Johanna Midelet

Afaf H El-Sagheer

Tom Brown

Antonios G Kanaras
email: a.kanaras@soton.ac.uk

Anne Débarre
email: anne.debarre@lac.u-psud.fr

Martinus H V Werts
email: martinus.werts@ens-rennes.fr

Spectroscopic and hydrodynamic characterisation of DNA-Linked gold nanoparticle dimers in solution using two-photon photoluminescence

Introduction

Deoxyribonucleic acid (DNA) is a versatile building block for the nanoscale engineering of nanoparticle-based materials. [1] Since the introduction of thiolated oligonucleotides as linkers for gold nanoparticle assembly, [2,3] various potential applications of oligonucleotidefunctionalized nanoparticles in nanomedicine, [4] metamaterials [5] and nanoelectronics [6] have been investigated. Plasmonic gold nanoparticles exhibit specific optical and electronic properties depending on their size, shape and arrangement. [7] Thus, their assemblies could be described as 'plasmonic molecules' [8,9] with adjustable response correlated to their unique structures.

Conceptually, nanoparticle dimers are the simplest example of assembled structures of nanoparticles. They have been extensively studied as sensors or plasmonic rulers using absorbance or scattering spectroscopy. [10][11][12] However, a key disadvantage of these spectroscopic methods is that they cannot effectively detect the interactions between the nanoparticles when the interparticle distance is too large or when the particles are too small in size. The localised surface plasmon resonance is progressively damped out for small particles (<30 nm) which drastically decreases their light scattering response; such particles may be considered 'weakly plasmonic'. For instance, at the plasmon resonance peak maximum, 20 nm gold nanospheres (AuNP) scatter less than 1% of the incident photons. [13] For biomedical applications of gold nanoparticles, it is particularly important to get a better understanding of their interactions with cells and complex biological structures. This requires the ability to track their location and distribution in these systems. [14] Often, the method used to image and track gold nanoparticles in cells is dark field microscopy, which has recently been extended to hyperspectral [15] and SERS [16] imaging. These imaging methods, which rely on plasmon-assisted light scattering, are hampered by the lower limit on the size of metal nanoparticles they can detect.

Here we demonstrate an alternative method for tracking DNA oligonucleotide-coated nanoparticles in liquid media by combining multiphoton-excited emission spectroscopy and fluctuation correlation spectroscopy (FCS). Whereas multiphoton-excited photoluminescence fluctuation correlation spectroscopy of individual luminescent silicon nanoparticles [17] and individual gold nanoparticles [18] have been reported, the applicability of FCS to analyze multiparticle assemblies has not yet been explored.

In the present work, two-photon photoluminescence (TPPL) emission spectra of DNA-gold nanosphere assemblies are obtained via photon time-of-flight spectroscopy [19,20] (PTOFS). We show that two-photon-excited emission spectroscopy detects plasmonically small (12 nm average diameter) gold nanospheres with single-particle sensitivity, since it probes their localized surface plasmon resonance spectrum. We also extend the TPPL spectroscopy to two-photon photoluminescence fluctuation correlation spectroscopy (TPPL-FCS), yielding a sensitive measurement that simultaneously probes the plasmonic spectroscopy and the hydrodynamics of nano-assemblies. Our work opens interesting opportunities for detection, imaging and in situ characterization of molecularly linked nanoparticle assemblies. This may offer a new optical read-out mode for nanoparticle-based nucleic acid detection.

Results and discussion

The experiments were carried out on various well-defined 12 nm AuNP-DNA monoconjugates and corresponding linked AuNP dimers. Through monofunctionalization of gold nanospheres with four different single-stranded DNA (ssDNA) strands we generated four "monomers": AuNP-A, AuNP-B, AuNP-C and AuNP-D. Two DNA-linked dimers were then obtained by hybridisation of the complementary DNA sequences,: the 'short-link' dimer AD (26 base-pair (bp) interparticle distance) and the 'long-link' dimer BC (146 bp). The collection of 4 AuNP-monoconjugates and 2 dimers is schematized in Figure 1.

Optical extinction and scattering spectra

The linear optical extinction spectra of all ssDNA-AuNP monoconjugates and the DNAlinked AuNP dimers were very similar in shape, displaying the well-known plasmonic resonance near 520 nm for 12 nm AuNP (Figure 2). The short-link dimer AD and long-link dimer BC did not show any significant alteration of the plasmon resonance band compared to the monomers. This is illustrated by the position of the extinction maximum, which was consistently found to be at 521 nm (Table 1). From the similarity of the extinction spectra between monomers and dimers, we infer that there are no significant plasmonic interactions between the constituent gold nanospheres in the dimer. The absence of significant plasmonic interaction indicates that the interparticle distance in both types of dimers (AD and BC) is too large for such interaction to occur. It has been demonstrated that such plasmonic interaction critically depends on the interparticle gap and also on the nanoparticle diameters. [21][22][23][24] Jain et al. [21] found that the fractional wavelength shift of the plasmon band in homodimers depends on the particle diameter and the surface-to-surface gap

(1)

In the present study we used 12 nm gold nanospheres. Using the above formula, we estimate that interparticle gaps beyond half that distance (6 nm) lead to undetectable plasmonic interactions. In addition to light extinction, nanoparticles (NP) and NP assemblies display light scattering properties depending on their shape, size, and core material. Light scattering provides further information on the plasmonic properties of the objects. As described previously, [13,23] a corrected light scattering spectrum of a nanoparticle solution can be obtained in a conventional right-angle fluorimeter configuration using white light as the illumination source, and correcting the raw sample light scattering spectrum using the spectrum of a Ludox reference sample according to Equation (2),

Sufficiently diluted Ludox is a good light scattering reference since it is a perfect Rayleigh scatterer. [25] In order to account for batch-to-batch variations in the Ludox concentration, the Ludox reference sample is characterised by an optical density parameter such that each of their extinction spectra is described by Equation (3).

(

) 3
While the corrected light scattering spectrum has the spectral shape of the scattering cross section spectrum and does not depend on any instrumental parameters, its intensity still depends on the nanoparticle concentration, which is usually not precisely known for purified nanoparticle solutions. Here, we propose to normalize the corrected light scattering spectrum using the Ludox density parameter and the optical density OD of the nanoparticle sample at the wavelength where its scattering is maximal (Equation 4).

(

) 4
It can be readily shown that reproduces the shape of the light scattering cross section spectrum , and that its maximum gives the scattering (quantum) efficiency at that wavelength.

(

) 5
We call this the quantum-efficiency normalized light scattering (QENLS) spectrum. It describes the intrinsic light scattering behavior of the nanoparticle in solution, independent of concentration, specific illumination or spectrometer properties. It allows light scattering of different nanoparticles to be compared directly, both in terms of the spectral shape and the scattering efficiency.

As stated above, the concentration independence is interesting for nanoparticle characterization, since it is often difficult to precisely know the concentration of nanoparticle sample preparations. Moreover, QENLS spectra may be obtained theoretically from the scattering and extinction cross section spectra, calculated using analytic [START_REF] Bohren | Absorption and Scattering of Light by Small Particles[END_REF] or numerical [START_REF] Yurkin | [END_REF][28][29][30][31][32] electromagnetic models. This allows for a direct comparison between experiment and theoretical models and helps to establish structure-property relationships for these plasmonic assemblies.

Figure 3 shows the QENLS spectra of the purified ssDNA-AuNP monoconjugates and DNAlinked dimers in pure water. The scattering efficiency is low, below 1%, as expected for 'plasmonically small' gold nanoparticles. While the scattering by the nanoparticles is weak, it can still be discerned in the light scattering spectrum by the plasmon-resonant band near 540 nm. We emphasize that these spectra are obtained from diluted bulk solutions in cuvettes using a bright white light source and are not single-particle spectra. The measurement of this weak scattering is relatively sensitive to even minor quantities of scattering impurities and tiny air bubbles. Care was taken to avoid these, by careful filtration and also by letting the samples rest and equilibrate before measurement. The experimental scattering efficiencies at the scattering maximum are included in Table 1, and are between 3 x 10 -3 and 5 x 10 -3 . A simple, idealized-model calculation on isolated 12 nm diameter perfect gold nanospheres in a medium of refractive index 1.33 (water) using Mie theory (see Supporting Information) yields 2 x 10 -3 , which is close to the experimental values.

