Adrien Le Guillou
email: adrien.leguillou@univ-brest.fr

Simona Niculescu

Guillou A Le

Author

Niculescu S Author

Schmullius C Author

Adrien Le

Machine and deep learning methods for Detection and Mapping of coastal wetlands of Crozon Peninsula (Brittany, France) used metric and sub-metric spatial resolution

Keywords: Wetland, Remote sensing, Machine learning, Deep learning, hydrology

    Machine and deep learning methods for detection and mapping of coastal wetlands of Crozon Peninsula (Brittany, France) used metric and sub-metric spatial resolution

INTRODUCTION

Wetlands cover about 6% of the Earth's surface. [START_REF] Erwin | Wetlands and global climate change: the role of wetland restoration in a changing world[END_REF] These ecosystems are sources of numerous ecosystem services and benefit human society. [START_REF] Clarkson | Wetland ecosystem services," Ecosystem services in New Zealand: conditions and trends[END_REF] The number of wetlands has drastically decreased due to human pressure [START_REF] Boesch | Scientific assessment of coastal wetland loss, restoration and management in louisiana[END_REF] .These areas have gradually been converted into farmland or urbanised areas. These changes affect biodiversity and contribute to the depletion of flora and fauna. Furthermore, wetlands help limit the impact of climate change. [START_REF] Salimi | Impact of climate change on wetland ecosystems: A critical review of experimental wetlands[END_REF] The first definition of a wetland in France came from the Water Act of 3 January 1992. This text defined wetlands as "land, whether used or not, that is usually permanently or temporarily flooded or inundated with fresh, salt, or brackish water; where vegetation exists, it is dominated by hygrophilous plants for part of the year" in Article L211-1 of the Environment Code. A number of criteria identify a wetland, e.g. vegetation specific to wetlands and/or soil that shows signs of waterlogging for at least part of the year. The criteria for delimiting a wetland can be found in the decree of 24 June 2008 * .

Wetlands can be found on all types of land. These areas are located in the 283 communes of Finistère and account for 10% of the department's surface area (Conseil général du Finistère, 2011). Wetlands are found in The advantages of CNNs in remote sensing are many. CNNs are capable of learning hierarchical features, meaning they can detect complex patterns at different levels of abstraction. In order to achieve this, convolutional layers use filters to identify local features from the input data, such as edges, textures, or even shapes in images. [START_REF] Albawi | Understanding of a convolutional neural network[END_REF][START_REF] Koushik | Understanding convolutional neural networks[END_REF][START_REF] Yoo | Deep convolution neural networks in computer vision: a review[END_REF] In this way, small objects, such as buildings or vehicles, as well as larger structures, such as rivers or forests, can be identified 2324 .

Remote sensing is a powerful tool for monitoring wetlands. [START_REF] Guo | A review of wetland remote sensing[END_REF][START_REF] Demarquet | Long-term wetland monitoring using the landsat archive: A review[END_REF] Thanks to its remote approach, it can acquire data over vast geographical areas, providing extensive spatial coverage and a global view of wetlands. With sensors mounted on satellites, aircraft or drones, images can be obtained at different resolutions, [START_REF] White | Remote sensing technologies for enhancing forest inventories: A review[END_REF] allowing vegetation, hydrology and other environmental parameters to be characterised accurately and regularly.

One of the main advantages of remote sensing is its ability to provide data with high spatial and temporal resolution. [START_REF] Li | Generating a series of fine spatial and temporal resolution land cover maps by fusing coarse spatial resolution remotely sensed images and fine spatial resolution land cover maps[END_REF] This makes it possible to observe seasonal and interannual changes in wetlands, detect variations in water extent, track changes in vegetation and monitor anthropogenic pressures. [START_REF] Wuver | The impact of human activities on biodiversity conservation in a coastal wetland in ghana[END_REF] This temporal resolution makes it possible to obtain up-to-date information on the condition of wetlands and understand their dynamics, [START_REF] Qin | Evolution of wetland landscape disturbance in jiaozhou gulf between 1973 and 2018 based on remote sensing[END_REF] which is essential to supporting their conservation and sustainable management. [START_REF] Copeland | A geospatial assessment on the distribution, condition, and vulnerability of wyoming's wetlands[END_REF] Remote sensing offers the possibility of characterising wetland vegetation and habitats in detail [START_REF] Ozesmi | Satellite remote sensing of wetlands[END_REF] . [START_REF] De Roeck | Remote sensing and wetland ecology: a south african case study[END_REF] By using different spectral bands and vegetation indices, it is possible to distinguish and map different vegetation types, [START_REF] Huete | Vegetation indices, remote sensing and forest monitoring[END_REF] which allows a better understanding of their spatial distribution and interactions. In this way, changes in vegetation structure, land use and drainage networks can also be assessed, providing crucial information for water resource management and biodiversity conservation. [START_REF] Bastiaanssen | Remote sensing in water resources management: the state of the art[END_REF] This research aims to develop a reproducible methodology for the pre-location of wetlands using two methods. The first method is to locate wetlands using satellite images and elevation data. The second method is to be able to locate wetlands using an index calculated directly from elevation data (the topographic wetness index). Subsequently, a typology of wetlands using machine learning and deep learning methods will be produced. The objective of this research is also to better understand the dynamics of these areas and to study them on a sub-metric scale using Pleiades imagery (50 cm resolution).

Other research has been conducted on Crozon Peninsula. A study on the evolution of the peninsula's land use was carried out by Guanyao Xie and Niculescu 36 using machine and deep learning methods. Other paleontological research on Crozon has also been undertaken, such as that of Vidal 37 or Perroud. [START_REF] Perroud | Palaeomagnetism of the ordovician dolerites of the crozon peninsula (france)[END_REF] Numerous articles exist on the automatic mapping of wetland areas. Kulawardhana, proposed a methodology , including a two-part mapping. [START_REF] Kulawardhana | Evaluation of the wetland mapping methods using landsat etm+ and srtm data[END_REF] Niculescu et al., 2016 [START_REF] Niculescu | Synergy between lidar, radarsat-2, and spot-5 images for the detection and mapping of wetland vegetation in the danube delta[END_REF] showed that remote sensing contributes to the state of knowledge by understanding the interactions between optical signal, polarimetric radar signal, LiDAR measurements and wetlands in the Danube Delta. [START_REF] Niculescu | Synergy of high-resolution radar and optical images satellite for identification and mapping of wetland macrophytes on the danube delta[END_REF]. Niculescu et al., 2020 41 applied random forest from S2, Pleiades and S1 data and in situ observations for discrimination and mapping of reed against submerged aquatic vegetation (SAV), emergent macrophytes, some floating dicotyledonous plant communities and floating vegetation in deltaic lakes. In this study, a total of 67 classification models, in several combinations, with two sets of validation samples (with reed and without reed) were run. More recently in France, Rapinel et al., 2023 proposed similar research on a national scale, presenting a method for mapping wetlands using the topographic wetness index, among other techniques. [START_REF] Rapinel | National wetland mapping using remote-sensing-derived environmental variables, archive field data, and artificial intelligence[END_REF] Huang et al., 2014 and Mao et al;, 2020 have conducted research on wetland mapping using Landsat images, [START_REF] Huang | Wetland inundation mapping and change monitoring using landsat and airborne lidar data[END_REF][START_REF] Mao | National wetland mapping in china: A new product resulting from object-based and hierarchical classification of landsat 8 oli images[END_REF] while other researchers like Bhatnagar have pursued similar themes using Sentinel-2 images. [START_REF] Bhatnagar | Mapping vegetation communities inside wetlands using sentinel-2 imagery in ireland[END_REF] Kaplan et al., 2017 and Mahdianpari et al., 2018, among others, have also contributed research on wetland mapping using a Sentinel-1/Sentinel-2 synergy. [START_REF] Kaplan | Mapping and monitoring wetlands using sentinel-2 satellite imagery[END_REF][START_REF] Mahdianpari | The first wetland inventory map of newfoundland at a spatial resolution of 10 m using sentinel-1 and sentinel-2 data on the google earth engine cloud computing platform[END_REF] This study explores this subject in greater depth by adopting a methodology tailored to the study area, proposing a two-part cartographic approach, and exploring high spatial resolution imagery (Sentinel-2, ESA) as well as very high resolution imagery (Pléiades, Airbus DS). In addition, this study makes a scientific contribution to understanding land use in the wetlands of Finistère, a region that has been little studied on this subject until now. No sub-metre-scale study of wetland mapping using satellite images has been carried out in Brittany to date.

STUDY AREAS AND WETLANDS

Study area

The Crozon Peninsula is located in the far west of France, in the Brittany region. It is an integral part of the Parc naturel régionale d'Armorique. It is also a very maritime area, surrounded by the sea on all sides: the Brest Roadstead to the north, the Iroise Sea to the west and the Bay of Douarnenez to the south. Crozon is located at latitude 48.2477°N and longitude -4.4861°W. This area includes several towns and villages, such as the town of the same name, Crozon, as well as Roscanvel and Camaret-sur-Mer. The study area covers 104 km² of land. The topography of the peninsula is characterised by coastal diversity. There are numerous rocky cliffs, pebbled beaches, rocky foreshores, and fine sandy beaches. Land use is characterised by forests, moorland, meadows, farmland and urban areas. According to the Corine Land Cover database, there are 18 km² of urbanised areas, and according to BD Forêt®, there are 53 km² of woodland and shrubland, including 33 km² of moorland and 16 km² of deciduous land. Finally, according to RPG® 2021, there are 14 km² of agricultural land, mainly meadows. In Crozon, the urban fabric is not as predominant as in the rest of Brittany. Its natural areas are fairly well preserved thanks to the numerous military installations that have limited urban sprawl in Crozon. [START_REF] Jalbert | Coastal wetlands[END_REF] The altitude varies, with a range of 329 m from the sea to Ménez Hom in the far east of the peninsula. The study area is not characterised by high altitudes, but the relief can still be marked by large degrees of slope. According to Météo France, the annual rainfall in 2021 was 1,043 mm (the national average in 2021 was 799 mm), with 1610 h of sunshine (the national average in 2021 was 1994 h). According to the Koppen classification, Crozon is classified as a "Cfb", or temperate oceanic climate. [START_REF] Kottek | World map of the köppen-geiger climate classification updated[END_REF]

Wetland typology

There are many different types of wetlands, and each wetland can be divided into numerous ecological units. Habitat typologies such as CORINE biotopes, soil typologies such as GEPPA [START_REF]Ministère de l' Écologie, du Développement Durable et de l' Énergie, Groupement d'Intérêt Scientifique Sol[END_REF] which assesses soil hydromorphy), and environmental typologies such as RAMSAR 51 allow for more precise definitions of what constitutes a wetland. The wetland typology used in this study synthesises the different typologies mentioned above. The typology of these areas also focuses on the term "ecosystem", commonly defined as "a biological community interacting with organisms and their physical environment":

• Wet forests (or temperate rainforests) are characterised by abundant annual rainfall and moderate temperatures. [START_REF] Ellis | Oceanic and temperate rainforest climates and their epiphyte indicators in britain[END_REF] They are generally found in coastal regions, where oceanic air masses provide constant humidity, or in mountainous areas. [START_REF] Dellasala | Just what are temperate and boreal rainforests?[END_REF] These forests consist of evergreen trees, such as conifers and broadleaf trees, which form a dense canopy.

