Tianming Lu
email: lu@isir.upmc.fr.

Écile Pacoret

David H Ériban
email: david.heriban@percipio-robotics.com

St éphane R égnier Abdenbi Mohand-Ousaid
email: abdenbi.mohand@femto-st.fr

Fellow, IEEE Vincent Hayward
email: hayward@isir.upmc.fr.

Stéphane Régnier
email: regnier@isir.upmc.fr.

Cécile Pacoret
email: cecile.pacoret@unige.ch

KiloHertz Bandwidth, Dual-Stage Haptic Device Lets You Touch Brownian Motion

Keywords: Haptic interface design, dual-stage architecture, dynamic modeling, compensation. !

This paper describes a haptic interface that has a uniform response over the entire human tactile frequency range. Structural mechanics makes it very difficult to implement articulated mechanical systems that can transmit high frequency signals.

Here, we separated the frequency range into two frequency bands. The lower band is within the first structural mode of the corresponding haptic device while the higher one can be transmitted accurately by a fast actuator operating from conservation of momentum, that is, without reaction forces to the ground. To couple the two systems, we adopted a channel separation approach akin to that employed in the design of acoustic reproduction systems. The two channels are recombined at the tip of the device to give a uniform frequency response from DC to one kHz. In terms of mechanical design, the high-frequency transducer was embedded inside the tip of the main stage so that during operation, the human operator has only to interact with a single finger interface. In order to exemplify the type of application that would benefit from this kind of interface, we applied it to the haptic exploration with microscopic scales objects which are known to behave with very fast dynamics. The novel haptic interface was bilaterally coupled with a micromanipulation platform to demonstrate its capabilities. Operators could feel interaction forces arising from contact as well as those resulting from Brownian motion and could manoeuvre a micro bead in the absence of vision.

INTRODUCTION

The human sense of touch is exquisitely sensitive to vibrations, and this over a significant band of frequencies reaching one kHz in healthy adult individuals [START_REF] Verrillo | Effect of contactor area on the vibrotactile threshold[END_REF]. Although the displacement detection threshold is function of numerous factors including finger temperature [START_REF] Verrillo | The effects of skin temperature on the psychophysical responses to vibration on glabrous and hairy skin[END_REF], contact condition [START_REF] Brisben | Detection of vibration transmitted through an object grasped in the hand[END_REF], age [START_REF] Verrillo | Age related changes in the sensitivity to vibration[END_REF], perceptual learning [START_REF] Dinse | Adaptation of inputs in the somatosensory system[END_REF], hydration [START_REF] Verrillo | Effects of hydratation on tactile sensation[END_REF], health, for a review see [START_REF] Skov | Effect of age and height on vibrotactile threshold among 1,663 u.s. workers[END_REF], among numerous other factors, people remain through their lives extraordinarily sensitive to small oscillatory and transient mechanical perturbations, especially when applied to the hand. As a result, haptic interfaces ought to be able to transmit high frequency signals to the hand, lest the information that these signals contain be lost or tainted.

Problem Addressed

The transmission of high frequency movements is a longstanding problem in mechanical design. Owing to structural properties, any mechanical structure is subjected to an interplay between elastic properties and mass distribution.

Although it is an infinite dimensional system, in a frequency band a mechanical structure may be characterized by a finite number of modes that are reflected in its spectral response to excitation. The presence of mechanical modes corresponding to resonances and anti-resonances are generally undesirable for accurate motion transmission. Thus, structural engineers usually restrict the range of transmission of frequencies from static loading to an upper limit set well below the first resonant or anti-resonant mode.

A simple thought experiment makes the problem at hand quite evident. Take a 15 cm-long, 5mm-diameter rod made of carbon fiber composite, the lightest and strongest material available today. The first mode of such a cantilevered beam is already at about 300 Hz and will get lower if anything is attached to the extremity.

A well accepted design wisdom aimed at increasing the mechanical bandwidth of an articulated structure calls for using parallel kinematic arrangements since the actuators can be grounded. These arrangements must nevertheless include cantilevered segments to achieve mobility. The result is that is hardly possible to design system with first modes at frequencies higher than one kHz, unless these arrangements have very small workspaces. It is difficult to achieve a bandwidth greater than 300 Hz [START_REF] Campion | The Pantograph Mk-II: A haptic instrument[END_REF] and some highend devices exhibit modes as low as 30 Hz [START_REF] Campion | Fundamental limits in the rendering of virtual haptic textures[END_REF].

To overcome this problem we constructed a dual-stage haptic interface design that achieves a flat frequency response in the whole haptic range. Low frequency movements are transmitted by a conventional kinematic arrangement up to its first resonant mode. Above a few hundred Hertz vibratory amplitudes become small, falling below one millimeter. Thus, higher frequency oscillations can be reproduced by an inertia-based, ungrounded actuator at the tip operating on the basis of conservation of momentum. Using a crossover technique combined with dynamic modeling, identification, and frequency compensation, an overall flat response over the target range was achieved.

Previous Works

The literature on the design of haptic devices is abundant, so only some pertinent designs are mentioned here. The frequency response of a device, although it is a key factor of performance [START_REF] Hayward | Performance measures for haptic interfaces[END_REF] [START_REF] Laycock | Recent developments and applications of haptic devices[END_REF], is rarely discussed, let alone measured, but a few numbers can be collected in the literature. These numbers are summarized in Table 1, as they are claimed by the corresponding references, although the method of measurement is rarely specified as recommended in [START_REF] Hayward | Performance measures for haptic interfaces[END_REF] in order to ensure a level playing field.

Dual-stage robotic design can be traced a long way back. The research work [START_REF] Sharon | The macro/micro manipulator: An improved architecture for robot control[END_REF] proposed a macro/micro manipulator architecture to enhance dynamic performance, but it was mainly focused on overall stability, accuracy improvement, and cycle-time reduction. The coarse-fine approach [START_REF] Stocco | A coarse-fine approach to forcereflecting hand controller design[END_REF] proposed a novel parallel coarse platform combined with maglev device to obtain both large workspace and desirable force capability. However, the evaluation of overall haptic bandwidth was absent. The Distributed Macro-Mini (DM 2 ) method described in the research work [START_REF] Zinn | Large workspace haptic devices-a new actuation approach[END_REF] suggested a straight-forward parallel control structure to partition the input control torques into low and high frequency components based upon low frequency base actuator's low pass filter characteristics. However, this approach strongly depends on the dynamics of actuators for channel separation and further control scheme must be established in order to achieve uniform response over desired bandwidth. Moreover, this method was not validated experimentally. Before us some authors proposed to augment devices with tip-mounted vibrotactile actuators as in [START_REF] Wall | A high bandwidth interface for haptic human computer interaction[END_REF], but as far as we know, vibrotactile performance was the only factor which was tested. A single degree-of-freedom dual-stage device achieving a wide bandwidth was described in reference [START_REF] Millet | The ultimate haptic device: First step[END_REF] [21] with a small motor coupled to a large one via a viscous transmission with the primary objective to reduce the overall apparent inertia. This approach, although effective to simultaneously improve several factors of performance, does not lend itself easily to be extended to multiple degrees of freedom. This is because achieving extra degrees of freedom implies adding additional structure, which will increase the overall apparent inertia and degrade the performance such as transparency and bandwidth. Other researchers developed high frequency devices taking advantage of feedback to extend the mechanical bandwidth as in [START_REF] Lee | A high-bandwidth force-controlled haptic interface[END_REF]. However, new design trade-offs arose between performance and the number of degrees of freedoms since the integration of multiple degrees-of-freedom reintroduces the issues related to the transmission of high-frequency movements.

In this paper, a new technique is proposed that aims to extend the bandwidth of haptic devices with uniform magnitude by the addition of a vibrotactile crossover. Commercial devices as well as homemade devices keep their full DOF and workspace while their frequency is extended at few cost. This technique is demonstrated here with a Pantograph and a ready-to-use vibrotactile device.

SYSTEM DESCRIPTION

Hardware

The haptic interface design proposed here is based on a dual-stage architecture comprising a proximal and a distal stage.

The proximal stage is a Pantograph haptic interface [START_REF] Campion | The Pantograph Mk-II: A haptic instrument[END_REF], see Fig. 1a, which is based on a planar parallel mechanism with two actuated degrees-of-freedom. The closed chain structure with grounded motors, and a stiff, light-weight transmission design provide optimized dynamic performance. It was shown in [START_REF] Campion | The Pantograph Mk-II: A haptic instrument[END_REF] that the Pantograph is able to resolve 2D displacements of the order of 10 µm.

The distal stage is a vibration transducer, Fig. 1 (right), (Haptuator, Tactile Labs, Montréal, Canada) operating on the principle of conservation of momentum as described in [START_REF] Yao | Design and analysis of a recoiltype vibrotactile transducer[END_REF]. This device comprises an internal moving magnet guided axially with respect to the case and actuated by a Laplace force acting between the magnet and the case. This actuator is efficient for high frequency and transient haptic feedback.

To couple these two stages to the load (user finger), the scheme given in Fig. 1c is chosen among the several configurations described in [START_REF] Mohand-Ousaid | Haptic interface transparency achieved through viscous coupling[END_REF]. Starting from the left, the Pantograph is grounded and coupled in series with the vibration transducer through an elastic element. In this part, the rectangular box and spring elements represent respectively the Pantograph's inertia and the elastic connection. Meanwhile, the vibration transducer, integrated inside the terminal assembly, is ungrounded and acts as an inertial actuator. Both stages are considered as a controllable source of force that acts on the last element of the scheme, the load. As a consequence of this arrangement, the Pantograph supplies the largest portion of rendered force covering low frequencies. While, the vibration transducer is responsible for transient effect covering high frequencies. The finger plate also included a three-axis MEMS accelerometer (MMA7361L, Freescale Semiconductors, Austin, TX, USA) to measure the signal transmitted to the finger on scale of -6 g to +6 g. This sensor was used for system identification and was essential for evaluating the performance of the whole interface. The device was interfaced to a computer via a signal acquisition hardware (DAQ PCIe 6259, National Instruments, Austin, TX, USA). The computer hosted a realtime Linux (RTAI) environment running signal processing algorithms at a 10 kHz sampling rate.