The experimental values are marginally higher than the theoretical values, due to the particle size distribution, deviations from spherical shape, and the local refractive index of the ligand shell. These are not taken into account by the simple theoretical model. The Mie calculation further confirms the spectral shape of the QENLS spectrum (Supporting Information, Figure S5). This demonstrates the relevance of the QENLS spectrum for the characterization of plasmonic nanostructures in solution.

There is very little difference in the light scattering by the DNA-linked AuNP dimers compared with the 'monomer' ssDNA-AuNPs monoconjugates. Similarly to the extinction spectra, the scattering spectra do not show any distinct features that would indicate strong plasmonic interaction between the nanoparticles in these dimer structures. The DNA linkers create interparticle distances which are too large for such plasmonic interactions to occur. As discussed above, plasmonic interactions critically depend on the interparticle distance and the plasmonic properties of the particles.

Microfluidic measurement of diffusion coefficients

In order to ensure that the absence of changes in the extinction and scattering spectra was not due to unexpected dissociation of the dimers, we studied the diffusion behavior of the nanoparticle dimers in solution. We modified our previously described [33] microfluidic method for measuring diffusion coefficients to include a spectroscopic flow cell. The method is based on measuring the (lateral) diffusive mass transfer of analyte from the analyte solution to the pure solvent while both liquids are flowing side-by-side in parallel laminar flow inside a (rectangular) microfluidic channel. Both liquids are injected continuously, at equal volumetric flow rates, and the measurement is done at steady-state.

This method is different from the more well-known Taylor Dispersion Analysis (TDA), which is also based on microfluidic laminar flow. TDA has been used for instance to measure diffusion coefficients of small molecules, [34] polymer particles, [35] and inorganic nanoparticles. [36] In TDA, a short plug of analyte solution (ideally, a 'delta' pulse) is injected into solvent flow pumped through a long capillary tube (0.5 ... 5 m, typically). The injected analyte pulse broadens as a result of the combination of Fickian diffusion and the Poiseuille flow velocity profile in the (cylindrical) tube. [37] The effective diffusion of the analyte is longitudinal, along the axis of liquid flow. The broadening analyte peak (which approaches a Gaussian shape for long enough tube lengths) is measured using typical chromatographic detectors (UV absorbance flow cell, fluorescence, refractive index, conductivity), and analysis of its shape gives the diffusion coefficient. Measurement times are several tens of minutes.

In contrast to TDA, the diffusion of the analyte in the present microfluidic measurement takes place perpendicularly to the axis of liquid flow. It is a steady-state technique with continuous injection of both the analyte solution and the pure solvent. The length of the microfluidic coflow channel is 5 cm, which is short compared to the length of the capillary in TDA. The typical measurement times are of the order of a minute, altough the present set-up requires additional time to reach a stable steady-state before measurement due to dead volume and pump instabilites. The NP solution and the solvent are in contact and in parallel laminar flow at a specified flow rate in the central channel of microfluidic 'H'-circuitry (see Supporting Info), allowing NPs to diffuse laterally from the NP solution flow to the solvent flow.

Extending the original work, [33] we developed an improved analysis protocol in which diffusion coefficients are directly determined from individual optical extinction measurements at selected flow rates using the spectrometric flow cell. This new protocol is described in the experimental section.

The diffusion coefficients obtained through microfluidic measurement are listed in the first column of Table 2. Compared to small molecules, the diffusion of the gold nanoparticles is at least one order of magnitude slower; this requires very low flow rates in our set-up. We found that these were difficult to stabilize and prolonged times were necessary to reach a stationary state after changing the flow rate. This explains the large error bars, which particularly handicaps the determination for dimer-BC. The stability of the microfluidic measurement can be improved by further temperature stabilization, use of pressure-driven flow instead of syringe pumps and reduction of dead volume by integrating the observation flow cell in the microfluidic structure.

In spite of this experimental difficulty, we observe that the diffusion coefficient of bissulfonato(phenyl)-phenylphosphine (BSPP)-coated AuNPs was in line with the value expected for a 13 nm diameter sphere (12 nm core + 0.5 nm ligand shell), using the Stokes-Einstein-Sutherland relation, i.e. 3.8 x 10 -11 m 2 s -1 . Moreover, we observed that ssDNA-AuNP monoconjugates have a significantly lower diffusion coefficient than BSPP-AuNP. The diffusion coefficient is further reduced in the case of a dimer.

Two-photon photoluminescence

The DNA-linked AuNP dimers cannot readily be distinguished from the ssDNA-AuNP monoconjugates when steady-state light extinction and scattering spectroscopies are used.

Straightforward detection of the dimers is further complicated by their weak light scattering.

Microfluidic measurement of diffusion coefficients does indeed distinguish (hydrodynamically) between monomer and dimer, but this requires a separate experiment.

Below, we will show that the intrinsic multiphoton-excited luminescence from the AuNP monomers and dimers in solution provides a more sensitive and rapid "one pot" method for detecting and characterizing such samples.

Upon excitation of the nanoparticle solutions with 100 fs pulses of 800 nm light from a Tisaphhire laser (80 MHz repetition rate, 4.5 mW average power on the sample, 60x NA 1.2 water immersion objective), an upconverted emission band is observed in the 450-700 nm range. This emission is attributed to two-photon excited photoluminescence (TPPL). [18,38,[START_REF] Wang | Proc. Natl. Acad. Sci[END_REF] The TPPL of all monomers and dimers studied was similar, in terms of spectral shape and in terms of intensity. This was always in the same order of magnitude, varying by less than a factor of 2. Small differences in TPPL emission intensity between samples were observed, but these were not characterized and studied in detail.

In Figure 4 we show the TPPL spectra for the DNA-linked AuNP dimers, obtained using photon time-of-flight spectroscopy [18,20] (PTOFS). The TPPL emission was a broad band peaking near 540 nm, and reproduced the spectral shape of the linear light scattering spectrum. Such spectral similarity between photoemission and resonant light scattering is a general observation with plasmonic nanostructures. [20,[START_REF] Yorulmaz | [END_REF]41] The mechanisms underlying light emission by plasmonic nanostructures are still under debate, both for Stokes ('one-photon excitation') [20,[START_REF] Yorulmaz | [END_REF]42,43] and anti-Stokes upconversion ('multi-photon excitation') [14,18,44] emission which have been observed for plasmonic nanostructures. The TPPL mechanism has been far less studied in comparison to one-photon excited photoluminescence (OPPL). Similarly to OPPL, the resemblance of the luminescence spectra with the corresponding scattering spectra suggests that the mechanism is plasmonmediated. In a first step, a two-photon absorption process excites an electron from the d-band to the sp-band. Two models have been suggested for the mechanism of photon emission. In the first model, the emission results from the interband electron-hole recombination, which is amplified at the frequencies of the surface plasmon. [45,46] In the second one, luminescence originates from the radiative intraband deexcitation of the surface plasmons. [47,48] However, recent work [49] suggested that the term 'photoluminescence' should not apply, as in the case of plasmonic structure displaying very small interparticle gaps, the light emission might originate from an inelastic scattering process. Such a process would be similar to Raman scattering, with the difference that hot electrons in the gradient plasmon field mediate the energy exchange, instead of the vibrations that fulfill this role in 'standard' Raman scattering. The theoretical model from that work predicts a 100-fold increase in (one-photon excited) light emission going from monomer to dimer, which is not in agreement with experimental observations where monomers and dimers display similar light emission intensities. [42,43] Interestingly, the authors do suggest interband-mediated photoluminescence (PL) to be operative in monomeric plasmonic particles.

Agnostic about the exact photophysical mechanism, we choose to refer to the upconverted light emission observed under multi-photon excitation conditions as "two-photon excited photoluminescence" (TPPL). This is also the term most regularly used in recent literature to refer to this phenomenon. However, we do acknowledge that "upconverted light emission" may be a more fitting and general term.

