Frédéric Cao

Patrick Bouthemy

Ronan Fablet

Keywords:

come

Problem statement

The acquisition of age and growth data is of key interest for marine living stock assessment and ecology applications. It relies on the interpretation of calcified structures, mainly otoliths (inner ears of the fish), routinely and manually performed by experts for several thousand of samples a year. Digital imaging offers new possibilities to ease the processing of these tedious tasks in a fully or partially automatic way [START_REF] Morison | An integrated system for production fish aging: image analysis and quality insurance[END_REF][START_REF] Small | Computer-assisted age and growth pattern recognition of fish scales using a digitizing tablet[END_REF]. As illustrated by Fig. 1 for a plaice otolith, otolith interpretation for ageing purposes comes to the analysis of yearly alternated opaque and translucent concentric rings. Determining the position of the otolith growth center is obviously a crucial issue, since it serves as the reference point. However, methods targeted at imagebased automatic ageing [START_REF] Fablet | Robust timefrequency model estimation in otolith images for fish age and growth analysis[END_REF][START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF][START_REF] Robertson | Development of an artificial neural network for automated age estimation[END_REF][START_REF] Traodec | Use of deformable templates for otolith 2D growth ring detection by digital image processing[END_REF][START_REF] Welleman | Automatic ageing of Plaice otoliths by means of image analysis[END_REF] generally ignore this step to focus on the detection of the rings given the location of the otolith nucleus (also referred as the otolith center in the subsequent).

This paper presents a new and well-founded framework to reliably determine the position of the otolith center, such that it can be used for further analysis. This topic has only been considered in [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF][START_REF] Welleman | Automatic ageing of Plaice otoliths by means of image analysis[END_REF]. The solution proposed in [START_REF] Welleman | Automatic ageing of Plaice otoliths by means of image analysis[END_REF] simply resorts to the detection of the darkest point within a predefined area of interest set a priori. Experiments will show its rather low robustness. In [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF], the detection of the otolith center is a by-product of the extraction of 2D growth rings. Though interesting, its main drawback lies in the overcomplex parametrization of the underlying multi-agent system. Contrarily, our scheme combines morphological features to the a contrario setting to perform a parameterless detection of otolith nucleus. The subsequent is organized as follows. Section 2 details the proposed morphological approach. Experiments, in particular a quantitative evaluation including a comparison to previously proposed approaches [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF][START_REF] Welleman | Automatic ageing of Plaice otoliths by means of image analysis[END_REF] for a large set of Plaice otoliths, are presented in Section 3.

Proposed method 2.1 Topographic map

Let be a grey level image. Its upper (resp. lower) level set at value

¡ is ¢ ¤£ ¦¥ ¨ § © ¤ ¦ ¦ ¥ ! § #" ¡ %$ (resp. ¢ £ ¥ % § &© ' ( ) 0 ¤ ¦ ¦ ¥ ! § 21 ¡ 3$
). It is a classical result of Mathematical Morphology [START_REF] Matheron | Random Sets and Integral Geometry[END_REF][START_REF] Serra | Image Analysis and Mathematical Morphology[END_REF] that these level sets give a complete representation of , which, in addition, is invariant with respect to global contrast changes. Level lines are the topological boundaries of connected components of level sets, and the topographic map is the collection of all level lines. The topographic map also characterizes the image, up to an increasing contrast change. Since level sets are nested, they can be embedded in a tree structure, computed by an Frédéric Cao, Patrick Bouthemy, Ronan Fablet efficient algorithm due to Monasse and Guichard [START_REF] Monasse | Fast computation of a contrast invariant representation[END_REF]. They call shape the interior of any level line. There are superior (resp. inferior) shapes, following whether they are obtained from an upper (resp. lower) level set. The denomination of shapes is due to the fact that they often correspond to shapes or part of shapes in real images [START_REF] Caselles | Topographic maps and local contrast changes in natural images[END_REF].

Nucleus detection

Let us first remark that the otolith itself can be easily extracted as the largest shape in the image, that we shall denote by 4 %5 . This is not very strict an hypothesis, since the acquisition of otolith images is well controlled, and the otolith is usually observed as it lies on a nearly constant background. To detect the nucleus, let us state the following qualitative facts: otoliths are vaguely elliptic, and nucleui correspond to a dark region close to the longest principal axis of the otolith. This region is also basically elliptic and no too excentric.

Maxima removal

Let us first express the fact that the nucleus corresponds to a dark region. Let 6 5 be the shapes included in 4 5 (that is, part of the otolith). We also denote by 6 87 the set of shapes in 6 35 that does not contain any superior shape. In other terms, shapes in 6 7 do not contain any local maxima. Of course, this is a bit strict, since noise creates lots of them. Thus, we first apply a grain filter [START_REF] Vincent | Grayscale area openings and closings, their efficient implementation and applications[END_REF][START_REF] Monasse | Morphological Representation of Digital Images and Application to Registration[END_REF], to the image, which consists in removing shapes whose area is less than a given threshold. This scale parameter is the unique parameter of our method. Its value is not sensitive since the size of the nucleus is always of few hundreds pixels. The size of the grain filter was set to the same value for all our experiments. Grain filter and maxima elimination leave of few dozens candidate shapes.

Principal axis proximity

Let us now denote by 9 the first principal axis of the otolith. Let @ be a perpendicular axis to 9 , and ¥ BA DC § C BE GF be a finite family of connected compact sets. Let A be one of the A C . We say that A has a minimal distance to 9 on @ if and only if @ IH DA QP © SR and

T ¥ U@ IH V9 @ IH VA § 8© XW `Y ba C BE GF T ¥ B@ IH c9 @ IH dA C § fe (1)
In (1), we measure the distance between a point (@ gH h9 ) and and set (@ iH cA C ). This condition simply means that if we restrict the observation on @ , then A is the closest to 9 . Finally, we say that 4 6 if 4 6 ¤7 and if for any axis @ , perpendicular to 9 such that 4 pH q@ rP © sR , then there exists 4 8t 6 7 such that 4 8t has a minimal distance to 9 on @ among the shapes of 6 7 and 4 vu w4 8t .

The interpretation is much simpler that this formal geometrical definition: basically, if we start from 9 and move along its normal, then the first dark shape that we encounter must contain 4 .

While the first step remove bright shape, this second one removes elongated shapes that turn around the nucleus, while staying afar. (See Fig. 2.)

∆ S 0 Figure 2.
Proximity to principal axis. The black-filled shape is in x since in any direction orthogonal to y , the only shape closest to y contains it. For the same reason, the white shape belongs to x . On the contrary, one can find a normal to y such that the grey-filled shape is not the closest to y . Thus it does not belong to x .

Geometrical statistical selection

Among the remaining few candidates, we would like to choose the largest, the closer to 9 and the most circular shape. Fixing thresholds for geometrical quantities may be a bit dangerous since, even though otolith images are perceptually very alike, they enjoy a great variability of details.

The two preceding steps are only qualitative, and avoid any threshold. They are also quite general and experimentally very stable. We now aim at 1. finding the best nucleus candidate.

2. giving a reliability measure to this detection.

Let us define three functions ¥ U C § C b 7 representing the three geometrical qualities of a good nucleus. The first one is the area

7 ¥ U4 § © I 4 e (2)
The second one is

¥ 4 § © 4 W E T ¥ 9 § e (3)
This function is scale invariant and measure how 4 is close to 9 , relatively to its size.

Let us now denote by @ ¥ 4 9 d § the diameter of the projec- tion of 4 on the orthogonal direction to 9 . We define

¥ 4 § e© 4 @ ¥ U4 9 d § e (4)
This value is also dimensionless, and describes the "flatness" of 4 with respect to the direction 9 . Let us remark that a good nucleus candidate will simultaneously yield large values of the C , in the case our geometrical qualitative assumptions hold. Let us make the a contrario hypothesis that the C are statistically independent. This assumption is reasonable for any shape except for the nucleus. We define the nucleus s as the shape in 6 such that q ¥ Bs § e© XW `Y ba ¦E t q ¥ U4 § fe [START_REF] Monasse | Fast computation of a contrast invariant representation[END_REF] This definition means that the best candidate is the less probable under the independence assumption. Of course, it may happen that only one of the probabilities j C is small.

Nevertheless, since the number of shape that are used in the histogram learning is small, we cannot estimate very small marginal probabilities. Thus, the most efficient way to have a small value of q is to have small values of j C for all i .

In practice, we learn the histogram on a set of about 100 shapes, yielding positive marginals greater than f u wv . In practice, the minimizer of q in our experiments assumes a value between f u xv !y and f u xv !z . Remark that, following Desolneux et al., q provides a rejection threshold.

Definition 2

We call number of false alarms (NFA) of 4 the number s p{ }| ~¥ U4 § © m 6 # q ¥ U4 § fe [START_REF] Morison | An integrated system for production fish aging: image analysis and quality insurance[END_REF] We also say that 4 is -meaningful if s { }| ¥ U4 § .

The additivity of expectation immediately gives the following result (see [START_REF] Desolneux | A grouping principle and four applications[END_REF]).

Proposition 1 The expectation of the number of - meaningful shapes in the independence model is smaller than .

As a consequence, if we choose " f and observe that a shape has a NFA larger than , we cannot conclude that it contradicts the independence assumption since the expected number of such an event may be comparable to .

3 year old otolith 10 year old otolith Figure 3. Two examples of the detection of otolith center using our morphological approach: the red line depicts the contour of the selected shape, the blue star the estimated position of the otolith center, and the magenta circle its true position. The first row displays the image of the whole otolith, while the second row zooms in to the region close to the otolith center.

Results

Examples

We first display two examples of the detection of the nucleus within otolith images for plaice samples. Fig. 3 reports these two detections, the first one for a 3 years old otolith and the second one for a 10 years old one. The red line outlines the shape selected by our morphological approach, the blue star the estimated position of the nucleus and the magenta circle its actual position manually pointed out. The second row zooms in around the otolith center. In both cases, the selected shape is actually located within the first translucent ring. Consequently, an accurate estimation of the position of the otolith center is deduced. An important feature stresses by these two examples is the robustness of the morphological detection to the increase in image complexity in terms of the number of concentric seasonal rings.

