L Landrieu

C Mallet

M Weinmann

COMPARISON OF BELIEF PROPAGATION AND GRAPH-CUT APPROACHES FOR CONTEXTUAL CLASSIFICATION OF 3D LIDAR POINT CLOUD DATA

Keywords: Point cloud, classification, spatial regularization, belief propagation, graph-cut

In this paper, we focus on the classification of lidar point cloud data acquired via mobile laser scanning, whereby the classification relies on a context model based on a Conditional Random Field (CRF). We present two approximate inference algorithms based on belief propagation, as well as a graphcut-based approach not yet applied in this context. To demonstrate the performance of our approach, we present the classification results derived for a standard benchmark dataset. These results clearly indicate that the graph-cut-based method is able to retrieve a labeling of higher likelihood in only a fraction of the time needed for the other approaches. The higher likelihood, in turn, translates into a significant gain in the accuracy of the obtained classification.

INTRODUCTION

The automated analysis of acquired lidar point cloud data is a crucial task in photogrammetry, remote sensing, computer vision and robotics. In particular, the semantic classification of lidar point clouds acquired with terrestrial or mobile laser scanning systems in urban areas has received significant attention in recent years [START_REF] Munoz | Contextual classification with functional max-margin Markov networks[END_REF][START_REF] Weinmann | Semantic point cloud interpretation based on optimal neighborhoods, relevant features and efficient classifiers[END_REF][START_REF] Hackel | Fast semantic segmentation of 3d point clouds with strongly varying density[END_REF]. The main objective of this task is to associate a semantic label (e.g. Building, Ground, Tree Trunk or Foliage) to each 3D point of the considered point cloud and the main challenges are typically represented by the irregular distribution of 3D points, a high complexity of the observed scene and very different objects of interest (Fig. 1).

As the number of 3D points far exceeds the number of semantic objects in the scene, the semantic point cloud classification can be expected to display a high spatial regularity. Furthermore, transitions between different classes are not equally likely, e.g. Tree Trunk to Ground is more probable than Foliage to Building. Graphical probabilistic models are widely used in the literature to model the influence of these observations [START_REF] Niemeyer | Classification of urban lidar data using conditional random field and random forests[END_REF][START_REF] Shapovalov | Nonassociative Markov networks for 3d point cloud classification[END_REF]. In [START_REF] Niemeyer | Classification of urban lidar data using conditional random field and random forests[END_REF], for instance, a context model based on a Conditional Random Field (CRF) [START_REF] Lafferty | Conditional random fields: probabilistic models for segmenting and labeling sequence data[END_REF] is used, which is then solved with a belief propagation algorithm. In this paper, we argue that graph-cut-based approaches allow us to achieve a better approximation of the most likely configuration in a much shorter time.

RELATED WORK

The task of semantic point cloud classification typically relies on the use of geometric features like the ones presented in [START_REF] Weinmann | Semantic point cloud interpretation based on optimal neighborhoods, relevant features and efficient classifiers[END_REF][START_REF] Hackel | Fast semantic segmentation of 3d point clouds with strongly varying density[END_REF], but some investigations additionally involve complementary types of features such as echo-based features or fullwaveform features [START_REF] Chehata | Airborne lidar feature selection for urban classification using random forests[END_REF]. These features, in turn, are provided as input to a classification pipeline. For the latter, standard approaches for supervised classification such as a Support Vector Machine (SVM) classifier or a Random Forest (RF) classifier are typically applied. A comprehensive study focusing on the classification of mobile laser scanning data with a variety of such standard approaches relying on different learning principles can be found in [START_REF] Weinmann | Semantic point cloud interpretation based on optimal neighborhoods, relevant features and efficient classifiers[END_REF] and concludes that a RF classifier provides a good trade-off between classification accuracy and computational effort. However, such standard classification approaches are limited by the fact that the derived labeling is typically not spatially regular, although it should be taken into account that class labels of neighboring 3D points tend to be correlated.

To derive a labeling with a higher spatial regularity, a contextual classification is typically considered for which many approaches rely on the use of a Conditional Random Field (CRF) [START_REF] Niemeyer | Classification of urban lidar data using conditional random field and random forests[END_REF]. However, retrieving the classification of highest likelihood with such a model is a complicated combinatorial task, which can only be approximately solved. The authors of [START_REF] Niemeyer | Classification of urban lidar data using conditional random field and random forests[END_REF] use loopy belief propagation (LBP), a message-passing algorithm [START_REF] Yedidia | Understanding belief propagation and its generalizations[END_REF] to perform marginal inference, and then apply the maximum-a-posteriori (MAP) principle point by point to compute a smooth labeling.

As suggested in [START_REF] Tappen | Comparison of graph cuts with belief propagation for stereo, using identical MRF parameters[END_REF] for stereo shape estimation, graphcut-based approaches such as α-expansion [START_REF] Boykov | Fast approximate energy minimization via graph cuts[END_REF] can retrieve a labeling of higher likelihood and in shorter time. In this paper, we propose comparing these in terms of the likelihood of the produced labeling, computation time and quality of the derived labeling.