• The wet meadow (or wet grassland) is an herbaceous ecosystem characterised by periodic or permanent soil saturation with water (redox or reductive soil). It is often found in topographical depressions where water accumulates after heavy rainfall or seasonal flooding. [START_REF] Galatowitsch | The vegetation of wet meadows in relation to their land-use[END_REF] • Wet grasslands are home to a wide variety of herbaceous plants and grasses, such as rushes, that are specially adapted to waterlogged soils.

• A peat bog is an ecosystem characterised by an accumulation of partially decomposed organic matter, known as peat. It forms in regions where drainage conditions are very slow or nonexistent, allowing organic matter to be conserved. Peat bogs are rich in sphagnum moss and other plants adapted to acidic, nutrient-poor environments. They are essential habitats for specialised plant and animal species, and peat bogs are estimated to cover 3%-5% of the Earth's surface. [START_REF] Crowson | A comparison of satellite remote sensing data fusion methods to map peat swamp forest loss in sumatra, indonesia[END_REF] • Salt meadows (or salt marshes) are coastal ecosystems located between land and high tide (intertidal zone [START_REF] Van Beijma | Random forest classification of salt marsh vegetation habitats using quad-polarimetric airborne sar, elevation and optical rs data[END_REF] ) .This environment is subject to regular fluctuations in water levels and is characterised by soils rich in mineral salts. The plants that grow here must be able to tolerate saline conditions. These areas are home to sea asters (Tripolium pannonicum) and obiones (Obione portulaciodes).

• Mudflats are intertidal coastal areas that are periodically covered and uncovered by tides. [START_REF] Beninger | Mudflat ecology[END_REF] These areas of sediment accumulation are rich in organic matter and fine sediment . Mudflats are home to a wide variety of plants, such as cord grass (Spartina), and animals adapted to shallow water and soft substrate.

• Finally, lakes or reservoirs are freshwater bodies formed naturally or through the construction of dams.

DATA IMPLEMENTED

The data used for this study are of several types: satellite images, an altimetry database and a wetland inventory.

The satellite data used are as follows: Pleiades images (Airbus DS), Sentinel-2 images (Copernicus, ESA) and Sentinel-1 images (Copernicus, ESA).

Pleiades

The Pleiades constellation is a pair of Earth observation satellites. The constellation provides high-resolution satellite images captured by the Pleiades-1A and Pleiades-1B satellites. These satellites, initiated by Centre nationales d'études spatiales (CNES), provide a resolution of up to 0.5 m, making it possible to distinguish small details on the ground. The satellite images cover four spectral bands, ranging from the blue band in the visible spectrum to the near-infrared band. The high resolution enables detailed mapping, precise identification of objects and improved classification. This precision has many applications, including urban planning, environmental management and precision agriculture.

Sentinel

Sentinel-2 is a satellite mission for Earth observation within the European Union's Copernicus programme.

It comprises a pair of satellites, Sentinel-2A and Sentinel-2B, which provide high-resolution, wide-field-of-view optical imaging data. The Sentinel-2 satellites provide a spatial resolution of up to 10 m in the visible spectral bands and up to 20 m in the infrared bands. They capture data in 13 different spectral bands, ranging from the visible to the near and mid-infrared. The mission offers a five-day global revisit to the equator and allows regular observations of areas of interest. Sentinel-2 data can also be accessed free of charge and without restrictions (available here: https://scihub.copernicus.eu/). Sentinel-1 is a satellite mission within the European Union's Copernicus programme that provides radar imagery data. It consists of two satellites, Sentinel-1A and Sentinel-1B, and uses synthetic aperture radar (SAR) technology. The Sentinel-1 satellites have active radar imaging capability, which means that they emit radar signals and record the echoes returned by the Earth's surface. This technology enables image acquisition independent of weather conditions and continuous observation day and night. Sentinel-1 offers two imaging modes: the interferometric (IW) mode, with a spatial resolution of 5 m, and the extra-wide (EW) mode, with a spatial resolution of 20 m. These different modes enable obtaining high-quality radar images and covering large areas relatively quickly.

Auxiliary data & altimetry data

In addition, external data was used to generate training and verification data based on a reference system. An inventory of wetlands in Brittany was used. These data are produced by the various SAGE (Schéma d'aménagement de gestion des eaux -water management development schemes) and are used to spatially classify the different wetlands. The Estimation de l'hydromorphie des sols (Estimation of soil hydromorphy) as reference data (database produced by UMR SAS INRA-Agrocampus Ouest) was also used † . Altimetric data in the form of a digital terrain model is also available with a 1-m resolution (RGE® Alti). Data processing for this paper was carried out using Qgis 3.22.12 (GDAL, SAGA and GRASS), OrfeoToolbox and SNAP.

METHODOLOGY 4.1 Image processing

In remote sensing, image processing is very important, especially before making a calculation 58 (classification, segmentation, etc...) . The images must be ready for use in different algorithms. Sentinel-1 and Sentinel-2 images (cf. Table1) were processed to map the wetlands.

First, the Sentinel-1 images were processed using SNAP software developed by ESA. The batch processing tool and the graph builder tool were used to automate the data processing in order to process the 22 Sentinel-1 images as quickly as possible. The chain used to process the Sentinel-1 data is as follows: Apply-Orbit-File, ThermalNoiseRemoval, Calibration, SpeckleFilter and Terrain-Correction. Once the data has been processed, an extraction is performed with a mask corresponding to the study area, resulting in a ready-to-use Sentinel-1 image stack.

No specific processing was done for the Sentinel-2 images, as they were in L3A format. Since the L3A format is a monthly synthesis of Sentinel-2 L2A images, extensive image processing was performed in advance, resulting in a ready-to-use image after download. The L3A format provides a composite image made up of all the images captured on a Sentinel-2 tile over the month so that images with little or no cloud cover can be obtained. This is all thanks to the Sentinel-2 satellite's revisit capability.

However, in order to produce the best mapping of wetlands, many spectral indices have been calculated from Sentinel-2 images. Spectral indices are values calculated from reflectance measurements in different spectral bands of the Sentinel-2 images. These indices are used to characterise and analyse objects or phenomena in the images, such as vegetation, water resources and soils. They are calculated using specific mathematical formulas that exploit the differences in reflectance between the different spectral bands. In this case, we calculate mainly the spectral indices characterising vegetation and water resources to locate wetlands.

For the purpose of this article, seven spectral indices were calculated for the year 2021 based on the 30UUU tile:

• The normalised difference vegetation index (NDVI) [START_REF] Rouse | Monitoring the vernal advancement and retrogradation (green wave effect) of natural vegetation[END_REF] is the most widely used spectral index. It is used to assess the amount and condition of vegetation based on spectral data obtained from sensors on board satellites. The NDVI is calculated from reflectance measurements in the red (R) and near-infrared (NIR) spectral bands. The formula for calculating the NDVI is as follows:

N DV I = (N IR -R) (N IR + R) .
• The green normalised difference vegetation index (GNDVI) [START_REF] Gitelson | Use of a green channel in remote sensing of global vegetation from eos-modis[END_REF] is used to estimate photosynthesis. This index determines water and nitrogen uptake in the plant canopy. The index is based on reflectance measurements in the green (G) and near-infrared (NIR) spectral bands:

GN DV I = (N IR -G) (N IR + G) .
• The normalised difference water index (NDWI) [START_REF] Gao | Ndwi-a normalized difference water index for remote sensing of vegetation liquid water from space[END_REF] is one of the most widely used indices for delineating and evaluating water surfaces and resources and is particularly useful for detecting rivers and lakes. This index is based on short-wave infrared (SWIR) and near-infrared (NIR) bands:

N DW I = (N IR -SW IR) (N IR + SW IR) .
• The bare soil index (BSI) [START_REF] Rikimaru | Tropical forest cover density mapping[END_REF] is used in remote sensing to identify and assess areas of bare or unvegetated soil. The combination of these spectral bands makes it possible to quantify the mineral composition of the soil. This index is based on the red (R), short-wave infrared (SWIR), near-infrared (NIR) and blue (B) bands:

BSI = (R + SW IR) -(N IR + B) (R + SW IR) + (N IR + B) .
• The advanced vegetation index (AVI) [START_REF] Rikimaru | Tropical forest cover density mapping[END_REF] is used to identify vegetation similar to the NDVI. The AVI aims to complete vegetation type discrimination by coupling the NDVI and the AVI. The index uses the red and near-infrared spectral bands:

AV I = [N IR • (1 -R) • (N IR -R)] 1 3 .
• The automated water extraction index (AWEI) [START_REF] Baret | Tsavi: a vegetation index which minimizes soil brightness effects on lai and apar estimation[END_REF] is used to identify water resources in the same way as the NDWI. This index complements the information provided by the NDWI, particularly for river extraction.

The AWEI calculation is based on reflectance measurements in the green (G), near-infrared (NIR) and short-wave near-infrared spectral bands:

AW EI = 4 • (G -N IR) -(0.25 • N IR + 2.75 • SW IR).
• The transformed soil adjusted vegetation index (TSAVI) [START_REF] Baret | Tsavi: a vegetation index which minimizes soil brightness effects on lai and apar estimation[END_REF] is a vegetation index that attempts to minimise the influences of soil brightness by assuming that the soil line has an arbitrary slope and intercept, with X corresponding to the slope of the ground line, a corresponding to the intercept of the ground line and X corresponding to the adjustment defined to minimise ground noise. In this case, the value of s = 0.33, the value of a = 0.5 and the value of X = 1.5. The index uses the red (R) and near-infrared (NIR) bands:

T SAV I = s • (N IR -s • R -a) a • N IR + R -a • s + X • (1 + s 2 )
.

After all vegetation and water indices have been calculated, a stack is made between the Sentinel-1 and Sentinel-2 images in different combinations and the spectral indices (cf. Section 4.2).

Pre-location approach

In order to pre-locate and then map these areas, the method is divided into two parts. First, the wetlands are pre-located using altimetric and/or spectral data. This methodology allows the study area to be divided into two zones: "wetlands" and "non-wetlands". Two approaches were developed in order to achieve this methodology (cf. Figure 2).