Performance evaluation

We have carried out an evaluation of the proposed technique on a set of 250 images of Plaice otoliths belonging to age groups from 1 to 13. For each image, the position of the nucleus has been manually pointed out to provide the ground truth. To achieve a quantitative analysis of the detection performance, we define the rate of correct detection w.r.t. the threshold value ¡ as follows. Given an image, the detection of the otolith center is considered as correct Morphological method Multi-Agent method [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF] method [START_REF] Welleman | Automatic ageing of Plaice otoliths by means of image analysis[END_REF] Figure 4. Detection performance on a set of 250 Plaice otolith images. We evaluate the rate of correct detection for a range of values of the threshold (see text for details) for three techniques: the morphological approach presented in this paper (red line), the multi-agent technique introduced in [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF] (blue -line) and the scheme used in [START_REF] Welleman | Automatic ageing of Plaice otoliths by means of image analysis[END_REF] (cyan -. line). in terms of difference between the true and predicted positions of the otolith center. Markers refer to the results supplied by the scheme used in [START_REF] Welleman | Automatic ageing of Plaice otoliths by means of image analysis[END_REF], while the detections performed by our approach are displayed by markers . The three methods need a CPU time about 1s per image.

if the distance between the detected nucleus and the actual one is lower than ¡ times the distance from the actual nucleus center to the first translucent ring. For ¡ from 0 to 0.3, a correct detection can be regarded as very accurate. Besides, for ¡ © f , it indicates whether or not the estimated position of the nucleus is within the first translucent ring. In addition, we compare the proposed morphological approach to the ones proposed in [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF] and [START_REF] Welleman | Automatic ageing of Plaice otoliths by means of image analysis[END_REF]. Fig. 4 depicts the overall evaluation in terms of rate of correct detection with ¡ h u u e .

With correct detection rates close to for

¡ © u e and to for ¡ © f , the morphological approach performs robust and accurate detection of the otolith center. These promising results indicate that this scheme could be used as a preprocessing for further analysis, such as automatic ageing [START_REF] Fablet | Robust timefrequency model estimation in otolith images for fish age and growth analysis[END_REF][START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF], or for routine ageing issues. Compared to previously proposed approaches, the morphological scheme largely outperforms the heuristic one used in [START_REF] Welleman | Automatic ageing of Plaice otoliths by means of image analysis[END_REF], which simply consists in retrieving the darkest point within a predefined window, and also shows better performances than the multi-agent technique [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF] (respectively, G e e f n and of correct detection for ¡ © u e ). The close comparison of the morphological and multi-agent frameworks indicates that the latter is significantly less robust to detect the nucleus region, but may be more accurate when this detection points out to the relevant area of interest. Besides, whereas multi-agent systems are known to involve quite complex parametrization, the proposed morphological can be regarded as parameterless. It only requires to set the parameter value of the grain filter, used to filter out small regions. In our experiments, this value was set to 500 and the detection performances were shown to remain stable for a grain parameter within f (u Gu g u u .

Figure 1 .

 1 Figure 1. Illustration of Plaice otolith interpretation for a 4 year old individual. a) Image of the Plaice otolith acquired under a binocular with transmitted light. The interpretation of the winter translucent rings is displayed by the markers set on the radial drawn on the main reading axis. b) Associated growth pattern (distance from the otolith center to the last ring as a function of the age).

  A natural way to detect this independence violation is as follows: let us fix some values ¡ C and calculate, under the independence assumption, the expected number of shapes assuming values of the C larger than ¡ C . Whenever this value is lower than f and a shape 4 satisfies GC g¥ 4 § h" ¡ C , then chance alone cannot explain the observation. This is related to the Helmholtz principle, introduced by Desolneux, Moisan and Morel[START_REF] Desolneux | A grouping principle and four applications[END_REF]. For i © f , 2, 3, let j C g¥ lk §


Ronan Fablet
email: rfablet@ifremer.fr£@www.ifremer.fr

Nicolas Le Josse

Abdesslam Benzinou

Automatic fish age estimation from otolith images using statistical learning

In this paper, we investigate the use of statistical learning techniques for fish age estimation from otolith images. The core of this study lies in the definition of relevant imagerelated features. We rely on the characterization of a 1D signal summing up the image content within a predefined area of interest. Fish age estimation is then viewed as a multiclass classification issue using neural networks and SVMs. A procedure based on demodulation and remodulation of fish growth patterns is used to improve the generalization properties of the trained classifiers. We also investigate the combination of additional biological and shape features to the image-related ones. The performances are evaluated for a database of several hundred of plaice otoliths.

Problem statement

Fish age-length keys are at the core of stock assessment and marine ecology issues. Acquiring fish age data is mainly performed by interpreting fish otoliths, which are the inner ears. These calcified structures are formed through an accretionary process, which results in alternated translucent (winter) and opaque (summer) rings, as illustrated by Fig. 1 for a plaice otolith. Fish age is then determined by counting the number of winter rings. This tedious task is achieved by expert readers, who typically interpret several thousand of otoliths a year. Computer-assisted tools are then sought to help in the acquisition of age-length keys and in the storage of otolith interpretation [START_REF] Morison | An integrated system for production fish ageing: image analysis and quality insurance[END_REF].

In this paper, we investigate the use of statistical learning techniques, namely neural networks and Support Vector Machines (SVM), to infer fish age from otolith images. The results obtained in [START_REF] Robertson | Development of an artificial neural network for automated age estimation[END_REF] demonstrated the interest of neural approaches for fish aging issues. However, it was shown that the proposed features extracted from otolith images did not bring significant improvement compared to using only biological data. This is somewhat in contradiction with the experience of expert readers, who mainly rely on otolith interpretation for fish aging. Biological information is only used for verification purposes. Our goal is then to define more relevant image-based features. In addition to biological and geometrical features detailed in Section 2, a new set of image-related features is introduced in Section 3 to actually characterize the otolith content in terms of alternation of opaque and translucent rings. Section 4 briefly presents the application of neural networks and SVMs to our multi-class classification issue. In particular, a procedure targeted at increasing the generalization properties of the classifiers is proposed. Results are reported in Section 5 for real Plaice otolith data.

Biological and geometrical features

Biological features

Biological information are usually available for fish otolith databases. We will use fish length and sex, and the catch date. If available, other information such as the sexual maturity or otolith weight could also be considered. Though relevant for aging issues [START_REF] Robertson | Development of an artificial neural network for automated age estimation[END_REF], these features are sufficient alone to provide accurate age estimates due to the huge growth variability among fish individuals.

Geometrical features

The second category of features we use relies on the characterization of the external shape of the otolith. We in Proc. of Int. Conf. on Pattern Recognition, ICPR'04 typically compute the perimeter, the surface, and the rate between the length along the two principal axis.

This type of feature is obviously not sufficient alone to infer fish age as shown in [START_REF] Fabosa | Fish Ageing by Otolith Shape Analysis[END_REF]. However, we aim at evaluating whether or not it can bring additional cues in combination to other feature types to improve fish age estimation.

Image-related features

The core of our study is the extraction of relevant features to represent the content of otolith images, in terms of alternation of translucent and opaque rings. We will investigate the use of two different feature sets: frequency-based and peak-based features.

From 2D image content to 1D representation

Otolith interpretation is usually performed by experts along a predefined reading axis, as shown by Fig. 1 for a Plaice otolith. The automatic analysis of the content of otolith images can then be restricted to a region around the main reading axis.

To this end, a template-based approach inspired from [9] extracts a one-dimensional signal depicting the 2D image content, relevant for interpretation purposes, within an angular sector around the considered reading axis. More precisely, given the otolith center ¤ and an angular sector ¥ , the following 1D signal ¦ ¨ § is computed:

¦ § © "! #© $ #© &% (' ) 0 21 3 § 4 5 (1)
where "! #© & is the median operator, 1 6 § is the template model used within ¥ , $ the image intensity function, and a scaling factor between 0 and 1. As in [START_REF] Traodec | Use of deformable templates for otolith 2D growth ring detection by digital image processing[END_REF], the template model 1 § is given by the sampled external otolith shape within ¥ . ¦ ¨ § © & 7 is then the median intensity value along the template 1 § scaled by w.r.t. the otolith center % . Since the scaling of the external otolith shape w.r.t. the otolith center provides a good approximation of the shape of the seasonal rings [START_REF] Traodec | Use of deformable templates for otolith 2D growth ring detection by digital image processing[END_REF], ¦ § depicts oscillations corresponding to the alternation of translucent and opaque rings within ¥ .

Growth-adapted filtering

Otolith growth is not linear but rather exponential. Therefore, rings tend to be thiner when the fish gets older. In terms of frequency content, the signal ¦ § is then highly nonstationary. In addition, the otolith is usually thiner close to its edge, what results in a low-frequency component in ¦ " § . Due to these two major issues, the straightforward use of FFT or DCT features computed from ¦ " § as in [START_REF] Robertson | Development of an artificial neural network for automated age estimation[END_REF] does not seem a relevant choice.

Contrarily, we develop a growth-adapted filtering to analyze ¦ § . Given a mean a priori growth model 8 @9 A© B 5 , with 8 the distance to the otolith center, and B the time variable in years, ¦ § is initially demodulated w.r.t. 9 :

¦ ¨C D § © B 5 ¦ E § © F9 A© GB 5 IH 8 P RQ TS VU (2)
where 8 2P RQ TS is the median length between the center of the otolith and the edge within ¥ . Though non-stationary, the demodulated signal ¦ C 2D § involves a more compact frequency content, what makes easier its analysis.

To remove the low-frequency component ¦ XW § from ¦ C 2D § , ¦ ¨W § is estimated using a convolution to a Gaussian kernel Y a`b with a large variance c 4d

W : ¦ eW § Y a"b 0 ¦ C D §
. Highfrequency noise can also be filtered out using a Gaussian kernel with a low variance c #f , such that the growth-adapted filtering finally comes to consider the filtered signal ¦ f § computed as:

¦ f § © GB 5 Y `g 0 ih ¦ C D § p ¦ W § rq (3)

Frequency-based representation

Given the demodulated and filtered signal ¦ f § , one can use its frequency content as a descriptor of the alternation of ridges and valleys within ¥ . The DCT transform is then applied to ¦ f § , and the s C ut W first DCT coefficients are stored to form the frequency-based feature vector.

Peak-based representation

Otolith interpretations performed by experts do not rely on the analysis of the image frequency content, but rather on the detection of ridge and valley structures corresponding to translucent and opaque rings. We then introduce a second kind of image-related features defined from the extrema of the signal ¦ f § . Given the positions of maxima (or equivalently the minima) of ¦ f § wv B Ix "U ey y y y y U 5B # , we define a new peak-based signal ¦ " 4 § by:

¦ 4 § © B 5 F v E © B p B 5 X T ¨ x T (4)
where is a distance kernel. The computation of v B Ix XU Ey y y y y U 5B # is based on the detection of the zero crossings of the first derivative of ¦ f § , estimated by finite differences. In practice, we use © Gd 6 2 fe ag B g u© d 3 hH "i . The resulting signal ¦ ¨ 4 § only depends on the extrema position. In particular, compared to ¦ f § , ¦ ¨ 4 § is invariant to the variability of intensity ranges over images.