Dynamic Modeling

For the system described above, a lumped parameter model of the system was developed, see Fig. 2. This model highlights the fact that the mechanical coupling of the two channels is more complicated than a mere acoustic summation, like in a network of loudspeakers. The system has three components, namely the vibration transducer-the Haptuator-a direct mechanical transmission-the Pantograph-and the finger of the user. Dynamic modeling was considered along one single axis, x, around a nominal position in the central region of the Pantograph's workspace, because the apparent masses depend on configuration. The parameters of the system are listed in Table 2. The windings of the motors of the Pantograph apply a force, f , to the entire system via transmission shafts whose elasticity combines with those of the proximal links giving a combined elasticity parameter, k 1 . The Haptuator produces a Laplace force, denoted by f v which is applied to the terminal assembly in contact with the finger. The force applied to the mass of the suspended magnet is thus -f v . The magnet itself is guided by membranes modeled by elasticity and damping. The total force applied to the terminal assembly of mass, m h , is thus the sum of the actions of the finger, the Haptuator's suspension, the Laplace force, and the distal links. All these effects can be collected in matrix form by, where

k f b f k v b v m h m v b 2 k 2 haptuator distal links proximal links nger pantograph x v x h m 2 x 2 x 1 b 1 k 1 m 1 f f v -f v
F = M Ẍ + C Ẋ + KX (1)
X =       x h x v x 1 x 2       , F =       f v -f v f 0       , M =       m h 0 0 0 0 m v 0 0 0 0 m l 0 0 0 0 m 2       , C =       b 2 + b v + b f -b v 0 -b 2 -b v b v 0 0 0 0 b 1 -b 1 -b 2 0 -b 1 b 1 + b 2       , and
K =       k 2 + k v + k f -k v 0 -k 2 -k v k v 0 0 0 0 k 1 -k 1 -k 2 0 -k 1 k 1 + k 2      
.

The system inputs are the torques applied to the motors lumped into a single signal, the desired haptic image expressed in workspace, and the output is the acceleration of the terminal assembly, ẍh , or equivalently, the superficial skin layers of the finger in contact with the terminal assembly.

CHANNEL SEPARATION, IDENTIFICATION AND COMPENSATION

Crossover Design

The signal path begins with frequency separation by a filtering method borrowed from audio engineering known as a crossover. Crossovers can be optimally designed according to several criteria. A well-known crossover approach, widely applied to perform spectral partition, is the Linkwitz-Riley Filter. Such filters, constructed by cascading two Butterworth filters which have -3 dB gain at cut-off frequency, are therefore characterized by -6 dB gain at cutoff frequency. This means that compared to Butterworth crossover, it gives an overall amplitude response that is optimally flat and which is combined with good phase behavior [START_REF] Linkwitz | Passive crossover networks for noncoincident drivers[END_REF]. Linkwitz-Riley filters are typically fourth order filters with slopes of 80 dB/decade. Figure 3 depicts the information flow in the system with the two-way crossover. The manner in which the signals recombine is not evident and thus merits further investigation. The crossover filters separate the signal into two paths with different frequency contents. Two different mechanical components receive the signals and recombine them to transmit movement to the finger interface. The whole system thus should behave like an all-pass, unity filter, i.e. the magnitude must be faithful to that of the original haptic signal [START_REF] Harris | An extension of the linkwitz-riley crossover filters for audio systems and their sampled data implementation[END_REF]. Figure 4 shows the magnitude response of the Linkwitz-Riley fourth order crossover at pulsation, ω c , defined as follows, Because the Pantograph and the Haptuator share an overlapping frequency band, the cut-off frequency was selected to be the highest that the Pantograph could allow in order to minimize the delay introduced by the filters. The cut-off frequency must be chosen to satisfy all-pass filter requirement. This was achieved through identification as discussed next.

L(s) = ω 4 c D(s) , H(s) = s 4 D(s) , L(s) + H(s) = s 4 + ω 4 c D(s) , where
D(s) = s 4 + 2 √ 2ω c s 3 + 4ω 2 c s 2 + 2 √ 2ω 3 c s + ω 4 c .

Identification

Our objective was to design a crossover method to separate the low and high frequency regions of haptic spectrum. The crossover method, Fig. 3, would be directly applicable insofar as the transducers could be assumed to have a flat response in their respective bands, which cannot be the case from the analysis of the previous section, see Fig. 2. It is therefore necessary to identify the responses of each transducer and cascade them with compensating filters.

The response of the low-frequency channel (activated Pantograph; inactivated Haptuator) was identified by measuring the Power Spectral Density (PSD) response to pseudo-random binary sequence input. Seen from Fig. 5, the original 300 Hz bandwidth [START_REF] Campion | The Pantograph Mk-II: A haptic instrument[END_REF] was reduced to 200 Hz in the present dual-stage arrangement, owing to the extra mass added at the tip.

The same method was applied to the high-frequency channel (inactivated Pantograph; activated Haptuator). This procedure was applicable as long as the system could be assumed to be linear and that the superposition principle applied. When coupled to the Pantograph, the Haptuator responds well to frequencies above 100 Hz and exhibits a smooth acceleration roll-off beyond 300 Hz. At high frequencies, one of our ongoing study suggests that human perception does not discriminate between directions of movement, so only one distal actuator was needed. In the frequency band from DC to 200 Hz, the Pantograph had an acceptably uniform magnitude response. A first, nicely damped antiresonance is clearly visible after 200 Hz. It is accompanied by a damped resonance at 300 Hz. Another resonance-antiresonance pair is seem around 800 Hz, but this time with a sharp peak. This behavior is explained by the model of Fig 2 with three masses connected by two damped springs [START_REF] Campion | Fundamental limits in the rendering of virtual haptic textures[END_REF]. Within the frequency band from DC to 200 Hz, the Pantograph may be identified as a static gain. Its transfer function is then approximated by

G L (s) ≈ G L 0 .
In the identification given with input signals only provided to the Haptuator, below 100 Hz the magnitude response (shown in dashed line) was not reliable since the device saturated with the motions of the internal moving mass exceeding its allowable range. For frequencies greater than 100 Hz the response was well approximated by the following model, G H (s) ≈ 250s + 6.40 10 5 s 2 + 2135s + 4.56 10 6 .

(2)

In the previous section, the lumped parameter model gave rise to an eight-order model but the consideration of a limited frequency band in the low frequency channel made it possible to ignore the high frequency modes, reducing the model complexity to a second order system. It can be observed from Fig. 5 that because of the interplay of masses and elasticities, the high frequency channel begins to roll-off at 300 Hz. Thus, this channel must be compensated to achieve uniform magnitude. After analysis and identification, the scheme of Fig. 3 becomes that of Fig. 6 where, L(s) and H(s) are the Linkwitz-Riley filters, C L and C H the compensating filters, and G L and G H the high and low frequency transfer functions of the coupled system respectively.

input signal acceleration G H (s) G L (s) C H (s) C L (s) H(s) L(s) crossover compensator coupled system
Fig. 6. System block diagram with compensation and crossover.

Compensation

The cross-over method assumes that the different channels have a uniform response in their respective bands, but that was not the case here. The channels had to be frequency and amplitude compensated in their respective bands for the haptic display fidelity that the magnitude of the transmission should not depend on frequency. From Fig. 5, it can be determined that the device had a sufficiently uniform magnitude response from DC to 200 Hz. Hence, the only required compensation was to regulate the gain as follows,

C L (s) = K sys G L 0 ,
where K sys stands for the desired overall gain and G L 0 is the estimated signal gain of the low frequency channel. The high frequency channel had a non-uniform magnitude response from 200 Hz to 1 kHz. Compensation for this channel could in principle be achieved by inversion of the identified model [START_REF] Verrillo | The effects of skin temperature on the psychophysical responses to vibration on glabrous and hairy skin[END_REF]. Unfortunately, straightforward inversion would have resulted in a physically non-realisable filter with ever increasing magnitude in the high-frequencies. A simple solution was to perform a band-limited inversion according to

C H (s) = K sys F (s) G H (s) ,
where F (s) was a desired realizable response chosen here to be a second-order low-pass filter with a frequency roll-off starting at 1.0 kHz.

Experimental Evaluation

The real-time sampling rate was set to 10 kHz and the acceleration magnitude response was measured for each third of octave in the frequency range of interest (63, 80, 100, • • • , 800, 1000 Hz). The results for the two individual channels and for the combined system are shown in Fig. 7. The system's response was indeed flat within a few dB from DC to 1000 Hz.

INTERACTING WITH THE MICRO-WORLD

To exemplify a new class of haptic interaction applications enabled by wide frequency haptic interfaces, we set up a micro-manipulation system where the manual interface was bilaterally coupled with an optical tweezer system [START_REF] Neuman | Optical trapping[END_REF].

Optical tweezers enable the manipulation of dielectric microscopic objects by steering them optically through a very steep axis-symmetric light intensity gradient produced by a highly focused laser. Bilateral tele-manipulation was enabled by simultaneously detecting the interaction force with the medium and surrounding objects through highspeed detection of the deflection of the microscopic objects away from their equilibrium position.

These instruments are very sensitive since the detected displacements can be as low as those induced by the ambient Brownian agitation and interactions forces can be detected in the picoNewton or nanoNewton range [START_REF] Pacoret | Touching the microworld with force-feedback optical tweezers[END_REF], [START_REF] Ni | 2d high speed force feedback teleoperation of optical tweezers[END_REF], [START_REF] Pacoret | Invited article: A review of haptic optical tweezers for an interactive microworld exploration[END_REF]. The user interface can be seen in Fig. 8. Here, we trapped a 3 µm bead in water and displaced it to move into contact with a larger fixed object.

Available Sensory Information

In the entire haptic range from DC to one thousand Hertz, the various types of forces at play during the interaction with micro-beads could be experienced: thermal, viscous, and proximity Coulomb and Van der Vaals interaction forces. In particular, thermal and contact interactions have interesting high-frequency characteristics for bilateral haptic feedback.

When the trapped bead was in free space, as in Fig. 9a, thermal agitation was experienced. The thermal force is linked to the random collisions of the surrounding water molecules with the particle [START_REF] Neuman | Optical trapping[END_REF]. The following property is observed in accordance with the equipartition theorem at equilibrium:

< ẋ(t) 2 >= k B T /m, (3)
Here x(t) is the trajectory of the particle in one dimension relative to the equilibrium position define by the center of the optical trap. m is its mass and 1/2k B T represent its thermal energy at an absolute temperature, T , and with k B the Boltzmann constant. The theory of Brownian motion describes the instantaneous motion of the bead in a harmonic optical trap potential by the Langevin equation [START_REF] Kubo | Statistical Physics[END_REF],

mẍ = (2k B γ 0 T ) 1/2 η(t) -γ 0 ẋ(t) -κx(t), (4)
given above in one dimension for simplicity. The Brownian interaction as a random force is necessary to obtain the equilibrium mention above. The stochastic process η(t) is introduced to render the effect of the collisions with molecules of the surrounding medium. The effect of this fluctuating force can be summarized by this stochastic variable verifying a Gaussian distribution and :

η(t) = 0 and η(t 1 )η(t 2 = δ(t 1 -t 2 ), ∀t 1 , t 2 ∈ R. (5)
The other forces counterbalance the Brownian diffusion and maintain the particle in the laser trap: the fluid friction with γ 0 the fluid friction coefficient, and the harmonic force from the trap with κ the trap stiffness.