The first method is based on the creation of a time series of Sentinel-1 and Sentinel-2 satellite images. The processed time series (calculation of spectral indices, Sentinel-1 processing on SNAP) is directly integrated into a random forest classification using training data from the inventory of wetlands (adapted to the scale of the Sentinel-2 30UUU tile) created for the Brittany region. The result is then post-processed with binary morphological erosion and thresholded with the RGE® Alti. Finally, after completing the entire processing chain, the best combination for pre-locating wetlands is selected. Six different combinations were tested (see Table 2).

The combination with the best metrics was kept (for validation, we used the wetland inventory described in Part 2.3). Another approach was developed to pre-locate wetlands in the study area. This approach primarily requires altimetric data in raster format. As mentioned previously, the RGE® Alti is used for processing (at a resolution of 1 m) in this case. From the RGE® Alti, we calculate the topographical wetness index 64 (cf. Figure 3) to estimate the areas where water will tend to merge and stagnate so that wetlands can be pre-located. When the results are available, thresholding is performed to extract all values corresponding to areas of stagnant water, resulting in a mask that pre-locates wetlands. This index is used to create a raster model of water flow based on topographical data and can be used to represent potential water accumulation zones in a given area. The wetland inventory and the soil hydromorphy database were used to calculate the metrics and validate the results. It is important to note that the calculation of the topographical moisture index has some limitations, as this index does not take into account the nature of surface deposits, so it is mainly used to pre-locate "potential" wetlands. [START_REF] Merot | A method for improving the management of controversial wetland[END_REF][START_REF] Rapinel | Mapping potential, existing and efficient wetlands using free remote sensing data[END_REF] To refine the result, we exclude the areas classified as wetlands that are located in impervious areas (urbanised areas or roads) by using a mask produced beforehand.

Mapping of wetlands

The second part of the methodology is based on a classification of land use in the two previously designated zones. There are now two zones, one corresponding to wetlands and the other to non-wetlands. It is important to note that only "continental" wetlands are considered in the wetland mask. Thus, we use the non-wetland mask to classify mudflats, as the topographical wetness index does not consider foreshores. The training data were generated using photo-interpretation of satellite images from 2021 (the date of classification) and external data such as BD Topo®, BD Ortho® and BD Forêt® (available free of charge on the Géoservice website ‡ ).

A homogeneous number of polygons (see Table 3) was implemented at the scale of the study area. The surface area of the training data was implemented as uniformly as possible, according to the type of land use in Crozon, as there are fewer peat bogs than in urban areas at the scale of the zone, so there is less surface area in training. This distribution also avoids overlearning and creating bias in the training data. Two land-use classifications are then produced. One was based on the "wetland" mask and the other on the "non-wetland" mask, and the two results were then merged to produce a complete map of the study area. Three types of classification were performed: two with machine learning algorithms and one with a deep learning algorithm. A pixel-by-pixel random forest classification and an object-based image analysis (OBIA) random forest classification were produced for the machine learning classifications. The convolutional neural network was chosen for the deep learning classification to create the land cover classification (cf. Figure 4). The neural network architecture is based on the documentation for the Orfeotoolbox TensorFlow tool § . [START_REF] Cresson | A framework for remote sensing images processing using deep learning techniques[END_REF]

MACHINE LEARNING

Random forest -Pixel by pixel and OBIA

The random forest is a reference model of machine learning for image processing. Proposed by Leo Breiman in 2001, this algorithm is based on a combination of decision trees. It is the model most often used for classification, given its performance and speed of execution compared to other machine learning algorithms. [START_REF] Adugna | Comparison of random forest and support vector machine classifiers for regional land cover mapping using coarse resolution fy-3c images[END_REF] The random forest also has the advantage of being easy to use. [START_REF] Zhu | Analysis on the applicability of the random forest[END_REF] Random forest functions as a set of decision trees used to predict a quantity or probability. The decision tree alone is a tool in the form of a tree (which can resemble a flowchart), where each node is a test for an attribute, and the branch is an outcome. A tree is divided into a "source" set and then into subsets. This process is repeated for each subset in recursive form.

We need three "hyper-parameters" 70 (fixed parameters) to be defined before training. These are the size of the trees (maximum number of nodes), the number of trees and finally, the number of features to be sampled (number of random variables selected from the explanatory variables in each mixture). The first step involves implementing the "bagging" principle, [START_REF] Breiman | Bagging predictors[END_REF] i.e. creating numerous random subsamples on a subset of the data. The second step is to develop individual decision trees for each sample. The different trees are trained by a random portion to make a prediction. It is important to note that each decision tree works individually and independently. Finally, the third step corresponds to the results of the predictions and is the result of the majority vote, which is the final prediction. Our random forest has the following parameters: maximum number of decision trees: 200, minimum number of samples per class: 20, and maximum depth of decision trees: 10. A time series of five Pleiades images was used for the random forest approach. As part of this research, random forest was implemented with two different classification methods: the pixel approach and the object approach.

Pixel approach

The pixel approach uses a learning algorithm to automatically extract the characteristics of pixels and associate them with classes (in this case, land-use classes). The principle of this approach is to use the spectral information of the pixels in one or more satellite images that have already been labelled and are therefore known. Once a sufficient number of pixels have been labelled, they are implemented in a machine-learning model to produce a trained model. Once the model has been trained, it can be applied to an entire satellite image (or time series), and a class prediction is made for each pixel in the image.

Object approach

In the object approach, [START_REF] Blaschke | Object based image analysis for remote sensing[END_REF][START_REF] Hay | Geographic object-based image analysis (geobia)[END_REF] neighbouring pixels with similar characteristics are grouped together (e.g. a house consisting of pixels with a similar spectral response is grouped to form an "object"). Colour, texture and spatial context can all influence the creation of the "object". There are many different segmentation algorithms, e.g. mean shift 74 or nearest neighbour. [START_REF] Mehta | Segmentation-based projected clustering of hyperspectral images using mutual nearest neighbour[END_REF] Once the objects have been segmented, specific descriptors are extracted for each object, considering characteristics such as size, shape, texture, colour, etc. These descriptors are used as inputs for the object and then as inputs for machine learning algorithms, in our case, random forest. The meanshift method was used for our object approach. We chose the following parameters to produce our segmentation: spatial radius: 10, range radius: 30, maximum number of iterations: 50, minimum "region" size: 200, minimum object size: 5, and polygon simplification: 0.5.

Deep learning principles

Deep learning is a discipline of artificial intelligence that uses deep artificial neural networks to solve complex problems. [START_REF] Wu | Development and application of artificial neural network[END_REF][START_REF] Zhang | Multivariate time series analysis in climate and environmental research[END_REF][START_REF] Zhu | Deep learning in remote sensing: A comprehensive review and list of resources[END_REF][START_REF] Zhang | Deep learning for remote sensing data: A technical tutorial on the state of the art[END_REF] These networks are capable of learning from raw data and extracting abstract representations. Deep learning is based on iterative supervised or unsupervised learning processes where networks are trained on labelled data or to discover structures in unlabelled data. [START_REF] Lecun | Deep learning[END_REF] Deep learning has wide applications in areas such as computer vision [START_REF] Voulodimos | Deep learning for computer vision: A brief review[END_REF] ,natural language processing, 82 speech recognition, [START_REF] Bae | Voice recognition based on adaptive mfcc and deep learning[END_REF] machine translation and robotics. [START_REF] Singh | Machine translation using deep learning: An overview[END_REF] For example, deep neural networks are used in computer vision § To use OTBTF: https://otbtf.readthedocs.io/en/latest/ for object detection, [START_REF] Zhao | Object detection with deep learning: A review[END_REF] facial recognition and image segmentation. [START_REF] Garcia-Garcia | A review on deep learning techniques applied to semantic segmentation[END_REF] In natural language processing, deep learning is used for tasks such as text classification, [START_REF] Minaee | Deep learning-based text classification: a comprehensive review[END_REF] text generation and machine translation. [START_REF] Young | Recent trends in deep learning based natural language processing[END_REF] However, deep learning also presents challenges and limitations. One major challenge is the need for large amounts of labelled data to efficiently train deep neural networks. The interpretability of learned models is also challenging, as deep neural networks are often considered "black boxes" due to their complexity. [START_REF] Hussain | Deep learning black box problem[END_REF] In addition, deep learning can face the problems of overlearning [START_REF] Panchal | Determination of over-learning and over-fitting problem in back propagation neural network[END_REF] and limited generalisation in situations where the training data differs from the real data

Architecure of the CNN

The CNN model proposed in this article consists of several layers for processing the input images (see Figure 4). The training data were generated from a Pleiades image, for which 5000 16-by-16 patches were extracted for each land cover class, and 5000 additional patches were used for validation. The architecture of CNN is as follows: The image patches have a resolution of 16 x 16 and are subjected to a series of three convolution layers. The first convolution layer with 16 filters of size 5 x 5 is followed by a ReLU activation function and a pooling layer of size 2 x 2. A second convolution layer with 16 filters of size 3 x 3 is then applied, followed by another pooling layer. Finally, a third convolution layer with 32 filters of size 2 x 2 is used. A test with 64 x 64 patches is also performed. The extracted features are then reshaped into a vector and fed into a fully connected layer. This latter layer consists of six or seven neutrons (depending on the "wetland" or "non-wetland" mask, which is not characterised by the same classes) corresponding to the predicted classes. The predicted class was determined by selecting the index of the neuron with the highest output value (e.g. a probability). The model is trained by minimising the loss using the cross-entropy cost function. The optimisation is performed with the Adam optimiser. The first step in the wetland classification methodology was to locate all the wetlands, for which two methods were developed. The first method was based on spectral indices (see Section 4.1), and the second on the topographical wetness index (TWI). The method using the TWI works best. The wetland inventory (made by local actors) ¶ and soil hydromorphy map (made by Agrocampus Ouest, INRA SAS) ‖ were used as validation datasets to evaluate the best method. The metrics show higher scores for the TWI, with a difference of +0.04 for the F1-score, +0.26 for the kappa, and +.10 (cf. Table 5) for the overall accuracy. Visually, the pre-location also appears better, with more relevant flow lines. In addition, the TWI method has the advantage of being less costly in terms of computation time, as it does not require classification with an extensive training dataset but only calculations based on altimetric data. In order to validate the different results, a validation dataset independent of the training dataset was created. For this purpose, 30% of the polygons initially intended for training were separated to form the validation dataset. Next, 1,000 points per land-use class were extracted for validation. The same validation dataset was used for the different approaches to have comparable reference data. Three classifications were tested with three different approaches. The pixel-by-pixel random forest approach achieved the best results of the different classifications, followed by the convolutional neural network and, finally, the OBIA random forest approach (cf. metric table). The only exception is the F-1 score, for which the CNN achieved the best score with a difference of 0.01 compared to the pixel approach. By looking more closely at the metrics using the confusion matrix (a matrix produced with the "Compute-ConfusionMatrix" tool in OrfeoToolbox), it is possible to examine the confusion between classes. Wetlands are well classified overall, thanks in part to the "wetland" mask, which prevents confusion between the "wet forest" and "forest" classes or between the "wet meadow" and "agricultural land" classes.