METHODOLOGY

We consider a point cloud V , whose local neighborhood structure is encoded in the graph G = (V, E), where the edge set E encodes the adjacency between nodes. For each point, we observe a feature vector. Our objective is to find a labeling x ∈ K V , where K is the finite set of semantic labels. We denote the set of features for all points in V by f , and the feature vector associated with the point i by f i .

Feature extraction

To adequately describe each considered 3D point i with geometric features, the local 3D structure at i is considered which is given in the spatial arrangement of 3D points within the local neighborhood of i. Accordingly, the local neighborhood of i has to be recovered first and, subsequently, all 3D points within that local neighborhood can be used to derive respective geometric features describing the local 3D structure at i.

The recovery of local neighborhoods can generally rely on different neighborhood definitions such as spherical or cylindrical neighborhoods which, in turn, can be parameterized with a specific scale parameter (e.g. a radius or the number of considered nearest neighbors). In this regard, the selection of the scale parameter often remains a crucial step since (1) the selection typically involves prior knowledge about the scene and/or the data and (2) typically an identical value of the scale parameter is used for all 3D points of the considered point cloud. For the consideration of general scenes with very different types of objects and classes of interest, however, a data-driven selection of the scale parameter seems to be desirable. Furthermore, it should be taken into account that 3D points belonging to different classes might favor a different neighborhood size [START_REF] Weinmann | Semantic point cloud interpretation based on optimal neighborhoods, relevant features and efficient classifiers[END_REF], and therefore an approach is to be preferred that allows for locally adapting the size of the local neighborhood for each individual 3D point. In the scope of our work, we apply the definition of a local neighborhood that is formed by the k nearest neighbors of i. To select the optimal scale parameter k opt for each 3D point i, we focus on eigenentropy-based scale selection [START_REF] Weinmann | Semantic point cloud interpretation based on optimal neighborhoods, relevant features and efficient classifiers[END_REF] which has proven to be favorable compared to other alternatives. Accordingly, we first calculate the eigenentropy for different scale parameters k and then select the optimal scale parameter k opt that corresponds to the minimal eigenentropy (i.e. to the minimal disorder of 3D points).

Based on the recovered local neighborhoods, a variety of geometric features can be extracted. In particular, the local 3D shape features are widely used as they provide a rather intuitive description of the local 3D structure with a single value per feature. These local 3D shape features are derived from the eigenvalues of the 3D structure tensor and represented by linearity, planarity, sphericity, omnivariance, anisotropy, eigenentropy, sum of eigenvalues and change of curvature [START_REF] Weinmann | Semantic point cloud interpretation based on optimal neighborhoods, relevant features and efficient classifiers[END_REF]. Furthermore, we extract geometric 3D properties of the local neighborhood that are given by the height of the 3D point i, the radius of the local neighborhood, the local point density, the verticality, and the maximum difference as well as the standard deviation of the height values of those points within the local neighborhood [START_REF] Weinmann | Semantic point cloud interpretation based on optimal neighborhoods, relevant features and efficient classifiers[END_REF]. As urban environments are typically composed of a variety of man-made objects with almost perfectly vertical structures, we also consider a 2D projection of the point i and its k opt nearest neighbors onto a horizontally oriented plane. Based on this 2D projection, local 2D shape features are defined by the sum and the ratio of the eigenvalues of the 2D structure tensor [START_REF] Weinmann | Semantic point cloud interpretation based on optimal neighborhoods, relevant features and efficient classifiers[END_REF]. Finally, we also define geometric 2D properties which are represented by the radius of the local 2D neighborhood in the projection plane and the point density in 2D.

Classification

To derive the initial labeling, we use a standard Random Forest (RF) classifier [START_REF] Breiman | Random forests[END_REF] that also allows for a soft labeling in terms of class probabilities. Subsequently, we use a CRFbased context model to impose spatial regularity on the initial labeling. More specifically, a CRF-based model like the one presented in [START_REF] Niemeyer | Classification of urban lidar data using conditional random field and random forests[END_REF] leverages contextual information to improve the semantic classification of 3D point clouds. In this model, the logarithm of the conditional likelihood of a labeling x given the observed features f is expressed as follows:

(x | f ) ∝ i∈V ψ(x i , f ) + (i,j)∈E φ(x i , x j , f ). (1)
This posterior probability is split into two parts: a data term and an interaction potential. The function ψ(x i , f ) encodes the influence of the observed feature on the label, without contextual information. We take ψ(x i , f ) as the logarithm of the probability given by the RF classifier. The interaction potential φ(x i , x j , f ) encodes the adequation between the labels of two adjacent nodes i and j. In [START_REF] Niemeyer | Classification of urban lidar data using conditional random field and random forests[END_REF], a classifier is trained to predict the probability of each transition given the difference of feature vectors. We argue here that the training of such a classifier poses certain difficulties as the number of transition classes is quadratic in the number of semantic classes, and hence would require a much larger training set to obtain a prediction of reasonable quality, as well as more intensive computations. Furthermore, this would require a point-perfect precise annotation of the training set, which is difficult as irregularities in the density of the acquisition make the precise localization of the interface between classes a complicated task. In this paper, we chose to forego the influence of features when it comes to transitions, and take φ(x i = k, x j = l, f ) = log(M k,l ), where M is the matrix of empirical transition probabilities in our training set. This model allows us to assess the adequation of a given labeling with the observed features while taking contextual information into account. MAP inference, i.e. retrieving the labeling of highest likelihood, is a complicated task and in fact NPhard. However, approximate solutions can be provided using message-passing algorithms or graph-cut-based methods.