Statistical learning

Fish age estimation is regarded as a pattern classification issue. Given an otolith image , we aim at mapping the associated feature vector j to an age class k . To cope with this multi-class classification, we consider two different statistical learning techniques: neural networks and SVM.

Neural networks

Neural networks have been widely used for pattern recognition issues [START_REF] Bishop | Neural Networks for Pattern Recognition[END_REF]. They are aimed at optimizing the interconnection weights between neurons to minimize the mean square error. Here, a back propagation neural network with one hidden layer is chosen. The decision function is a sigmoid. The number of neurons of the hidden layer has been empirically optimized, and set to fifty. In our experiments, we use the Netlab Matlab toolbox [START_REF] Nabney | Netlab: Algorithms for Pattern Recognition[END_REF].

SVM

Kernel-based techniques such as SVMs [START_REF] Scholkopf | Learning With Kernels: Support Vector Machines, Regularization, Optimization and Beyond[END_REF] are among the most efficient approaches for pattern recognition. The key idea of SVMS, which are maximum margin classifiers, is to map the original feature space to a higher dimensional. The selected mapping l has to verify that the dot product between two points in the new feature space l © j x e rm l © j d can be rewritten as a kernel function n © j x "U j d

. The binary SVM classification then resorts to determine the hyperplane separating the two classes within the feature space associated to the kernel function. We let the reader refer to [START_REF] Scholkopf | Learning With Kernels: Support Vector Machines, Regularization, Optimization and Beyond[END_REF] for further details.

In our study, we will use a Gaussian kernel, n © j 4x U j d j o © p © j d p j d d H pe c 6d . The binary SVM classification is extended to a multi-class classification using a one vs. all strategy. We use the libSVM package [START_REF] Chang | LibSVM: a library for Support Vector Machines[END_REF] to test for two different SVM techniques: C-SVM and nu-SVM [START_REF] Chang | LibSVM: a library for Support Vector Machines[END_REF][START_REF] Scholkopf | Learning With Kernels: Support Vector Machines, Regularization, Optimization and Beyond[END_REF].

Training issues

Given a training set q of otolith images and the associated feature vectors v j er F s (j possibly refers to frequency-based, peak-based, biological or geometrical features, or a combination of these features), we first apply a Principal Component Analysis (PCA) to retain the first s t ut components. The resulting feature set is denoted by v j t rt " ¨ s . Statistical learning is then performed within the associated feature space.

To increase the robustness of the learning stage, we virtually increase the number of elements within the training set q as follows. Each element v within q is associated to a growth pattern 8 w9 © B 5 provided by the interpretation of the otolith made by the expert. Given v yx zq , the templatebased signal ¦ § (cf. Eq.1) is demodulated w.r.t. the growth model 8 {9 © GB 5 and remodulated w.r.t. growth models randomly chosen within v 9 s . The image-related features computed for these virtual signals are then combined to the original ones to create a larger training set. The remodulation is typically performed with five growth models. Thus, the size of the training is multiplied by a factor 6six. This is expected to improve the generalization performed by the statistical learning techniques.

Experiments

Training and test sets

The experiments are carried out for a database of 300 images of plaice otoliths from age group 1 to 6. Due to the lower number of samples in age groups 5 and 6, we merge both groups to end up with a five-class issue: 1 to 4 and 5+. This grouping can also be motivated by the fact that age groups 4 and less usually represent more than 85% of the commercial landings. The ground truth for fish age estimation was provided by the interpretation of an expert in plaice otolith readings. The training set is formed by selecting the three fourth of the images of each age class, while the remaining images are used for the test set. For each image, image-related features are extracted for five nonoverlapping angular sectors of width i uH p| ¤ around the main reading axis. Angular sectors, for which information required to interpret the otolith is missing due to ring discontinuities or local artifacts, are discarded from the training set, but no such checking is carried out over the test set. We resort to training and test sets including respectively 1500 and 600 elements. Using the virtual growth-based signal generation, the training set finally comprises 8000 elements.

Classification results over the test set

We evaluate the performances of the proposed approach using different feature sets and classifiers. The performances, reported in Fig. 2 are analyzed in terms of mean correct classification rate w.r.t. the five age groups over the test set. The overall evaluation shows that the best results (86%) are obtained by C-SVMs [START_REF] Scholkopf | Learning With Kernels: Support Vector Machines, Regularization, Optimization and Beyond[END_REF] combined to the peakbased features and the remodulation procedure within the training set. Thus, this configuration is used as the reference in the subsequent. Fig. 2.a highlights the need for non-linear techniques to cope with the considered classification task, and shows that C-SVMs outperform the neural nets and nu-SVMs [START_REF] Bishop | Neural Networks for Pattern Recognition[END_REF][START_REF] Scholkopf | Learning With Kernels: Support Vector Machines, Regularization, Optimization and Beyond[END_REF].

In Fig. 2.b, we compare different feature types: peakbased features, peak-based features (PB), frequency-based features combined to the remodulation procedure (FB), DCT coefficients of the signal ¦ X} as used in [START_REF] Robertson | Development of an artificial neural network for automated age estimation[END_REF] (DCT), biological features (B) and geometrical features (G). We also analyze the relevance of the remodulation process (Rem) to synthesize new examples within the training set. Fig. 2.b first indicates that biological and geometrical features are far too simple to provide alone relevant cues to infer fish age. The influence of the growth-adapted filtering is also demonstrated by the rather low performance achieved using the DCT features from the raw signal. Besides, it proves the superiority of PB features over FB features and validates the interest of the remodulation procedure, which brings a sig- nificant improvement from 82.8% to 86% of mean correct classification rate when using PB features. We also manage to combine biological and geometrical features to PB features. Surprisingly as reported in Fig. 2.c, this does not bring any improvement compared to PB features alone. This combination indeed tends to decrease the mean correct classification rate, while the mean-square error is slightly lowered. This is certainly due to the high overlapping in terms of length and shape features between the different age groups, which decreases the discriminant power of these features.

Extension to image classification

From this overall evaluation over the test set, the best configuration is to combine C-SVMs to PB features and to exploit the remodulation procedure. Besides, we can supply a more robust image classification by combining the classes assigned to several angular sectors. To this end, we use a voting procedure: given the age groups assigned to five angular sectors of the tested image around the main reading axis, this image is classified as belonging to the age group with the maximum number of votes. Tab.1 reports the confusion matrix of the resulting image-based classification. The mean correct classification rate is 88%, and only age group 4 has a classification rate just below 80%. These results are very promising for an application to routine aging, since they are in the range of the levels of agreement observed between expert readers.

Compared to previous work using statistical learning for fish aging [START_REF] Morison | An integrated system for production fish ageing: image analysis and quality insurance[END_REF], the reported classification rates are much greater due to the definition of more relevant image-based features. Besides, as reported in [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF], previously proposed 1D and 2D techniques are both outperformed by the proposed statistical learning scheme with respectively 50% and 80% of correct classification. Besides, compared to 2D approaches which require about one minute per image, the SVM classification from PB features just needs a few seconds on a 2.4GHz PC in a Matlab implementation.

Figure 1 .

 1 Figure 1. Illustration of Plaice otolith interpretation for a 4 year old individual. The interpretation of the winter translucent rings is displayed by the markers set on the radial drawn on the main reading axis.

Figure 2 .

 2 Figure 2. Overall evaluation of fish age estimation for the plaice test set in terms of rate of correct classification. a) Given the peak-based feature vectors, we compare four different classifiers: C-SVMs, nu-SVMs, neural nets (NN) and linear SVMs. b) using C-SVM, we evaluate the relevance of four feature vectors: peak-based features (PB), frequency-based features (FB), biological features (B) and geometrical features (G). c) Using C-SVM, we compare combinations of peak-based, biological and geometrical features: PB, PB+B, PB+G, PB+B+G. In all cases, we use the remodulation procedure over the training set.

Table 1 .

 1 Confusion matrix of the results of fish aging for each image of the test set by combining the classifications of individuals angular sectors.

		1	2	3	4	5+	error in [-1,+1]
	1	91.6	8.3				100
	2		91.1	5.8		2.9	97
	3		4.1	91.6	4.1		100
	4		4.3	13	78.2	4.3	95.5
	5+			5.8	5.8	88.2	94.1

Acknoledgments :

The authors wish to thank André Ogor from for his help in the acquisition of otolith images, and Marie-Line Manten who provides the expert interpretation of the image of plaice otoliths.


Ronan Fablet

EXTRACTION ADN INTERPRETATION OF RING STRUCTURES IN IMAGES OF BIOLOGICAL HARD TISSUES: APPLICATION TO FISH AGE AND GROWTH ESTIMATION

This paper presents a general framework for the automated estimation of age and growth from images of biological materials depicting concentric ring-like structures such as tree trunks, corals, bivalve seashells, fish scales or otoliths. This interpretation task can be seen as a ring segmentation issue, where growth rings are associated to image ridge and valley structures. This is stated as the Bayesian selection of a subset of partial ring curves extracted using a semi-local template-based growth-adapted scheme. The application to fish otolith interpretation provides a consistent and convincing validation of the proposed framework.

PROBLEM STATEMENT AND RELATED WORK

Age and growth data acquired from the analysis of ring-like structures in biological hard tissues (fish otoliths, shells of sea shells, tree trunks, corals,...) are key information for a broad range of scientific issues such as marine stock assessments, marine ecology, paleoclimatology or archeology. We provide examples of such images involving ring-like structures in Fig. 1 and in Fig. 4. The deposit of ring structures is mostly periodic (mainly seasonal or daily depending). Counting growth rings then leads to an estimation of the age, whereas growth increments can be estimated from the distance between successive rings. Since large collections of biological data are needed (typically, several thousands of samples per year for fish stock assessment), computeraided tools [START_REF] Morison | An integrated system for production fish aging: image analysis and quality insurance[END_REF] are being sought. Our work is dedicated to the automation of age and growth estimation from the analysis of images of biological hard tissues. The key issues, as illustrated in Fig. 1, lie in the use of growth information both to design a robust ring extraction framework taking into account growth non-linearity, and to discriminate actual growth rings from irrelevant ones. Previous work [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF][START_REF] Traodec | Use of deformable templates for otolith 2D growth ring detection by digital image processing[END_REF][START_REF] Welleman | Automatic ageing of Plaice otoliths by means of image analysis[END_REF] has mainly focused on the information extraction step but have not tackled the actual interpretation task. The latter is a complex issue as stressed by the the results of the European workshop on plaice otolith interpretation held in Fig. 1. Example of growth ring structures observed on a plaice otolith illustrating the complexity of the interpretation of growth rings due to the presence of false rings (eg, between the first and second rings), and to the non-linearity of the associated growth pattern (the last two rings tend to be closer and hard to distinguish). The positions of actual growth rings are depicted by the markers set on the radial drawn from the otolith center to the edge.