The convolutional neural network showed better metrics for the "mudflat" class, with less confusion with the "rock/cliff" class than the random forest classification. Conversely, the "forest" class performed worse for the neural network than the random forest, with high confusion with the "dry heat" class. This is probably due to the similar reflection of shrubby areas in moorlands and small trees in forests.

The random forest classification with the pixel approach shows very good metrics overall, as does the OBIA approach. However, there is some confusion between the "rock/cliff" and "artificial land" classes. This confusion is quite understandable, given the similar reflectance between a rocky coastline and roads. This confusion can also be observed with CNN, but to a lesser extent. Confusion is also visible between the "sand" and the "artificial land" classes, both at OBIA and in the pixel approaches.

In short, the random forest approach shows better discrimination for land-use classes linked to wetlands, while the neural network performs better for areas outside wetlands. This is primarily due to better discrimination between the "sand", "artificial land" and "rock/cliff" classes.

Visually (cf. Figure 5), the random forest pixel approach shows a more accurate mapping than the OBIA or CNN classification. CNN tends to have a "salt and pepper" effect. This effect may be due to the size of the patches entered, which does not allow for sufficiently precise segmentation at the scale of the resolution of the Figure 5: Confusion matrix for the three wetlands classifications Pleiades images. Finally, the OBIA classification provides a visually relevant map, but one that exhibits tiling effects (i.e. a spatial discontinuity between two land cover classes). This effect is particularly noticeable between the "lake" class and the "deep water" class, where it is possible to see pixels classified as "lake" in the form of a square in an area that should normally be "deep water". The OBIA classification also tends to overrepresent the "artificial land" class (predominance of red on the map). Many pixels are classified as "artificial land" when, in fact, they are "sand" or "rock/cliff" that can be seen directly on the coastline or beaches.

Discussion

The results therefore show that the methodology described in this article is capable of mapping wetlands. With scores ranging from 0.76 (OBIA, F1-score) to 0.90 (pixel, kappa), the metrics show fairly satisfactory results, with an OA of 89% for the pixel random forest approach. The two-stage approach involves pre-locating wetlands using spectral indices or the topographical moisture index (TWI). By mapping the different wetland typologies using the pre-location mask, it is then possible to reduce the confusion between the different land-use classes. The best classification is the pixel-by-pixel random forest classification, although this approach is similar to that of the neural network (in terms of metrics). These two classifications have a difference of 0.04 for the kappa, 0.02 for the overall accuracy (in favour of the RF) and 0.01 for the F1-score (in favour of the CNN). Nevertheless, the pixel-by-pixel random forest classification visually appears better than the OBIA and CNN approaches. Numerous research studies have shown that deep learning is able to obtain better scores as a general rule compared with more "traditional" machine learning algorithms. [START_REF] Belgiu | Random forest in remote sensing: A review of applications and future directions[END_REF][START_REF] Storie | Deep learning neural networks for land use land cover mapping[END_REF][START_REF] Abdi | Land cover and land use classification performance of machine learning algorithms in a boreal landscape using sentinel-2 data[END_REF][START_REF] Günen | Performance comparison of deep learning and machine learning methods in determining wetland water areas using eurosat dataset[END_REF] However, in the case of this article, the pixel approach shows slightly higher scores. This may be due to the architecture of the neural network, which could be improved by integrating more convolution and hidden layers. It is also possible to integrate patches with larger entries (64x64, 128x128 for example) or to integrate more images in the Pleiades time series. It is also important to note that the computation time for deep learning is significantly higher than for machine learning algorithms and requires more hardware resources (graphics card). This energy cost is not to be overlooked, and may call into question the use of this tool depending on the real need for it. [START_REF] Martineau | Shrinking deep learning's carbon footprint[END_REF] Improvements can still be made to the methodology. The use of new spectral indices or new algorithms could probably refine the results for pre-locating wetlands. For the classification and typology of wetlands, neural networks could offer significant potential for improvement. To this end, a comparative study of the best deep learning algorithm architectures can be carried out with a view to implementing them in a land use classification.

This study shows good results for the wetland classes studied. For the random forest pixel method, the wetland classes achieve an average Overall Accuracy score of 93% (see comparative table of scores). A similar study by Ouyang et al. was published, investigating the comparison between a pixel-based approach and an Object-Based Image Analysis (OBIA) approach for saltmarsh vegetation mapping. This study shows scores (in Overall Accuracy) ranging from 78% to 82% for their approach, using QuickBird images for a similar class study as ours (Mudflat with Spartina and Saltmarsh with Phragmites). [START_REF] Ouyang | A comparison of pixel-based and object-oriented approaches to vhr imagery for mapping saltmarsh plants[END_REF] Another more recent study by Mahdianpari et al., on urban wetland mapping, was published. This study shows results similar to ours, achieving an OA of 91% for similar wetland land cover classes. The study utilizes WorldView-4, GeoEye-1, and LiDAR data to characterize wetlands into five classes: Bog, Fen, Swamp, Marsh, and Open Water. [START_REF] Mahdianpari | Smart solutions for smart cities: Urban wetland mapping using very-high resolution satellite imagery and airborne lidar data in the city of st. john's, nl, canada[END_REF]

Perspectives

There are possible avenues for improvement in this work. Initially, the convolutional neural network is the best candidate for improvement. Many improvements can be made to the neural network's architecture, such as implementing more convolution layers or changing the gradient descent. In short, it is possible to conduct research that focuses entirely on neural networks and try out the architecture that would be most suitable [START_REF] Boonpook | Deep learning semantic segmentation for land use and land cover types using landsat 8 imagery[END_REF] so that architectures such as the U-Net, [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] the VGG-Net 100 and the LoopNet can be evaluated. Besides the deep learning aspect, it is also possible to delve deeper into the machine learning aspect by trying other algorithms, such as support vector machines. [START_REF] Vapnik | The nature of statistical learning theory[END_REF] It is also possible to implement a larger input dataset. The training dataset was 5,000 t per land-use class; it is possible to use 10,000 t per land-use class to investigate whether an improvement is visible with a larger input dataset.

In the case of the pre-location of wetlands, it is also possible to try new approaches or new indices. If the goal is still to use spectral information for pre-location, indices like the modified soil-adjusted vegetation index (MSAVI) [START_REF] Qi | A modified soil adjusted vegetation index[END_REF] or the enhanced vegetation index (EVI) [START_REF] Matsushita | Sensitivity of the enhanced vegetation index (evi) and normalized difference vegetation index (ndvi) to topographic effects: a case study in high-density cypress forest[END_REF] can be included in the methodology to determine how useful their contributions are. The use of other wetness indices can also be tested, as not only the topographic wetness index can be used to spatially delineate areas that are likely to be wet. The vertical distance to channel network (VDCN) [START_REF] Shahrayini | Modeling and mapping of soil salinity and alkalinity using remote sensing data and topographic factors: a case study in iran[END_REF] is also an algorithm that can be used to model flow lines to identify areas that are likely to be wet or under water.

CONCLUSION

The proposed methodology made it possible to map wetlands in various ways and with different approaches, with an accuracy between 76% and 90%. The aim of this research was also to develop a reproducible methodology for as many different landscapes as possible. In this way, the methodology can be reused in different areas using altimetric data and satellite images, regardless of the spatial and spectral resolution of the sensor. The advantage of pre-locating wetlands is that the study can be divided into two parts, reducing the confounding of land-use classes with similar spectral responses. By dividing the study area into two groups (wetland mask and non-wetland mask), confusion between forest and wetland forest classes could be avoided, allowing for better classification. This article highlights a number of significant strengths resulting from in-depth analyses. The methodologies used have produced convincing results in the analysis and fine mapping of wetlands, making a contribution to the field of study. With precise data and good results, this article provides additional elements in the spatial understanding of wetlands, opening up promising new prospects for this theme. Land-use classes for wetlands based on several typologies (RAMSAR, GEPPA) make it possible to discriminate between wetlands with precision. This typology also provides a methodology that can be reproduced in several stages to produce its own wetland maps. Mapping in two stages (pre-location and mapping) has the advantage of being able to improve discrimination between wetlands and non-wetlands. It also provides geospatial information for the area under study (Crozon, France).

Figure 1 :

 1 Figure 1: Location map of the Crozon peninsula

Figure 2 :

 2 Figure 2: The two methodologies for pre-locating wetlands

Figure 3 :

 3 Figure 3: Methodology for Topographic Wetness Index calculation

Figure 4 :

 4 Figure 4: Architecture of the CNN

Figure 6 :

 6 Figure 6: The three land use classifications

Table 1 :

 1 Satellite image data

	Satellite	Number of image	Spectral bands	Spatial resolution
	Sentinel-2	12 (L3A Format)	1,2(Blue),3(Green),4(Red),	10 to 20m
			5,6,7,8(NIR),8A,9,10,11,12
	Sentinel-1	22 (IW Format)	VV/VH	5x20m
	Pléiades	5	1 (Blue), 2 (Green), 3 (Red), 4 (NIR)	0.50m
	RGE Alti (DEM)	1		1m

Table 2 :

 2 The different combinations for the first pre-location methodology

	Method

Table 3 :

 3

	Wet meadow	26 899m²
	Mudflat	24 908m²
	Salt meadow	7 222m²
	Pond	28 484m²
	Marsh / Bog	6 074m²
	Wet Forest	29 003m²
	Rock / Cliff	17 692m²
	Urban / Artificial	140 912m²
	Arable Land	335 513m²
	Dry Heath	62 639m²
	Sand	113 223m²
	Deep water	920 764m²
	Forest and shrubland	57 767m²

Training data surface area Class Area surface of training sample (m²)

Table 4 :

 4 Score of the two methods for pre-loating wetlands

	Methods Spectral index TWI
	F1-Score	0.82	0.86
	Kappa	0.64	0.90
	OA	0.82	0.92

Table 5 :

 5 Score for the three wetlands mapping approaches

		OBIA RF Pixel by Pixel RF CNN
	OA	0.85	0.89	0.87
	Kappa	0.84	0.90	0.86
	F1-Score	0.76	0.82	0.83

† You can find the methodological guide for inventorying wetlands at the local level in the Finistère department at the following address:https://www.finistere.fr/var/finistere/storage/original/application/e17e923ab8d8c903be015a08e1c7c52f.pdf

‡ https://geoservices.ign.fr/catalogue

¶ https://bretagne-environnement.fr/donnees-zones-humides-bretagne ‖ Hydromorphy soil : https://sols-de-bretagne.fr/inventaire-et-cartographie-sols/applications-thematiques/192hydromorphie-des-sols.html

ACKNOWLEDGMENTS

This research was funded by the the project CNES (Centre national d'études Spatiales) / TOSCA 7618.


