroom. The tetrakis(dimethylamido)titanium (TDMAT) precursor was preheated to 75 °C. TE membranes were heated to 140 °C within the deposition chamber at 1 x 10 -5 torr. The deposition recipe is shown in Table S1. 100 cycles were used to deposit ≈5 nm TiO 2 on the 10 nm and 25 nm diameter pores, while 200 cycles deposited ≈10 nm TiO 2 in the 50-200 nm diameter pores. These thickness of TiO 2 deposited was checked by depositing under the same growth conditions on to silicon wafer (200 cycles = 9.6 nm) using a Woollam M-2000XI ellipsometer.

Calcium Sulfate Precipitation within TE membranes
Glassware was piranha cleaned by immersing in a solution of 7 parts 95+ % sulfuric acid and 3 parts 30 % hydrogen peroxide for >2 hours, rinsed 5 times with water, then dried with a stream of air. A 1 cm 2 membrane was cut out and plasma cleaned in air for 2 minutes (Atto plasma cleaner, Diener). The clean membrane was then immersed in EtOH (2 minutes), then water (2 minutes) before mounting between the two halves of the clean glass U-tubes. This apparatus was sealed using PTFE tape (12 m x 12 mm x 0.075 mm) and the U-tube arms clamped in position, and 1 mL water added to each arm to check for leaks and to keep the membrane hydrated. The water was removed, and 3 M solutions of CaCl 2 ·2H 2 O and (NH 4 ) 2 SO 4 were passed through 0.22 µm syringe filters, and 1 mL of each was added to the individual arms of the U-tube. The membrane was isolated after 1-16 hours and rinsed with water. Any surface crystals were removed by scraping with a glass cover slip, and any unmineralized areas of the membrane were trimmed off. The polycarbonate was then dissolved in 1.8 mL dichloromethane (DCM) in an Eppendorf tube and sonicated for 30 seconds. 200 µL water was floated on top of the DCM, and the tube vortexed to transfer the sample to the water-DCM interface. The DCM was removed and replaced 2 times, and then removed via pipette, leaving the sample stored in water.

Bulk Ethanolic Precipitation of Bassanite
This was carried out according to the method of Tritschler et al. (2015) 1 where a 50 mM solution of CaCl 2 ·2H 2 O and a 50 mM solution of (NH 4 ) 2 SO 4 were prepared and passed through a 0.22 µm filter. 2.5 mL of each solution was combined for 1 second before pouring the mixture into 45 mL EtOH to quench the reaction. This was shaken vigorously for 30 seconds, then left to rest for 5 minutes. The mixture was centrifuged (5 minutes, 4,000 xg), the supernatant removed, and the precipitate washed by resuspension in 50 mL EtOH. The particles were stored in 5 mL EtOH.

Sample Characterization
Sample morphologies were determined using Scanning Electron Microscopy (SEM). Particles were resuspended in 5 µL of solvent (water for bulk gypsum and TE membrane samples, EtOH for bulk bassanite samples) and applied to a 1 cm 2 piece of silicon wafer affixed to a SEM stub with copper tape. SEM images were recorded at 5 keV using an FEI Nova 450 NanoSEM using an in-lens secondary electron (SE) detector or a circular backscatter (CBS) detector, and energy dispersive X-ray (EDX) maps were recorded using a Bruker SDD-EDS detector at 18 keV. Transmission electron microscopy (TEM) was also used to characterize the particles, and in particular, to determine their structure using selected area electron diffraction (SAED). Samples were prepared by placing a 5 µL suspension of the prepared particles onto formvar (10 nm) and carbon (1 nm) coated copper grids (200 mesh) and allowed to dry. Analysis was carried out using a FEI Tecnai TF20: FEGTEM equipped with a Gatan Orius SC600A CCD camera operating at 200 keV using a spot size of 6 (electron dose ~30-50 e -Å -2 per image at 50,00 x magnification). Low dose TEM imaging and SAED patterns were recorded using an FEI Titan3 Themis 300: S/TEM with S-TWIN objective lens and monochromator (spread ~0.25 eV) operating at 300 keV and set to a screen current of 0.1-0.2 nA. This corresponded to an electron dose of ~2.5-5.0 e -Å -2 per image.
The structure of the calcium sulfate particles were also determined using powder X-ray diffraction (p-XRD) and Raman Spectroscopy. Sample in suspension were mixed with a silicon powder standard and dried onto a silicon substrate for p-XRD. Diffraction patterns were collected on a Brucker-AXS D8 series diffractometer using a Cu Kα source (40 kV, λ = 1.5406 Å) between 2θ = 2.0-50.0° (0.0196° and 3 seconds per step). These data were processed using Bruker-AXS Commander and EVA software, and the intensities normalized in OriginPro ver. 2018. Samples were dried onto silicon wafer to collect Raman spectra on a Horiba LabRAM HR Evolution Raman microscope using a green 532 nm 50 W laser at 5-10% power between 50-500 and 550-1200 cm -1 . The space in the spectrum collection between 500-550 cm -1 was selected to omit a very strong peak at 520 cm -1 from the silicon wafer substrate, and so avoid saturating the detector. The spectra were collected using LabSpec 6 software, with a spectral resolution of 0.2 cm -1 obtained using an 1800 grooves mm -1 grating and a 100 µm aperture, and plotted and normalized in OriginPro ver 2018.