2003: inter-reader agreement rates vary from 40% to 95% depending on readers' experience, whereas this rate is comprised between 85% and 95% for expert readers. As a first step, statistical learning has been recently investigated for automating age estimating from a training set of samples interpreted by experts [START_REF] Fablet | Automated fish age estimation from otolith images using statistical learning[END_REF]. However, this approach is limited to age estimation and cannot be straightforwardly extended to growth ring extraction and growth estimation.

A two-stage approach is proposed to bring new solutions to these issues. A semi-local growth-adapted templatebased scheme is first developed to robustly extract meaningful partial ring curves curves. Second, exploiting a priori growth information provided by a set of samples interpreted by an expert, the interpretation step is viewed as a Bayesian selection of a subset of the extracted curves. The subsequent is organized as follows. Sections 2 detail the semilocal approach proposed for the segmentation of partial 2D ring curves. The application to age and growth estimation is discussed in Section 3. Results are presented in Section 4.

EXTRACTION OF PARTIAL RING CURVES

Semi-local template-based framework

The first stage of our approach relies on the extraction of partial ring segments. As a result of the accretionary process leading to the formation of the hard tissues, the alternated translucent and opaque rings are rather concentric w.r.t. the growth center, and ring shapes can often roughly be approximated (at least locally) as scaled versions of a given template. Rather than exploring purely local techniques for ridge and valley detection [START_REF] Chalmond | Markov fusion of a pair of noisy images to detect intensity valleys[END_REF][START_REF] Lindeberg | Edge detection and ridge detection with automatic scale selection[END_REF], we then prefer investigating the use of the external shape as the parametric model of ridge and valley structures, and we extend the global template approach presented in [START_REF] Traodec | Use of deformable templates for otolith 2D growth ring detection by digital image processing[END_REF] to a semi-local framework.

The extraction of local elementary ridge or valley segments illustrated in Fig. 2 proceeds as follows. Given a set of overlapping angular sectors defined w.r.t. the known growth center, we aim at determining within each angular sector the scaling factors, such that the scaled local template approximately fits the local ridge and valley segments. This is stated as the computation of the zero crossings of the first-order derivative of the the median intensity along the scaled template. Let us stress that the computation of these derivatives needs to account for the time-frequency features of hard tissue due to the decrease in the width of the growth rings when the hard tissue gets older. To cope with this issue, we use a demodulation scheme w.r.t. a mean a priori growth pattern learned from training samples.

Extraction of 2D ridge and valley curves

Given the set of extracted elementary ridge and valley segments, we aim at merging these elementary segments to form meaningful curves. Numerous perceptual grouping algorithms have been developed to extract curves from candidate points or elementary segments [START_REF] Cao | Good continuations in digital image level lines[END_REF][START_REF] Guy | Inferring global perceptual contours from local features[END_REF]. These techniques rely on general geometric criteria such as good continuations [START_REF] Cao | Good continuations in digital image level lines[END_REF] or curve smoothness [START_REF] Guy | Inferring global perceptual contours from local features[END_REF]. When dealing with the analysis of growth rings within hard tissue images, three geometric features are of key interest: the growth rings are concentric; there is an alternation of opaque and translucent rings; opaque and translucent rings never cross each other.

The proposed grouping procedure exploits these features. More precisely, it proceeds as follows for elementary ridge segments (and, conversely for valley ring structures). For a given pair of elementary ridge segments associated to two neighboring angular sectors, the decision rule used to merge this pair of segments evaluates whether or not elementary valley segments within the neighboring angular sectors lie between the pair of tested segments in terms of distance to the growth center. Fig. 3 illustrates this decision rule for two cases: one where the merging is validated and the other one where it is rejected. A ridge curve is finally formed by the set of elementary ridge segments which can be linked by a path going through merged segments.

IMAGE INTERPRETATION FOR AGE AND GROWTH ESTIMATION

From a set of partial ring curves, the actual interpretation of the image content in terms of age and growth estimation comes to the selection of a curve subset corresponding to the actual growth rings. One should point out that several curve subsets might correspond to the correct interpretation, since an actual growth ring might be covered by several partial curves. Besides, some detected curves might not correspond to actual rings, but to false rings or might be due to noise patterns. To achieve this interpretation task, we rely on the protocols followed by expert readers. Mainly, it involves three different aspects: first, the detection of candidate ring-like structures; second, the evaluation of the significativity of any possible rings w.r.t. length and contrast information; third, the analysis of the spacial arrangement of the validated ring structures, which needs both to correspond to an alternation of translucent and opaque rings, and to conform to some a priori growth features.

To take off these protocols, the selection of a relevant curve subset is stated as a Bayesian labeling issue, where a binary label, "selected" or "rejected" is assigned to each extracted ridge or valley curve. Let us denote by C the set of extracted ridge and valley curves as described in the previous section. This set is sorted w.r.t. the distance between ring curves and the growth center (the computation of this distance needs to be direction-invariant ans is normalized w.r.t. the distance along the main reading axis). Let us also define L the binary label set {"selected", "rejected"}, e C the set of labels {e c } c∈C for a given labeling configuration, o C = {o c } c∈C the features computed for all ring curves c ∈ C to evaluate their significativity. The selection of the relevant curve subset then comes to retrieve the best labeling configuration êC maximizing the MAP crite-rion: êC = arg max

U 1 (L c , e c ) = 1 -s 1 (L c -ν 1 ), if e c = "selected" U 1 (L c , e c ) = s 1 (L c -ν 1 ), if e c = "rejected" ,
where s 1 () is a smooth step function rescaled between 0 and 1 and ν the length threshold. This parameter value is easy to set since it simply expresses from which length value a ring curve is regarded as visually significant.

In order to explicitly define the a priori term P (e C ), we further introduce g eC the growth pattern associated to the label configuration e C (i.e., the growth pattern computed for the selected ring curves S(e C ){c * ∈ C/e c * = selected}). P (e C ) is then evaluated as the likelihood that the growth pattern g eC is relevant w.r.t. a priori growth information: P (e C ) = P (g eC is relevant). This probabilistic model is learned from training samples using kernel logistic regression as presented in [START_REF] Fablet | Statistical learning applied to computer-assisted fish age and growth estimation from otolith images[END_REF].

Solving for the MAP criterion:

êC = arg max eC ∈L |C| P (o C |e C )P (ge C is relevant) (1)
cannot be achieved by testing over all possible configurations (since C typically involves about 50 curves, there are 2 |C| possible configurations). Therefore, this minimizarion is carried out in a causal manner by introducing one-by-one ring curves c ∈ C. At step k, provided the current set of labeling configurations, we evaluate the likelihood of the configurations generated by adding the k th ring curve in C once with the label "selected" and once with the label "rejected" to each configuration of the current configuration set. We then only retain the N max best configurations w.r.t. likelihood values P (e c |o c ). Typicaly, N max is set to 50.

EXPERIMENTS

For all the experiments reported in this Section, we use the same parameter setting. axis uniformly sampled. The angular sector used for each local template is ∆θ SL = π/90. Concerning the Bayesian labeling of the set of extracted ring curves, the threshold ν 1 is set to π/8 and β to 10.

Extraction and interpretation examples

We first report in Fig. 4 three examples of the extraction of meaningful ring curves within images of biological hard tissues: a plaice otolith, the shell of a bivalve seashell, and the section of a tree trunk. All these images share common characteristics in terms of rather concentric ridge and valley structures associated to a growth-based modulation.

As expected, the proposed template-based growth-adapted scheme extracts meaningful ring curves mainly corresponding to the actual growth rings.

For validation purposes, the emphasis is given to fish otoliths. Among the different kinds of biological hard tissues, they provide representative examples in terms of complexity of the interpretation task. This will also enable the quantitative comparison to previous work [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF][START_REF] Traodec | Use of deformable templates for otolith 2D growth ring detection by digital image processing[END_REF][START_REF] Welleman | Automatic ageing of Plaice otoliths by means of image analysis[END_REF]. Our evaluation set is formed by 400 hundred plaice otoliths from the fourth quarter collected by Ifremer at the fish-market of Boulogne/Mer in 1993 and 2000. Half of the dataset is used to train the a priori growth, whereas the other half is used for the evaluation of our approach.

To illustrate the behavior of the different stages of our approach, we provide in Fig. 5 the results for a six year old plaice otolith (seven translucent rings). Relevant ridge curves are extracted, and the selected interpretation is the same as the expert one. This example was chosen to illustrate the ability of our approach to extract ridge and valley structures close to the otolith edge thanks to the growth-adapted filtering used within the semi-local template framework. Concerning computational time, our approach runs under Matlab 7. The extraction of 2D ring curves runs in about 30 seconds on a 2.4GHz Pentium IV, whereas the Bayesian labeling needs a few seconds. interpretations, the second one the extracted ridge curves, the third one the curve subsets selected for age and growth estimation and the fourth one the estimated growth patterns compared to the ground truth ones. For each example, the ground truth is provided by the interpretation of an expert in Plaice otolith reading.

Quantitative evaluation

Using the second half of the collected set of plaice otoliths (i.e., a database of 200 otoliths), we have carried out a quantitative evaluation of the proposed approach. The age distribution of this database is reported in Fig. 6. This is representative of the age distributions estimated from commercial landings, where samples of age group six and less usually represent more than 90% of the total. Otoliths older than six can also be found. However, the number of samples for age groups greater than six is not sufficient to learn a relevant growth model. Consequently, they were not considered during our evaluation. The whole set of otoliths was interpreted by an expert in plaice age readings. We use these interpretations as the ground-truth to compute the class-by-class and overall age estimation errors. These results are given in Fig. 6. The agreement rate is comprised between 84% for age group five and 94% for age group two. The overall agreement rate of 89% shows that the proposed approach outperforms previous work, since the maximum overall agreement rate for the different 2D methods evaluated in [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF] was below 80% for a similar test set. These results stress the need for the Bayesian interpretation stage combined to the extraction of candidate ring curves. Besides, for the whole set of 200 otoliths, the estimation error is never greater than one. In addition, the obtained results are in the range of the interexpert agreement rates, what validates the interest of the proposed approach as an operational aging tool.

Fig. 2 .

 2 Fig. 2. Local template-based scheme for the detection of elementary ring segments

Fig. 3 .