Sofiane Schaack

Etienne Mangaud

Erika Fallacara

Simon Huppert

Philippe Depondt

Fabio Finocchi

When Quantum Fluctuations Meet Structural Instabilities: The Isotope-and Pressure-Induced Phase Transition in the Quantum Paraelectric NaOH

Anhydrous sodium hydroxide, a common and structurally simple compound, shows spectacular isotope effects: NaOD undergoes a first-order transition, which is absent in NaOH. By combining ab initio electronic structure calculations with path integrals, we show that NaOH is an unusual example of a quantum paraelectric: zero-point quantum fluctuations stretch the weak hydrogen bonds (HBs) until they become unstable and break. By strengthening HBs via isotope substitution or applied pressure, the system can be driven down to a broken-symmetry antiferroelectric phase. We also provide a simple quantitative criterion for HB breaking in layered crystals and show that nuclear quantum effects are crucial in paraelectric to ferroelectric transitions in hydrogen-bonded hydroxides.

Beyond the alteration of chemical equilibria and dynamical properties, with important consequences in geology and chemistry, [START_REF]Isotope Effects in Chemistry and Biology[END_REF] isotope effects can affect material properties. Changing the nuclear mass in ferroelectrics (FEs) [START_REF] Horiuchi | [END_REF] can actually trigger the mode instabilities in displacive phase transitions [3]. Understanding these transitions and finely tuning isotope substitution in FEs, which are used in nonvolatile memories and sensors [START_REF] Lines | Principles and Applications of Ferroelectrics and Related Materials[END_REF], is an active field of fundamental research with technological applications [START_REF] Narayan | [END_REF]. Here, we employ molecular dynamics, including quantum effects via path integrals, to explore the ferroelectric behavior of sodium hydroxide, which displays giant isotope effects.

Most studies on FEs focused on perovskites. Generally, the associated energy profile is a double well for the symmetry-broken FE phase, and becomes a single well for the higher-symmetry paraelectric (PE) phase [START_REF] Chandra | Physics of Ferroelectrics: a Modern Perspective[END_REF]. In some cases, the phonon zero-point energy moves below or above the barrier level when the nuclear masses vary. Accordingly, the FE phase can be quenched or restored, as in SrTiO 3 , a prototypical quantum paraelectric [START_REF] Muller | [END_REF][8][9]. More generally, nuclear quantum effects (NQEs) can govern the phase transition, resulting in a critical point that is tuned by variables other than temperature, such as nuclear mass and pressure. Quantum criticality (secondorder phase transitions taking place at 0 K) can occur in many systems [10][11][12] and motivated the inclusion of quantum fluctuations in Landau-like models [12].

In parallel to bulk and ultrathin perovskite films, [13,14] other FEs have been investigated, such as hydrogen-bonded crystals [15][16][17], whose properties are ruled by the peculiarities of hydrogen bonds (HBs) [START_REF] Li | Proc. Natl. Acad. Sci. U.S.A[END_REF]. Several studies have focused on crystals with strong and short HBs, such as KH 2 PO 4 [16]. In contrast, systems with weak and long HBs were scarcely studied. Among them, NaOH is a common material widely used in industrial chemistry [START_REF] Kurt | Ullmann's Encyclopedia of Industrial Chemistry[END_REF][START_REF] Yang | [END_REF]; a recent study shows evidence of NQEs on the proton transfer rates in water solutions containing NaOH [21]. However, there is scarce knowledge of the anhydrous NaOH and NaOD crystals, which ex- hibit several puzzling properties and spectacular isotope effects.

Anomalies in infrared (IR) [22], Raman [23] and NMR spectra [24] have been reported for NaOD, though absent in NaOH. X-ray, neutron diffraction and dielectric constant measurements reported a structural change of NaOD around T C 153K [25]. Below T C , NaOD is monoclinic with P 2 1 /a space group. Above T C , the struc-ture is orthorhombic with space group Bmmb [26]. Both structures are layered (Fig. 1) with NaOH (NaOD) stacks. A noticeable effect at the transition is the 0.5 Å expansion of the c axis, normal to the NaOD layers, while lateral parameters are little affected. Both heat capacity [27] and low-frequency dielectric constant [28] display anomalies in NaOD around T C , which are absent in NaOH down to 6 K. Although the H or D distributions were not experimentally determined, a microscopic model where the hydroxyl orientation changes from slanted to vertical was conjectured on the basis of the similarity between the NaOD transition at ambient pressure and 153 K and that in NaOH at 10 kbar and room temperature [29]. This similarity also raises the question of a quantum phase transition in sodium hydroxide [12]. Though both transitions were observed experimentally, the microscopic description of the transition mechanism encompassing the giant isotope effects is still lacking and the formation or rupture of interlayer HBs is equivocal.

In order to solve these issues, we investigate the behavior of NaOH and NaOD accounting for NQEs via pathintegral based simulations [30], using the i-PI package [31] with the PIGLET thermostat [30,32]. The atomic forces are computed by density functional theory in the Perdew-Burke-Ernzerhof (PBE) approximation [33], using the Quantum Espresso package [34]. Lattice parameters are optimized via cell relaxation enforcing a target hydrostatic pressure with residual stress tensor components within ±1 kbar. Supplemental Material (SM), Sec. A provides further computational details. [25] and NaOH [35]. ∆E is the energy increase per unit formula with respect to the AFE configuration. For comparison sake, we reported the halved a AFE lattice parameter. ∆E (meV) Classical picture. -First, we consider several static configurations at 0 K discarding all thermal and quantum nuclear effects (see SM, Sec. B): paraelectric (PE), ferroelectric (FE) and antiferroelectric (AFE). In the PE configuration [36], hydroxyls are parallel to c (θ 1 = θ 2 = 0). In the AFE (FE) configuration (Fig. 1), hydroxyls at x = 0 and x = 1/2 are slanted in opposite (parallel) directions along b with angles θ 1 = -θ 2 (θ 1 = θ 2 ). The corresponding optimized lattice parameters are reported in Table I. AFE is the lowest-energy configuration. The classical thermal energy k B T at the experimental transition tem-perature is 12meV, larger than the AFE/FE energy difference while smaller than the AFE/PE one. Although its c parameter is close to those measured for NaOD at 293 K and NaOH at all temperatures, the static PE is unstable as confirmed by perturbation theory at the harmonic level: the OH bending mode in the (bc) plane (θ oscillations) has imaginary frequency and drives the PE toward AFE or FE configurations, whose c lattice parameters severely underestimates the experimental ones, more than usual in the PBE approximation [37].

a b c OH O• • • H AFE 0 3.
To solve this apparent paradox and apprehend the interplay between hydroxyl angle θ and lattice parameter c, we compute the potential energy surface E(c, θ), shown in Fig. 1 for the AFE (a similar behavior is observed for the FE, see SM, Sec. C). The static equilibrium angle θ 0 (c) = min [START_REF] Costescu | [END_REF]. Computed elastic constants at 0 K confirm this picture: C 33 < 0 for c ∈ (11.2 -11.6) Å (SM, Sec. C). In this c range HBs, which are the main contribution to the interlayer cohesion, disrupt under stretching and become unable to hold the NaOH layers together. At 0 K, the classical crystal is thus elastically unstable [40] for these c values.

In order to appraise the role of classical thermal fluctuations, we optimized the lattice parameters between 77 and 400 K (Fig. 2) through several (N V T ) runs. At low temperature, the HBs display small fluctuations around the linear configuration and the lattice parameters are very close to those obtained at 0 K. When raising T , the HBs break and reform, as revealed by the analysis of O-H• • • O angles and distances. HBs stretch with T and the crystal expands along c with a huge coefficient of thermal expansion α c 2.5 × 10 -4 K -1 , that further increases beyond 350 K; this huge α c is the signature of weak interlayer HBs [41]. The classical picture thus reveals the onset of HB breaking. However, several major discrepancies with the experiments still hold: first, c(T ) remains underestimated and evolves with no abrupt changes, though some anomalies can be detected beyond 350 K (see SM, Sec. D); second, classical simulations cannot distinguish between NaOD and NaOH and are thus unable to describe the isotope-specific transition. We discuss below how nuclear quantum effects (NQEs) reshape the classi- cal picture and reconcile theory with experiments. Quantum picture. -The inclusion of NQEs via pathintegral molecular dynamics (PIMD) changes the classical scenario drastically. First, we optimize the lattice parameters through the same procedure as in classical MD (SM, Sec. E). As HBs are weak and elongated, lateral quantum fluctuations of H and D nuclei dominate over longitudinal ones and further destabilize the HBs [START_REF] Li | Proc. Natl. Acad. Sci. U.S.A[END_REF]42]. This yields a much larger lattice parameter c than the classical one, particularly for the lighter isotope: c(NaOH)=11.35 Å at 100 K, with α c 10 -4 K -1 between 100 and 300 K (Fig. 2). In NaOD, c increases linearly from 10.60 Å (77 K) to 10.96 Å (250 K) and abruptly jumps to 11.6 Å (300 K). At the same T , the a parameter drops by 0.02 Å, consistently with the experiments [25]. This correlated behavior is congruous to a first-order transition between 250 and 300 K in NaOD, though the transition temperature T C is overestimated with respect to the experimental 153 K value [25]. Noteworthy, the PIMD simulations faithfully reproduce the giant structural isotope effect and confirm the jumps in the c and a lattice parameters that could be hypothesized but not firmly asserted from the available experimental data.

The disruption of the interlayer hydrogen bonds modifies also drastically the orientation of the OD groups: from bimodal distributions with maxima at ±θ 0 ( 30 • ) for T < 250 K, the OD angular distributions display a single maximum at 0 • for T ≥ 300 K (Fig. 3). The structural transition in NaOD is therefore linked to a deep change of the dipole ordering; the distribution of the order parameter θ follows a universal Landau-like behavior as also found in the centering of the hydrogen bonds in KH 2 PO 4 [16] and ice under extreme pressures [43]. The absence of transitions in NaOH is confirmed by the persistence of a unimodal OH angular distribution at all temperatures here probed, with a flat profile at low T , typical of quantum paraelectrics [44]. The c abrupt change in NaOD correlates with a 5% discontinuity of the interlayer O-O distance d OO , due to the combined c expansion and in-plane relaxation of the O anions, concomitant to the HB weakening (SM, Sec. D). The joint probability P (θ, d OO ) shows a strong correlation between d OO and the OH polar angle θ (Fig. 4). In NaOD at 77 K, d OO = 3.14 Å, while d OO ≥ 3.57 Å at T ≥ 300 K, in a dynamical PE state where θ oscillates around 0 • . In contrast, NaOH shows a single probability maximum at θ = 0 • , with d OO ≥ 3.45 Å at all temperatures.