Loopy belief propagation (LBP), which is an extension of the exact Viterbi algorithm [START_REF] Forney | The Viterbi algorithm[END_REF] from trees to general graphs, is highly popular for its robustness and the simplicity of its implementation. However, it does not provide any proof of convergence or guarantees with respect to the global optimum. In [START_REF] Niemeyer | Classification of urban lidar data using conditional random field and random forests[END_REF], marginal inference is performed first using the sum-product LBP algorithm, and then each point is assigned the label of highest probability. In this paper, we also present the max-product version of the LBP algorithm, which allows us to directly compute the MAP inference.

Graph-cut-based algorithms, such as α-expansion, offer guarantees that the results will be close to the global optimum. Furthermore, α-expansion is also known for its impressive speed, in part due to the max-flow implementation [START_REF] Boykov | An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision[END_REF].

EXPERIMENTAL RESULTS

We evaluate the performance of different approaches on the Oakland 3D Point Cloud Dataset [START_REF] Munoz | Contextual classification with functional max-margin Markov networks[END_REF], a labeled benchmark dataset which has been acquired with a mobile laser scanning system in Oakland, USA. The ground truth (GT) labeling is provided with respect to five semantic classes given by Wire, Pole/Trunk, Fac ¸ade, Ground and Vegetation. Furthermore, a split into training data (about 36.9k labeled 3D points), validation data (about 91.5k labeled 3D points) and test data (about 1.3M labeled 3D points) is already provided.

First, we derive an initial labeling by using low-level geometric 3D and 2D features (cf. Section 3.1) as input for a standard Random Forest classifier. For training, we take into account that an unbalanced distribution of training samples per class might have a detrimental effect on the classification results and hence use a reduced training set comprising 1,000 randomly selected training examples per class [START_REF] Weinmann | Semantic point cloud interpretation based on optimal neighborhoods, relevant features and efficient classifiers[END_REF]. For testing, we evaluate the classification result achieved for the test set with respect to the GT labeling, where we obtain an overall accuracy of OA = 92.3%, a kappa value of κ = 83.0% and an unweighted average of the F 1 -score of F1 = 63.5%. The class-wise evaluation metrics of recall, precision and F 1 -score are provided in Table 1 and a visualization of the classified point cloud is given in Fig. 1. For the three MAP inference algorithms presented in Section 3.2, we use MEX implementations provided by [START_REF] Schmidt | A Matlab toolbox for probabilistic undirected graphical models[END_REF]. The respective results as well as the required processing times are provided in Fig. 2 and Tables 2-4, respectively. It can be observed that the use of contextual classification generally improves the classification results in terms of OA, κ and F1 . As expected, the α-expansion algorithm reaches a higher likelihood in a much shorter time. We remark that this improvement translates into a classification of higher quality, validating the relevance of the model.

CONCLUSIONS

In this paper, we have focused on the CRF-based classification of lidar point cloud data. We have presented two approximate inference algorithms based on belief propagation and a graph-cut-based approach represented by α-expansion.

The derived results reveal that the graph-cut-based approach is able to retrieve a labeling of higher likelihood and thus a higher classification accuracy, while it is also significantly faster than the other approaches. In future work, we intend to investigate further approaches for spatial regularization.

Fig. 1 .

 1 Fig. 1. Labeled point cloud (Wire: blue; Pole/Trunk: red; Fac ¸ade: gray; Ground: brown; Vegetation: green).

Fig. 2 .

 2 Fig. 2. Classification results derived with the sum-product version of LBP (top), the max-product version of LBP (center) and the α-expansion MAP inference (bottom).

Table 1 .

 1 Classification results derived with the initial labeling (OA = 92.3%, κ = 83.0%, F1 = 63.5%).

	Class	Recall [%] Precision [%] F 1 -score [%]
	Wire	84.6	10.2	18.2
	Pole/Trunk	77.4	25.2	38.0
	Fac ¸ade	68.2	86.5	76.3
	Ground	98.7	96.6	97.6
	Vegetation	80.6	94.9	87.2
	Class	Recall [%] Precision [%] F 1 -score [%]
	Wire	75.6	15.4	25.5
	Pole/Trunk	63.6	61.2	62.4
	Fac ¸ade	79.1	92.9	85.5
	Ground	99.3	97.3	98.2
	Vegetation	90.0	96.5	93.1

Table 2 .

 2 Classification results derived with the sum-product version of the LBP algorithm (OA = 95.4%, κ = 89.8%, F1 = 71.1%, = -2.08 • 10 6 , t = 85s for 30 iterations).

	Class	Recall [%] Precision [%] F 1 -score [%]
	Wire	62.7	16.0	25.5
	Pole/Trunk	49.9	65.6	56.7
	Fac ¸ade	72.3	92.8	81.2
	Ground	99.4	96.0	97.7
	Vegetation	88.1	94.0	90.9

Table 3 .