A particularly attractive feature of the confocal measurement of TPPL in our set-up is the possibility to simultaneously obtain information on the hydrodynamics of the particles by analyzing the TPPL intensity fluctuations in the confocal volume due to Brownian motion, i.e. performing TPPL fluctuation correlation spectroscopy (TPPL-FCS). TPPL-FCS is similar fluorescence correlation spectroscopy, [50][51][52][53] but instead of (monophotonic) fluorescence it uses the multi-photon excited light emission from the plasmonic structures for probing the dynamics of the confocal volume. Excitation of the intrinsic luminescence of the plasmonic structure is a useful alternative to the introduction of molecular fluorescent tags [54][55][56] in the structures. One-photon excited photoluminescence FCS has recently been applied to study the hydrodynamics of gold nanorods via their instrinsic photoexcited light emission. [41] Typical TPPL-FCS results for a ssDNA-AuNP monoconjugate and the corresponding DNAlinked AuNP dimer are shown in Figure 5. The autocorrelation curves of the TPPL intensity in the confocal observation volume clearly display different shapes between the AuNP-B monoconjugate and the AuNP dimer. The autocorrelation data for ssDNA-AuNP monoconjugates can be described using a model involving only translational diffusion (Eqn. 6), assuming a 3D Gaussian beam. 225 nm and q = 0.075. The diffusion coefficients obtained from TPPL-FCS are listed in Table 2.

We found that the autocorrelation data for both dimers AD and BC requires a model including a rotational term, described by rotational time constant (Eqn. 7), which can also be expressed by the rotational diffusion coefficient . [57] (7)

The rotational diffusion coefficients were found to be = 7 (±0.8) x 10 4 s -1 for dimer-AD, and = 5.5 (±0.8) x 10 4 s -1 for dimer-BC. There is much noise on the autocorrelation at very short time lags. This results in a sizeable uncertainty on the time constant for rotational diffusion. However, in combination with the observation of a longer diffusion time, the appearance of this rapid rotational contribution demonstrates the hydrodynamic difference between ssDNA-AuNP monoconjugates and DNA-linked dimers, due to their different sizes.

The values for the rotational diffusion coefficients and the translational diffusion coefficients obtained from TPPL-FCS may be compared to theoretical model values calculated for nanorods with diameter d = 12 nm and length L = 33 nm (AD) or L = 74 nm (BC), respectively. Following the hydrodynamic model by Tirado et al. [58] the expressions of the translation diffusion coefficient and of the rotation constant are:

(8) (9)
The calculation yields = 2 x 10 -11 m 2 s -1 and = 7 x 10 4 s -1 for "AD-like" nanorods, and = 1.3 x 10 -11 m 2 s -1 and = 1.4 x 10 4 s -1 for "BC-like" nanorods. These values are in the same order of magnitude and display the same trends as those experimentally obtained for the dimers (Table 2), despite the rough approximation related to the shape of the object. The agreement with the simple model is better for AD dimer than for BC dimer. The former has the shortest linker between the two nanospheres, which may explain the better agreement.

This result indicates that the hybridised DNA linker is indeed rigidly extended between the components of the structure.

The combined theoretical and experimental results on the translational diffusion coefficient of ssDNA-AuNP monoconjugates and DNA-linked AuNP dimers illustrate that the diffusion coefficient of elongated objects (L = 33 nm and L = 74 nm for a width of 12 nm) cannot be estimated simply from the Stokes-Einstein equation using the long axis as the hydrodynamic radius, but requires more elaborate hydrodynamic models. In the same vein, it has recently been shown that attaching a single long rigid rod-shaped DNA molecule (68 bp, 23 nm) to a 6 nm diameter nanosphere leads to only a small increase in effective hydrodynamic Stokes radius (3.2 nm to 5.8 nm), well below the additional length provided by the rod-like molecule. [59] It is interesting to compare the translation diffusion coefficients obtained through TPPL-FCS and microfluidics (Table 2). The two methods agree. The trend in diffusion coefficient between ssDNA-AuNP monogconjugates and DNA-linked AuNP dimers, and the order of magnitude of the coefficient, are reproduced by the microfluidic measurement. It should be noted that there is a large uncertainty on the microfluidic data, in particular for dimer-BC, which was measured at very low flow rates.

Beyond this direct comparison of the determination of hydrodynamic radii by the three different measurements described here, we can also look at studies of gravitational sedimentation [60][61][62] and analytical centrifigation [59,[63][64][65] of nanoparticle solutions. These also yield insight in the hydrodynamic behaviour of nanoparticles. Recently we studied the gravitational sedimentation of a DNA-linked dimer of 13 nm AuNPs. [62] This dimer has a structure similar to dimer BC, but a slightly different DNA linkage was used. At 277 K, we obtained D = 0.58 x 10 -11 m 2 s -1 , which, taking into account the change in viscosity of the water, would correspond to D = 1.1 x 10 -11 m 2 s -1 at 298K; this is in agreement with the values obtained by TPPL-FCS and microfluidics. In addition to the diffusion coefficient, such measurements yield the sedimentation coefficient, which also critically depends on particle shape. [59]

Conclusion

TPPL combined with PTOFS and FCS provides a sensitive method to detect and characterize even the 'weakly plasmonic' assemblies studied here which do not efficiently scatter light and whose plasmonic spectra do not show a clear difference between monomeric species and dimeric assemblies. In contrast to linear optical spectroscopy, which is carried out in typical spectroscopic cell volumes (3 mL), TPPL is measured in a small confocal volume, typically in the sub-picolitre range, the entire sample being a droplet (~ 50 µl). Such a confocal configuration is compatible with detection in capillaries, such as those found in microfluidics or analytical chromatography.

For the type of DNA-linked gold nanosphere dimers studied in this work, it is the hydrodynamic behavior measured using TPPL-FCS which carries the relevant information that allows monomeric and dimeric objects to be distinguished. The monomers and dimers were measured separately, after gel electrophoresis. It should be noted that it may be difficult to detect the simultaneous presence of monomers and dimers in a sample of unknown composition using either the microfluidic method or TPPL-FCS. Without prior knowledge on the diffusivity of either the pure monomer or the pure dimer, noise on the measurements will often lead to satisfactory fits to the data with single-component models and a single average diffusion coefficient. However, when prior knowledge about the behaviour of one component is available, changes in the measurements relative to the measurement of the pure component can then be interpreted in terms of a multi-component model indicating the presence of an additional species. Also, for series of samples of different monomer-to-dimer ratios one may be able to build global models, where all data are analyzed using the same set of diffusion coefficients for the different species.

In this context, it is of interest to envisage extension to even more complex samples consisting of several populations of NP assemblies. Whereas microfluidic diffusion experiments have as yet only addressed analysis of solutions containing mixtures of molecules and nanoparticles with large differences in diffusion coefficients, [66][START_REF] Werts | Proc. SPIE[END_REF][START_REF] Hatch | [END_REF] work in FCS has explored the analysis of samples containing several sizes of nanoparticles, [69][70][71] and demonstrated the possibility of distinguishing different populations of objects within a single sample. The success of such analyses is affected by experimental noise, and depends on the availability of a priori knowledge on the sample composition that can be included in the model for fitting the data. Identification of different populations in FCS and microfluidic experiments may be greatly facilitated if differences in optical spectra exist between these popuations, such as demonstrated earlier [23] for mixtures of monomers and dimers with different spectral response. For the present set of samples, however, such spectral distinction is not possible.

Our study shows that TPPL of small AuNPs is bright enough not only to detect and image AuNPs but also to study their spectral and hydrodynamic properties. We anticipate that this may find application in NP-based nucleic acid detection.

Experimental details

Synthesis and purification of ssDNA-AuNP monoconjugates and DNAlinked dimers

A schematic illustration of the route to make DNA-gold nanoparticle monomers and dimers is shown in Figure S1 (Supporting Information). In summary, four solutions of DNA-gold nanoparticle monoconjugates were prepared by mixing bis-sulfonato(phenyl)phenylphosphine (BSPP)-coated AuNPs with one of the four thiolated ssDNA in a 1:1 ratio.

These were subsequently purified by gel electrophoresis. The different ssDNA oligonucleotides are labeled A, B, C, D. The DNA sequences are shown in Supporting

Information, Table S1. The DNA-gold nanoparticle monoconjugates were then mixed to create nanoparticle dimers through DNA hybridisation of the complementary oligonucleotide strands (A + D resp. B + C). [72] Agarose gel electrophoresis was used to purify the samples.

This resulted in solutions of AuNP-dimer with a short (26 bp) DNA link (dimer-AD) and

AuNP-dimer with a long (146 bp) DNA link (dimer-BC). The synthetic details and characterization of the purified nanoparticles are given in the Supporting Information.