Stokes's law for a spherical particle gives γ 0 = 6πρνR, where ρ, ν, and R are the fluid density, fluid kinematic viscosity, and sphere radius, respectively. The characteristic time for the loss of kinetic energy through friction, ≈ 2.0 × 10 -6 s, is three orders of magnitude shorter than our experimental time resolution so we can drop the inertial term and the governing equation becomes,

ẋ(t) + 2πf c x(t) = (2D) 1/2 η(t), (6)
where the corner frequency of the damped optical trap (spring-damper system) is f c = κ/(2πγ 0 ) and D = k B T /γ 0 is a diffusion constant. Then, the particle displacement about the axis of the trap and its derivatives, see Fig. 9c, obey the form of a Gaussian distribution, with a mean value equal to zero and a variance that depends on the temperature, the trap stiffness, the fluid viscosity and other possible constraints.

Figure 9e shows the experimental histogram of the distribution of many samples read from the accelerometer which was mounted on the haptic handle, that is, the signal actually experienced by the user. This signal, indeed exhibiting a characteristic Gaussian profile, is nothing but a magnified representation of the movements of the micro bead bombarded by thermally agitated water molecules. When the bead was moved around, a micro-collision occurred if an obstacle happened to be present in its path, Fig. 9b. This collision was felt as an acceleration spike that can be seen in Fig. 9d.

At the vicinity of this fixed obstacle, the apparent fluid viscosity increased [START_REF] Neuman | Optical trapping[END_REF]. As a result, the variance of Brownian-induced agitation decreased and the distribution of acceleration due to molecular impacts became dramatically sharper as can be observed in the data collected in Fig. 9f.

These two high-frequency phenomena are experienced as tactile sensations by the operator helping her(him) to anticipate and adjust her(his) movements.

Sensorimotor Manoeuvres in the Dark Micro World

In order to assess the usability of the system, we asked five volunteers to manoeuvre micro-beads without the benefit of vision. Their task was to move a micro-bread about until they felt it to collide with an obstacle. At this point they had to move away from the obstacle in a direction normal to the surface on the basis of what they felt in the hand.

Inspection of Fig. 10 where five examples of trajectories are superposed onto a single image shows that the volunteers consistently succeeded at this task to a considerable degree. Trajectories that did not collide with any obstacle are not drawn in this figure. The ability to manipulate micro-objects when imaging is difficult shows considerable promise for many novel applications. Such as in [START_REF] Kim | Simultaneous 3d visualization and position tracking of optically trapped particles using optical diffraction tomography[END_REF] where objects are displayed under diffraction pattern or in [START_REF] Arai | Tying a molecular knot with optical tweezers[END_REF] where target structures are too small to be resolved in the microscope image, effective haptics can be introduced to improve manipulation intuitiveness.

Preliminary Validation

In order to validate the dual-stage approach experimentally, a set of experiments was designed as follows. Eight people, three females and five males, aged from twenty to thirty, volunteered to perform a test. They had limited knowledge and experience in haptics. They were asked to manipulate optical tweezers to circle around a spherical obstacle. The only instruction they were given was to maintain contact as long as possible between manipulated bead and obstacle. Each volunteer performed three sessions, each containing ten experimental trials. Each session had a different device configuration: in the first one, manipulation was performed under pure visual feedback (camera display of the scene) without haptics (V); the second one with visual feedback and haptic feedback from the conventional Pantograph (P); and the third one with visual feedback and haptic feedback from the dual-stage interface (D). For simplicity, these three conditions will be abbreviated in the following text and figures as V, P, and D respectively. The session order was randomized, and the volunteers were not informed beforehand. Before the experiment, they were engaged in a training session of ten to fifteen minutes to get familiar with all three conditions. During each trial, if the manipulated bead escaped the laser trap due to volunteers' manipulation, e.g. too much force was exerted, or if the contact was not maintained for a significant portion of the trajectory (> 50%), such manipulation would not be considered as successful and the related data were rejected.

Finally, the experiment was evaluated in terms of the number of successful trials, the average of the manipulation time per trial, the average force during trials, the average displacement error during trials. Results are plotted at the individual level in Fig. 11 and at the condition level in Fig. 12. It can be seen from Fig. 12 that the condition vision-only (V) has the lowest success rate, the longest manipulation time, the largest average exerted force and the highest displacement error. This means that in general the conditions with visual and haptic feedback (P and D) have much better performance than the condition vision-only (V). These results are highlighted in Fig. 12 on the number of successful trials and the displacement error which have significant difference according to a one-way ANOVA analysis on our small population (where assumptions of normality are not satisfied [START_REF] Hoekstra | Are assumptions of well-known statistical techniques checked, and why (not)?[END_REF]). The performance of the dual-stage device seems slightly better than the Pantograph in the tested configuration for maintaining an average force and minimizing the displacement error along the round trajectory. In Fig. 11d, it is interesting to note that the improvement due to the dualstage device is consistent across the subjects on the mean displacement error. The statistical tests do not reveal high significance, but show the potential for an improvement on the displacement error by the dual-stage device (p-value = 0.37, i.e. 63% probability of significant improvement) and motivate us for further investigation. This means that, when a task requires a low level of displacement error, the new device might be beneficial. A protocol that constrains user's strategy to minimize the displacement error could reveal this potential better than the present exploratory protocol. Further user studies should use this result in their experimental design and increase the tested population to study the gain on precision and accuracy due to the highbandwidth haptic devices.

CONCLUSION AND FUTURE WORK

This paper presented an approach to extend the frequency response of ordinary force-feedback haptic interfaces. The method consists of setting up a parallel structure with lowfrequency and high-frequency channels by signal crossover separation and using the intrinsic mechanics of a vibrotactile transducer to recombine the two signals paths. The combination of the low-frequency channel with the highfrequency channel realized by a recoil-type ungrounded high-frequency actuator results in a very simple design. Individual compensators could be implemented in order to equalize the overall magnitude response in frequency domain over the frequencies of interest to human perception. A key advantage of our approach is to enable the use of conventional force feedback devices for applications where high bandwidth response is desired. In our experiments, this large bandwidth haptic device has been tested in complex situations with several users. However, this first validation needs to be continued and further studies must investigate experimental designs with more specific instructions that constrain better user's exploration strategies. The impact on the displacement error promises interesting results when the trajectory accuracy and precision is important for the tasks, like avoiding delicate samples or contaminating agents. By rendering high dynamical interaction, better control is expected during a complex task such as an exploration at the dimension of live cells.

In future work, we plan to investigate the issues of closed loop stability of such systems which are immediately amenable to a channel separation approach [START_REF] Prattichizzo | Cutaneous force feedback as a sensory subtraction technique in haptics[END_REF]. We plan to extend this technique to several other force-feedback haptic devices.

Fig. 1 .

 1 Fig. 1. System components and coupling scheme. The Pantograph (a) has a finger plate containing a vibrotactile actuator (b), oriented as indicated by the arrow. The finger plate also includes an accelerometer for monitoring. The coupling scheme is described by (c) [21].

Fig. 2 .

 2 Fig. 2. System model. Lumped parameter model reflecting the main mass concentration, each corresponding to a mode.

Fig. 3 .

 3 Fig. 3. System with crossover filters.

Fig. 4 .

 4 Fig. 4. Magnitude plot of the crossover's channels.

Fig. 5 .

 5 Fig. 5. Magnitude response from PSD analysis (Welch method).

Fig. 7 .

 7 Fig. 7. The magnitude response of the combined interface.

Fig. 8 .

 8 Fig. 8. Operator interacting with a 3 µm glass bead (black arrow) via the dual-stage interface. Obstacles (bigger spheres) are 10 µm glass bead attached to the coverslip.

Fig. 9 .

 9 Fig. 9. Tangible differences between free space and contact in the micro world. (a) Manipulated bead in free space. (b) Bead brought into contact. (c) Molecular agitation felt through the interface. (d) Sharp transient at time 55 ms caused by a collision. (e) The distribution of acceleration magnitudes felt through the interface displays the hallmark of molecular interaction. (f) Dramatic reduction of agitation magnitude when the bead is pressed against an obstacle. (g) The distribution of acceleration magnitudes felt through the interface when the bead is pressed against an obstacle.

Fig. 10 .

 10 Fig. 10. Five examples of trajectories where volunteers blindly steered a micro-bead until it collided with an obstacle. The bead was then moved away from the obstacle.

Fig. 11 .Fig. 12 .

 1112 Fig. 11. Experiment results for each of the eight volunteers. The bars and whiskers represent the mean and standard deviation for each value respectively. (a) The number of successful trials. (b) The average manipulation time. (c) The average force. (d) The average displacement error. (V: visual feedback; P: visual feedback plus the Pantograph interface; D: visual feedback plus the dual-stage interface.)

TABLE 1

 1 Frequency bandwidth of some haptic devices.

	Model	Origin	DOFs Workspace [mm] Max. Force [N] Bandw. [Hz] Source
	Two finger grasp	Tech. Univ. Madrid	6	100×160	3	8	[10]
	Freedom 7	McGill University	7	170×220×330	2.5	30	[11]
	Phantom Desktop Sensable	3	160×120×120	7.9	30	[9]
	Maglev	Butterfly Haptics, LLC 6	24	40	75	[12]
	Pantograph	McGill University	2	100×160	5	300	[8]
	ERGOS	Ergos Technologies	1	50	60	20 k	[13]

TABLE 2

 2 Lumped mechanical parameters.

	Parameters Description
	m h	mass of terminal interface assembly
	mv	mass of Haptuator's moving magnet
	m 1	combined mass of motor windings
	m 2	apparent mass of links
	kv, bv	stiffness and damping of Haptuator
	k 1 , b 1	combined stiffness and damping of proximal links
	k 2 , b 2	combined stiffness and damping of distal links
	k f , b f	stiffness and damping of finger [24]
	x h	displacement of the terminal assembly
	xv	displacement of moving magnet
	x 1	displacement of motors
	x 2	equivalent displacements of links

ACKNOWLEDGMENT

The authors would like to thank Percipio Robotics for their contribution and support on this research project.