 3 Classification results derived with the max-product version of the LBP algorithm (OA = 94.4%, κ = 87.3%, F1 = 70.4%, = -2.09 • 10 6 , t = 95s for 30 iterations).

	Class	Recall [%] Precision [%] F 1 -score [%]
	Wire	64.7	37.8	47.7
	Pole/Trunk	38.2	84.8	52.6
	Fac ¸ade	74.5	92.1	82.3
	Ground	99.6	96.7	98.1
	Vegetation	95.8	97.4	96.6

Table 4 .

 4 Classification results derived with α-expansion MAP inference (OA = 96.2%, κ = 91.4%, F1 = 75.5%, = -1.39 • 10 6 , t = 9s).


T Jane Stockmann

Jean-Marc Noël

Ali Abou-Hassan

Catherine Combellas

Frédéric Kanoufi
email: frederic.kanoufi@univ-paris-diderot.fr

Facilitated Lewis Acid Transfer by Phospholipids at a (Water|CHCl 3 ) Liquid|Liquid Interface Toward Biomimetic and Energy Applications

Proton and metal ion interaction with phospholipids are of considerable interest to biological applications (e.g. chemical communication, drug transport, etc.). Herein, H + and Li + coordination to a typical phospholipid are examined electrochemically at the water|chloroform micro-interface, which reveals two coordination stoichiometries towards protons that were 2 thermodynamically quantified using cyclic voltammetry. The thermodynamics of phospholipid facilitated proton transfer are further confirmed through Comsol Multiphysics simulations.

Insight into H + -phospholipid coordination/interaction has valuable implications towards cellular communication (such as vesicle systems that mimic living cells) and vesicle micro-reactor synthetic applications; however, the utility of the H + /phospholipid coupled water|organic solvent system is exemplified herein towards the batch generation of solar fuels through shake-flask experiments.

INTRODUCTION

Many cellular processes, such as those involved in the cell energy machinery, depend on the transport of ions across phospholipidic biological membranes. An illustration is the transfer of protons to generate ATP involved in cellular respiration. In addition to the well-known role of proton pumps (or ion channels), recent experiments 1 and molecular dynamics simulations [START_REF] Wolf | Anomalous Surface Diffusion of Protons on Lipid Membranes[END_REF] suggest that the phospholipid itself, even devoid of protonable moieties, presents a high proton affinity, ensuring a high H + concentration at the water/phospholipid interface. In principle this concept can be generalized to alkali metal ions and to biomimetic analogs of living cells such as vesicles or simple/double emulsion systems employing phospholipids. These artificial cell-like platforms are largely employed in various applications and are particularly a key-ingredient for the compartmentalization of (bio)chemical information or chemical reactions in droplet-based microfluidics. [START_REF] Van Swaay | Microfluidic methods for forming liposomes[END_REF][START_REF] Tomasi | Chemical communication between liposomes encapsulating a chemical oscillatory reaction[END_REF][START_REF] Tompkins | Testing Turing's theory of morphogenesis in chemical cells[END_REF] By the encapsulation of chemical systems, vesicles become a powerful utility, particularly with respect to a generalized view of how chemical species interact with the lipid bilayer, [START_REF] Tomasi | Chemical communication between liposomes encapsulating a chemical oscillatory reaction[END_REF][START_REF] Tompkins | Testing Turing's theory of morphogenesis in chemical cells[END_REF][START_REF] Torbensen | Interaction of the Belousov-Zhabotinsky Reaction with Phospholipid Engineered Membranes[END_REF] through their transport between vesicles. The importance of the transport (or permeability) of H + , and that of related Lewis acids, through phospholipid layers is particularly challenged by the recent reports on the high affinity and fast diffusion of H + within the lipids comprising the vesicle membrane. [START_REF] Brändén | Localized proton microcircuits at the biological membrane-water interface[END_REF][START_REF] Wolf | Anomalous Surface Diffusion of Protons on Lipid Membranes[END_REF] For a specific understanding, it is necessary to analyze the various components in isolation: e.g. the specific interaction of protons with phospholipids. This can be accomplished by depositing phospholipids in mono-or bilayers at the liquid/air [START_REF] Zhang | Proton Diffusion at Phospholipid Assemblies[END_REF][START_REF] Cannan | Scanning Electrochemical Microscopy (SECM) Studies of Oxygen Transfer across Phospholipid Monolayers under Surface Pressure Control: Comparison of Monolayers at Air/Water and Oil/Water Interfaces[END_REF] and liquid|liquid interfaces 4,8- 15 and electrochemically stimulating that interface with a probe or through the charge transfer of different chemical species; e.g. protons, particularly in the case of the latter.