Optical spectroscopy

Optical spectroscopy was carried out at ambient temperature (298 K) on air-equilibrated samples contained in standard 1 cm quartz or plastic fluorescence cuvettes. UV-visible extinction spectra were measured using an optical fiber-based system (Ocean Optics) incorporating a CCD spectrometer (USB4000-VIS-NIR) and a tungsten-halogen light source (LS1, 6.5 W, 3100 K) equipped with a BG34 colour correction filter.

Light scattering measurements were performed according to the methodology that we described previously. [13,20,23] The method uses a right-angle configuration, measuring only light scattered around 90°, assuming that the angular distribution of light scattering by the samples and the reference is identical. This is valid for gold particles smaller than about 100 nm. [73] The sample solutions were illuminated with white light (LS-1 tungsten-halogen light source). The scattered light was collected at a fixed angle of 90°, and analysed using a backthinned CCD spectrograph (Ocean Optics QE65000). All samples were diluted such that the optical density remains well below 0.05. A solvent background was subtracted from all recorded spectra, and the background-subtracted raw spectra were corrected using Ludox as the perfect Rayleigh scatterer. [25] In the present work, the light scattering spectra were normalized such that the maximum has the value of the scattering quantum yield at that wavelength, as explained above.

The Ludox reference sample consisted of the supernatant of a Ludox SM30 (Aldrich) suspension centrifuged for 1 h at 9700 x g, which was diluted 200 times in 0.05 M NaCl. For each measurement series, three Ludox reference samples were prepared, and each reference sample was characterised using its value, by fitting the function to the experimental Ludox extinction spectrum. The baseline value enables for correction for very small differences in baseline, but should be very close to zero. If this is not the case, a new reference sample is prepared. Finally, it was verified that all three Ludox samples gave identical scattering spectra, in both shape and intensity. The average value of the three Ludox samples was used.

Where appropriate, the extinction and scattering spectra were smoothed using the Whittaker-Eilers (WE) algorithm [74] to reduce noise and bring out the spectral shape more clearly. The WE smoother, which conserves both spectral shape and peak intensity and is simpler and more efficient than the Savitsky-Golay [75] filter, was programmed in Python using the scientific 'numpy' and 'scipy' libraries [76] (see Supporting Information).

Microfluidic measurement of diffusion coefficients

The microfluidic measurement of diffusion coefficient is based on the microfluidic 'H-filter'. [77] We adapted our previously described microfluidic method for measuring diffusion coefficients [33] to include a spectroscopic flow cell (SMA-Z-10 Ultem, FIAlab Instruments, Seattle WA, USA) which was used to measure the optical extinction spectrum using the fiber-coupled spectrometer cited above. The long (1 cm) path length of the flow cells enables precise measurement of optical density (OD), even at low concentrations.

The measurement is based on determining the extent of the diffusive mass transfer from the flow of nanoparticle solution to the flow of pure solvent, which are continuously injected at separate inputs of the microfluidic circuit (Supporting Information, Figure S6) and flow parallel after meeting at a 'T'-junction, enabling diffusive mass transfer to occur. At the end of the interaction zone, the flow is split in two by another 'T'-junction (thus constituing an 'H'filter circuit). The extent of diffusive transfer between the two flows can be determined from the gain in OD of the exiting solvent flow (which will carry the subscript "B"), and/or from the loss in OD from the exiting nanoparticle solution flow (subscript "A"). We measured the OD of the solvent flow, . The extent of diffusion is defined here in terms of the concentrations of nanoparticles in the flows exiting the H-filter, and (their sum is equal to the injected nanoparticle concentration). For a measurement of the concentration at exit "B", we have Equation 10.

(

) 10
Note that this definition is (slightly) different from the definition in our initial work; [33] the present definition leads to in case of no diffusive transfer occurring, and to for diffusive transfer being complete. The overall concentration of the injected nanoparticle solution ( ) was measured by stopping the injection of the pure solvent, causing only the pure nanoparticle solution to exit at both exits and traverse the flow cell. On the other hand, when injecting only pure solvent, the baseline for the extinction measurement was recorded.

At a given volumetric flow rate (m 3 s -1 ; this is the sum of the two entering flow rates), we can theoretically calculate the extent of diffusion for a given diffusion coefficient . For this, it is convenient to convert the flow rate into a (device-independent) measure of the interaction time, (Equation 11), using channel length , channel width , and channel height .

(

) 11
Using the analytic solution of the diffusion equation, [33] we obtain Equation 12for the presently defined . This sum has to be evaluated numerically. For sufficiently large values of the series converges rapidly, in which case only a few terms are needed for a reliable result (sometimes even only the first term). [33] (12)

When has experimentally been measured at a certain specified flow rate , can be found by solving for D. This needs to be done numerically, for example using the secant method, since there is no direct inverse expression for Equation 12. (When only the first term of the series in Equation 12 is significant, there is a direct analytic inverse expression, but this feature is not used here.)

The experimental flow rates were chosen such that the measured was in the range 0.1 ... 0.7.

For each sample, several determinations of were carried out, at various flow rates over

Two-photon excited photoluminescence (TPPL)

The set-up for TPPL has been described previously. [20] Briefly, the experiments use a scanning stage confocal microscope. They are performed in air and at ambient temperature in a droplet of sample deposited on a clean coverslip. The sample is illuminated by a a titanium-sapphire femtosecond laser (wavelength 800 nm, 80 MHz repetition rate, 100fs pulse duration) through a high numerical aperture water-immersion objective (N.A.=1.2, 60x Nikon). The luminescence of the particles diffusing inside the excitation volume is collected by the same objective and is directed to a 50% fiber coupler after passing through a dichroic mirror (Semrock FF720SDiO1). Matching between the collected beam profile and the fiber core is ensured by a telescope. The collected light is filtered by a short pass filter (Semrock FF016-680/SP) to remove the residual laser light.

One fiber of the coupler is directly connected to an avalanche photodiode. This path allows detecting the bursts of luminescence of the freely diffusing particles. A long additional fiber (length 100 m) is inserted in the path of the second fiber before the signal is detected by a second avalanche photodiode. This path is devoted to the spectral analysis of the bursts of luminescence by the photo time-of-flight method as already described previously. [19,20] In PTOFS, the photons that travel into the long fiber have a transit time that depends on their wavelength according to the chromatic dispersion in the long fiber. As a result, the light flash that is detected by the APD connected to this path is stretched and the profile of the output signal is directly related to the spectrum of the incoming flash. The recording of the temporal traces of the emitted photons uses a time-correlated single photon counting. The correlation function used for FCS and the spectra of the data are derived by post processing with homemade software.

Quantum-efficiency normalized light scattering spectrum: comparison of experiment with Mie theory

. QENLS spectrum calculated using Mie theory and idealized 12 nm gold nanospheres in pure water (dotted line), comparison with experimental QENLS spectrum for monomeric "A" DNA-modified AuNPs (solid red line). The spectra have not been re-scaled, and come directly from theory and experiment, respectively, demonstrating that they are within the same order of magnitude (scattering efficiency at maximum ~ 10 -3 ). The Mie calculation was realized using a previously published Python computer program. [S6] Microfluidic diffusion coefficient measurements

Figure 1 .

 1 Figure 1. Single-stranded DNA-gold nanosphere monoconjugates (AuNP-A, AuNP-B, AuNP-C, AuNP-D), and the corresponding DNA-linked dimers with interparticle links of 26 ('short link' AD) resp. 146 bp ('long link' BC). DNA base sequences can be found in the Supporting Info.

Figure 2 .

 2 Figure 2. Normalized extinction spectra of ssDNA-gold nanoparticle monoconjugates and their resulting DNA-linked dimers in aqueous solution, average gold core diameter 12 nm. Top: short-link dimer AD; Bottom: long-link dimer BC. There is virtually no difference in the extinction spectra of the monomer AuNP and the dimers.

Figure 3 .

 3 Figure 3. Quantum-efficiency normalized light scattering (QENLS) spectra of ssDNA-AuNP monoconjugates and their corresponding DNA-linked dimers in aqueous solution. Top: AD dimer; Bottom: BC dimer.

Figure 4 .

 4 Figure 4. Two-pĥoton photoluminescence spectra from DNA-linked dimers (concentration 3.5 nM in water, excitation: 800 nm, 80 MHz, 100 fs pulses). The dotted lines are the corresponding linear light scattering spectra, scaled for comparison.