The joint probability P (θ 1 , θ 2 ) (Fig. 5) of the polar angles of parallel HB chains at x = 0 and x = 1/2 crystal coordinates (Fig. 1) reveals angular correlations, with remarkable differences between NaOH and NaOD. At 77 K, NaOD is AFE. For increasing T , the joint probability also displays tiny secondary maxima corresponding to FE configurations, consistently with the 3.4 meV classical energy difference between the two configurations (Table I). The PE configuration is always a local minimum for T ≤ 250 K. At 250 K, the angular correlations in NaOD become strongly blurred and at 300 K the two maxima merge into a single one at θ 1 = θ 2 = 0 (the paraelectric state). In contrast, the NaOH distribution shows this single maximum at all temperatures and a slightly more elliptic distribution at low T with the main axis along the θ 1 = -θ 2 AFE line. This is characteristic of a quantum PE [44] in which the AFE ordering is prevented by zero-point fluctuations (larger for H than for D).

NaOH under pressure. -The phase transition can be recovered in NaOH by an external pressure that brings the layers (and the facing O anions) closer together and potentially restores hydrogen bonds. The experimental compressibility is anisotropic, with an abrupt ∼ 7% volume contraction at P c = 10 kbar upon increasing pressure [29]. We simulated NaOH under a 10 Kbar hydrostatic pressure, which mainly impacts the lattice parameter c that recovers its computed value for NaOD at 77 K and ambient P (Table II). The computed volume contraction of NaOH between 0 and 10 kbar amounts to 9%, close to the 12% as measured at 297K [29]. The atomic distributions show that the contraction of the interlayer distance under pressure actually reinforces the HBs in NaOH and displaces its ground state toward a combination of AFE and FE configurations. The joint probability P (θ 1 , θ 2 ) (Fig. 5) indeed displays four comparable maxima around θ 1 = -θ 2 = ±30 • (AFE) and θ 1 = θ 2 = ±30 • (FE). The HBs in NaOH under pressure and room temperature are restored; however, the polar angle ordering contrasts with that in NaOD at low T . Indeed, at room temperature, the dipole-dipole interaction that would favor the AFE ordering is negligible with respect to the thermal activation energy [START_REF]The energy difference between the static AFE and FE configurations roughly corresponds to 40 K (Table I)[END_REF]. In passing, we note that pressure induces the symmetrybreaking transition in NaOH, while it has opposite effect in KH 2 PO 4 [16] and in ice VII [42,43]. This apparent contradiction can be explained by the nature of HBs [START_REF] Li | Proc. Natl. Acad. Sci. U.S.A[END_REF], which are very weak in NaOH but strong in both KH 2 PO 4 and ice VII. Our findings corroborate the observed phase transition in pressure [29] and suggest that NaOH is close to a quantum critical point for the AFE-FE-PE transitions, in which pressure has partly analogous effects to the H → D substitution. Further studies, beyond the scope of this paper, are necessary to locate the critical point [START_REF] Chandra | Physics of Ferroelectrics: a Modern Perspective[END_REF]12].

Conclusions. -Sodium hydroxide displays a complex behavior that stems from very weak interlayer hydrogen bonds (HBs). Our analysis of the classical potential energy surface provides a precise criterion for the transition from elastically stable to unstable HBs under stretching, and locates at the inflection point the critical O-O distance. This criterion can be generalized to other layered hydroxides, such as LiOH and KOH [START_REF] Pagliai | [END_REF]47]. In sodium hydroxyde, interlayer O-O distances are close to their critical value. Quantum fluctuations drive NaOH into the elastically unstable range, where HBs are unable to ensure the interlayer cohesion, in sharp contrast with the classical picture. The order parameter OH polar angle distribution displays a single maximum at all temperatures here probed, and NaOH can be characterized as a quantum paraelectric. Deuteration reduces quantum fluctuations and restores weak HBs in NaOD, which is antiferroelectric at low T . Further thermal fluctuations besides the quantum ones destabilize HBs: our simulations indicate that NaOD undergoes a first-order phase transition in temperature, as marked by a jump in the interlayer spacing. We emphasize that the isotope-and pressure-driven phase transitions in sodium hydroxide escape classical statistical mechanics. Neither the proton nor the deuterium behaviors can be captured by harmonic zero-point corrections on top of a classical picture: the potential energy surface is highly anharmonic and sensitive to mode coupling. The consistent treatment of the intrinsically quantum difference between H and D via path-integrals instead provides a comprehensive picture of isotope and pressure effects. Our study suggests that NaOH is close to a quantum critical point [12] and opens perspectives for tuning the transition in sodium hydroxide by doping, isotope substitution, pressure and coupling to other, more conventional, ferroelectrics. In addition, because of its structural simplicity, anhydrous NaOH is also a prototype to study the relation between hydrogen bonding and mechanical properties, which is crucial in supramolecular materials, such as hand-twistable crystals [48], azaheterocycles with wavelike topology [49] and self-healing tricarboxylic acid [50].

FIG. 1 .

 1 FIG. 1. The static 0 K picture. Panel a: static antiferroelectric (AFE) orthorhombic structure. Na in blue, O in red and H(D) in white. The unit cell is doubled along b, to show the hydrogen bonds as dashed lines. The OH groups form angles θ1 and θ2 with c axis. Panel b: AFE potential energy surface E(c, θ) versus angle θ = θ1 = -θ2 and lattice parameter c. θ0(c) = min θ E(c, θ) is plotted in olive green.

  θ E(c, θ) follows an almost perfect square root dependence θ 0 (c) = ± (ξ -c)/α for c ≤ ξ = 12.1 Å and is null for c ≥ ξ. The order parameter θ 0 (c) thus adopts a Landau-like behavior with a transition toward the PE configuration (θ = 0) for c ≥ ξ. A Morse potential nicely fits the minimum energy at fixed c, E(c) ≡ E[c, θ 0 (c)]. As the HB length (O• • • H) is directly correlated to the c lattice parameter (SM, Sec. D) E(c) provides a suitable and general criterion to pinpoint the HB breaking in NaOH [38]. The critical c value is located at the inflection point of the Morse curve: c cr 11.2 Å, which corresponds to a maximum for the interlayer attractive force at a threshold (O• • • H) cr 2.4 Å. Below value, the HBs resist to rupture, whereas for (O• • • H)>(O• • • H) cr they can be considered as broken

FIG. 2 .

 2 FIG. 2. Lattice parameters a, b, c in Å vs T as given by PIMD for NaOH (red), NaOD (blue) and classical Langevin dynamics (magenta). The dashed lines are a guide for the eye. Experimental values from Ref. 25 for NaOD (blue triangles) and Ref. 35 for NaOH (red triangles).

FIG. 3 .

 3 FIG.3. PIMD Distributions P (θ) at various temperatures in NaOH and NaOD at ambient pressure; the NaOH case at T = 300 K under 10 kbar pressure is also shown.

FIG. 4 .

 4 FIG. 4. Joint interlayer O-O distance and OD (OH) polar angle probability distributions P (θ, dOO) in NaOD (NaOH) at various temperatures and ambient pressure. Top right panel: NaOH at 300 K under 10 Kbar hydrostatic pressure. The horizontal lines denote the mean distance dOO .

FIG. 5 .

 5 FIG. 5. Joint probability distribution of the polar angles of hydroxyl groups at x = 0 (θ1) and x = 1/2 (θ2) in NaOH (top) and NaOD (center and bottom) at various temperatures and ambient pressure. Top right panel: NaOH at 300 K under 10 kbar hydrostatic pressure.

TABLE I

 I

	. Lattice parameters, OH (ionic-covalent) and O• • • H
	(hydrogen) bond lengths in Å as obtained via structural op-
	timization at 0 K in the AFE, FE and PE configurations vs.
	measured lattice parameters for NaOD

TABLE II .

 II Computed lattice parameters for NaOH at P = 10 ± 1 kbar and 300 K and NaOD at P = 0 ± 1 kbar and 77 K.

		a ( Å)	b ( Å)	c ( Å)
	NaOH	3.449	3.401	10.59
	NaOD	3.463	3.398	10.60

ACKNOWLEDGMENTS

We thank Sara Bonella for fruitful discussions and for her critical reading of the manuscript, and the referees for constructive criticisms. This work was granted access to the HPC resources of CINES under the allocation A0050906719 and of TGCC under the allocation A0130906719, made by GENCI.


Yuwen Meng
email: yuwen.meng.etu@univ-lemans.fr

Taco Nicolai
email: taco.nicolai@univ-lemans.fr

The effect of the contact angle on particle stabilization and bridging in waterin-water emulsions

Keywords: water-in-water emulsion, aqueous two phase system, microgel, bridging, network

Hypothesis

Water-in-water (W/W) emulsions formed by mixing incompatible polymers in aqueous solution can in some cases be stabilized by adding particles that adsorb spontaneously at the W/W interface. The importance of the contact angle of the particles with the interface on the stability of W/W emulsions is still an outstanding issue. We hypothesize that if the contact angle with the continuous phase is smaller than 90°, particles can bridge dispersed droplets, which enhances the stability of the emulsion.

Experiments

The W/W emulsions consisted of a dispersed poly(ethylene oxide) (PEO) phase in a continuous dextran phase or vice versa. Gelatin microgels were added and their contact angle was varied by varying the pH. The morphology during aging was observed by microscopy.

Findings

The contact angle of the microgels with the PEO phase varied between 110° close to neutral pH and 0° at pH 3 and pH 11. The W/W emulsions were stable only when the contact angle with the continuous phase was smaller than 90°. In this case, microgels could form bridges between dispersed droplets creating a network of droplets.