Liquid|liquid electrochemistry, [START_REF] Herzog | Recent developments in electrochemistry at the interface between two immiscible electrolyte solutions for ion sensing[END_REF][START_REF] Samec | Charge-transfer processes at the interface between hydrophobic ionic liquid and water Pure[END_REF][START_REF] Liu | Electrochemistry at micro-and nanoscopic liquid/liquid interfaces[END_REF] at the interface between two immiscible electrolytic solutions (ITIES), offers a valuable biomimetic approach since the interface, typically between water and an organic solvent (w|o), e.g. water|1,2-dichloroethane (w|DCE), [START_REF] Poltorak | Electrochemically Assisted Generation of Silica Deposits Using a Surfactant Template at Liquid/Liquid Microinterfaces[END_REF] is similar to the water|lipid biological interface. Indeed, it has been used to investigate ion transfer reactions of significant biomolecules [START_REF] O'sullivan | Stripping voltammetric detection of insulin at liquid-liquid microinterfaces in the presence of bovine albumin[END_REF][START_REF] Colombo | Nanopipet-Based Liquid-Liquid Interface Probes for the Electrochemical Detection of Acetylcholine, Tryptamine, and Serotonin via Ionic Transfer Anal[END_REF][START_REF] Hartvig | Formation of Dielectric Layers and Charge Regulation in Protein Adsorption at Biomimetic Interfaces[END_REF] and understand the interaction of ions with nanopore [START_REF] Sairi | Electrochemical Characterisation of Nanoscale Liquid|Liquid Interfaces Located at Focused Ion Beam-Milled Silicon Nitride[END_REF][START_REF] Kim | Ion Permeability of the Nuclear Pore Complex and Ion-Induced Macromolecular Permeation as Studied by Scanning Electrochemical and Fluorescence Microscopy Anal[END_REF][START_REF] Kim | Nanoscale Mechanism of Molecular Transport through the Nuclear Pore Complex As Studied by Scanning Electrochemical Microscopy[END_REF] structures common in living cells. By functionalizing the w|o interface with phospholipids, kinetic and thermodynamic insight through direct electrochemical measurements can be gained concerning ion transfer, [START_REF] Velický | Mechanism of Ion Transfer in Supported Liquid Membrane Systems: Electrochemical Control over Membrane Distribution Anal[END_REF] ion adsorption, [START_REF] Mareček | Mechanism of Lecithin Adsorption at a Liquid|Liquid Interface[END_REF] or facilitated ion transfer reactions. [START_REF] Mareček | Mechanism of Lecithin Adsorption at a Liquid|Liquid Interface[END_REF][START_REF] Kim | Nanoscale Mechanism of Molecular Transport through the Nuclear Pore Complex As Studied by Scanning Electrochemical Microscopy[END_REF][START_REF] Stockmann | Electrochemical assessment of water|ionic liquid biphasic systems towards cesium extraction from nuclear waste Anal[END_REF][START_REF] Reymond | Facilitated ion transfer reactions across oil|water interfaces. Part II. Use of the convoluted current for the calculation of the association constants and for an amperometric determination of the stoichiometry of MLjz+ complexes[END_REF][START_REF] Diba | Amperometric sensing of sodium, calcium and potassium in biological fluids using a microhole supported liquid/gel interface[END_REF] However, phospholipids are difficult to analyze due to their lack of solubility in conventional liquid|liquid electrochemical solvents. They are usually dissolved in low polarity solvents, such as chloroform (CHCl 3 , ε = 4.81), [START_REF] Wohlfarth | CRC Handbook of Chemistry and Physics[END_REF] which are often avoided owing to their high resistivity for electrochemical measurements. [START_REF] Ohde | Some factors in the voltammetric measurement of ion transfer at the micro aqueous | organic solution interface[END_REF] An active area of research [START_REF] Olaya | Ion transfer across the water|trifluorotoluene interface[END_REF][START_REF] Toth | Novel organic solvents for electrochemistry at the liquid/liquid interface[END_REF] consists in overcoming such limitations through the use of (i) micro-ITIES coupled with (ii) an ionic liquid (IL) as the supporting electrolyte. [START_REF] Ohde | Some factors in the voltammetric measurement of ion transfer at the micro aqueous | organic solution interface[END_REF] Furthermore, by using chloroform, appreciable concentrations of 1,2dimyristoyl-sn-glycero-3-phosphocholine (DMPC) -employed herein as a model phospholipidcould be analyzed thus improving the response signal.

Herein, we have studied by cyclic voltammetry (CV) the interaction between a Lewis acid (H + or Li + ) and a phospholipid (DMPC) at a w|CHCl 3 micro-interface. CV demonstrates that DMPC facilitates the transfer of H + and Li + across the interface; furthermore, this process is thermodynamically favourable. In order to highlight a potential application, the facilitated, catalytic transfer of H + has been demonstrated towards solar fuel generation (i.e. for O 2 reduction or H 2 evolution) through shake-flask experiments, where decamethylferrocene ( * 2

Cp Fe(II) ) was employed as a sacrificial electron donor.

EXPERIMENTAL

Reagents were obtained commercially and used as received, including lithium sulfate (Li 2 SO 4 , VWR, Fontenay-sous-Bois, FR), and sulfuric acid (Alfa Aesar, Ward Hill, US), while octyltriethoxysilane, tetramethylammonium bromide (TMABr), decamethylferrocene (

* 2
Cp Fe(II)

), tetradecylammonium tetrakis(para-chlorophenyl)borate (TDATPBCl), chloroform (for HPLC, ≥99.9%) and sodium tetraphenylborate (NaTPB) were bought from Sigma-Aldrich/Fluka (L'Isle d'Abeau Chesnes, FR). 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) was sourced from Echelon Bioscience (Le Perray en Yvelines, France). All aqueous solutions were prepared using Milli-Q ultrapure water (≥ 18.2 MΩ•cm).