Figure 5 .

 5 Figure 5. TPPL-FCS (excitation 800 nm, 4.5 mW). Top and middle: TPPL intensity autocorrelation curves for ssDNA(B)-AuNP monoconjugate and long-link dimers BC, and fit using translational and rotation-translational diffusion, respectively. Bottom: best fits for monomer and dimer TPPL autocorrelation, rescaled to enable direct comparison, demonstration the longer translational time of the dimers and the presence of a rotational component at short time lag.

( 6 )

 6 photon excitation. Furthermore, with being the longitudinal waist of the observation volume. N is the mean number of particles diffusing simultaneously inside the excitation volume. Calibration of the focal volume using Rhodamine 6G in water gives =

  several days, giving access to the statistical uncertainty on the diffusion coefficient. The connection of the flow cell to the microfluidic system introduced a sizeable dead volume, which resulted in long times for the reading of the OD to stabilize, in particular at low flow rates. Drift and fluctuations during this time contribute to the relatively large confidence interval. The temperature was close to 298K, but fluctuated somewhat (±2 K) during measurement.The microsystem used had an interaction channel of height 140 µm, width 200 µm and length 50 mm. The precise microfluidic circuit is shown in the Supporting Info. Prior to each experiment the system was washed with Milli-Q water (200 µL) at a flow rate of 4 µL/min. Milli-Q water (Entry B) and the sample studied (Entry A) were introduced in the microsystem using two syringes (d= 2.5 mm) mounted on individual syringe pumps. The system was left to stabilize for one hour at the flow rate selected for each experiment (typically between 1 x 2 µl/min and 10 x 2 µl/min).

Figure S6 .

 S6 Figure S6. Microfluidic circuit used for the determination of diffusion coefficients. Blue arrows indicate fluid flow direction. The length of the flow interaction zone is 50 mm, with width 200 µm and height 140 µm. After splitting the flow, each channel follows a long serpentine channel for additional hydrodynamic resistance.

Table 1 .

 1 Spectroscopic data. Linear optical extinction and scattering maxima (λmax ext resp. λmax sca ), and scattering yield at the wavelength of maximum scattering cross section (φsca max ). Wavelength of maximum two-photon photoluminescence (TPPL)

	emission (	)
		extinction		scattering	TPPL
				(λ exc 800 nm)
		λ max ext	λ max sca	φ sca max
		[nm]	[nm]

Table 2 .

 2 Translational diffusion coefficients from microfluidics and from TPPL-FCS.

	Temperature was 298 K.
		microfluidics	TPPL-FCS
		D (m 2 s -1 )	D (m 2 s -1 )
	AuNP-BSPP	4.1 (±1.3) x 10 -11	n.m.
	AuNP-A	2.0 (±0.8) x 10 -11	2.3 (±0.2) x 10 -11
	AuNP-B	n.m.	2.0 (±0.1) x 10 -11
	AuNP-C	n.m.	2.3 (±0.2) x 10 -11
	AuNP-D	n.m.	2.2 (±0.2) x 10 -11
	short-link dimer AD	n.m.	1.6 (±0.1) x 10 -11
	long-link dimer BC	0.6 (±0.5) x 10 -11	1.1 (±0.3) x 10 -11
	n.m. = not measured

Acknowledgments

This work was supported by Dstl (UK) in the framework of the France-UK Ph.D. programme. AD and MW acknowledge funding by the Agence Nationale de la Recherche (France), grant ANR-2010-JCJC-1005-1 (COMONSENS).

SUPPORTING INFORMATION

Oligonucleotide synthesis and purification

Standard DNA phosphoramidites, solid supports, and additional reagents were purchased from Link Technologies Ltd, Glen Research and Applied Biosystems Ltd. All oligonucleotides were synthesized on an Applied Biosystems 394 automated DNA/ RNA synthesizer using a standard 0.2 μmole phosphoramidite cycle of acid-catalyzed detritylation, coupling, capping, and iodine oxidation. Stepwise coupling efficiencies and overall yields were determined by the automated trityl cation conductivity monitoring facility and in all cases were >98.0%. All -cyanoethyl phosphoramidite monomers were dissolved in anhydrous acetonitrile to a concentration of 0.1 M immediately prior to use. The coupling time for normal A, G, C, and T monomers was 60 s, and the coupling time for the thiolmodifier C6 S-S CE phosphoramidite monomer (from Link Technologies Ltd, 2126-F100) was extended to 600 s. Cleavage of the oligonucleotides from the solid support and deprotection was achieved by exposure to concentrated aqueous ammonia solution for 60 min at room temperature followed by heating in a sealed tube for 5 h at 55 °C.

The oligonucleotides were purified by reversed-phase HPLC on a Gilson system using an XBridge TM BEH300 Prep C18 10M 10x250 mm column (Waters) with a gradient of acetonitrile in ammonium acetate (0% to 50% buffer B over 30 min, flow rate 4 mL/min), buffer A: 0.1 M ammonium acetate, pH 7.0, buffer B: 0.1 M ammonium acetate, pH 7.0, with 50% acetonitrile. Elution was monitored by UV absorption at 300 nm. After HPLC purification, oligonucleotides were desalted using NAP-10 Sephadex columns (GE Healthcare). All oligonucleotides were characterised by negative-mode electrospray HPLCmass spectrometry in water, using a Bruker Daltronics micrO-TOF mass spectrometer, using an Acquity UPLC BEH C18 1.7 μm HPLC column (Waters), with a gradient of TEAA/CH 3 CN in TEAA/HFIP buffer, increasing from 5-40% buffer B over 14 minutes, with a flow rate of 0.1 mL min -1 (buffer A: 10 mM TEAA, 100 mM HFIP (H 2 O); buffer B: 20 mM TEAA (CH 3 CN)). Raw data was processed/deconvoluted using the DataAnalysis function of the Bruker Daltronics CompassTM 1.3 software package. Synthesis and characterization of ssDNA-AuNP monoconjugates and DNA-linked AuNP dimers Spherical gold nanoparticles of 12 ± 3 nm diameter were synthesised using the well established Turkevich et al. [S1] method modified later on by Frens et al. [S2] A solution of sodium tetrachloroaurate (100 mL, 1 mM) was brought to 100 °C with mild stirring. Once boiling, a warm solution of trisodium citrate (5 mL, 2% wt/V) was added with vigorous stirring. A colour change occurred from yellow to colourless to dark purple and finally to red. Once the red colour was obtained, the boiling and the stirring were maintained for 15 additional minutes before allowing the reaction mixture to cool down to room temperature.

Transmission electron microscopy (TEM) analysis of the citrate AuNPs is shown in Figure S2. Particles were then incubated with BSPP to increase the stability by replacing the citrate (15 mg). [S3] After overnight stirring, NaCl was added to aggregate the particles. Aggregation was confirmed by a colour change from red to dark blue. The aggregated particles were then subject to centrifugation at 25,000 x g for 30 min at 25 °C and re-suspended in phosphate buffer (20 mM phosphate, 5 mM NaCl) prior to DNA functionalization.

Two types of dimers with different linker lengths were assembled through DNA hybridisation. AuNPs (12 ± 3 nm) dissolved in phosphate buffer were incubated in a 1:1 ratio with disulfide-functionalized oligonucleotides (A, B, C or D, Table S1). An aqueous solution of BSPP (bis(p-sulfonatophenyl)phenylphosphine dihydrate dipotassium salt, 10 µL, 1 mg/20 µL) was added to the solution of disulfide-terminated oligonucleotide. This mixture was left while shaking for 1 h prior to being added to the nanoparticle solution. The AuNPoligonucleotide monoconjugates of each strand were purified using agarose gel electrophoresis (1.75% in 0.5xTBE) run at 100 V for 45 minutes. After diffusion from the gel the monoconjugates were centrifuged for 20 min at 25 000 x g and redispersed in hybridization buffer ( The ssDNA-AuNP monoconjugates and DNA-linked dimers were analyzed by agarose gel electrophoresis. As seen in the Figure S4a, both the short-link and long-link AuNP dimers (Lane 3 -AD and Lane 4 -BC, respectively) are delayed compared to BSPP-coated AuNPs or ssDNA-AuNP monoconjugates due to the increase in size of the assemblies. A further delay is noticed for BC dimers compared to AD dimers. This is attributed to their larger interparticle distance. After purification the dimer assemblies were characterised using transmission electron microscopy (Figure S4b).