Frank Nitsche
email: fnitsche@uni-koeln.de

Helge Abuldhauge Thomsen

Daniel J Richter

Helge Abildhauge Thomsen

Bridging the gap between morphological species and molecular barcodes -exemplified by loricate choanoflagellates

Keywords: Acanthoecids, Bicostata, Calliacantha, Diaphanoeca, Crinolina, SSU, LSU

HAL is

Introduction

The group of acanthoecid (loricate) choanoflagellates is compromised of at present more than 115 described morphospecies [START_REF] Leadbeater | The Choanoflagellates -Evolution[END_REF]. In general they are ubiquitously found in brackish and marine waters, where they can reach high abundances of up to 3.5 x 10 6 cells per l -1 /Bering Sea (e.g. [START_REF] Sukhanova | Choanoflagellida on the southeastern Bering Sea shelf[END_REF]). The systematics and taxonomy of this group of organisms have undergone substantial changes when analysed with molecular data, in particular the small and large subunit (SSU and LSU) of the ribosomal DNA (rDNA) locus. In several cases within choanoflagellates (both loricates and craspedids), it was necessary to modify morphology based taxonomy based on results from molecular phylogeny [START_REF] Carr | Molecular phylogeny of choanoflagellates, the sister group to Metazoa[END_REF]. Within the acanthoecid choanoflagellates, two groups were established based on both developmental traits, such as the lorica assembly, and on confirming molecular data. In some cases, species described by morphology and assigned to the same genera do not form a monophyletic group when sequence data produced are analyzed in a phylogenetic tree. An example therefore is Helgoeca nana, which was transferred from the tectiform genus Acanthocorbis to the new, nudiform genus Helgoeca based on phylogenetic and morphologic studies [START_REF] Leadbeater | A new genus, Helgoeca gen. nov., for a nudiform choanoflagellate[END_REF]).

In addition, only 10% of acanthoecid choanoflagellate species have thus far been analysed regarding their molecular identity, in particular with reference to one of the most frequently used and appropriate marker genes, the SSU of the rDNA locus [START_REF] Pawlowski | CBOL Protist working group: Barcoding eukaryotic richness beyond the animal, plant, and fungal kingdoms[END_REF]. This lack of molecular data prevents an assignment of next generation sequencing (NGS) data from ongoing molecular barcoding surveys at the species level. In particular, the vast majority of acanthoecid barcodes within the global dataset of the Tara Oceans expedition could not be assigned at the species level. Questions arising when analysing acanthoecid choanoflagellate sequences from public databases include: how many species are there? How variable is the analysed marker gene? How should a species be defined based on this data? This work is aimed to demonstrate the importance of combining morphological and molecular data to understand ecological processes occurring in the complex microbial food web.

Material and Methods

Sampling was done in Denmark, in September 2014 and February 2015 according to previous records of acanthoecids from this area [START_REF] Thomsen | Studies on marine choanoflagellates II. Fine-structural observations on some silicified choanoflagellates from the Isefjord (Denmark), including the description of two new species[END_REF][START_REF] Thomsen | Loricabaerende choanoflagellater (Kraveflagellater)[END_REF]Thomsen et al. 2016).

In addition to surface samples from Isefjord (at Tempelkrogen and Kyndby), a Niskin bottle was used from board of the RV Ophelia to sample underneath the halocline at the field station of DTU Aqua at Helsingoer, The Sound (Table 1). Samples were transported back to the laboratory in a thermically isolated container and immediately processed. In the laboratory, about 500ml were concentrated on a 2µm Millipore filter using gravity for filtration. Half of this concentrate was transferred in to a petri dish for single cell picking. A micromanipulator was used to pick and transfer the morphologically identified single cells to a PCR tube. The other half was further concentrated by centrifugation (5 min at 2000g) and the resulting pellet was fixed using osmium tetroxide vapour for 1 min on a cover slide. These samples were used for identification and microphotography. Schematic drawings were done based on drawings by [START_REF] Thomsen | Loricabaerende choanoflagellater (Kraveflagellater)[END_REF] using Blender 2.77. Single cells were amplified using two step PCR. For the first PCR the primer set 42F

(5'-CTC AAR GAY TAA GCC ATG CA-3') and 1510R (5'-CCT TCY GCA GGT TCA CCT AC-3') were used, re-amplification was done using the primer set 82F (5'-GAA ACT GCG AAT GGC TC-3') and 1630R (5'-ACC TAC GGA AAC CTT GTT ACG-3') (final primer concentration 0.02µM). For both reactions the following program was applied: 2 min 98°C denaturation followed by 35 cycles of 30 sec at 95°C denaturation, 30 sec at 48°C and 30 sec at 52°C annealing, 2 min at 72°C elongation and a final elongation at 72°C for 7 min. For LSU rDNA single cells were amplified using the primer set NLF184/21(5'-ACC CGC TGA AYT TAA GCA TAT-3') and NLR3535/22 (5'-MRG GCT KAA TCT CAR YRG ATC G -3') in the first amplification and NLF1105/22 (5'-CCG AAG TTT CCC TCA GGA TAG C -3') and NLR2098/24

(5'-AGC CAA TCC TTW TCC CGA AGT TAC -3') for the reamplification. The PCR program was the same as for SSU, only elongation time was set to 4 min in the first PCR and 1.5 min for the reamplification.

PCR products were purified using the Qiagen PCR purification kit according to the manufacturer's instructions. Each purified SSU rDNA PCR product was initially sequenced directly with an ABI 3130xl DNA Sequence Analyzer using the primer C6F (5'-GAC TCA ACA CGG GRA AMC TYA CCA -3'). Positive sequences were sequenced further either by direct sequencing with three additional primers, 82F (5'-GAA ACT GCG AAT GGC TC -3'), V4F (5'-CCA GCA SCY GCG GTA ATT CC -3'), and 1630R (sequence given above), or in cases where the amount of DNA in the PCR product was insufficient for the multiple sequencing reactions that were necessary to produce a complete 18S assembly (C. ventriosa, D. undulata and P. minima) by cloning with the TOPO® TA Cloning® Kit into the pCRTM4-TOPO® vector from Life Technologies, according to the manufacturer's instructions, followed by sequencing with V4F and the standard vector-based M13F and M13R primers.

LSU rDNA amplicons were treated accordingly only using the primers NLF184/21, NLF1105/22 and NLR2098/24 for sequencing.

Fragments were assembled manually using Bioedit [START_REF] Hall | BioEdit: a user-friendly biological sequence alignment editor and analysis program for Windows 95/98/NT[END_REF]. The obtained sequences of SSU and LSU rDNA were used to build a concatenated two gene (SSU and LSU rDNA sequence Table 2), 4470bp (manually corrected) alignment by Kalign2 (gap open penalty 90, gap extention penalty 4, terminal gap penalties 3 and bonus score 0) [START_REF] Lassmann | Kalign2: high-performance multiple alignment of protein and nucleotide sequences allowing external features[END_REF]. This alignment was analysed using Maximum likelihood (ML) and Bayesian inference (BI) methods. ML analysis was computed by RAxML [START_REF] Stamatakis | A Rapid Bootstrap Algorithm for the RAxML Web Servers[END_REF]) using the RAxML GAMMA+P-Invar model of rate heterogeneity, as suggested by MrAic [START_REF] Ronquist | MrBayes 3: Bayesian phylogenetic inference under mixed models[END_REF] and run using a GTR+I model and a four-category gamma distribution to model among-site rate variation, 1000 bootstrap replicates (rapid bootstrapping). The Bayesian inference search, computed by MrBayes 3.2.6 [START_REF] Ronquist | MrBayes 3: Bayesian phylogenetic inference under mixed models[END_REF] consisted of two parallel chain sets run at default temperatures with a sampling frequency of 10, run until the average standard deviation of split frequencies dropped below 0.01. The analysis consisted of 3,500,000 generations, with a burnin of 87,500, before calculating posterior probabilities. The choanoflagellates were rooted with a clade consisting of two ichthyosporean taxa [START_REF] Nitsche | Stephanoeca arndti spec. nov -First cultivation success including molecular and autecological data from a freshwater acanthoecid choanoflagellate from Samoa[END_REF].

In order to identify Tara Oceans OTUs corresponding to the 9 species we sequenced, we extracted the V9 region of the 18S sequence for each species. We then searched for matching OTUs in the Tara Oceans data using a similar strategy to the one implemented in order to construct the OTUs [START_REF] Mahé | Swarm: robust and fast clustering method for amplicon-based studies[END_REF][START_REF] De Vargas | Eukaryotic plankton diversity in the sunlit ocean[END_REF]. We searched within the database of Tara Oceans V9 barcodes for either perfect matches or for matches with exactly one difference between our nine new sequences and a Tara Oceans V9 barcode using the alignment software Sumatra version 1.0.10 (https://git.metabarcoding.org/obitools/sumatra/wikis/home). We visualized these matches using network diagrams (Figure 4) with Cytoscape version 3.2.1 [START_REF] Shannon | Cytoscape: a software environment for integrated models of biomolecular interaction networks[END_REF]. The idea of this approach is that many rare barcodes may be present in a sample simply due to PCR error, because of the massive amount of barcodes that were sequenced. If this is true, then when we build a network of barcodes, drawing connections between barcodes if there is exactly one DNA sequence difference between them, then the "true" barcode will be highly abundant, and will be surrounded by a "swarm" of much less abundant sequences that represent sporadic PCR errors (which may also be errors occurring on intermediate PCR products that already contained one or more errors). To create maps for each newly affiliated Tara Oceans OTU, we used the GPS coordinates of each sampled station provided by the Tara Oceans Consortium (Tara Oceans Consortium, 2014, Pesant et al., 2015) and relative abundances for each OTU for the 0.8-5 µm and 5-20 µm size fractions [START_REF] De Vargas | Eukaryotic plankton diversity in the sunlit ocean[END_REF]. Although several of the species we describe may construct loricae measuring larger than 5 µm (or even larger than 20 µm), we found the majority of the abundance for each species within the 0.8-5 µm size fraction, and nearly all of the abundance within the 0.8-5 µm and 5-20 µm size fractions. We hypothesize that this occurs due to the filtration process, during which cells are likely pulled out of their loricae. There were only four cases in which a species was observed in either the 20-180 µm or 180-2000 µm size fractions, but not in the two smaller size fractions; in three of these cases, only 1 total barcode was observed outside the two smaller size fractions, and in one case, 4 barcodes were observed, amounts we considered to be below the threshold required to present the data on a map. We created the maps using R version 3.3.0 (R Core Team, 2016) using the following packages: data.table version 1.9.6 [START_REF] Dowle | data.table: Extension of Data.frame. R package version 1[END_REF], ggplot2 version 2.1.0 [START_REF] Wickham | ggplot2: Elegant Graphics for Data Analysis[END_REF] and maps version 3.1.0 [START_REF] Brownrigg | maps: Draw Geographical Maps. R package version 3.1.0[END_REF].