The tetraoctylphosphonium tetrakis(pentafluorophenyl)borate ionic liquid (P 8888 TB) was prepared through a metathesis reaction between tetraoctylphosphonium bromide (Sigma-Aldrich) and tetrakis(pentafluorophenyl)borate lithium etherate (Boulder Scientific, Longmont, CO) in dichloromethane as described elsewhere. [START_REF] Stockmann | Tetraoctylphosphonium Tetrakis(pentafluorophenyl)borate Room Temperature Ionic Liquid toward Enhanced Physicochemical Properties for Electrochemistry[END_REF] Tetramethylammonium tetraphenylborate (TMATPB) was prepared similarly by combination of TMABr and NaTPB in a 1:1 molar ratio in water (99% yield), subsequently rinsed with water, dried, and structurally confirmed through 1 H-NMR (CD 3 CN, 400 MHz) δ (ppm): 3.04 (s, 12 H), 6.84 (t, 4 H), 6.99 (t, 8 H), 7.27 (m, 8 H) which agrees well with that shown previously. [START_REF] Li | Alkali metal and ammonium cationarene interactions with tetraphenylborate anion Supramol[END_REF] UV/Visible spectra were acquired using a Perkin Elmer Lambda 1050 UV/Vis/NIR Spectrometer equipped with 3D WB Detection Module (Waltham, MA).

Electrochemical measurements were recorded using a potentiostat from CH-Instruments (model#720, Austin, Texas) and the electrochemical cells illustrated in Scheme 1. The aqueous phase was back-filled into a pulled borosilicate glass capillary (the fabrication of which has been described in detail elsewhere [START_REF] Stockmann | Electrochemical assessment of water|ionic liquid biphasic systems towards cesium extraction from nuclear waste Anal[END_REF][START_REF] Stockmann | Electrochemical behavior of ferrocenes in tributylmethylphosphonium methyl sulfate mixtures with water and 1,2-dichloroethane Can[END_REF] ). The capillary was in-turn fixed inside a modified pipette holder (HEKA Instruments, Nova Scotia), [START_REF] Stockmann | Interfacial Complexation Reactions of Sr2+ with Octyl(phenyl)-N,N-diisobutylcarbamoylmethylphosphine Oxide for Understanding Its Extraction in Reprocessing Spent Nuclear Fuels[END_REF] and filled from the back with the aqueous phase so that the w|CHCl 3 interface was positioned at the tip of the capillary using a syringe. The tip was then immersed in the CHCl 3 phase. The w|CHCl 3 interface was continuously monitored using a CCD camera attached to a 12× zoom lens assembly (Navitar, Rochester, NY). The diameter of the immiscible interface between the two electrolytic solutions (ITIES) was determined to be 25 µm via an optical microscope. The potential scale was referenced relative to the ion transfer potential of tetramethylammonium (TMA + ), 0.208 V, which was added at a concentration of 0.5 mM of TMACl to the aqueous phase. The formal ion transfer potential for TMA + was estimated by using the point-of-zero-charge (PZC) from a blank CV, without TMACl added, and using 5 mM Li 2 SO 4 as the aqueous phase supporting electrolyte.

The PZC, in turn, was taken to be the midpoint between the two polarizable potential limits at a micro-ITIES.

RESULTS AND DISCUSSION

Figure 1A illustrates the CVs obtained through Cell 1 (Scheme 1 and Figure 1B), at a scan rate of 0.020 V s -1 and with increasing [DMPC] (y), from 0 to 1 mM, while z was maintained at 5 mM H 2 SO 4 . In the blank curve (dashed black trace) the polarizable potential window (PPW) is limited at positive and negative potentials by the transfer of H + and SO 4 2-(or HSO 4 -), respectively, from w to o. After addition of 0.25 mM of DMPC to the CHCl 3 phase, two sigmoidal, or s-shaped, waves appear in the forward and reverse scans with half-wave potentials

( 1/2 w o  
) between 0.000-0.050 V for the first and 0.290-0.350 V for the second wave. Meanwhile, the baseline corrected steady-state current (i ss ) for each wave increases linearly with [DMPC] for both waves. Since i ss is positive, it can be concluded that a cation is transferring from w to o.

However, because the pipette geometry is asymmetric, its CV response for simple ion transfer is also asymmetric (Figure S1 in SI); therefore, this is an organic phase diffusion limited process and it can be concluded that DMPC is facilitating proton transfer from w to o. [START_REF] Samec | Charge-transfer processes at the interface between hydrophobic ionic liquid and water Pure[END_REF][START_REF] Rodgers | Cyclic voltammetry at micropipet electrodes for the study of ion-transfer kinetics at liquid/liquid interfaces Anal[END_REF] Furthermore, the appearance of two curve features suggests that there are multiple proton to DMPC coordination ratios and at least two protons are exchanged. All other parameters are the same as those described in Figure 1. See also Figure S2 in the SI.