 3 Fig. 3. Decision rule for merging a pair of neighboring elementary ridge segments: a) validated merging, b) rejected merging. The pair of tested segments is displayed by a solid line, and neighboring elementary valley segments by dashed lines.

  eC ∈L |C| P (o C |e C )P (e C ), where P (o C |e C ) is the data-driven term and P (e C ) integrates an a priori knowledge on growth variability. The data-driven likelihood P (o C |e C ) is intended to evaluate the significativity of each ring curve given a labeling configuration e C : P (o C |e C ) = c∈C P (o c |e c ). As previously mentioned, experts mainly rely on the perception of contrast and ring continuity. Since contrast information is already implicitly used to extract ring curves, the likelihood P (o c |e c ) is defined from the angular length L c of the curve c. Using an energy setting, P (o c |e c ) is expressed as: P (o c |e c ) ∝ exp[-U 1 (L c , e c )]. The energy function U 1 is designed to favor the selection of ridge and valley curves with a large length value:

Fig. 6 .

 6 Fig. 6. Age estimation errors for the test set of 200 images of Plaice otoliths.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Examples of extraction of meaningful ring structures within images of biological hard tissues depicting growth ring structures. Thefirst image displays an application to a fish otolith, the second one to the shell of a bivalve seashell and the third one to the section of a tree trunk.Otolith images partial ring curves selected ring curves Estimated growth pattern


Elise Azar

Christophe Blanc

Ahmad Mehdi

Maurizio Nobili

Antonio Stocco
email: stocco@unistra.fr

Mesoporous Silica Colloids

Keywords: Wetting, Surface Diffusion, and Cationic Surfactant Adsorption

come

INTRODUCTION

Cationic surfactants are widely used in many industrial and fundamental research fields ranging from cosmetics, fabrics, nanoparticles synthesis, DNA folding, self-assembly and mesoporous material fabrication. [START_REF] Heinz | Nanoparticle Decoration with Surfactants : Molecular Interactions , Assembly , and Applications[END_REF][START_REF] Paria | A Review on Experimental Studies of Surfactant Adsorption at the Hydrophilic Solid -Water Interface[END_REF] Besides these applications, the fate of cationic surfactants and the resulting waste in water is an important issue, since cationic surfactant contamination of water represents an real environmental problem. [START_REF] Olkowska | Occurrence of Surface Active Agents in the Environment[END_REF] Current methods to remove surfactants from water involve the use of organophilic clays, flocculants or carbon beds. [START_REF] Li | Counterion Effects on the Sorption of Cationic Surfactant and Chromate on Natural Clinoptilolite[END_REF][START_REF] Kotti | Removal of Cationic Surfactants from Water by Adsorption on Attapulgite[END_REF][START_REF] Maria-Hormigos | Carbon Nanotubes-Ferrite-Manganese Dioxide Micromotors for Advanced Oxidation Processes in Water Treatment[END_REF][START_REF] Das | Prospects of Biosynthesized Nanomaterials for the Remediation of Organic and Inorganic Environmental Contaminants[END_REF][START_REF] Yang | Application of Graphene-Based Materials in Water Purification: From the Nanoscale to Specific Devices[END_REF] In many separation methods, surfactant removal by adsorption onto solid substrates is required. Hence, both large surface areas and an effective attraction between the surfactant and the solid are necessary to drive soluble surfactants adsorption on the solid boundaries.

Adsorption of cationic surfactants on planar solid surfaces has been investigated for several surfactantsubstrate systems. For cetyltrimethylammonium (CTA + ) surfactants on silica surfaces, different adsorption regimes are found as a function of the surfactant concentration, surface charge and hydrophobic interaction. [START_REF] Goloub | Adsorption of Cationic Surfactants on Silica . Surface Charge Effects[END_REF][START_REF] Atkin | Mechanism of Cationic Surfactant Adsorption at the Solid -Aqueous Interface[END_REF] At low concentrations, surfactant may adsorb onto the silica surface as a monolayer, as defective bilayers or as surface micelles. [START_REF] Rennie | Structure of Cationic Surfactant Layer at the Silica-Water Interface[END_REF][START_REF] Tyrode | Adsorption of CTAB on Hydrophilic Silica Studied by Linear and Nonlinear Optical Spectroscopy[END_REF] These micellar structures are flattened by the surface and possess a thickness of 3.5 nm and a lateral size of 9 nm. [START_REF] Atkin | Mechanism of Cationic Surfactant Adsorption at the Solid -Aqueous Interface[END_REF] Upon increasing the concentration, bilayers may form due to the interaction between the hydrophobic chains. It is important to notice that the interfacial self-assembled structures usually appear at a concentration lower than the usual critical micellar concentration (CMC) in the volume. [START_REF] Rennie | Structure of Cationic Surfactant Layer at the Silica-Water Interface[END_REF] For CTA + surfactants at concentrations C lower but close to CMC, surface excess concentrations  between 1 and 2 mg/m 2 have been reported. [START_REF] Rennie | Structure of Cationic Surfactant Layer at the Silica-Water Interface[END_REF][START_REF] Atkin | Adsorption Kinetics and Structural Arrangements of Cationic Surfactants on Silica Surfaces[END_REF][START_REF] Biswas | Kinetics of Adsorption of Cationic Surfactants at Silica-Water Interface[END_REF][START_REF] Wangchareansak | Coadsorption of Low-Molecular Weight Aromatic and Aliphatic Alcohols and Acids with the Cationic Surfactant, CTAB, on Silica Surfaces[END_REF] As pointed out before, solid substrates with large specific areas are required for adsorption in order to separate surfactants from clean water. In this context, porous particles are ideal candidates given the large surface/volume ratio, which can be tuned by the pore size and volume fraction. [START_REF] Lehman | Zeolite and Mesoporous Silica Nanomaterials: Greener Syntheses, Environmental Applications and Biological Toxicity[END_REF][START_REF] Tang | Efficient Removal of Both Antimonite (Sb( Iii )) and Antimonate (Sb( v )) from Environmental Water Using Titanate Nanotubes and Nanoparticles[END_REF] However, adsorption inside a pore strongly differs from the adsorption on a planar interface. Pore size and morphology affect the adsorption process, which depends on differences in pressure and physicochemical properties inside and outside the pores. [START_REF] Liu | Gibbs Ensemble Monte Carlo Simulation of Adsorption for Model Surfactant Solution in Confined Slit Pores[END_REF] Non-ionic surfactants adsorption onto mesoporous silica particles has been widely investigated by Findenegg and coworkers. [START_REF] Shin | Surfactant Self-Assembly in Cylindrical Silica Nanopores[END_REF][START_REF] Shin | Structural Characterization of Surfactant Aggregates Adsorbed in Cylindrical Silica Nanopores[END_REF][START_REF] Qiao | 2H NMR Investigation of the Structure and Dynamics of the Nonionic Surfactant C12E5 Confined in Controlled Pore Glass[END_REF][START_REF] Müter | Adsorption and Depletion Regimes of a Nonionic Surfactant in Hydrophilic Mesopores : An Experimental and Simulation Study[END_REF] Bilayers formation and other structures inside the pores has been reported. Very few experimental investigations can be found in the literature for the adsorption of cationic surfactants onto mesoporous silica. A small angle neutron scattering investigation reported some preliminary experiments for 8 nm pore size mesoporous silica at pH=9 where an increase of cationic surfactant adsorption occurs if the ionic strength is increased. [START_REF] Shin | Surfactant Adsorption in Ordered Mesoporous Silica Studied by SANS[END_REF] Cationic surfactant interacting with silica nanoparticles have been also recently investigated. [START_REF] Heinz | Nanoparticle Decoration with Surfactants : Molecular Interactions , Assembly , and Applications[END_REF][START_REF] Kumar | Size-Dependent Interaction of Silica Nanoparticles with Different Surfactants in Aqueous Solution[END_REF][START_REF] Sharma | Adsorption of Nonionic Surfactant on Silica Nanoparticles : Structure and Resultant Interparticle Interactions[END_REF][START_REF] Ahualli | Adsorption of Anionic and Cationic Surfactants on Anionic Colloids : Supercharging and Destabilization[END_REF] Here, we have investigated the wetting and diffusion of porous silica colloids, and the adsorption of cationic surfactants on porous colloidal particles. Porous colloids of different pore sizes are deposited both in the bulk and at the interface. By varying pore size, surfactant concentration and investigating counterion effects we aim at controlling CTA + cationic surfactant adsorption. These results could be used in order to develop a strategy to clean the surface and the volume of water with micron sized particles, which are small enough to perform Brownian motion and rapidly diffuse at the interface (and in the volume) but also large enough to slowly sediment. These porous colloids may be ideal candidates for an efficient removal of surfactants at low concentrations and present the advantage to be easily removed after decontamination by sedimentation or flotation. Note that larger particles are difficult to adsorb at the interface and may sediment very fast; whilst nanoparticles may remain dispersed in water due to the strong Brownian motion and cannot be separated by gravity or adsorption on bubbles as in flotation.

MATERIALS AND METHODS

Materials. All chemicals, except for the in-house synthetized colloids, were purchased from Sigma Aldrich and used without further purification. Two surfactants were investigated: cetyltrimethylammonium bromide CTA + Br  (CAS 57-09-0, molecular weight M w = 364.45 g/mol) and cetyltrimethylammonium hydroxide CTA + OH  (10 wt.% in H 2 O, CAS 505-86-2, M w = 301.55 g/mol). Three different batches of porous silica particles were also employed. The first two consist of spherical mesoporous silica colloids (CAS 7631-86-9) with an average radius = 1.23 ± 0.10 µm (measured by scanning electron microscopy, SEM) and nominal pore diameter d = 2 nm and d = 4 nm and a specific area S A = 1000 ± 100 m 2 /g for d = 2 nm and S A = 350 ± 50 m 2 /g for d = 4 nm. A third batch of nonspherical mesoporous silica particles was synthetized in the laboratory. These last particles are currently called Santa Barbara amorphous-15 silica (SBA-15). The average pore diameter is larger than the previous ones: d =7 nm measured by volumetric nitrogen sorption isotherms. Stable particle dispersions were obtained by sonication of 1.2 mg/mL dispersions in an ultrasound bath for one hour. We measured the Feret diameter [START_REF] Tsubaki | A Proposed New Characterization of Particle Shape and Its Application[END_REF] of these particles by scanning electron microscopy, which leads to an equivalent radius = 1.96 ± 0.97 µm (i.e. half of the Feret diameter). The pores are about a micron long and connected via mesoporous walls. A total specific area of 750 ± 50 m 2 /g was evaluated by Brunauer-Emmett-Teller (BET) method. Pore size distributions were determined by the (Barrett, Joyner, Halend) BJH method. [START_REF] Mouawia | From Simple Molecules to Highly Functionalised Lamellar Materials[END_REF] Mesoporous walls contribute significantly to the total specific area in terms of microporosity (size < 1-2 nm). We evaluate a total specific area S A = 225 ± 25 m 2 /g for the d =7 nm pore size (See Figure S1 in Supporting Information, SI).

NaOH, NaBr, NaCl salts were used as received. Fresh Milli-Q water was used throughout this work. Experiments were carried out at room temperature T = 22 °C.