Computational Studies
The potential model of Byrne et al. (2017) 5 was used to produce the free energies of water transport in bassanite. The structure of bulk bassanite was built based on AMCSD #6909. 6 {001} and {110} surfaces were generated using the METADISE code. 7 Slabs were ≈30 Å thick, and hydrated with water occupying approximately 30 Å on either side. MD simulations were performed using the LAMMPS code 8  Lattice equilibration was performed in an NPT ensemble employing a Nosé-Hoover thermostat set to 300 K and barostat set to 0 bar 10, 11 with relaxation times of 0.1 and 1.0 ps respectively. All lattice vectors in bulk bassanite were allowed to vary, whereas in the slab calculations, only the lattice vectors in the plane of the slab were allowed to vary. The systems were allowed to relax under the target conditions for 100 ps before the lattice vectors were averaged every 100 fs for 500 ps. Before the PMF calculations were performed, the lattice vectors were fixed at their NPT average. A water molecule was inserted/removed as required for the mechanism under study and the lattice vectors were assumed not to change from the fully hydrated value.
The Potential Mean Force (PMF) calculations were performed by constraining an atom in a position using a harmonic well and recording the average force the well applies during an MD simulation. 12 The average force exerted by the harmonic well is exactly opposite that being applied by the rest of the system on the atom of interest. The integral of the average force as a function of position gives the free energy profile associated with the pathway. All our PMF calculations used a spring constant of 10.0 eV Å -2 applied in one direction only. All PMF calculations were performed in an NVT ensemble using a Langevin thermostat 13 with a 0.1 ps relaxation time. Forces were averaged every 10 fs. Slab calculations were simulated for 1 ns to allow thorough exploration of the 2D surface. Bulk calculations were simulated for 100 ps. Integration of the average force to obtain the free energy profiles was performed using the trapezoidal rule.
To analyze the flux to a growing crystal, the advection-diffusion equation was solved using COMSOL Multiphysics (ver. 5.5). This was done for (1) confinement within pores by using two large reservoirs connected by a narrow cylindrical channel with a crystal positioned at its center and (2) for a bulk solution using a crystal in the middle of a large reservoir. A concentration of 1 Mol m -3 and 0 Mol m -3 were assigned to the top and bottom of the large reservoirs ( Figure 9a). Initially, the concentration at the surface of the crystal was also set to 0 Mol m -3 . A diffusion coefficient of 1 x 10 -9 m 2 s -1 was used throughout and was taken as representative of the diffusion coefficients of 0.79 x 10 -9 m 2 s -1 for Ca 2+ and 1.10 x 10 -9 m 2 s -1 for SO 4 2-, 14 and the properties of the fluid taken as water. The boundary conditions represent a sink for the transported ions, under the limit of fast growth. In practice this is a simplification of the crystallization process, nevertheless measuring the diffusive flux at the crystal surface allows the relative transport of ions to be compared, and the importance (or not) of the geometry to be elucidated.  Figure S2. Raman spectra of calcium sulfate precipitates. Left shows as collected and right shows normalized zoomed area to highlight shifts in ν 1 symmetric sulfate peak for gypsum at 1008 cm -1 to bassanite at 1015 cm -1 in Raman spectra. 15,16 Blank silicon wafer substrate (grey), TE membrane (orange), bulk gypsum precipitate (magenta), bulk ethanolic bassanite control (cyan), rods from 200 nm diameter pores (dark yellow), and rods from 100 nm diameter pores (green). It was not possible to collect spectra from the samples formed in the smaller diameter pores as their signal was too low.   Supplementary Table S5. Calcium sulfate rod diameters quoted in this manuscript. TE membrane pores show a small variability about the diameter quoted as purchased. As such, measurements of the mineral rods that were used for diffraction were recorded from TEM images. 10 measurements of the rod diameter across the area selected for diffraction were recorded in imageJ2, 3, with the error quoted one standard deviation of these values.* Samples were from the same area but imaged after a minimal exposure of 30-50 e-Å 2 s -1 (S3a ≈1 sec) and after a longer exposure (S3c 2-3 min). + Edge of tube / rod unclear so not measured.