Results

Based on sampling from Danish waters, we were able to isolate, sequence and neotypify nine previously unsequenced morphospecies and five yet unsequenced genera of acanthoecid choanoflagellates: Bicosta minor, Calliacantha longicaudata, C. natans, Cosmoeca ventricosa, Crinolina isefiordensis, Diaphanoeca sphaerica, D. undulata, Pleurasiga minima and P. reynoldsii. All species could be maintained for a few days only in mixed cultures, containing environmental bacteria and other protists. Bicosta minor (Reynolds) [START_REF] Leadbeater | Renaming of Salpingoeca Sensu Grontved[END_REF]Fig. 1A Additional references: Bérard-Therriault et al. 1999;[START_REF] Manton | A reinvestigation of collared flagellates in the Genus Bicosta Leadbeater with special reference to correlations with climate[END_REF][START_REF] Marchant | Choanoflagellates[END_REF][START_REF] Thomsen | Planktonic Choanoflagellates from Disko Bugt, West Greenland, with a survey of the marine nanoplankton of the area[END_REF][START_REF] Tong | Choanoflagellates in Southampton water, including the description of three new species[END_REF] Global distribution in Tara Oceans Data: no identical or nearly identical match in the Tara Oceans V9 database (Table 3). Calliacantha longicaudata (Leadbeater) Leadbeater 1978; Fig. 1C Additional references: [START_REF] Bérard-Therriault | Guide d'identification du phytoplancton marin de l'estuaire et du Golfe du Saint-Laurent, incuant également certains protozoaires[END_REF][START_REF] Leadbeater | The Choanoflagellates -Evolution[END_REF][START_REF] Marchant | Choanoflagellates[END_REF][START_REF] Mckenzie | Distribution and abundance of choanoflagellates (Acanthoecidae) in the coastal cold ocean of Newfoundland, Canada[END_REF][START_REF] Thomsen | Planktonic Choanoflagellates from Disko Bugt, West Greenland, with a survey of the marine nanoplankton of the area[END_REF][START_REF] Thomsen | Loricabaerende choanoflagellater (Kraveflagellater)[END_REF][START_REF] Thomsen | Choanoflagellates (Acanthoecidae, Choanoflagellida) from the Weddell Sea, Antarctica, taxonomy and community structure with particular emphasis on the ice biota; With preliminary remarks on choanoflagellates from Arctic Sea Ice (Northeast Water Polynya, Greenland)[END_REF] Global distribution in Tara Oceans Data: no identical or nearly identical match in the Tara Oceans V9 database (Table 3).

Remarks: Marine tectiform acanthoecid, found at Kyndby (Table 1). Identification based on the original description, neotypified to relate a morphotype to genotype.

Emended diagnosis: Tectiform, cells solitary, lorica without stalk 11-18 µm in length, composed of five longitudinal costae each composed of two costal strips. Two transverse costae are linked to the anterior longitudinal strips, leaving the ultimate tips of the anterior costae as projecting spines. The pedicel is composed of a variable number of costal strips (Figs. 1C and2E).

The closest relative of the SSU rDNA sequence in NCBI GenBank, based on nucleotide BLAST results, is an uncultured choanoflagellate from the Scotia Sea (KC488358) at 99.6% identity.

Neotype sequence data: The SSU and LSU rDNA sequences of C. longicaudata have been deposited in the GenBank database with the accession numbers KU587840 and KU587841, respectively.

Calliacantha natans (Grøntved) Leadbeater 1978; Fig. 1B Additional references: [START_REF] Bérard-Therriault | Guide d'identification du phytoplancton marin de l'estuaire et du Golfe du Saint-Laurent, incuant également certains protozoaires[END_REF][START_REF] Buck | Protists from the ice-edge region of the Weddell Sea[END_REF][START_REF] Leadbeater | Ultrastructural observations on some marine choanoflagellates from the coast of Denmark[END_REF][START_REF] Leadbeater | The Choanoflagellates -Evolution[END_REF][START_REF] Manton | Some critical qualitative details of lorica construction in type species of Calliacantha Leadbeater (Choanoflagellata)[END_REF][START_REF] Marchant | Choanoflagellates[END_REF][START_REF] Thomsen | Planktonic Choanoflagellates from Disko Bugt, West Greenland, with a survey of the marine nanoplankton of the area[END_REF][START_REF] Thomsen | Loricate Choanoflagellates (Acanthoecidae, Choanoflagellida) from the Weddell Sea, Antarctica[END_REF][START_REF] Throndsen | The planktonic marine flagellates[END_REF][START_REF] Tong | Choanoflagellates in Southampton water, including the description of three new species[END_REF] Global distribution in Tara Oceans Data: Fig. 5A (Table 3).

Remarks: Marine tectiform acanthoecid, found at Kyndby and Tempelkrogen (Table 1). Identification based on the original description, neotypified to relate a morphotype to genotype.

Emended diagnosis: Tectiform, cells solitary, lorica 20-60 µm in length, formed by six longitudinal costae and two transverse costae, one of which forms the anterior ring.

Posterior end of lorica chamber tapers and joins with a single spine, while three spines emerge from the anterior transverse ring (Figs. 1B and2F). Additional references: [START_REF] Bérard-Therriault | Guide d'identification du phytoplancton marin de l'estuaire et du Golfe du Saint-Laurent, incuant également certains protozoaires[END_REF][START_REF] Booth | Choanoflagellates from the Sub-Arctic North Pacific-Ocean, with Descriptions of 2 New Species[END_REF][START_REF] Leadbeater | The Choanoflagellates -Evolution[END_REF][START_REF] Marchant | Choanoflagellates[END_REF][START_REF] Thomsen | Loricate Choanoflagellates (Acanthoecidae, Choanoflagellida) from the Weddell Sea, Antarctica[END_REF][START_REF] Tong | Choanoflagellates in Southampton water, including the description of three new species[END_REF] Global distribution in Tara Oceans Data: no identical or nearly identical match in the Tara Oceans V9 database (Table 3).

Remarks: Marine tectiform acanthoecid, found at Helsingør, 20m (Table 1).

Identification based on the original description, neotypified to relate a morphotype to genotype.

Emended diagnosis: Tectiform, cells solitary, lorica 23-32 µm in length, barrel-shaped, composed of 3 transverse costae and 8-12 longitudinal costae. Two almost equally sized anterior transverse costae located at the anterior end of the lorica chamber and at the level of the joints between the second and the third longitudinal costal strip.

Same number of strips in anterior transverse costae as there are longitudinal costae.

Third transverse costa narrower, formed by 3-4 costal strips, positioned between the third and fourth longitudinal strip (Figs. 1D and2G). 3).

Remarks: Marine tectiform acanthoecid, found at Tempelkrogen (Table 1).

Identification based on the original description, neotypified to relate a morphotype to genotype. Global distribution in Tara Oceans Data: no identical or nearly identical match in the Tara Oceans V9 database (Table 3).

Remarks: Marine tectiform acanthoecid, found at Tempelkrogen and Kyndby (Table 1). Identification based on the original description, neotypified to relate a morphotype to genotype. 3).

Remarks: Marine tectiform acanthoecid, found at Helsingør, 20m (Table 1).

Identification based on the original description, neotypified to relate a morphotype to genotype.

Emended diagnosis: Tectiform, cells solitary, lorica up to 30 µm in length without posterior pedicel, with posterior pedicel up to 50 µm long. 11-12 longitudinal costae, composed of 5 costal strips and three transverse costae form the lorica chamber.

Anterior transverse costa crosses longitudinal costae at the junction between the first and second strip, leaving the first strips as free projecting spines. The middle transverse costa, which has an undulating appearance, crosses anterior to the joints between the second and the third longitudinal costal strip (Figs. 1F and2K).

The closest relative of the SSU rDNA sequence in NCBI GenBank, based on nucleotide BLAST results, is an uncultured choanoflagellate from the Arctic Ocean, north of Barrow, Alaska (KJ762435) at 98% identity.

Neotype sequence data: The SSU rDNA sequence of D. undulata has been deposited in the GenBank database with the accession number KU587848. Pleurasiga minima Throndsen 1970; Fig. 1H Additional references: [START_REF] Bérard-Therriault | Guide d'identification du phytoplancton marin de l'estuaire et du Golfe du Saint-Laurent, incuant également certains protozoaires[END_REF][START_REF] Hallegraeff | Scale-bearing and loricate nanoplankton from the East Australian current[END_REF][START_REF] Manton | Further observations on finestructure of marine collared flagellates (Choanoflagellata) from Arctic Canada and West Greenland -Species of Parvicorbicula and Pleurasiga[END_REF][START_REF] Marchant | Choanoflagellates[END_REF][START_REF] Thomsen | Studies on marine choanoflagellates II. Fine-structural observations on some silicified choanoflagellates from the Isefjord (Denmark), including the description of two new species[END_REF][START_REF] Thomsen | Planktonic Choanoflagellates from Disko Bugt, West Greenland, with a survey of the marine nanoplankton of the area[END_REF][START_REF] Thomsen | Choanoflagellate diversity with particular emphasis on the Acanthoecidae[END_REF][START_REF] Tong | Choanoflagellates in Southampton water, including the description of three new species[END_REF] Global distribution in Tara Oceans Data: Fig. 5D (Table 3).

Remarks: Marine tectiform acanthoecid, found in Tempelkrogen (Table 1).

Identification based on the original description, neotypified to relate a morphotype to genotype.

Emended diagnosis: Tectiform, cells solitary, lorica 10-14 µm in height and 10-12 µm in width, amphora-shaped, two transverse, nearly equally wide costae, 7 longitudinal costae composed of 3 costal strips. Costal strip connections are, anteriorly, T-joints (Figs. 1H and2L).

The closest relative of the SSU rDNA sequence in NCBI GenBank, based on nucleotide BLAST results, is an uncultured choanoflagellate from the Arctic Ocean, north of Barrow, Alaska (KJ763316) at 97% identity.

Neotype sequence data: The SSU and LSU rDNA sequences of P. minima have been deposited in the GenBank database with the accession numbers KU587849 and KU587850, respectively. Pleurasiga reynoldsii Throndsen 1970; Fig. 1I Additional references [START_REF] Marchant | Choanoflagellates[END_REF][START_REF] Thomsen | Planktonic Choanoflagellates from Disko Bugt, West Greenland, with a survey of the marine nanoplankton of the area[END_REF][START_REF] Thomsen | Choanoflagellate diversity with particular emphasis on the Acanthoecidae[END_REF][START_REF] Throndsen | The planktonic marine flagellates[END_REF][START_REF] Throndsen | Marine planktonic Acanthoecaceans (Craspedophyceae) from Arctic waters[END_REF] Global distribution in Tara Oceans Data: Fig. 5E (Table 3).

Remarks: Marine tectiform acanthoecid, found in Tempelkrogen (Table 1).

Identification based on the original description, neotypified to relate a morphotype to genotype.