Surface tension and sessile drop contact angle. Surface tension was used to measure surfactant adsorption on porous particles. All measurements were performed in a 9 cm diameter polystyrene Petri dish containing a volume V = 35 mL of surfactant solutions at different concentrations C and a fixed mass (1.2 mg) of porous particles. For planar aqueous surfaces contained in a Petri dish, surface tension was measured by the Wilhelmy plate method (KSV NIMA, Biolin Scientific) using a filer paper plate. In order to evaluate the interfacial tensions of the silica-surfactant solutions-gas systems, we also measured the surface tension of aqueous solutions and the advancing contact angle  of sessile drops by a profile analysis tensiometer (PAT, Sinterface, Germany). A typical volume of the aqueous drop in PAT experiments is 15 mm 3 . Series of experiments were repeated at least three times and show a good reproducibility. For interfacial tension measurements, the standard deviations of the data obtained in different experimental campaigns lay between 1 and 3 mN/m, which can be related to the experimental protocols: particle deposition, aging of particle dispersions and surfactant solutions (i.e. maximum 5 days).

Particle dispersion deposition.

The final chosen method adopted to deposit porous particles at the interface is to drop 1 mL of a 1.2 mg/mL particle suspension on a tilted glass slide placed at the air-water interface and let it slip. [START_REF] Lotito | Self-Assembly of Single-Sized and Binary Colloidal Particles at Air/Water Interface by Surface Confinement and Water Discharge[END_REF] Particle density at the interface can be calculated by counting the particle number using optical microscopy. For all porous particle systems, we evaluated an average surface coverage of 6.5±2 particles per mm 2 (if 1.2 mg of silica porous particles are added in the Petri dish). From the latter value, one can estimate the ratio between the total number of particles N tot and the ones trapped at the surface N s : N tot / N s  10 6 , which is very high, meaning that only few particles stay at the interface. We have put many efforts to find protocols to increase the number of particles remaining at the airaqueous solution interface and try several methods. However, protocols involving spraying or the use of additional volatile solvents were discarded since they do not allow the control of the particles numbers or introduce additional sources of contamination and uncertainties. It is important to note that even if N tot /N s  10 6 , the amount of particles at the interface is non-negligible for the adsorption of soluble surfactants, which accumulate preferentially at the interface but they are also present in the bulk, see Figure S2 in SI.

Particle contact angle by gel trapping. We measured the particle contact angle of porous silica colloids using a gel trapping technique. [START_REF] Paunov | Novel Method for Determining the Three-Phase Contact Angle of Colloid Particles Adsorbed at Air -Water and Oil -Water Interfaces[END_REF] Few microliters of a diluted solution of particles were added to a gelled solution of Phytagel (CAS 71010-52-1, Sigma Aldrich) in a small container. After heating up the gel to the liquid state, the particles get trapped at the interface. Going back to the room temperature, a UV-glue was used to transfer the particles from the gel to the glue substrate. The contact angle was measured using scanning electron microscopy images of the transferred particles on the solidified glue at their complementary contact angle positions.

Particle tracking. Bright field optical microscopy was used for particle tracking. Experiments were performed in an upright Leica optical microscope mounted on an anti-vibration table. Images of isolated particles were recorded using a CMOS camera (Orca Flash 4.0, Hamamatsu) at rates of 80 or 100 frames per second using objectives of different magnifications (×63 and ×100). Tracking of the particle location was done by an IDL routine or by using an image correlation-based approach (''Stat Tracker St. Andrews'') implemented in Labview (National Instruments).

Zeta potential and pH measurements. We measured the zeta potential  (Zetasizer Nano ZS, Malvern Instruments) and the pH of the particle dispersions in pure water or in the presence of surfactants. For porous silica colloids dispersions, a pH = 6.4 was always measured in pure water.

RESULTS AND DISCUSSION

Interfacial tensions of CTA + Br  and CTA + OH  at the liquid-gas and solid-liquid interfaces We started characterizing the adsorption of CTA + surfactants on non-porous silica by evaluating the interfacial tension between silica and the aqueous surfactant solutions,  SL . Young equation for a sessile drop of aqueous surfactant solutions on a silica substrate in air reads:

 SG =  SL   LG cos, (1)
where the subscripts S, L and G represent solid, liquid and gas respectively. One can evaluate  SL measuring the interfacial tension  LG , the sessile drop static contact angle and assuming that  SG is a constant (and does not vary with the surfactant concentration). Surface tension at the air-aqueous solution interface  LG for CTA + Br  and CTA + OH  surfactant was measured by the Wilhelmy plate technique and pendant drop tensiometry. The two methods lead to very similar results as shown for a series of experiments in Figure 1A. The evolution of  LG as a function of the surfactant concentration C for both surfactants shows no significant difference. In addition,  LG values are stable and do not change in a typical experimental time range of 3000 s (inset of Figure 1A). Sessile drops made with surfactants solutions were deposited on clean glass slides and their contact angles were also evaluated by imaging the drop profile (and the cos is plotted in the inset of Figure 1B for a series of experiment). [START_REF] Zorin | Influence of Cationic Surfactant on the Surface Charge of Silica and on the Stability of Aqueous Wetting Films[END_REF] Hence,  SL can be calculated from eq. 1 with  SG = 68.5 mN/m as reported by Binks et al. [START_REF] Binks | Solid Wettability from Surface Energy Components: Revelance to Pickering Emulsion[END_REF] for silica surfaces showing water contact angle similar to our experiments. Unexpectedly the silica-aqueous solution interfacial tension  SL shows a non-monotonic behavior if the surfactant concentration is increased. [START_REF] Haidara | A Direct Method of Studying Adsorption of a Surfactant at Solid-Liquid Interfaces[END_REF][START_REF] Haidara | Kinetics and Thermodynamics of Surfactant Adsorption at Model Interfaces : Evidence of Structural Transitions in the Adsorbed Films[END_REF] For C ≥ 0.1 mM,  SL increases if C increases, instead of decreasing as  LG . Hence, the Gibbs adsorption valid for ideal dilute solutions for C < CMC ( 0.8-0.9 mM) [START_REF] Atkin | Mechanism of Cationic Surfactant Adsorption at the Solid -Aqueous Interface[END_REF][START_REF] Monticone | Coadsorption of Phenoxyalchohols and Cationic Surfactans with Various Headgroups at the Silica/Water Interface[END_REF] can be applied only for the air-liquid interface, where a surface concentration   1 mg/m 2 at the CMC can be evaluated. [START_REF] Stocco | Interfacial Behavior of Catanionic Surfactants[END_REF] For C < 0.1 mM at the solidliquid interface, one could also observe a tiny decrease of the interfacial tension which could correspond to an increasing accumulation of non-interacting surfactants at the solid-liquid interface. [START_REF] Pyter | Wetting of Solids by Surface-Active Agents : The Effects of Unequal Adsorption to Vapor-Liquid and Solid-Liquid Interfaces[END_REF] However for C ≥ 0.1 mM, the increase of  SL points to the formation of self-assembled structures as bilayers [START_REF] Rutland | Surface Forces between Silica Surfaces in Cationic Surfactant Solutions : Adsorption and Bilayer Formation at Normal and High PH[END_REF] or surface micelles, which form because of the hydrophobic interactions between surfactant tails. Note that the concentration at which the interfacial tension  SL increases is about 10 times lower that the CMC. [START_REF] Atkin | Mechanism of Cationic Surfactant Adsorption at the Solid -Aqueous Interface[END_REF] An increase of the interfacial tension  SL reveals that the surface is increasing in hydrophobicity due to the presence of hydrophobic surfactant groups. As already pointed out in the Introduction, the presence of bilayers or surface micelles on planar silica surfaces has been widely reported but to the best of our knowledge was never connected to a minimum in the interfacial tension  SL .

Porous particles at the interface

The contact angle of porous particles at the gas-liquid interface was measured by a gel trapping method (see Materials and Methods). Figure 2 shows images of particles at their complementary contact angle positions. We have also observed some crater shape footprints on the solidified substrate, which correspond to particles possessing very low contact angles. For spherical porous particle, we measured particle contact angle  = 47° ± 6° for d = 2 nm and  = 52° ± 14° for d = 4 nm (Figure 2A andB). Nonspherical porous particles show also a finite immersion at the air-water interface that is comparable to the contact angle observed for the spherical porous particles. It is important to notice that the measured contact angle of a sessile water drop on silica,   26°, is significantly lower than the contact angles of porous silica particles shown in Figure 2:  In order to explain this result, we start discussing the partial wetting state of porous particles and compare it to the reference case of a bare solid spherical particle, see Figure 3. For a bare particle, the equilibrium of interfacial tensions leads to the Young equation (see equation 1). For smooth and homogenous surfaces, the bare solid micron-sized particle contact angle should be identical to the contact angle of a sessile liquid drop on a flat solid substrate:     In the framework of the Cassie-Baxter model valid for composite interfaces, two different scenario can be considered for porous particles at the interface.

In the first case, we consider that the pores of the particles are completely filled by the liquid. In this case, the particle interfacial tensions  SG and  SL change if compared to the bare particle case. The interfacial tension of the particle exposed to the liquid will be reduced from  SL to f SL , where f is the solid area fraction on the particle surface, see Figure 3. The particle surface exposed to the gas phase can be regarded as a composite interface made of solid and liquid.  The resulting equilibrium of interfacial tensions reads:

f SG +(1f) LG = f SL +  LG cos (2)
Except for f, all the other variables in equation 2 are measured. In pure water,  SG = 68.5 mN/m,  LG = 72.5 mN/m and  SL = 4 mN/m (Figure 1). According to equation 2,  decreases if f decreases and the Young equation is recovered if f =1. Actually for porous particles with pores completely filled by the liquid, the particle contact angle is expected to be low,  , which explains the observation of crater footprints in SEM images and the large number of particles in the volume with respect to the particles present at the interface (see Particle dispersion deposition section). Note also that the interfacial energy  gain associated to the adsorption of a bare particle at the interface  LG A 0 due to the removal of a bare fluid interface area (A 0 =R 2 sin 2 ) is strongly reduced for a porous particle given the presence of liquid inside the particle.  A second scenario can be considered to explain the results shown in Figure 2, where   (Figure 3)In this case, the liquid is not present on the porous particle surface exposed to the gas phase. Hence, the external surface can be regarded as a composite surface made of solid and air, and the interfacial tension of this surface becomes f SG . The resulting equilibrium of interfacial tensions reads:

f SG = f SL +  LG cos (3)
In this second case, the contact angle of a porous particle can be higher than the contact angle of an equivalent bare particles. Equation 3 can be rewritten in the form (see equation 1), which leads to solid area fraction f = 0.76 for 2 nm and f = 0.68 for 4 nm pore size porous particles.