These results agree with recent molecular dynamics simulations of both the w|CHCl 3 39,40 and w|DMPC 2 interfaces. The former was shown to be highly polarized, with a dipole pointing from the water side towards the CHCl 3 one. This apparent positive charge on the water side explains the reported preferred physisorption of HO -at w|o interfaces. [START_REF] Zangi | Physisorption of Hydroxide Ions from Aqueous Solution to a Hydrophobic Surface[END_REF] It also suggests H + or Li + are expelled from the interface, in agreement with the large overpotential required for their direct transfer to CHCl 3 . Moreover, simulations at the w|DMPC interface 2 evidenced a high binding affinity for H + and DMPC; particularly, two binding sites (the lipid's phosphate and carbonyl)

and two energy minima are described. These overall simulated pictures fit with the role of DMPC facilitating H + (equivalently Li + ) transfer at the w|CHCl 3 interface.

They also favor a mechanism of facilitated ion transfer through interfacial complexation (TIC)

(see Figure S3 in SI for description of possible mechanisms), summarized by:

(1)

Here, m and n are the stoichiometric coefficients of protons and DMPC, respectively.

The thermodynamics of facilitated proton transfer was further investigated by changing the acid concentration in Cell 2 while [DMPC] was maintained (y = 0.75 mM). In the resultant CVs (Figure S4), as [H 2 SO 4 ] was increased from 25 to 150 mM for curves a-e, the half-wave potential of waves 1 and 2 shifts from -0.120 to -0.260 V and 0.200 to 0.120 V, respectively. As the concentration of protons increases the applied potential (i.e. the amount of energy or driving force) required to elicit charge transfer decreases, in good agreement with previous reports. [START_REF] Stockmann | Electrochemical assessment of water|ionic liquid biphasic systems towards cesium extraction from nuclear waste Anal[END_REF][START_REF] Reymond | Facilitated ion transfer reactions across oil|water interfaces. Part II. Use of the convoluted current for the calculation of the association constants and for an amperometric determination of the stoichiometry of MLjz+ complexes[END_REF][START_REF] Nestor | Facilitated Li+ ion transfer across the water/1,2-dichloroethane interface by the solvation effect[END_REF] For an acid in excess compared to DMPC, the half-wave potential of the complex ( is the formal proton transfer potential at the w|CHCl 3 interface (estimated to be 0.580 V based on the formal proton transfer at a w|DCE interface [START_REF] Olaya | Voltammetric determination of extreme standard Gibbs ion transfer energy[END_REF] ):

(2) R, T, z, and F have their usual thermodynamic significance. Eq. 2 is established assuming that the most abundant DMPC species near the w|o interface is the fully protonated form as depicted in (1). It provides access to the overall constant, β, of complexation, along with the ligand stoichiometry (n, m). If one assumes a value of n = 1, then whatever the value of m, Eq. 2 reduces to a linear relationship with one variable on the left-hand side, a slope of 1, and a yintercept equal to lnβ:

  '* 1/2,H-DMPC HH zF 1 ln ln RT w w o oo c m           (3)
The half-wave potentials measured using Cell 2 (CVs in Figure S4 S1 (SI). The slope for both waves is ~1.

Therefore, the H-DMPC + complex is likely operating at a 1:1 ratio with H + coordinating in discreet events to two different sites on the DMPC molecule with varying coordination strengths.

These sites likely include the phosphine oxide and carbonyl moieties with the former being the more highly coordinating, as previously demonstrated. [START_REF] Stockmann | Interfacial Complexation Reactions of Sr2+ with Octyl(phenyl)-N,N-diisobutylcarbamoylmethylphosphine Oxide for Understanding Its Extraction in Reprocessing Spent Nuclear Fuels[END_REF][START_REF] Ogura | Voltammetric study on the transfer of alkali and alkaline earth metal ions at the aqueous/organic interface facilitated by phosphine oxides Bull[END_REF] In another experiment, P 8888 TB was replaced with tetradecylammonium tetrakis(para- indicates that H + in the water phase is no longer in excess and is substantially consumed at the interface. The IL incorporated TB -(tetrakis(pentafluorophenyl)borate) is known to show little interaction or ion pairing, [START_REF] Lesuer | Improved Electrochemistry in Low-Polarity Media Using Tetrakis(pentafluorophenyl)borate Salts as Supporting Electrolytes Angew[END_REF] as well as being highly stable in acidic media; [START_REF] Rosatzin | Lipophilic and immobilized anionic additives in solvent polymeric membranes of cation-selective chemical sensors Anal[END_REF] this is not the case for TPBCl -, which decomposes readily in an acidic solution(Figure S6 in SI). Furthermore, the formation of HTPBCl was observed electrochemically and with the naked eye by H + transfer through a phospholipid coated droplet. [START_REF] Mareček | Mechanism of Lecithin Adsorption at a Liquid|Liquid Interface[END_REF] Therefore, it is likely that TPBCl -interferes with DMPC facilitated proton transfer, artificially altering the In previous studies at large scale (cm 2 ) w|DCE interfaces, [START_REF] Navrátil | Electrochemical Measurements on Supported Phospholipid Bilayers: Preparation, Properties and Ion Transport Using Incorporated Ionophores[END_REF][START_REF] Mareček | Mechanism of Lecithin Adsorption at a Liquid|Liquid Interface[END_REF][START_REF] Holub | Proton transfer across a liquid/liquid interface facilitated by phospholipid interfacial films[END_REF] the analysis relied on capacitance measurements with no clear ion transfer waves and only catalytic concentrations (µM) of the phospholipid. For example, Mareček et al. investigated the proton-phospholipid interaction using CV at a 20-26 mm 2 w|DCE interface; 47 however, they only employed a modicum (25 µM) of phospholipid and observed an adsorption wave that was resolved at moderate scan rates (0.5-3 V s -1 ). Through a rigorous data treatment analysis, they suggested a five-part mechanism involving the adsorption of the proton and phospholipid species at the interface as well as the eventual coordination of protons to an anionic species in the organic phase. 47 S5, the formal proton transfer potential (0.580V -estimated from the value at a w|DCE interface [START_REF] Olaya | Voltammetric determination of extreme standard Gibbs ion transfer energy[END_REF] ), and the initial proton concentration in the aqueous phase, respectively.