Emended diagnosis: Tectiform, cells solitary, lorica up to 23 µm in height and up to 22 µm in width, amphora-shaped, posterior transverse costae about 1/3 wider than anterior costae composed from 7 costal strips, 7 longitudinal costae between anterior and posterior costae composed by two costal strips, merging branch like into 4 terminal costae (Figs. 1I and2M). We detected 5 operational taxonomic units (OTUs) within Tara Oceans V9 hypervariable region SSU data perfectly matching one of the 9 newly sequenced species [START_REF] De Vargas | Eukaryotic plankton diversity in the sunlit ocean[END_REF]. Each OTU was previously classified as a choanoflagellate, but lacked a species identification. These OTUs correspond to C. natans, C. isefiordensis, D. undulata , P. minima and P. reynoldsii (Table 3, Fig. 4).

We did not detect perfect matches for B. minor, C. longicaudata, C. ventricosa or D. undulata, although in each case our new sequence was an equal or better match to the Tara OTU sequence than any existing sequences in GenBank. One of the newly identified species, C. natans, is the second most globally abundant choanoflagellate present within Tara Oceans V9 data. Its 18S V9 sequence is distantly related to any sequence currently in GenBank (the closest match is to Didymoeca costata at 88% identity). A network-based analysis comparing our new sequences to Tara V9 barcodes showed that, in all cases except for one, these sequences matched the most abundant barcode within the OTU identified. In the case of P. reynoldsii, it is possible that our new sequence might contain a single error, since there are no other sequences within 1 difference of any sequences within this OTU in the Tara V9 database (Fig. 4).

The five newly sequenced species present in Tara Oceans data display a range of distributions in a global context. Calliacantha natans (Fig. 5A), the second most abundant choanoflagellate in Tara Oceans data (Table 3), and Diaphanoeca undulata, the 16 th most abundant (Fig. 5C) are found in nearly every station and ocean basin studied, with the exception of the northern Indian Ocean (where the craspedid Monosiga brevicollis appears to be the dominant choanoflagellate; de [START_REF] De Vargas | Eukaryotic plankton diversity in the sunlit ocean[END_REF]. Both of these species are also found at their highest relative abundances in the cold water stations of the Antarctic, the South Atlantic, and the cold water coastal upwelling off the Horn of Africa (Supplementary Figs. S1 andS2).

The two newly sequenced Pleurasiga species, P. minima and P. reynoldsii, are detected in the South Atlantic and the Antarctic, at the boundary between the Indian Gyre and the South Atlantic Gyre off the coast of South Africa, at an upwelling station off the west coast of South America, and in the Mediterranean (Figs. 5D,E). As is the case for C. natans and D. undulata, the two Pleurasiga species are also observed at their highest relative abundances in the cold water stations of the southern hemisphere (Supplementary Figs. S4,S5). Crinolina isefiordensis, by far the least abundant of the newly sequenced species, is found in only two stations world-wide (Fig. 5B, Supplementary Fig. S3).

Discussion

Within a short time and with comparably little effort we were able to roughly double the number of acanthoecid choanoflagellates with sequence data available in public databases. The genus Diaphanoeca is a good example of consensus between morphology and phylogenetic analysis, as all species form a well-supported cluster (Fig. 3). The presence of Crinolina within this cluster may be well justified by the similar morphology of the two genera. The genus Crinolina, in particular the type species C. isefiordensis, was characterized by the lorica being open posteriorly.

Although it is closely related to Diaphanoeca [START_REF] Thomsen | Studies on marine choanoflagellates II. Fine-structural observations on some silicified choanoflagellates from the Isefjord (Denmark), including the description of two new species[END_REF] in its morphology, it is well distinguishable. As, at present, there is no sequence from the type species C. aperta available, we refrain from transferring C. isefiordensis to the genus Diaphanoeca, as it might instead turn out to be a sister genus when additional sequence data become available. In addition the nested position of C. isefiordiensis lacks strong phylogenetic support.

Pleurasiga and Calliacantha also form highly supported clusters (Fig. 3). Thus, the phylogeny created with concatenated sequences of SSU and LSU rDNA confirmed the coherence of both genera. However, within our data set the monophyletic origin of the Stephanoecida cannot be considered robustly resolved on phylogenetic grounds. Adding housekeeping genes like HSP90 or -tubulin might help to resolve this issue [START_REF] Leadbeater | A new genus, Helgoeca gen. nov., for a nudiform choanoflagellate[END_REF][START_REF] Nitsche | Higher Level Taxonomy and Molecular Phylogenetics of the Choanoflagellatea[END_REF], but these genes could not be analysed in this study. Nevertheless, the nudiform species, Acanthoecida, are recovered as a monophyletic group. A future enhancement to our single-cell sequencing approach could include whole genome amplification of single cells to obtain sufficient DNA for the analysis of other marker genes [START_REF] Krabberød | Radiolaria divided into Polycystina and Spasmaria in combined 18S and 28S rDNA phylogeny[END_REF].

Despite the fact that our sampling was conducted exclusively in Danish waters, we detect an essentially global distribution for the species we sequenced with matching OTUs in the Tara Oceans expedition (which did not directly sample Danish waters). This result echoes previous observations of choanoflagellates as ubiquitous in aquatic environments, while providing evidence that single species are also found across all ocean basins. In addition, this highlights the fact that a local sampling approach can be translated via sequence barcodes to information on species distributions at a global level. Using these sequences, it should now be possible to link previous descriptions of species distribution using morphology directly to distributions from Tara and other surveys based on ribosomal sequence data. Within our sequences, we succeeded in providing an identification for the second most globally abundant choanoflagellate in Tara Oceans data, Calliacantha natans. C. natans and the other species we identify in Tara Oceans data display their highest relative abundances in cold water Tara sampling stations. The highest relative abundance for any newly sequenced species is that of C. natans in the 0.8-5 µm size fraction at the surface located off the coast of Argentine Patagonia, where it represents nearly 1% of the total abundance of all 2,828 OTUs detected, and is the seventh most abundant OTU. Thus, within our sample of only five newly sequenced loricate choanoflagellates, we are able to detect a global distribution for each species and to attest to the importance of individual species within individual microbial food webs.

In addition, our approach should also be applicable to other groups of microbial eukaryotes whose morphology is species-specific but which lack extensive associated molecular barcoding data. Depositing ribosomal sequence data, such as those we collected in this study, into curated databases like the Protist Ribosomal Reference database [START_REF] Guillou | The Protist Ribosomal Reference database (PR2): a catalog of unicellular eukaryote Small Sub-Unit rRNA sequences with curated taxonomy[END_REF]) is a valuable and necessary addition to help resolve the flood of data acquired by High Throughput Sequencing technologies.

Concluding we can answer the questions posed in the introduction -the number of described acanthoecid morphospecies, 115, and the number of acanthoecid OTUs from Tara Ocean data, 129 correlate well. This result indicates that about 10 % of loricates have not been described yet. Therefore we find that the SSU rDNA is a suitable marker gene for species determination as shown in previous studies [START_REF] Nitsche | Comparison of similar Arctic and Antarctic morphotypes of heterotrophic protists regarding their genotypes and ecotypes[END_REF][START_REF] Pawlowski | CBOL Protist working group: Barcoding eukaryotic richness beyond the animal, plant, and fungal kingdoms[END_REF]. On the other hand we find that for species characterisation, morphology and sequence data still need to be supplemented with autecological data as salinity and temperature tolerance are required to interpret for example global distribution patterns. For each newly sequenced species, we searched the V9 portion of the 18S locus against the set of Tara Oceans V9 metabarcodes. Tara OTU Match %: the percent identity of the best match; Tara OTU Abundance Rank: the rank abundance of the matched Tara OTU within all choanoflagellate OTUs sequenced; Tara OTU GenBank Best Match: the best match within described choanoflagellate species in GenBank for the Tara V9 OTU; Tara OTU GenBank Match %: the percent identity of the match between the Tara OTU and the GenBank sequence.

  An isolation and establishment of monocultures was not successful. For all species, schematic 3D drawings for clear lorica architecture (Fig1A-I) and LM micrographs (2A-M) are provided alongside phylogenetic analysis based on SSU and LSU rDNA (Fig 3).

  Remarks: Marine tectiform acanthoecid, single cell isolated from a Kyndby sample collected 23 February 2015 (Table1). Identification based on the original description, neotypified to relate a morphotype to genotype. Emended diagnosis: Tectiform, cells solitary, lorica 11-45 µm in length, composed of seven costal strips arranged as two longitudinal costae, and by two costal strips each with tapered tips anteriorly and a posterior spine. (Fig 1A and 2A-C). The closest relative of the SSU rDNA sequence in NCBI GenBank, based on nucleotide BLAST results, is an uncultured choanoflagellate from the Scotia Sea (KC488357) at 98% identity. Neotype sequence data: The SSU rDNA sequence of B. minor has been deposited in the GenBank database with the accession number KU587839.

  The closest relative of the SSU rDNA sequence in NCBI GenBank, based on nucleotide BLAST results, is an uncultured choanoflagellate from the Scotia Sea (KC488358) at 98% identity.Neotype sequence data: The SSU and LSU rDNA sequences of C. natans have been deposited in the GenBank database with the accession numbers KU587842 and KU587843, respectively.Cosmoeca ventricosaThomsen 1984 in Thomsen and Boonruang 1984; Fig. 1D

  The closest relative of the SSU rDNA sequence in NCBI GenBank, based on nucleotide BLAST results, is an uncultured choanoflagellate from the Baltic Sea (FN690465) at 99% identity.Neotype sequence data: The SSU rDNA sequence of C. ventricosa has been deposited in the GenBank database with the accession number KU587844.Crinolina isefiordensis Thomsen 1976; Fig.1EAdditional references:[START_REF] Bérard-Therriault | Guide d'identification du phytoplancton marin de l'estuaire et du Golfe du Saint-Laurent, incuant également certains protozoaires[END_REF][START_REF] Leadbeater | The Choanoflagellates -Evolution[END_REF][START_REF] Thomsen | Planktonic Choanoflagellates from Disko Bugt, West Greenland, with a survey of the marine nanoplankton of the area[END_REF][START_REF] Throndsen | The planktonic marine flagellates[END_REF][START_REF] Tong | Choanoflagellates in Southampton water, including the description of three new species[END_REF] Global distribution in Tara Oceans Data: Fig.5B(Table

  Emended diagnosis: Tectiform, cells solitary, lorica 25-30 µm in length, skirt-shaped, open anteriorly and posteriorly. 14-15 longitudinal costae composed of 6-7 costal strips. Anteriorly longitudinal spines from two costal strips protrude above anterior transverse ring, posteriorly longitudinal costae slightly project beyond the transverse ring (Figs. 1E and 2H). The closest relative of the SSU rDNA sequence in NCBI GenBank, based on nucleotide BLAST results, is an uncultured choanoflagellate from the Arctic Ocean, north of Barrow, Alaska (KJ762435) at 96% identity. Neotype sequence data: The SSU rDNA sequence of C. isefiordensis has been deposited in the GenBank database with the accession number KU587845. Diaphanoeca sphaerica Thomsen 1982; Fig. 1G Additional references: Marchant 2005; Marchant and Perrin 1986.