Introduction

Mixing aqueous solutions of incompatible polymers leads to the formation of water-in-water (W/W) emulsions [START_REF] Frith | Mixed biopolymer aqueous solutions -phase behaviour and rheology[END_REF]. Contrary to oil/water emulsions, W/W emulsions cannot be stabilized against droplet coalescence with molecular surfactants, because the W/W interface is thicker and W/W emulsions have a much lower interfacial tension [START_REF] Ding | Interfacial tension in phaseseparated gelatin/dextran aqueous mixtures[END_REF][START_REF] Forciniti | Interfacial tension of polyethyleneglycol-dextran-water systems: influence of temperature and polymer molecular weight[END_REF][START_REF] Scholten | Interfacial tension of a decomposed biopolymer mixture[END_REF][START_REF] Balakrishnan | Particles Trapped at the Droplet Interface in Water-in-Water Emulsions[END_REF]. W/W emulsions can, however, in some cases be stabilized by adding particles [START_REF] Nicolai | Particle stabilized water in water emulsions[END_REF][START_REF] Esquena | Water-in-water (W/W) emulsions[END_REF][START_REF] Dickinson | Particle-based stabilization of water-in-water emulsions containing mixed biopolymers[END_REF] that adsorb at the interface, forming so-called Pickering emulsions. The driving force that maintains a particle at the interface is the gain of free energy (ΔG) due to the decrease of the interfacial tension. The free energy of particle absorption of spherical microgels with radius R depends on the interfacial tension between phase A and phase B (γ AB ) and the contact angle (θ) of the microgels with the interface [START_REF] Binks | Colloidal particles at liquid interfaces[END_REF][START_REF] Aveyard | Emulsions stabilised solely by colloidal particles[END_REF]: ΔG = -πR 2 γ AB (1-|cos(θ)|) 2 (1)

θ is determined by the interfacial tension between the particles and the two phases (γ PA and γ PB ):

cos(θ) = |γ PA -γ PB |/γ AB (2)
If γ AB > |γ PA -γ PB |, the particles will spontaneously adsorb to the interface. However, this is not sufficient to inhibit coalescence. A major unresolved issue in this area of research is to understand why, contrary to oil/water emulsions, adsorption of particles at the interface is not sufficient to stabilize W/W emulsions. A striking observation reported for many systems is that the stability depends on which phase is the dispersed phase even if the composition of the phases and therefore the interfacial tension is the same [START_REF] Gonzalez-Jordan | Enhancement of the particle stabilization of water-inwater emulsions by modulating the phase preference of the particles[END_REF][START_REF] Nguyen | Stabilization of Water-in-Water Emulsions by Addition of Protein Particles[END_REF][START_REF] Gonzalez-Jordan | Influence of the protein particle morphology and partitioning on the behavior of particle-stabilized water-in-water emulsions[END_REF][START_REF] Merland | Thermo-induced inversion of water-in-water emulsion stability by bis-hydrophilic microgels[END_REF][START_REF] Peddireddy | Stabilization of Water-in-Water Emulsions by Nanorods[END_REF][START_REF] Nguyen | pH-responsive water-in-water Pickering emulsions[END_REF]. It has been suggested that W/W emulsions are better stabilized if the microgels have a stronger preference for the continuous phase and thus stick out more from the droplet surface [START_REF] Gonzalez-Jordan | Enhancement of the particle stabilization of water-inwater emulsions by modulating the phase preference of the particles[END_REF][START_REF] Nguyen | Stabilization of Water-in-Water Emulsions by Addition of Protein Particles[END_REF]. However, the particles used in these studies were too small to be able to visualize their position at the interface and to determine the contact angle. In order to investigate the relationship between the contact angle and the stability of the emulsion, the particles should be sufficiently large and their contact angle should be varied without changing the composition of the two phases.

Recently, we showed for a three-phase system consisting of dextran (DEX) and liquid gelatin (GEL) phases dispersed in a continuous PEO phase, that the interfacial tension between the GEL and the PEO (γ GP ) and DEX (γ GD ) phases can be tuned by the pH [START_REF] Meng | Exploiting multiple phase separation to stabilize water in water emulsions and form stable microcapsules[END_REF]. In fact, GEL was observed to disperse into the PEO phase below pH 3 and above pH 11, implying that γ GP became zero. The reason for this phenomenon is that GEL becomes strongly positively and negatively charged at low and high pH,

respectively. Here we exploit this phenomenon in order to modify the contact angle of spherical solid GEL microgels at the PEO/DEX interface and investigate the influence of the contact angle on the capacity of these microgels to stabilize W/W emulsions.

Elsewhere, it was shown that microgels of GEL can be produced by forming a W/W emulsion of liquid bovine GEL droplets in a concentrated PEO or maltodextrin solution [START_REF] Kong | Preparation of gelatin microparticles using water-inwater (w/w) emulsification technique[END_REF][START_REF] Beldengrun | Gelatin/maltodextrin water-in-water (w/w) emulsions for the preparation of cross-linked enzymeloaded microgels[END_REF]. Above 30°C, the GEL phase forms small liquid droplets that can be jellified by rapidly reducing the temperature.

They can subsequently be covalently crosslinked using the enzyme transglutaminase. The microgels that are formed in this manner are spherical and sufficiently big (10 µm) to visualize with confocal laser scanning microscopy (CLSM) at the DEX/PEO interface and to determine the contact angle.

Another advantage of using GEL microgels is that the contact angle that they make with the DEX/PEO interface can be varied by varying the pH.

The objective of this study was to investigate to what extent the contact angle determines the morphology and the stability of the W/W emulsion. In particular, we will show the influence of the contact angle on the possibility for a single microgel to bridge two neighboring droplets and that bridging can lead to the formation of a stable network of droplets. The possibility of bridging by particles between liquid droplets has not been reported before. Bridging can be important because it helps not only to inhibit coalescence, but also to slow down creaming or sedimentation of the dispersed droplets.

Materials and methods

Sample preparation

The emulsions used in this study were composed of PEO (M w = 2.0 × 10 5 g.mol -1 ) and DEX (M w = 1.6 × 10 5 g.mol -1 ). Enzymatically crosslinked GEL microgels were prepared utilizing phase separation as reported in the literature [START_REF] Kong | Preparation of gelatin microparticles using water-inwater (w/w) emulsification technique[END_REF][START_REF] Beldengrun | Gelatin/maltodextrin water-in-water (w/w) emulsions for the preparation of cross-linked enzymeloaded microgels[END_REF]. Gelatin from bovine skins (Type B , 225 g Bloom) and PEO at pH 7.3 were mixed, leading to the formation of droplets of the GEL phase containing 13 wt% GEL dispersed in a continuous PEO solution. The emulsion was cooled in an ice bath for 10 minutes to rapidly jellify the GEL droplets. However, the system was not sensitive to details of the cooling rate. 5 g/L transglutaminase (TGase, ~100 U/g), which was a kind gift of Ajinomoto Foods Europe S.A.S co., was added in order to covalently crosslink the GEL microgels. After stirring overnight, the emulsions were heated briefly at 80°C to inactivate the enzyme. PEO was removed after precipitating the microgels by centrifugation and repeatedly washing with ultrapure water. The microgels were subsequently freeze-dried. All chemicals were purchased from Sigma-Aldrich.

Stock solutions of GEL microgels at 5 and 10 wt% were prepared by dispersing the powder in ultrapure water, followed by ultrasonication to break up residual dispersed aggregates of microgels.

Stock solutions of PEO (15wt%), DEX (30wt%) and GEL microgels were mixed in the required amounts [START_REF] Balakrishnan | Particles Trapped at the Droplet Interface in Water-in-Water Emulsions[END_REF]. Different amounts of GEL microgels were added to these emulsions.

The pH of the solutions was adjusted by dropwise addition of HCl or NaOH at 0.1 or 1 mol/L.

Sample characterization

The morphology of the emulsions was observed with a Zeiss LSM800 CLSM microscope (Carl Zeiss Microscopy GmbH, Germany). Two different water immersion objectives: HC × PL APO 63× (NA = 1.2) and a HC × PL APO 25× (NA = 0.7) were used. The morphology of the samples was visualized by adding rhodamine B (5 ppm), which partitioned differently between the phases. For observation, the samples were inserted between slides and coverslips and sealed using a double-sided sticker. The sealed slides were stored vertically in a holder and then observed horizontally at different positions.

When creaming or sedimentation occurred the images were taken within the creamed or sedimentated layer. The droplet size distribution was measured manually from several images and was used to determine the number average diameter and the standard deviation.

The contact angles between the phases were determined by the method described in [START_REF] Nicolai | Effect of the Interfacial Tension on Droplet Association in Aqueous Multiphase Systems[END_REF].

Circles were drawn to trace the different interfaces and the distance between the centers of the circles and their radii were used to compute the contact angles. An example is shown in fig. 1, where the angle of the continuous PEO phase ( ) was determined from the radii of the circles (r D and r G )

and the distance between the centers of the circles (d DG ) :

cos( P )= -(r D 2 + r G 2 -d DG 2 )/2r D r G (3)
For correct measurements, it is important to select images where both dispersed phases are imaged near the center in the same horizontal plane. The average angle and the standard deviation were obtained from several independent measurements. makes with the GEL microgels (white) and the DEX droplets (dark).

Results and discussion

pH dependence of the contact angle

CLSM images of emulsions of the DEX phase dispersed in the continuous PEO phase at different pH containing 0.15 wt% GEL microgels are shown in Fig. 2. The contact angle that the PEO phase makes with the GEL and DEX phases ( ) was determined as described in section 2 and is plotted in Fig. 3 (a) as a function of the pH. The contact angle of the spherical solid GEL phase is obviously constrained to independent of the pH and that of the DEX phase is given by:

. A sharp decrease of was observed below pH 4 and at pH 2.8 the microgels no longer adsorbed at the interface, but dispersed fully in the PEO phase. Interestingly, the effect of the pH on the contact angle could be reversed by adding NaCl. In the presence of 0.1 M NaCl, the microgels adsorbed at the interface at pH 2.8 with the same contact angle as at pH 7.3 in the absence of salt. The effect of charge on the interfacial tension has been discussed in detail by Vis et al. for mixtures of fish gelatin and DEX [START_REF] Vis | Decreased interfacial tension of demixed aqueous polymer solutions due to charge[END_REF]. It was found that the interfacial tension was lower when the gelatin was more strongly charged, which was attributed to the Donnan potential between the charged gelatin phase and the neutral DEX phase. The addition of salt eliminates this effect.

For comparison we also show the contact angles of the liquid GEL, PEO and DEX phases as a function of the pH in mixtures with the same composition that was reported elsewhere [START_REF] Meng | Exploiting multiple phase separation to stabilize water in water emulsions and form stable microcapsules[END_REF]. In this case is not constrained and the relative interfacial tensions determine the contact angle that each phase makes with the two other phases [START_REF] Rowlinson | L. Benyahia, Water-in-water emulsion gels stabilized by cellulose nanocrystals[END_REF]. where it preferred the PEO phase over the GEL phase.

Effect of the contact angle on the stability

We investigated the effect of adding microgels on the stability and morphology at different pH for an emulsion containing 15 v% of the DEX phase and 1.5 wt% microgels, see Fig. 4. The pH of the emulsions was adjusted to 7.3, 4.5 and 3.5 for which was approximately 110°, 90° and 70°, respectively. In all cases, a layer of microgels formed at the surface of the dextran droplets. The initial number average droplet diameter (d) did not vary significantly with the pH: 41 ± 8, 37 ± 15 and 39 ± 10 µm at pH 7.3, 4.5 and 3.5, respectively.

The stability of these emulsions was followed for a period of 10 days. At pH 7.3, at which the microgels preferred the DEX phase with  110°, the emulsion destabilized quickly and 6 h after preparation large DEX domains were observed that sedimented. Small PEO droplets can also be seen trapped within the larger DEX domains that remained there for at least 10 days. At pH 4.5, at which the microgels preferred each phase similarly so that ≈ 90°, coalescence of the DEX droplets was significantly slower than at pH 7.3 (d = 56 ± 7 µm after 6 h), but large DEX domains were still formed eventually. At pH 3.5, at which the microgels preferred the PEO phase with ≈ 70°, the DEX droplets grew in size during the first 6 h (d = 60± 1 µm), but then remained stable for at least 10 days when d = 72 ± 20 µm. The reason for the initial growth is that the DEX droplets were not yet sufficiently covered, because when more microgels were added to the emulsion, the growth stopped sooner so that the stable DEX droplets were smaller, see Fig. 5, with d = 27 ± 5, 28 ± 6, 30 ± 5 and 30 ± 5 µm after 0 h, 6 h, 1 day and 10 days, respectively. Macroscopically, slow sedimentation of the droplets was observed.