All samples were deposited on Carbon Film 400 Mesh Copper grids for transmission electron microscopy (TEM) imaging. All TEM images were obtained on a Hitachi H7000 transmission electron microscope operating at a bias voltage of 75 kV. On the TEM images the difference between the interparticle distance (26 bp for dimer-AD and 146 bp for dimer-BC) cannot be noticed. Since in duplex DNA, each base pair ideally adds a length of 0.34 nm, the AuNP dimers should theoretically be separated by at least 8.84 nm (i.e. the theoretical length of the double stranded part of the linkers). However, the TEM image shows AuNPs in the dimers in close proximity. This observation is the result of the capillary drying forces and Van der Waals nanoparticle attractions occurring during the TEM grid drying and is not representative for the distance in solution. [S4]

Whittaker-Eilers smoother

The Whittaker-Eilers smoother was implemented in Python 3.6.1 with the numpy 1.12.1 and scipy 0.19.0 extensions (Anaconda Python Distribution, Anaconda, Inc., Austin, Texas, USA). The original Matlab program by Eilers [S5] uses the sparse Cholesky solver for solving the matrix equation involved in the smoothing procedure, but since a sparse Cholesky solver is not available in the 'scipy' sparse matrix library, we chose the sparse LU-decomposition based solver instead ('scipy.sparse.linalg.splu'). Our Python implementation was tested with the data provided with the original publication, [S5] and gave identical smoothing results. The core function is given here. """ Implementation of the Whittaker smoothing algorithm, based on the work by Eilers [1].

[1] P. H. C. Eilers, "A perfect smoother", Anal. Chem. 2003, (75), 3631-3636

The larger 'lmbd', the stronger the smoothing.

This implementation applies to complete data series (no missing points), sampled at equal intervals.


Florian Bouville

Etienne Portuguez

Yunfei Chang

Gary L Messing

Adam J Stevenson

Eric Maire

Loic Courtois

Sylvain Deville

Templated grain growth in macroporous materials

We demonstrate a facile method to produce crystallographically textured, macroporous materials using a combination of modified ice templating and templated grain growth (TGG). The process is demonstrated on alumina and the lead-free piezoelectric material Sodium Potassium Niobate (NKN). The method provides macroporous materials with aligned, lamellar ceramic walls which are made up of crystallographically aligned grains. Each method showed that the ceramic walls present a long range order over the entire sample dimensions and have crystallographic texture as a result of the templated grain growth process. We also present a modification of the March-Dollase equation to better characterize the overall texture of materials with textured but slightly misaligned walls. The controlled crystallographic and morphologic orientation at two different length scales demonstrated here can be the basis of multifunctional materials.

I. Introduction

Single crystals are used in many applications to take advantage of crystallographic anisotropy that maximizes the physical properties of materials along specific crystal directions. Single crystals are, however, frequently difficult to grow with adequate size, shape, compositional homogeneity, and cost. For this reason, a group of processing strategies has been developed to produce polycrystalline ceramics with crystallographically aligned, or textured, grains.

One particularly promising approach that has been widely applied is Templated Grain Growth 1 (TGG). For TGG, a small population of large template particles (5-50 µm) is dispersed in a fine particle matrix. The templates are aligned during green forming, usually by tape-casting, and epitaxial grain growth from the templates results in microstructures constituted of large and aligned grains. The texture quality of the final material is a function of the template alignment after green forming, the composition of the system, and the sintering conditions.

To date, TGG and texturing methods have produced monolithic ceramics and microstructure composites with improved properties (e.g. mechanical, piezoelectric) relative to random ceramics. Such processing strategies are nevertheless unable to produce some types of composite architectures that combine controlled macroscopic porosity with textured ceramic layers. We propose here a modified ice templating approach to fabricate porous, composite TGG structures.

Ice templating is a well-established processing route for porous materials 2, 3 where a temperature gradient across a suspension causes ice crystals of the liquid to nucleate and grow, rejecting the solid particles and forming the template of a porous structure. Subsequently, the ice crystals are removed by sublimation, leaving behind pore spaces separated by densely packed walls of the primary particles from the original suspension. Subsequent processing, like sintering, can be used to control the microstructure of the particle walls imparting strength or other desired physical properties.

Ice templating is also a promising approach for hierarchical assembly of complex structures [START_REF] Deville | Ice templating, freeze casting: Beyond materials processing[END_REF] because it can be used to simultaneously control several different size scales in the materials. Particles on the nm-µm scales are consolidated within walls that are µm-mm scale, and the samples obtained have dimensions in the millimeter to centimeter range. This hierarchical aspect makes it an ideal tool to realize composites with various connectivities and, at the same time, control the microstructure of each component. For instance, ice-templating was used to obtain 3-1 piezoelectric composites [START_REF] Lee | Piezoelectric Properties of PZT-Based Ceramic with Highly Aligned Pores[END_REF] where the ceramic phase was a randomly oriented polycrystal. Such materials have the electromechanical coupling coefficient of a bulk material combined with adaptive acoustic impedance.

In order to combine the composite architectures possible by ice templating with oriented ceramics made by TGG, it is necessary to align template particles during the ice templating process. Recently, anisotropic particles such as graphene [START_REF] Qiu | Biomimetic superelastic graphene-based cellular monoliths[END_REF] and alumina platelets [START_REF] Hunger | Platelets self-assemble into porous nacre during freeze casting[END_REF] were aligned by ice templating, but the alignment has always been obtained only locally; anisotropic particles within each wall were aligned relative to one another, but misorientation between the individual walls meant that the texture was not observed over the entire sample . In order to extend the texture developed within the individual walls to the entire sample, the walls need to be ordered over the entire sample. Such a lamellar structure can be the basis for 2-2 and 3-2 composites. Some modifications of the process have been developed to obtain lamellar pores in samples of large dimensions 8 but have proved hard to replicate.

In this study we present a method that combines ice templating and TGG. We first demonstrate how to make textured, macroporous alumina as a model system and then apply the process to sodium potassium niobate, NKN, a promising lead-free piezoelectric composition. We also show that the ceramic walls produced during ice templating can be aligned based on the application of a second thermal gradient during the freezing to produce 2-2 type composites with ordered lamellar macropores between textured NKN layers. Because of the complex interconnections and morphologies of the textured and ice templated materials, standard tools like XRD rocking curve analysis or Lotgering factor are insufficient to characterize the structure. Therefore, we propose a different strategy that couples X-rays diffraction (XRD) and morphological descriptors with a modification of the March-Dollase equation.

II. Experimental procedure

For the alumina samples, commercially available alumina platelets (RonaFlair White Sapphire; produced by Antaria ltd, sold by Merck KGaA) with 8 µm diameter and 500 nm thickness were used as template particles and isotropic alumina (TM-DAR, Taimicron) of 100 nm as matrix particles. Nanoparticles of silica (Nexsil 20K, diameter 20 nm, provide by Nyacol) and calcium carbonate (Sigma Aldrich) were added as liquid phase precursors in 75:25 molar ratio of SiO2:CaO. The matrix powder, liquid phase precursors and a binder (PEG20M, 4 wt. % of the powder mass, Sigma Aldrich) were mixed with distilled water and ball-milled for 20h and the template particles were added only three hours before the end of the milling step to avoid any excessive breakage of the particles.

For conventional ice templating, the slurry contained 20 vol.% of solid which comprised 9.8 vol% of templates, 88.5 vol.% of matrix powder, and 1.7 vol.% of liquid phase SiO2+CaO. The slurry was then poured into a cylindrical Teflon mold and placed in contact with a copper cold plate. Temperature was controlled by circulating refrigerated silicone oil through the copper plate, and the freezing rate was -1°C/min. Once the sample was completely frozen, it was removed from the mold and freeze dried for at least 48 h in a commercial freeze-dryer (Free Zone 2.5 Plus, Labconco, Kansas City, Missouri, USA) to ensure a complete removal of the ice crystals.