Figure 3. Sketches of a bare non-porous particle (left), a porous particle with pores completely filled by the liquid (center) and a porous particle with pores partially filled by the liquid (right) in mechanical equilibrium at the gasliquid interface.

Influence of particle pore size on surfactant adsorption

In order to measure the surfactant adsorption on porous silica colloids we performed surface tension experiments using a Wilhelmy plate apparatus. Starting from a stable interfacial tension measurement at a given surfactant concentration C, porous colloids are deposited at the air-aqueous solution interface via a tilted glass slide. Note that the addition of few porous colloids (1.2 g in 35 mL water) in absence of surfactants does not affect the interfacial tension  LG . As a consequence of the addition of mesoporous particles, we record an increase of the liquid-gas interfacial tension connected to a surfactant removal from the aqueous solution due to the adsorption on porous silica colloids.

In Figure 4 we show a series of surface tension experiments of CTA + Br  and CTA + OH  solutions at different surfactant concentrations in the presence of a fixed number of porous silica particles of 4 and 7 nm pore diameters d. For CTA + OH  in the presence of the d = 4 nm (Figure 4A) and 7 nm (Figure 4B) porous silica particles, we measured a significant increase in the surface tension, which is a clear evidence of surfactant removal from the aqueous solution. When adding d = 4 nm porous silica colloids, the interfacial tension increases by 8 mN/m, 5 mN/m and 4 mN/m for 0.25 mM, 0.5 mM and 0.7 mM respectively. As for the d = 7 nm porous silica colloids, the surface tension increases by 12 mN/m, 9 mN/m and 7 mN/m for 0.25 mM, 0.5 mM and 0.7 mM respectively. Surprisingly, no apparent increase in the surface tension with CTA + Br  was observed, which will be further analyzed and discussed in the following sections. No adsorption for both CTA + Br  and CTA + OH  was also observed for d = 2 nm porous silica colloids, see Figure 5. Surface tension measurements showed no variation before and after adding the d = 2 nm porous particles (Figure 5), leading to the conclusion that a pore size of 2 nm is too small for CTA + cationic surfactant adsorption. This result agrees with the increase of  SL shown in Figure 1B and connected to the formation of surface micellar structures at concentrations much lower than the CMC. Surfactants may adsorb inside the pores as micellar structures and not as single molecules. The size of micelles in the bulk [START_REF] Atkin | Mechanism of Cationic Surfactant Adsorption at the Solid -Aqueous Interface[END_REF] (for C  CMC) is between 2.6 and 4.7 nm; and for C < CMC the thickness of surface micelles is about 3.5 nm for CTA + Br  . Hence, these dimensions are always larger than the size of 2 nm and explain why adsorption is not observed in d = 2 nm porous particles.

Figure 6B shows  S as a function of CTA + OH  concentration for d = 4 and 7 nm porous silica particles.

For C = 0.1 mM, we measured a weak adsorption of surfactants on porous silica particles  S = 1-3 mg/m 2 , which is equivalent to the surface excess of CTA + surfactant forming dense monolayers at the interface.

For non-spherical silica particles with d = 7 nm,  S increases up to 10 mg/m 2 at intermediate concentrations and slightly decreases if C approaches the CMC (0.9 mM). For spherical silica particles with d = 4 nm, the surface concentration increases up to  S  4 mg/m 2 and significantly decreases if C approaches the CMC. It is interesting to note that at low concentrations,  S is proportional to the pore size, meaning that pores are filled with surfactants. In this pore size range and for surfactant concentrations far from the CMC, the larger the pore diameter the larger the surfactant adsorption. Close to the CMC however surfactants start to self-assemble in the form of micelles in the volume. As a consequence, a competition between the self-assembly of surfactants in the volume and the adsorption inside the pores of the silica particles is expected. This competition may also depend on the confinement dictated by the pore size. If the pore confinement effect is very strong, micelles in the volume could hinder surfactant adsorption inside the particles' pores. For d = 4 nm porous particles, the decrease of  S as a function of concentration seems in agreement with this scenario. For pore size d = 7 nm, the pore confinement effect is weaker than for d = 4 nm given that the micellar dimensions are about 3.5 nm, i.e.

the half of the pore size, which explains the weak decrease of  S as a function of concentration close to the CMC, see Figure 6B.

Porous particle diffusion at the gas-liquid interface

At the single colloidal particle level, we have also noticed striking differences in the translational diffusion of spherical d = 4 nm porous particle at the gas-liquid interface in the absence and the presence of CTA + surfactants. Tracking the particle center of mass at the air-water interface, we observed Brownian trajectories (see inset Figure 7A) and measured the mean squared displacement (MSD), which is plotted as a function of the lag time t in Figure 7A. Translational diffusion coefficients at the surface, D s : can be calculated by MSD = 4 D s t.

In absence of surfactants, D s for d = 2 and 4 nm pore particles agrees with the hydrodynamic prediction for partially immersed particles at clean and flat fluid interface, see Figure 7B: 40

, ( 5
)
where k B T is the thermal agitation energy,  is the liquid viscosity and k t is the drag factor accounting for the particle immersion or contact angle at the interface: [START_REF] Aaron | Drag and Diffusion Coefficients of a Spherical Particle Attached to a Fluid Interface[END_REF] (for 0< <90°) .

For the particle diffusing in the bulk our experimental results agree with the Stokes-Brownian diffusion = 0.174 µm 2 /s. In absence of surfactants, the good agreement between the 1.4 < D S /D 0 < 1.5

experiments and the prediction shows that no additional dissipation due to contact line fluctuations (as observed for bare silica colloids with 1.2 < D S /D 0 < 1.3) 41 occur on partially wetted porous particles. As pointed out before the external porous particle surface can be regarded as a composite surface made of hydrophilic silica and fluids. Hence, this surface presents less defects than the surface of a bare particle, which may explain the negligible line friction due to surface defects. [START_REF] Boniello | Brownian Diffusion of a Partially Wetted Colloid[END_REF] As a perspective, one may wonder if these porous particles could be good probes for passive surface microrheology since the only sources of dissipations seem to be the viscosity.

Surface diffusion coefficients of porous particles change significantly in the presence of CTA + OH  (C = 0.5 mM): 1.1 < D S /D 0 < 1.2, and in CTA + Br  (C = 0.5 mM) aqueous solutions: D S /D 0 ≈ 0.3, see Figure 7.

The experiments are performed at times ≈ 3000 s, where an increase of the gas-liquid interfacial tension of 5 mN/m for CTA + OH   and no change for CTA + Br  were measured, see Figure 4. Hence the presence of surfactants affect strongly the porous particle translational diffusion at the surface. For porous particles in the presence of CTA + OH  ,adsorption of surfactants inside the pores occurs during the porous particle Brownian motion, whilst in the presence of CTA + Br  no adsorption dynamics occurs. In order to quantify the decrease of the surface translational diffusion D S , we use a model describing the drag felt by a spherical particle straddling a viscous and incompressible interface possessing a surface viscosity  S at low Boussinesq numbers < 1. The drag factor in equation 5 in this case reads: 42 ,

For CTA + Br  (C = 0.5 mM) aqueous solutions, a surface viscosity  S  10 8 Pa.s.m fits well the experimental result. In the literature, a large range of values of  S , from 10 8 to 10 6 Pa.s.m, are reported for soluble monolayers by surface macrorheology. [START_REF] Langevin | Surface Shear Rheology of Monolayers at the Surface of Water[END_REF] Usually a large difference is also measured between surface macro-and micro-rheology ( S = 10 10 …10 9 Pa.s.m), [START_REF] Sickert | Single-Particle Brownian Dynamics for Characterizing the Rheology of Fluid Langmuir Monolayers[END_REF] which could be due to additional dissipations or some boundary conditions not included in the analysis of the results. [START_REF] Shlomovitz | Measurement of Monolayer Viscosity Using Noncontact Microrheology[END_REF][START_REF] Stocco | Rotational Diffusion of Partially Wetted Colloids at Fluid Interfaces[END_REF] Recent experiments using noncontact microrheology, with completely wetted particles as probes, report  S 10 8 …10 7 Pa.s.m, 45 which agree with our results for CTA + Br   For CTA + OH  instead our results  S  5.10 10 Pa.s.m are comparable to passive surface microrheology using partially wetted particles as probe particles. [START_REF] Sickert | Single-Particle Brownian Dynamics for Characterizing the Rheology of Fluid Langmuir Monolayers[END_REF] Given that the liquid-gas interfacial tensions are similar for CTA + Br   and CTA + OH  , one possible explanation of the difference in D S between the two surfactant solutions is related to the surfactant dynamics occurring at the porous particle surface. As already pointed out before, the adsorption of CTA + OH  surfactants inside the pores could lead to a local depletion of the surfactant concentration close to the external surface of the porous particle and therefore in a smaller surface viscosity felt by the particle. 373

Influence of the counterion on surfactant adsorption

We start this section by analysing the remarkable difference in surfactant adsorption on porous particles observed between CTA + OH  and CTA + Br  . For planar non-porous interfaces, both interfacial tensions at the liquid-solid and liquid-gas point to a very similar behaviour for CTA + surfactants, independently from the counterions. However, CTA + Br  surfactants do not adsorb on d = 4 and 7 nm porous particles, while To explain this striking different behavior we started to look at the pH of the solution. Adding CTA + OH  surfactants in the solution in fact alters the pH of water, which changes from 6.4 to 10.5 for C = 0.5 mM. It is also well known that for planar silica surfaces, cationic surfactant adsorption usually increases if the pH increases because of the increase negative charge of the silica surface. [START_REF] Monticone | Coadsorption of Phenoxyalchohols and Cationic Surfactans with Various Headgroups at the Silica/Water Interface[END_REF] In order to test this hypothesis, we have added Na + OH  to a CTA + Br  solution (C = 0.5 mM) in the presence of porous particles. The final pH measured is very similar (pH = 10.7) to the pH of CTA + OH  surfactants where a strong adsorption was observed. However also in this case, CTA + Br  surfactants do not significantly adsorb on porous silica particles, see Figure 8. It is also important to notice that for planar interfaces, CTA + Br  adsorb on silica even if the pH remains around 6. [START_REF] Monticone | Coadsorption of Phenoxyalchohols and Cationic Surfactans with Various Headgroups at the Silica/Water Interface[END_REF] If OH  ions are not sufficient to trigger surfactant adsorption on porous particles, we consider the opposite scenario for which the ion Br  is able to hinder CTA + adsorption on silica. Therefore, in the presence of porous particles, we measure the surface tension of CTA + OH  solution adding 1 mM of Na + Br  . In this case, we observe that the surface tension of CTA + OH  (in the presence of porous particles) remains constant instead of increasing, see Figure 8. Thus, it confirms that CTA + do not adsorb inside the pores of d = 4 and 7 nm silica particles if Na + Br  is present in the aqueous solution. In order to verify if this effect is specific to Na + Br  , we have also tested another salt: Na + Cl  . The surface tension of CTA + OH  (in the presence of porous particles) in this case increases only by 1 to 3 mN/m, which confirms a salt hindrance effect on adsorption (see Figure 8).