  Emended diagnosis: Tectiform, cells solitary, lorica 22-30 µm in length and 16-17 µm in diameter, bell-shaped, formed by 13-15 longitudinal costae composed of 9-10 strips each, and three transverse costae. In the two anterior transverse costae the number of strips equals the number of longitudinal costae, whereas the posterior transverse costa contains fewer strips. Posterior lorica end with irregularly arranged costal strips. Large colony formations frequently found (Figs. 1G and 2I, J). The closest relative of the SSU rDNA sequence in NCBI GenBank, based on nucleotide BLAST results, is Diaphanoeca grandis (AF084234) at 99% identity. Neotype sequence data: The SSU and LSU rDNA sequences of D. sphaerica have been deposited in the GenBank database with the accession numbers KU587846 and KU587847, respectively. Diaphanoeca undulata Thomsen 1982; Fig. 1F Additional references: Thomsen 1992 Global distribution in Tara Oceans Data: Fig. 5C (Table

  The closest relative of the SSU rDNA sequence in NCBI GenBank, based on nucleotide BLAST results, is an uncultured choanoflagellate from the Gulf Stream, North Atlantic (KJ759457) at 95% identity.Neotype sequence data: The SSU and LSU rDNA sequences of P. reynoldsii have been deposited in the GenBank database with the accession numbers KU587851 and KU587852, respectively. Species from the genus Diaphanoeca form a well-supported cluster in the concatenated SSU and LSU analysis (Fig.3). D. sphaerica and D. undulata branch together with D. grandis and D. spiralifurca. Crinolina isefiordensis, a morphologically similar species, clusters within the same group, indicating a possible paraphyly or polyphyly (neither state is robustly supported) of Diaphanoeca.The two species from the genus Calliacantha, C. longicaudata and C. natans, form a monophyletic group with high bootstrap support. The genus Pleurasiga, represented by P. minima and P. reynoldsii, also forms a monophyletic group with strong support.Finally, Cosmoeca ventricosa and Bicosta minor cluster together with Acanthocorbis unguiculata. Although this branching pattern has high bootstrap support, the different morphology of these species indicates that a subsequent incorporation of additional sequences representing each genus may cause the pattern to change.

Figure 1 .

 1 Figure 1. Schematic drawings of the species from this study. (A) Bicosta minor, (B) Calliacantha natans, (C) C. longicaudata, (D) Cosmoeca ventricosa, (E) Crinolina isefiordensis, (F) Diaphanoeca undulata, (G) D. sphaerica, (H) Pleurasiga minima, (I) P. reynoldsii. Scalebar 5µm

Figure 3 .

 3 Figure 3. Molecular phylogeny of choanoflagellates based on a concatenated twogene dataset. The tree shown was derived by Maximum likelihood analysis based on a combined SSU and LSU rDNA nucleotide sequence alignment. Branches are drawn proportional to the number of nucleotide substitutions per site as indicated by the scale bar at the lower left. Branches receiving 100% maximum likelihood bootstrap percentages (mlBP) and 1.00 Bayesian Inference posterior probabilities (biPP) support are denoted by an *. mlBP and biPP values are otherwise given above and below branches respectively, only values above 50% are shown.

Figure 4 .

 4 Figure 4. Network diagrams of previously unidentified Tara Oceans V9 OTUs matching a newly sequenced species in this paper. Nodes represent individual barcodes and edges are present between barcodes if there is exactly one DNA sequence difference between them. The barcode within each OTU matching our new sequence is in red, and all other Tara Oceans barcodes are in blue. Node sizes are proportional to barcode global abundance.

Figure 5 A

 5 Figure 5 A-E. Presence (red) or absence (white) of newly sequenced species that were identified as matching a V9 OTU in the Tara Oceans data set within the 0.8-5 μm or 5-20 µm size fraction, either at the surface or at the deep chlorophyll maximum (DCM) for all Tara sampling stations with available data. A Calliacantha natans; B Crinolina isefiordensis; C Diaphanoeca undulata; D Pleurasiga minima and E

  Fig.1

Fig. 3

 3 Fig.3

Fig. 4

 4 Fig.4

Fig. 5

 5 Fig.5

Table 1 .

 1 Relative abundances in percentage for the different sampling sites and species.

Table 2 .

 2 Nucleotide sequences used to create the multigene phylogeny shown in Fig.3. Reference Numbers are GenBank Accession.

Table 3 .

 3 Matches of V9 18S barcode sequences in the Tara Oceans OTU data set.

Table 1

 1 Station between Elsinore and Hälsingborg 24 Sep. 2014 20 m Tempelkrogen 23 Feb. 2015 surface Kyndby 23 Feb. 2015 surface

	Bicosta minor (Reynolds 1976) Leadbeater 1978	2.0	14.9 16.7
	Calliacantha longicaudata (Leadbeater 1975) Leadbeater 1978		13.3 14.2
	Calliacantha natans (Grøntved 1956) Leadbeater 1978		5.3	4.3
	Cosmoeca ventricosa Thomsen 1984	20.3
	Crinolina isefiordensis Thomsen 1976	3.7	x
	Diaphanoeca sphaerica Thomsen 1982		3.2	4.3
	Diaphanoeca undulata Thomsen 1982	2.4
	Pleurasiga minima Throndsen 1970	1.2	32.4 33.3
	Pleurasiga reynoldsii Throndsen 1970		12.2 6.8

Table 3 Species Tara OTU Match % Tara OTU Abundance Rank Tara OTU GenBank Best Match Tara OTU GenBank Match %

 3

	Bicosta minor	97	23	Didymoeca costata	83
	Calliacantha longicaudata	96	7	Didymoeca costata	87
	Calliacantha natans	100	2	Didymoeca costata	88
	Cosmoeca ventricosa	99	15	Didymoeca costata	89
	Crinolina isefiordensis	100	101	Diaphanoeca grandis	90
	Diaphanoeca sphaerica	94	11	Diaphanoeca grandis	94
	Diaphanoeca undulata	100	16	Savillea micropora	91
	Pleurasiga minima	100	27	Didymoeca costata	92
	Pleurasiga reynoldsii	100	39	Didymoeca costata	89

Acknowledgements

We thank colleagues at the University of Copenhagen Marine Biological Section (Elsinore), in particular Per Juel Hansen and Lasse Riemann, for providing us with excellent laboratory facilities during our Sept. 2014 field campaign. We also thank colleagues at the University of Copenhagen Marine Biological Section (Copenhagen), in particular Gert Hansen, for providing us with excellent laboratory facilities during our Feb./March 2015 field campaign. The Natural History Museum of Denmark, University of Copenhagen, kindly gave us access to their DNA laboratories. Special thanks goes to Nina Lundholm and Charlotte Hansen. We acknowledge Marie-José Garet-Delmas for assistance with Sanger sequencing. We also thank Stéphane Audic and Nicolas Henry for assistance in searching databases and preparing figures based on Tara Oceans data. We thank two anonymous reviewers for their comments that improved this manuscript. DJR was supported by a postdoctoral fellowship from the Conseil Régional de Bretagne, and the French Government "Investissements d'Avenir" program OCEANOMICS (ANR-11-BTBR-0008).


A Avellan

C Levard

Corinne Chaneac

D Borschneck

Francis R A Onofri

Jérôme Rose

A Masion

Fabrice R A Onofri

Accelerated microwave assisted synthesis of alumino-germanate imogolite nanotubes

INTRODUCTION

Tubular nanomaterials are increasingly popular in a number of applications e.g. to improve mechanical strength, pack high surface areas in a limited volume… If carbon nanotubes remain the most publicized materials in this category, much of the focus now shifts towards inorganic nanotubes/nanofibers. Among these, imogolites (Al2SiO7H4) are nanotubes occurring naturally in volcanic soils, which can be synthesized with simple aqueous sol gel processes. 1,[START_REF] Suzuki | Inorganic and Metallic Nanotubular Materials[END_REF] However these protocols have in common very poor yields (millimolar concentrations) and slow kinetics (several days of growth). Yield is no longer an issue, since large quantities of Ge analogues, isostructural to imogolite (Al2GeO7H4, hereafter called Ge-imogolites) are readily obtained with initial reagent concentration in the molar range. [START_REF] Levard | [END_REF] The diameter (3-4.5 nm) is a function of wall multiplicity, which is easily controlled with the initial concentrations. 4 These hydrophilic tubes can be functionalized on both the internal and external tube surfaces. 5,6 Like silicon-based imogolite, the synthesis of Ge-imogolites is an aqueous phase process where the room-temperature based hydrolysis of a mixture of Al and Ge monomers results in the nucleation of roof-tile shaped proto-imogolites (ca. 5nm). Although not entirely elucidated, the mechanisms of tube growth, during a growth step at moderate temperature for several days, are thought to include the formation of annular structure from proto-imogolite upon heating, followed by tube growth via tip-to-tip collisions. 7 Under these conditions, average tube length is a few tens of nanometers with a maximum length typically not exceeding 150 nm. Some microsized Ge-imogolites were obtained using urea instead of NaOH during hydrolysis. 8 However the growth still requires a week, and it is unclear to what extent the formation of long tubes is a quantitative process. Predominantly short tubes (< 200 nm) and long growth duration are detrimental characteristics of all the Ge-imogolite syntheses available in the literature. To overcome these limitations, at least partly, we investigated the improvements that microwave (MW) heating could offer in comparison to conventional heating in an oven. MW is widely used for the synthesis of organic materials and, to a lesser extent, for the synthesis of minerals. Using conventional heating (CH), thermal energy is delivered to the material surface by radiant and/or convection heating and is transferred to the bulk solution via conduction. During MW processing, polar water molecules tend to align with the changing alternating electric field, and energy is transferred by rotation, friction and collision. As a result, heat can be generated homogenously throughout the volume. 9 In the literature, MW synthesis have increased reaction rates, improved yield and narrowed nanoparticle size distribution. [10][11][12][13][14] These improvements cannot be explained solely by a rapid heating effect, and therefore various authors postulate the existence of a "specific microwave effect". 15 In the present study, we report the effects of MW heating on the formation of Ge-imogolite as a function of reaction time and temperature.