In order to align the ceramic walls during ice-templating, freezing took place while the slurry flowed over the freezing surface. A rectangular mold (2 x 10 x 3 cm 3 ) made of silicon rubber was placed on an inclined copper plate. The slurry was then introduced at the top end of the mold and allowed to flow down the inclined plane of the copper plate as it froze. Slurry that reached the bottom of the mold was recirculated using a peristaltic pump. Up until the completion of the freezing, the flow was maintained at 70 cm 3 /min. A cooling rate of -1°C/min was used for all the samples. Once a first layer (of around 5 mm in thickness) of aligned crystals was frozen, the slurry recirculation was turned off, the copper plate was leveled, and the mold was filled with the remaining slurry. A thermal camera (ThermaCAM E45, FLIR, Croissy-Beaubourg, France) was used to measure the temperature of the flowing suspension during the solidification of the first layer. This camera has a sensitivity of 0.1°C and can measure temperature down to -10°C. Once freezing was completed, the samples were freeze-dried under conditions identical to those used for conventional ice templated alumina.

The sintering cycle of alumina samples frozen at -1°C/min was chosen in accordance with the study by Pavlacka et al. [START_REF] Pavlacka | Processing and mechanical response of highly textured Al2O3[END_REF] with a sintering step at 1550°C for 90 minutes. For SEM observations, the samples were fractured and thermally etched at 1450°C for 20 minutes to better reveal the grain boundaries.

For NKN samples, anisotropic sodium niobate (NNT) platelets 15 µm in diameter and 1 µm thick were synthesized for use as template particles, and as well as sodium potassium niobate (NKN) particles 0.5 µm in diameter were produced to be used as the primary particles. The NNT particles were prepared by Topochemical Microcrystal Conversion [START_REF] Poterala | Mechanistic Interpretation of the Aurivillius to Perovskite Topochemical Microcrystal Conversion Process[END_REF][START_REF] Saito | Lead-free piezoceramics[END_REF] of bismuth niobate seeds according to the procedure detailed by Chang et al [START_REF] Chang | Microstructure development and piezoelectric properties of highly textured CuO-doped KNN by templated grain growth[END_REF] . The NKN particles were made by a conventional mixed oxide synthesis [START_REF] Chang | Microstructure development and piezoelectric properties of highly textured CuO-doped KNN by templated grain growth[END_REF] . 1 mol % of copper oxide (Sigma Aldrich) was added as liquid phase precursor. The slurry preparation conditions and freezing conditions for NKN were identical to that of alumina. The sintering cycle of the NKN sample was chosen in accordance with the study of Chang et al. [START_REF] Chang | Microstructure development and piezoelectric properties of highly textured CuO-doped KNN by templated grain growth[END_REF] , with a sintering step at 1115°C for 4h and an annealing step at 1125°C for 3h.

SEM pictures were taken with a Supra 55 microscope (Zeiss) on gold coated samples. Samples were scanned on a Phoenix tomograph with a 3.4 µm 3 voxel size on a disk sample of 3 mm diameter and 3 mm in high. The directionality measurement was made with the plug-in named "directionality" of the free software Fiji [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF] . XRD measurements were performed on a D5000 device (Brüker).

III. Results and discussions (1) Platelet Alignment in a Particle Matrix by Ice Templating

There are several examples where the growth of ice crystals effectively organizes anisotropic particles [START_REF] Qiu | Biomimetic superelastic graphene-based cellular monoliths[END_REF][START_REF] Hunger | Platelets self-assemble into porous nacre during freeze casting[END_REF] , but for TGG a minor fraction of platelets must be aligned within a powder matrix. Fig. 1a shows that the platelets in the green body are generally aligned in the same direction as the ceramic wall, although some degree of misorientation is observed. We believe that compaction between the growing crystals aligns the platelets, similar to the alignment of platelets during unidirectional pressing. The most important differences between the two situations are the magnitude of the compaction force and the fact that ice templating takes place in a colloidal suspension. The key parameters to act on platelet orientation are interparticle forces, steric impingement, and, in some special cases, preferential surface interactions between the platelets/ice crystals.

The resulting microstructure is shown in Fig. 1b and Fig. 1c. These samples have a lamellar structure where 10-20 µm thick lamellar pores are separated by 5-10 µm thick ceramic layers. In Fig. 1b, large tabular grains are easily observed within the ceramic walls, and the orientation of such grains is generally parallel to the border of the walls. The grains keep their preferred orientation even when the wall itself is divided or wavy. Fig. 1c shows a higher magnification image of the ceramic walls, and most of the grains in the wall are aligned within 15° of the wall orientation. This measure was evaluated by analyzing the grain orientation on SEM pictures [START_REF] Jeulin | Segmentation of 2D and 3D textures from estimates of the local orientation[END_REF] within the ceramic walls on thermally etched microstructures.

(2) Control of the lateral wall orientation by freezing under flow Fig. 2a shows a microstructure typical of ice templated ceramics. The sample microstructure is divided into individual domains where the walls present a short range order, but the orientation distribution of the walls over the entire sample is random (Fig. 2c ande). No long range order is present. While the images in Fig. 1 show that TGG is possible within individual walls by ice templating, we must also align the walls to benefit from texture over the whole sample.

Controlling the lateral orientation of the ceramic walls is an important challenge in ice templating and is critical to realizing the improved properties we seek from the textured ceramic walls. Previously, the alignment of ice templated walls has been achieved by combining a patternedice nucleation surface with gentle vibration during freezing [START_REF] Launey | Designing highly toughened hybrid composites through natureinspired hierarchical complexity[END_REF][START_REF] Münch | Architectural Control of Freeze-Cast Ceramics Through Additives and Templating[END_REF] . Because this process is inherently linked to a specific freezing setup and has proven difficult to replicate, we developed a different and hopefully more robust alignment technique.

Since ice crystal orientation is intimately related to the direction and magnitude of the applied temperature gradient [START_REF] Waschkies | Investigation of structure formation during freeze-casting from very slow to very fast solidification velocities[END_REF] , so adding a second gradient could orient the crystal growth in a direction imposed by the linear combination of the two gradients. Obviously, a second temperature gradient could be imposed externally, but we developed a simpler process where a temperature gradient is naturally generated as the slurry flows along a cooling plate.

Because suspensions are viscous, a parabolic velocity gradient occurs during flow (Fig. 3), and the slurry cools more rapidly along the sides of the mold (where the viscosity is very low) than in the center (where the viscosity is high). Thermograms (Fig 4a) taken at the beginning of the freezing process showed that the temperature difference between the side and the center can be up to 20°C with a maximum lateral temperature gradient approaching 50°C/cm. The temperature profile is asymmetric (Fig. 4d) because the slurry is introduced at a corner of the mold and flows both down the incline and across the width of the mold.

During ice templating, the local temperature gradient dictates the solidification front velocity and consequently the ice crystal size [START_REF] Waschkies | Investigation of structure formation during freeze-casting from very slow to very fast solidification velocities[END_REF] , so the microstructure of ice template samples may change if the temperature gradient changes during the process. Fig. 4e shows the temperature profile and lateral gradient after 5 minutes of freezing under flow, and the maximum lateral temperature gradient remains around 50 °C/cm (Fig. 4e). The maximum lateral temperature gradient increases significantly in the last solidification steps, where it can reach 120°C/cm (Fig. 4f) because there is no longer any fluid flow, which helps maintain the constant temperature gradient throughout most of the process, at this late stage of the process. In the samples presented here using the freezing under flow method, the microstructure is similar from one side to the other in the material due to the fact that the process is self-regulating and maintains the same lateral temperature gradient. Domains can still be found in the microstructure (Fig. 2d) but their orientation mismatch is small compared to samples frozen under the typical static conditions (Fig. 2e and Fig. 2f). Thus, a significant benefit of the freezing under flow process is that the maximum lateral temperature gradient is constant throughout most of the process.

In order to characterize the alignment between the ceramic walls, we imaged the samples using X-ray tomography (Fig. 5a), computed the wall orientations [START_REF] Jeulin | Segmentation of 2D and 3D textures from estimates of the local orientation[END_REF] , and fit the data with a Gaussian distribution to obtain the wall orientation distribution function (Fig 5b andc). We also evaluated the wall orientation distribution function as a function of depth in the sample, and the standard deviation of the orientation distribution function shifts from 16° to 10° (Fig. 5d) in the solidification direction. Such dispersion could arise from the sample preparation or microstructure evolution during the freezing. We note that the changing microstructure observed here is in the vertical direction, and is thus not caused by the lateral temperature gradient imposed by the freezing under flow process. In all measurements, more than 80% of the sample volume is textured. Freezing under flow is thus able to induce a long range order of ice crystals over a large sample by creating a second self-regulating gradient during the solidification.