Effect of the phase composition

To test whether the effect of the pH on the stability is related to the contact angle and not to the charge density of the GEL, we prepared the inverse emulsion at pH 7.3 containing 15 v% PEO dispersed in the continuous DEX phase and added 2.3 wt% microgels. The composition of the phases was the same, and therefore was again approximately 110°. However, in this case, DEX is the continuous phase with a contact angle of around 70°. Contrary to the DEX droplets dispersed in PEO, the PEO droplets in DEX did not coalesce, but remained stable for at least 10 days, see Fig. 6, with d = 27 ± 5, 28 ± 6, 30 ± 5 and 30 ± 5 µm after 0 h, 6 h, 1 day and 10 days, respectively. Macroscopically, slow creaming was observed. It is clear that if the microgels prefer the continuous phase and thus stick out from the droplet surface, they better stabilize the emulsion regardless of the charge density of the microgels.

A similar observation was reported elsewhere [START_REF] Gonzalez-Jordan | Enhancement of the particle stabilization of water-inwater emulsions by modulating the phase preference of the particles[END_REF] for the same emulsions in the presence of latex microgels. The surface of the latex microgels was modified by the adsorption of more or less proteins and it was found that the emulsions were more stable when the microgels preferred the continuous phase. However, in that study, the microgels were too small to clearly visualize at the interface and the contact angle could not be determined. Here we showed that the contact angle can indeed be the determining factor for the stability of a W/W emulsion. It is important to stress, however, that the preference of the particles for the continuous phase is neither a sufficient nor a necessary condition for stability, as was illustrated, for instance, in ref. [START_REF] Merland | Thermo-induced inversion of water-in-water emulsion stability by bis-hydrophilic microgels[END_REF].

Droplet bridging by microgels

In this investigation, we observed a new phenomenon that has so far not yet been recognized, viz. that one microgel can bridge between two dispersed droplets. This is only possible if the contact angle of the continuous phase is significantly less than 90°C, otherwise, the bare surface of the second droplet will simply completely wet the surface of the microgel, leading to coalescence as is schematically illustrated in Fig. 7. The possibility to form bridges will help to stabilize the emulsion, but it can also lead to clustering of the droplets. This is most clearly seen for the PEO in DEX emulsions at pH 7.3 shown in Fig. 6, but bridging can also be seen in the DEX in PEO emulsions at pH 3.5 in Fig. 4. Fig. 7 Illustration of droplet coalescence or bridging depending on the contact angle of the continuous phase. The dispersed liquid phase is shown in blue and the microgels are shown in yellow.

For bridging to occur, a droplet covered with microgels needs to encounter the bare surface of another droplet. Therefore, the extent of bridging will depend on the amount of microgels, as in the presence more microgels the droplets present less bare surface. Adding fewer microgels leads to more bridging, which in turn causes the formation of denser clusters. However, adding fewer microgels also leads to more coalescence due to more contact between bare surfaces, and therefore to the formation of larger droplets. By increasing the volume fraction of the dispersed phase and fine-tuning the amount of microgels, bridging may lead to the formation of a network that fills the whole space and forms a W/W emulsion gel that resists creaming or sedimentation. This is illustrated in Fig. 8

Conclusion

Earlier investigations showed that the capacity of particles to stabilize W/W emulsions depends on the affinity of the particles for each aqueous phase and is better when the particles prefer the continuous phase [START_REF] Gonzalez-Jordan | Enhancement of the particle stabilization of water-inwater emulsions by modulating the phase preference of the particles[END_REF][START_REF] Nguyen | Stabilization of Water-in-Water Emulsions by Addition of Protein Particles[END_REF]. The contact angle could not be determined for these emulsions, but it was suggested that the larger stability was due to a smaller contact angle of the particles with the continuous phase. Here we showed that the contact angle of GEL microgels at the PEO/DEX interface can be varied and controlled by the pH. W/W emulsions formed by mixing PEO and DEX were stable only when the contact angle with the continuous phase was smaller than 90° confirming the hypothesis that the contact angle can indeed be a determining factor for the stability of W/W emulsions. It may explain why the stability in some cases depends on which phase is the dispersed phase. This study also showed that if the contact angle with the continuous phase is significantly smaller than 90°, a single particle can bridge two dispersed droplets. By fine-tuning the quantity of the dispersed phase and the particle a percolated network of the dispersed droplets can be formed that resists creaming or sedimentation without crosslinking the particles. This offers an alternative to the method reported in the literature [23][START_REF] Ganley | Stabilisation of water-in-water emulsions by montmorillonite platelets[END_REF][START_REF] Gonzalez-Jordan | Cold gelation of water in water emulsions stabilized by protein particles[END_REF] to avoid creaming or sedimentation of dispersed droplets by forming an emulsion gel through crosslinking the stabilizing particles. Further research is needed to establish the mechanical properties of this network of bridged liquid droplets and to apply the findings reported here for a model W/W emulsion to other types of W/W emulsions that have potential applications in areas such as food and cosmetics. where it preferred the PEO phase over the GEL phase. Photographs of the emulsions after 10 days are also shown.

  using a vortex stirrer to form the W/W emulsions. The duration and intensity of vortex stirring did not have an influence on the morphology of the emulsions as long as the components were thoroughly mixed. Emulsions were prepared according to the phase diagram shown in ref. [13] at three different volume fractions of the PEO and DEX phases. The emulsions at 15/85, 25/75 and 85/15 v% PEO/DEX contained 1.2/13.7, 2.0/12.1 and 6.8/2.4 wt% PEO/DEX, respectively. The PEO phase contained 8 wt% PEO and the DEX phase contained 16 wt% DEX with negligible quantities of PEO and DEX in the DEX and PEO phase, respectively. All three emulsions were positioned on the same tie-line and therefore had the same interfacial tension between the PEO and DEX phase of approximately 75 µN.m -1

Fig. 1

 1 Fig.1 Illustration of the determination of the contact angle ( ) that the continuous PEO phase (grey)

8 Fig. 2

 82 Fig. 2 CLSM images of emulsions of the DEX phase dispersed in the continuous PEO phase with 0.15 wt% of GEL microgels at different pH. The fluorophore rhodamine B partitioned more to the GEL microgels (white) than to the PEO phase (grey) and least to the DEX phase (dark) except at pH 2.8

Fig. 3 (

 3 Fig. 3 (a) Contact angles of the DEX ( , blue circles) and PEO ( , red diamonds) phases in emulsions with GEL microgels as function of the pH with their standard deviation. The contact angle of the GEL phase was fixed at 180°C. (b) Angles of the DEX, PEO and GEL (green triangles) phases as a function of the pH in an equivalent liquid triphasic DEX/GEL/PEO mixture, reproduced from [17].

Fig. 4

 4 Fig. 4 CLSM images (220 × 220 µm) of emulsions containing 15 v% of the DEX phase (dark) dispersed in the PEO phase (grey) with 1.5 wt% of microgels (white) at different pH and aging times.

Fig. 5

 5 Fig. 5 CLSM images (220 × 220 µm) of an emulsion containing 15 v% of the DEX phase (dark) dispersed in the PEO phase (grey) with 2.3 wt% of microgels (white) at pH 3.5 and at different aging times.

Fig. 6

 6 Fig.6CLSM images (511 × 511 µm) of emulsions at pH 7.3 containing 15 v% of the PEO phase (grey) dispersed in the DEX phase (dark) with 2.3wt% microgels (white) at different aging times. The zoomin shows bridged droplets. Photographs of the fresh emulsion and after 10 days are also shown.

Fig. 1

 1 Fig.1Illustration of the determination of the contact angle ( ) that the continuous PEO phase (grey) makes with the GEL microgels (white) and the DEX droplets (dark).

Fig. 2

 2 Fig.2CLSM images of emulsions of the DEX phase dispersed in the continuous PEO phase with 0.15 wt% of GEL microgels at different pH. The fluorophore rhodamine B partitioned more to the GEL microgels (white) than to the PEO phase (grey) and least to the DEX phase (dark) except at pH 2.8

Fig. 3 (

 3 Fig. 3 (a) Contact angles of the DEX ( , blue circles) and PEO ( , red diamonds) phases in emulsions with GEL microgels as function of the pH with their standard deviation. The contact angle of the GEL phase was fixed at 180°C. (b) Angles of the DEX, PEO and GEL (green triangles) phases as a function of the pH in an equivalent liquid triphasic DEX/GEL/PEO mixture, reproduced from [17].

Fig. 4

 4 Fig. 4 CLSM images (220 × 220 µm) of emulsions containing 15 v% of the DEX phase (dark) dispersed in the PEO phase (grey) with 1.5 wt% of microgels (white) at different pH and aging times.

Fig. 5 Fig. 6

 56 Fig. 5 CLSM images (220 × 220 µm) of an emulsion containing 15 v% of the DEX phase (dark) dispersed in the PEO phase (grey) with 2.3 wt% of microgels (white) at pH 3.5 and at different aging times.

Fig. 7 Fig. 8

 78 Fig. 7 Illustration of droplet coalescence or bridging depending on the contact angle of continuous phase.

  which shows emulsions containing 15 v% or 25 v% of the PEO phase dispersed in the continuous DEX phase with 2.3 wt% or 4.6 wt% microgels. Increasing the amount of microgels or decreasing the volume fraction of the dispersed phase led to smaller droplets and a more homogeneous network that better resisted creaming, see photographs in Fig.8. In earlier investigations, W/W emulsion gels were formed by crosslinking particles adsorbed at the interface as well as those still free in suspension[23][START_REF] Ganley | Stabilisation of water-in-water emulsions by montmorillonite platelets[END_REF][START_REF] Gonzalez-Jordan | Cold gelation of water in water emulsions stabilized by protein particles[END_REF]. No particle crosslinking is involved in the formation of the emulsion gels investigated here. As a consequence, these W/W emulsion gels flow very easily since the bridges between the droplets are easily broken. CLSM images (511 × 511 µm) of emulsions at pH 7.3 containing 25 v% or 15 v% of the PEO phase (grey) dispersed in the DEX phase (dark) with 2.3 wt% at 4.6 wt% microgels (white) at different aging times. Photographs of the fresh emulsions and after 7 days are also shown.

	Fig.8
	25 v%
	2.3
	wt%
	25 v%
	4.6
	wt%
	15 v%
	4.6
	wt%
	Fresh	7 days