Attempting to rationalize these finding, we consider some specific ionic phenomena related to adsorption phenomena. Some properties of OH  Br  Cl  and Na + are listed in table 1.The main differences between the three negative ions are their hydration numbers (3 for OH  , 2 for Cl  and just 1 for Br  ) and their

A B

Jones-Dole viscosity B coefficients connected to their ability to weaken or strengthen the interfacial water structure close to hydrophobic molecules such as the surfactant tails. Cl  is at the border (B  0 M 1 ) between chaotropic Br  (B = 0.04 M 1 ) and kosmotropic OH  (B = 0.18 M 1 ) behaviors. [START_REF] Marcus | Effect of Ions on the Structure of Water[END_REF] Hence OH  may favor hydrophobic interactions between CTA + hydrophobic groups, which supports the adsorption of surface micelles; whereas Br  leads to a weakening of these hydrophobic interactions. We have also measured the zeta potential  on bare porous particles, [START_REF] Kozak | Electrokinetics of Concentrated Suspensions and Porous Media. 1. Thin Electrical Double Layers[END_REF][START_REF] Kozak | Electrokinetics of Concentrated Suspensions and Porous Media. 2 Moderately Thick Electrical Double Layers[END_REF] which shows always negative values: 28.5 mV for d = 4 nm and 7.8 mV for d = 7 nm; as expected for hydrophilic silica. [START_REF] Allen | Stability of Colloidal Silica. II Ion Exchange[END_REF] For CTA + OH  surfactants, remains negative for C = 0.25 mM: mV for d = 4 nm andmVfor d = 7 nm particles. On the contrary, in the presence of CTA + Br   positive zeta potentials were measured at the same concentration (C = 0.25 mM):  mV for d = 4 nm and mV for d = 7 nm particles, which points to the accumulation of positive charges on the external surface of the porous silica colloids. Hence, CTA + from CTA + Br  (or H 3 O + ) may accumulate on the silica portion of the porous particle outer surface. This outer silica surface is very small with respect to the total porous particle surface, which may explain the negligible change of the interfacial tension (or pH) observed in the experiments. Both the chaotropic effect of Br  and the repulsion due to the positive  lead to a hindrance of CTA + adsorption inside the pores, which could explain the weak adsorption of CTA + Br  surfactants on porous silica colloids.

Some additional specific ion effects occur on the surface of silica, where silanol groups are known to undergo ion exchange reaction: 50,51 X + + SiOH = X(SiO) + H + for pH < 8, where X + is a cation (H 3 O + , Na + or CTA + ), and for pH > 8, SiOH + OH  SiO  Hence a competition between H 3 O + , Na + or CTA + cations is also expected. Na + from Na + Br  and Na + Cl  in fact competes with CTA + in the adsorption on silica, [START_REF] Dimov | Adsorption of Ionic Surfactants on Solid Particles Determined by Zeta-Potential Measurements : Competitive Binding of Counterions[END_REF] which can explain the weakening of CTA + OH  adsorption in the presence of a sodium salt (see Figure 8). Note that similarly to OH  , Na + possesses an elevated hydration number and a positive B coefficient corresponding to a kosmotropic behavior, see Table 1.

Table 1

CONCLUSIONS

We have herein reported some fundamental aspects of the wetting and surface diffusion of porous particles at the liquid-gas interface and explored the mechanisms underlying cationic surfactant adsorption inside the particle's pores. Contact angle of porous particles at the gas-liquid interface can be described in the framework of the Cassie model in partial wetting, and it depends strongly on the presence of the liquid inside the pores of the particle. For pores completely filled by the liquid, the particle contact angle is expected to be very low and porous particles may detach from the interface and diffuse in the bulk. Particle translational diffusion at the pure water interface agrees with the hydrodynamics prediction, OH  Br  Cl  Na + Bare ion radius (nm) [START_REF] Israelachvili | Intermolecular and Surface Forces[END_REF] 0.176 0.195 0.181 0.095 Hydrated radius (nm) [START_REF] Israelachvili | Intermolecular and Surface Forces[END_REF] 0.3 0.33 0.291 0.36 Hydration number (+/1) [START_REF] Israelachvili | Intermolecular and Surface Forces[END_REF] 3 1 2 4-5 B (M 1 ) [START_REF] Marcus | Effect of Ions on the Structure of Water[END_REF] +0.18 0.04 0.01  which makes these particles ideal probes for interfacial microrheology. Porous silica colloids are already able to adsorb efficiently CTA + OH  surfactants without any chemical surface treatments on silica. We determined a significant adsorption of CTA + OH  surfactant on d = 4 and 7 nm pore size colloids. The lack of adsorption for d = 2 nm porous particles agrees with the presence of surface micelles and not monolayers of surfactants inside the pores of silica. We quantified CTA + OH  surface concentration and showed that for C < CMC, the adsorption increases with the pore size. Therefore, we investigated the effect of the counterion on surfactant removal in order to understand the opposite adsorption behaviour observed between CTA + OH  and CTA + Br  on porous silica colloids. pH and surface charge effects are not able alone to explain our experimental findings, which points to the importance of kosmotropic/chaotropic counterion character. Surfactant adsorption on the porous particle affects also the particle translational diffusion at the interface, which points to different boundary conditions on the particle external surface. Finally, these results can be used to implement an environmental friendly strategy to remediate the surface of water from soluble and insoluble pollutants. Yet for future investigations, we plan to functionalize porous silica particles with hydrophobic groups to target contaminants that accumulate preferentially only on the water surface. Moreover, based on our expertise on self-propelled Janus silica particles at the interface, [START_REF] Wang | Enhanced Active Motion of Janus Colloids at the Water Surface[END_REF][START_REF] Wang | Janus Colloids Actively Rotating on the Surface of Water[END_REF] we plan to investigate the role of enhanced active diffusion on the kinetic of surfactant removal. [START_REF] Safdar | Light-Driven Micro-and Nanomotors for Environmental Remediation[END_REF] Attention will be paid to the effect of ionic species present in the aqueous medium on the self-propulsion particle behavior. [START_REF] Uygun | Self-Propelled Chelation Platforms for Efficient Removal of Toxic Metals[END_REF][START_REF] Eskandarloo | Nano-and Micromotors for Cleaning Polluted Waters: Focused Review on Pollutant Removal Mechanisms[END_REF]

Figure 1 .

 1 Figure 1. (A) Liquid-gas interfacial tension of CTA + Br  (+, ) and CTA + OH  (, ) as a function of the concentration obtained by pendant drop tensiometry (+,) and by Wilhelmy plate method (, ); inset: interfacial tension as a function of time for pure water () and CTA + Br  (+) and CTA + OH  () at C = 0.5 mM. (B) Solid-liquid

Figure 2 .

 2 Figure 2. SEM images of gel trapped = 1.23 µm spherical mesoporous silica colloids d = 2 nm (A) and d = 4 nm (B); and a non-spherical silica particle of equivalent radius = 1.96 µm (diameter = 3.92 µm) and d =7 nm (C).

Figure 4 .Figure 5 .

 45 Figure 4. Liquid-gas interfacial tension as a function of time after the deposition of d = 4 nm porous silica particles (A) and d = 7 nm particles (B) at different CTA + OH  surfactant concentrations: C = 0.25 mM (), 0.5 mM (), 0,7 mM (); and CTA + Br  concentration C= 0.7 mM (). 1.2 g of particles were added in 35 mL solution.

Figure 6 .

 6 Figure 6. Adsorption amount (A) and surfactant excess concentration on the total silica Area (B) for d = 7 nm (), and d = 4 nm () solid particles as a function of CTA + OH  initial concentration.

Figure 7 .

 7 Figure 7. (A) Mean squared displacement as a function of the lag time for d = 4 nm porous particles at the gas-liquid interface in pure water (), in C = 0.5 mM CTA + OH  aqueous solution () and in C = 0.5 mM CTA + Br  aqueous solution (). The inset shows a typical particle Brownian trajectory at the surface. (B) Ratio between the surface and the bulk diffusion coefficients as a function of the particle contact angle for the same systems shown in (A) and for d = 2 nm porous particles at the gas-liquid interface in pure water (). Solid line is the hydrodynamic prediction for a bare and clean interface. Dashed and pointed lines are drawn from a model valid for viscous and incompressible interfacial layers with a given surface viscosity  S .

Figure 8 .

 8 Figure 8. Salt effect on the liquid-gas interfacial tension as a function of time after porous particle deposition for d = 4 nm particles (A) and d = 7 nm particles (B). The surfactant concentration is fixed, C =0.5 mM, CTA + OH  data () are the same as in Figure 2. Data for CTA + Br -+ NaOH (), CTA + OH  + [NaBr] = 1 mM (), CTA + OH  + [NaCl] = 1 mM () and CTA + Br  + [NaCl] = 1 mM () as a function of time are also shown.

  OH  surfactants adsorb with very high surface excess concentrations  4-10 mg/m 2 for C around 0.5 mM.

		CTA +
	A	0.10		4			B		2.0
	MSD / m	0.05	y / µm	2 0	0	x / µm 2	4	D s /D 0	1.5 1.0	d=4 nm/CTA d=4 nm/water + OH -d=2 nm/water	 S =5.10	-10 Pa.s.m
						d=4 nm /Water d=4 nm /CTA + OH -		0.5	d=4 nm/CTA	+ Br	-	 S =10 -8 Pa.s.m
		0.00 0.00	0.05	0.10	d=4 nm /CTA	0.15 -+ Br		0.0	0	50	100
			t / s									 / °
													14

ACKNOWLEDGEMENTS

This article is dedicated to the memory of Giancarlo Stocco (1941Stocco ( -2019)). We acknowledge Labex Chemisyst (ANR-10-LABX-05-01) and the University of Montpellier for financial supports. We want also to thank Thomas Zemb, Olivier Diat, Gaelle Gassin, Martin In, Julian Oberdisse and Michael Gradzielski for discussions. We acknowledge Clarence Charnay for zeta potential experiments and Frederic Fernandez "University of Montpellier, Platform MEA" for the SEM microscopy. Finally, financial supports from the ANR SURFANICOL ANR-14-CE07-0039-01 is also acknowledged.

ASSOCIATED CONTENTS

Supporting information

Non-spherical mesoporous silica particles pore size distribution, Particle deposition protocols.