(3) Texture measurement in composite, layered materials

The final texture of the composite is a result of the superimposition of two distinct alignments present at two length-scales: (1) the grain alignment in the wall and (2) the wall alignment in the composite. The orientation of grains in bulk textured materials can be measured by several XRD methods, like pole figure or rocking curve [START_REF] Brosnan | Texture Measurements in 001> Fiber-Oriented PMN-PT[END_REF] , but these methods provide information on the first microns below the sample surface due to the limited depth of penetration of X-rays, which in our case corresponds only to the first wall. Thus, XRD based methods are able to measure the grain alignment within the wall, but they cannot characterize the alignment of the ceramic walls throughout the composite. Any functional property of a textured material is directly linked to the dispersion of crystallographic orientation of the whole sample, not just the texture measured in the first few layers. Thus, XRD measurement only provides partial information on the texture of the macroporous sample synthetized here.

One method of characterizing the orientation distribution in materials made by templated grain growth is the March-Dollase (MD) distribution [START_REF] Brosnan | Texture Measurements in 001> Fiber-Oriented PMN-PT[END_REF][START_REF] Pavlacka | Processing and mechanical response of highly textured Al2O3[END_REF] (1).

𝑀𝐷 𝑓, 𝑟, 𝜔 = 𝑓 𝑟 2 𝑐𝑜𝑠 2 𝜔 + 2 -3/2 + (1 -𝑓) (1)
The porous material made here can be considered as a combination of layers, each one of those slightly misoriented with respect to the surface (2), as depicted in Fig. 6a. Equation 1 can be extended to account for the misalignment of an individual ceramic wall by introducing an angle, a n , which characterizes the angle between the ceramic walls and the reference frame of the sample/measurement:

𝑊 = 𝑓 𝑟 2 𝑐𝑜𝑠 2 (𝜔 -𝛼 ) + 2 ( -) -3/2 + (1 -𝑓) (2)
Because a represents the shift between the reference frame and the wall orientation, it follows the Gaussian distribution of wall orientations determined by tomography (Figure 4). By adding a large number of MD functions with f and r parameters determined for a single wall by XRD, but shifted by an angle, following the Gaussian distribution determined in Figure 4, one can model the behavior of a textured composite (3).

𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 = 𝑓 𝑟 2 𝑐𝑜𝑠 2 (𝜔 -𝛼 ) + 2 ( -) -3/2 + (1 -𝑓) 1 (3)
𝛼 " ~𝑁(0, 𝜎), where N is a Gaussian distribution of mean 0 and standard deviation s .

As we know the MD functions and the Gaussian distribution of the wall, we can calculate the FWHM of composite distribution but also model its evolution with the Gaussian and MD parameters. The FWHM of the composite as produced in this study is 36° (see Fig. 6b), which is relatively high compared to the measurements made on tape cast materials and even compared to the theoretical grain orientation (see Fig. 6b). This value is greater than both the FWHM of Gaussian distribution and MD function, 28° and 5.7° respectively.

To better understand the interplay between the wall alignment and grain alignment within the walls, we calculated the evolution of the composite FWHM versus the two parameters, the FWHM of the macrostructure of the walls and the FWHM of the grains within one individual wall in Fig. 6c.

As expected, reducing the FWHM of both distributions tends to decrease the FWHM of the composite. From our experimental data, it is clear that better aligning the individual ceramic walls during ice templating, rather than improving the texture within the walls, is more important for obtaining high texture quality composites in the future. The wall orientation distribution function could be reduced by optimizing the freezing under flow process by increasing the magnitude of the lateral temperature gradient (thus an increase in the flow velocity). Indeed, the texture quality within the walls could theoretically be improved by improving template alignment within the walls, but it would be a relatively small increase given that the level of misorientation between the walls themselves is much greater (the smallest FWHM reported to date with alumina is 4.6°9).

(4) Textured piezoelectric composite

Given the results presented above for alumina, it is clear that ice-templating can texture grains in ceramic walls of a macroporous body and align such walls in two directions in a single processing step. The same process has been applied to a NKN powder in order to demonstrate that textured composites, like those required in some sensor and transducer applications, can be made in a single processing step. The microstructure of the porous sample is presented in Fig. 7a and Fig. 7b. The microstructure obtained (Fig. 7a) is similar to the alumina sample because the ice templating process is not strongly influenced by composition (physical characteristics of the particles, platelets, and the suspension are much more important). The large grains present in the sintered wall (Fig. 7b) are cube shaped, due to the weakly orthorhombic crystallographic structure of NKN. As was the case in alumina, the ice crystal growth effectively aligned the NNT. Dense and textured walls are obtained after sintering.

The presence of preferred grain orientation has been investigated by XRD measurements. Two XRD patterns are shown in Fig. 7c: the bottom one represents a randomly-oriented sample obtained by conventional mixed oxide NKN powder and the top XRD pattern the porous textured composite. A clear texture of the <00l> plane is present in the sample made by ice-templating. However the texture is not as good as in samples made by tape-casting [START_REF] Chang | Microstructure development and piezoelectric properties of highly textured CuO-doped KNN by templated grain growth[END_REF] and the Lotgering factor of the sample is only 21%.

IV. Conclusions

We demonstrated that ice-templating combined with templated grain growth is an effective method to produce textured, macroporous materials. The growth of ice crystals was used to align platelets that are used afterward as seeds for templated grain growth. To retain the benefits arising from this local texture, a 'freezing under flow' method has been developed to control the long range order of the lamellar ice crystals and thus ensure both short and long range order of the grain orientation. This novel method is robust and independent of the material used. The original dispersion of orientation of the ice crystals compromises the optimization of the functional properties and needs to be reduced, as suggested by the model developed here. Such reduction could be achieved by modifying the freezing conditions, which requires a more comprehensive study of the process parameters. The principles demonstrated here could be the basis for hierarchical, multifunctional composite materials, including structural and piezoelectric ceramics.

Fig. 1 :

 1 Fig. 1: (a) SEM observations of the platelets (black and white arrows) alignment in the green body. (b) Close view of wall's organization after sintering, showing the correlation between wall and grain orientation. (c) SEM picture showing the high grain alignment.

Fig. 2 :

 2 Fig. 2: Comparison of randomly oriented ice-templated microstructure (a) and (b) oriented sample made by freezing under flow. Domains with long range ordered walls are represented with the same color in (c) and (d) for each sample, see reference 14 for details on the method. (e) and (f) represent the angular orientation histogram of pixel gradient in the image.

Fig. 3 :

 3 Fig. 3: Schematic representation of the freezing under flow setup, depicting the fluid velocity profile and a cross section perpendicular to the flow showing the two different orthogonal gradients.

Fig. 4 :

 4 Fig. 4: Thermal measurement during freezing under flow. The images represent the temperature of the flowing suspension at three different times: before the solidification starts (a), when nearly half of the layer is frozen (b) and before the end (c). The graphs (d), (e), and (f) represent the temperature profile in the middle of the sample and its derivative as a function of the distance for each selected time.

Fig. 5 :

 5 Fig. 5: Three-dimensional microstructure and morphological characterization of a sample made by freezing under flow. (a) Tomographic reconstruction of the sample. (b) Typical section of the reconstruction on which analysis is performed. (c) Histogram of the pixel fraction presenting a preferred orientation versus the considered angle of the image (b). A Gaussian fit is applied to this distribution and the lateral dispersion s, the amount of textured pixel and the fit accuracy are extracted. (d) Lateral dispersion as a function of the position in the sample.

Fig. 6 :

 6 Fig. 6: (a) Representation of the cubic grain textured wall slightly misaligned and the contribution of those walls in the material global orientation distribution. (b) Example of composites texture response for different conditions. (c) Evolution of the FWHM of the composite with respect to the FWHM of the constituent.

Fig. 7 :

 7 Fig. 7: (a) Microstructure of sample frozen under flow, showing the alignment of ceramic wall. (b) SEM picture of a wall showing the large grains. (c) Comparison of XRD pattern obtained with textured composite and non-textured sample (CMO stands for Conventional Mixed Oxide, reproduced from 12 ).

Acknowledgements

We acknowledge the financial support of the ANRT (Association Nationale Recherche Technologie) and Saint-Gobain through a CIFRE fellowship, convention #808/2010.