METHODS

Ge-imogolite precursors (proto-imogolites) were obtained by adding a germanium ethoxide solution to aluminum chloride (0.05 mol.L -l , nAl / nGe = 1.75). The solution was slowly hydrolyzed with a 0.05 mol.L -l NaOH solution (1ml/min) to a hydrolysis ratio (R=nOH/nAl) of 2. Proto-imogolites were refrigerated at 4°C before further use. Tubes growth was performed either under Conventional Heating (CH) in an oven with pressure resistant containers or under microwave (MW) irradiation (Anton Paar Synthos 3000 microwave, 2.45 GHz) under stirring. For both heating regimes, 3 temperatures (100, 150 and 200°C) and 2 durations (1h and 2 h) were tested; CH systems were also heated for 7 days, the CH system at 100°C during 7 days being a reference of current protocols. The final suspensions were dialyzed with a 1kDa pore size membrane against ultra pure water until the conductivity reached 2 µS.cm -1 . AFM images (Bruker INOVA) were obtained in tapping mode. Diluted samples (1mg.L -l ) were deposited on a mica sheet and dried several hours at 60°C prior to analysis. AFM images extraction and height profile thresholds were performed using Gwyddion 2.4 software. 16 Particle counting, length and height distributions were extracted using Fiji 2.0 plugin 17 and image J 1.46 software. 18 As opposed to height resolution (0.2 nm), lateral resolution was poor and limited to 25 nm by the dimensions of the AFM tip; therefore protoimogolites were determined on the basis of their height (ca. 1nm, vs. 3.5 for the tubes) and not their length which is indistinguishable from the shortest tubes. To this end, a threshold of 2.5 nm was applied using the Gwyddion software (cf. Fig. S2 in S.I. for details). X-ray diffraction patterns were obtained on freeze-dried dialyzed samples using an X'Pert Pro diffractometer (PANalytical) equipped with a rotating glass capillary (ø 300µm) and a mirror as a primary optics to produce a parallel beam. Cobalt Kα radiation (1.79Å) was used at 40kV and 40mA. Scans were performed in the scattering angle range 2θ =2-55° with steps of 0.05° and 15s per step.

RESULTS AND DISCUSSION

The reference sample, i.e. 7 days CH at 100°C, corresponds to the most common protocol described in the literature. The Xray diffraction patterns of the recovered tubes of this reference sample (Figure 1) corresponds to the pattern previously observed with Ge-imogolites. 6,19 As expected, average tube length as determined by Atomic Force Microscopy (AFM) is below 80 nm (Figure 2) and the maximum does not exceed 150 nm (Figure 3(a)). Increasing the temperature to 150°C and 200°C resulted in poorer results. While the diffraction patterns still display the signature of Geimogolite (Fig. 1), only very few tubes were detected by AFM (Fig. 2). Instead, the AFM images are dominated by globular structures, presumably aggregates of precursors and/or illordered aluminum (oxy)hydroxides at 150°C, and an additional boehmite contribution (AlOOH; ICDD PDF #74-1895) (Fig. 1) at 200°C, possibly resulting from the maturation of the species formed at 150°C. Figure 4 shows the proportions of proto-imogolite (i.e height <1nm), short tubes (i.e. length < 25 nm) and "long" tubes (i.e. length > 25 nm) as determined from AFM images analysis. Under CH conditions, no tubes are present at 100°C after 1 and 2 hours heating. Above 100°C, the proportion of tubes formed under CH conditions increases with the reaction temperature and reaction time to reach 90% at 200°C after 2 hours, short tubes (<25 nm) being the predominant structure. The X-ray diffraction patterns are consistent with Ge-imogolite formation. 19 (Fig. 1) To the best of our knowledge, this is the first report unequivocally documenting the early formation of Ge-imogolite (i.e. within one or two hours) under hydrothermal conditions. However, it appears that the formed Ge-imogolite cannot withstand prolonged maturation under these conditions since they become undetectable on the AFM images after 7 days (Fig. 2). Synthesis results obtained with MW contrast sharply their CH counterpart. The most striking result is that micron-sized tubes are detected at the lowest temperature and shortest time (100°C, 1 h) (Fig. 2). At this stage, there is still a majority of proto-imogolite present in the sample. Increasing the temperature and duration causes this proportion to gradually decrease, mainly to the benefit of long (> 25 nm) tubes, which are the only detected structures after 2 h at 200°C (Figs. 3 and4). Using MW, the reaction rate is accelerated by a factor close to 100 compared to CH protocols. This is accompanied by a shift in the tube length by approximately one order of magnitude (Fig. 3). To the best of our knowledge, there is no previous evidence of the synthesis of micron-sized Ge-imogolite in such a short time frame. Micron-sized Ge-imogolite was also obtained previously using urea as hydrolysis agent with considerably slower kinetics than the present study, i.e. 5 days of heating. 8 . The maximum lengths measured under these conditions were around 1 µm, which is also the case with our MW based protocol. This length might correspond to an "equilibrium" value since two different growth procedures lead to the same maximum value he systems hydrolyzed with urea was described as very polydispersed in length. 8 In the present case, the particle size distribution can be termed as bimodal with maxima around 300 and 800 nm (Fig. 3 and Fig. S1 in Supporting Information (S.I.)), and may be an improvement in term of length selectivity compared to the urea based protocol. However, a particle size distribution of the solids formed following this procedure is required to confirm this hypothesis Amara et al. hypothesize an urea mediated modification of the interactions between the tips of the tubes to explain the increased length, but did not give further details on the nature of the mechanisms involved. 8 The present results are consistent with a structuring role of urea during tube formation. Indeed, when the growth is conducted under similar conditions (viz. CH, 150°C for 7 days vs. 140°C for 5days for the urea based protocol), only negligible amounts of tubes are produced from NaOH hydrolyzed systems (Fig. 2), thereby suggesting that urea and/or its decomposition by-products not only promote tube lengthening, but also prevent the decomposition/destructuration of the short tubes formed in the initial stages of heating. In the present study, it is obvious that the enhanced tube growth under MW heating is the result of a different mechanism. The MW induced molecular motion of polar species causes homogenous heating throughout the sample volume, 20 but increased molecular mobility is not necessarily linked to thermal effects. 21 The fast and homogeneous increase in temperature under MW irradiation certainly increases the kinetics of tube formation. However this faster molecular motion is not sufficient to explain the observed enhancement of the tube length. As a matter of fact, it appears that prolonged heating at temperature above 100°C has even adverse effects on tube growth as shown by the quasi-absence of Ge-imogolites for the systems that underwent CH at 150 and 200°C during 7 days (Fig. 2). Interestingly, this temperature dependent destructuring of short Ge-imogolite tubes is not observed when MW are applied, and increasing proportions of long tubes are formed instead (Figs. 2 and4). Improvement of the tube growth could be achieved by favoring tip-to-tip collisions, since this has been hypothesized as major growth mechanism. 7 The most obvious way to accomplish this, is to restrict, at least partly, the randomness in particle collisions, i.e. promoting the alignment of the tubes within the sample, which equates to eliminating 2 degrees of liberty and thus a theoretical increase of the probability of effective collisions by 4 to 5 orders of magnitude depending on symmetry. In this context, a specific MW effect could be the alignment of imogolites tubes along the MW electric field streamlines. Recent experiments, carried out with polarized light extinction spectroscopy, 22,23 have clearly demonstrated that in the 0.3-6 MHz range, where the electrical properties of water are expected to be comparable to the GHz range, electric field gradients of 50V/mm are sufficient to align aqueous suspensions of imogolites nanotubes of a few tens of nanometers. On the other hand, for such moderate electric field gradients, electromagnetic calculations show that the induced dielectric force and dielectric moment are directly proportional to the particle electrical polarisability and thus, to the square of their length in the case of elongated particles such as nanotubes. As a consequence, the effect of the dielectric force induced by MW increases quadratically with the length of nanotubes, limiting their rotation induced by the Brownian motion and thus, to some extent, thermal effects. It is believed that such a mechanism would be most effective in promoting the tip-to-tip collisions between long tubes (and thus rare at the beginning of the process), leading to the formation of micrometer-long tubes rather than nanometer of a few tens nanometers long. For the MW systems at 100°C, proto-imogolite and long tubes are the major species while the proportion of short tubes is surprisingly low. This suggests an additional growth mechanism, according to which tubes grow from the addition of proto-imogolite. Since Ge is a good MW absorber (i.e. high equivalent electrical permittivity), 24 hotspots are likely to occur where Ge atoms are concentrated, i.e. the tubes and precursors, thus creating a favorable environment from an energy standpoint. Obviously, these two mechanisms probably take place simultaneously. They are also not fully inconsistent since, for instance, the forced orientation of the largest nanotubes should also promote the assembly at their tips of protoimogolites (which are probably less sensitive to the MW electrical field).

Conclusions

The use of MW is a significant step forward in the synthesis of Ge-imogolite (100 times faster and tubes 10 times longer than with CH), and could be the key to commercial applications of this material. A better control over the tube length might be required to tailor tubes to specific uses. This means a more indepth investigation of the mechanisms involved, their relative importance during the entire process. Here, it would be a matter of determining at which stage precursor addition or tube-tube collision are the predominant mechanism. To do so, monitoring particle orientation during the entire process is an essential piece of information. This aspect, which is far from being straightforward, is currently under investigation.

Figure 1 :

 1 Figure 1: X-ray diffraction patterns of samples grown at 100, 150 or 200°C under conventional heating (CH) or microwave (MW) irradiation for 1h, 2h or 7 days.

Figure 2 :

 2 Figure 2: AFM images under tapping mode for samples synthesized under conventional heating (CH) or microwave (MW) irradiation, at 100, 150 or 200°C. Scale bar = 500nm. Grey level is related to the height of the particles.

Figure 3 :

 3 Figure 3: Repartition in volume percentage of the length of Ge-imogolites nanotube measured from AFM images. At least 500 particles were considered excluding aggregates. Growth stages were performed under (a) conventional heating at 100°C for 7days or under microwave irradiation at 200°C (b) 1h or (c) 2h.

Figure 4 :

 4 Figure 4: Repartition in volume percentage and type: proto-imogolites, short tubes (length <25nm) or long tubes (length >25nm) measured from AFM images, for various temperatures, growing durations and the two heating conditions. CH: Conventional Heating, MW: MicroWave irradiation *: samples dominated by large aggregates preventing the determination of tube proportions.

J. Name., 2013, 00, 1-3 | 3

J. Name., 2013, 00, 1-3 | 5

Acknowledgements

We acknowledge support from the French National Research Agency (no. ANR-11-NANO-008-04; ANR-11-NANO-008-06). This work is also a contribution to the Labex Serenade (ANR-11-LABX-0064) funded by the «Investissements d'Avenir» French Government program of the French National Research Agency (ANR) through the A*MIDEX project (ANR-11-IDEX-0001-02).

Notes and references