The present system however, exhibits an array of advantages. By using chloroform, appreciable [DMPC] were made possible, thus increasing i ss to observable levels. At the same time, the cell was made conductive by employing a highly dissociative, inert IL as the supporting electrolyte. Most critically, the system employed herein allows for direct thermodynamic assessment of proton-DMPC interaction based on established liquid|liquid mechanisms. [START_REF] Reymond | Facilitated ion transfer reactions across oil|water interfaces. Part II. Use of the convoluted current for the calculation of the association constants and for an amperometric determination of the stoichiometry of MLjz+ complexes[END_REF] One can also estimate the pK a s of DMPC in CHCl 3 for waves 1 and 2 (since, K a = 1/β), with P 8888 TB as the supporting electrolyte (Figure S4 of the SI), as 13.1 and 8.5, respectively.

Furthermore, eq. 3 can be rewritten in terms of pK a : 48,49

     (4)
These results agree well with previous studies of ligand assisted ion transfer reactions at liquid|liquid interfaces. [START_REF] Nestor | Facilitated Li+ ion transfer across the water/1,2-dichloroethane interface by the solvation effect[END_REF][START_REF] Su | Evidence of tetraphenylporphyrin monoacids by ion-transfer voltammetry at polarized liquid vertical bar liquid interfaces[END_REF][START_REF] Matsuda | Facilitation effect of neutral macrocyclic ligands on the ion transfer across the interface between aqueous and organic solutions. I. Theoretical equation of ion-transfer-polarographic current-potential curves and its experimental verification[END_REF][START_REF] Bakker | Electroanalysis with Membrane Electrodes and Liquid-Liquid Interfaces Anal[END_REF][START_REF] Dassie | Facilitated proton transfer or protonated species transfer reactions across oil|water interfaces[END_REF][START_REF] Nishi | Facilitated transfer of alkali-metal cations by dibenzo-18-crown-6 across the electrochemically polarized interface between an aqueous solution and a hydrophobic room-temperature ionic liquid Anal[END_REF][START_REF] Langmaier | Voltammetry of Ion Transfer across a Polarized Room-Temperature Ionic Liquid Membrane Facilitated by Valinomycin: Theoretical Aspects and Application Anal[END_REF][START_REF] Kudo | Evaluation of overall extraction constants for the crown ether-complex ions of alkali and alkaline-earth metal with counter picrate ions from water into nitrobenzene based on their component equilibrium constants[END_REF][START_REF] Meng | Investigation of transfer behavior of protonated pyridine at the liquid/liquid interface using dual micropipettes[END_REF][START_REF] Cui | Anion Transfer at a Micro-Water/1,2-Dichloroethane Interface Facilitated by beta-Octafluoro-meso-octamethylcalix 4 pyrrole[END_REF] In order to explore this further, while taking into account the aqueous acid dissociation of H 2 SO 4 (pK a 's of -6.62 and 1.99), [START_REF] Haynes | CRC Handbook of Chemistry and Physics[END_REF] a simulation was constructed using Comsol Multiphysics software. H 2 SO 4 was chosen so as to improve the size of the potential window, while high [H 2 SO 4 ] (pH = 1.6-0.8) were used so that reaction was continuously limited by the diffusion of

DMPC; i.e. [H + ]>>[DMPC].
Additionally, since H 2 SO 4 was both analyte and supporting electrolyte, lower concentrations would elicit additional effects from increased solution resistivity. The TOC/TIC mechanism was incorporated into the simulation (Figure S3 of the SI), while the two-dimensional axial symmetric micropipette geometry employed, along with the generalized theory of facilitated and simple ion transfer, has been described in detail elsewhere. [START_REF] Stockmann | Tetraoctylphosphonium Tetrakis(pentafluorophenyl)borate Room Temperature Ionic Liquid toward Enhanced Physicochemical Properties for Electrochemistry[END_REF][START_REF] Nishi | Facilitated transfer of alkali-metal cations by dibenzo-18-crown-6 across the electrochemically polarized interface between an aqueous solution and a hydrophobic room-temperature ionic liquid Anal[END_REF] Figure S7A , the pK a 's can similarly be calculated from the y-intercept; these were found to be 13.2 and 8.6 for waves 1 and 2, respectively, and agree well with the experimentally determined values. This simulation also provides a physical insight into the interaction of these two diprotic species, H 2 SO 4 and DMPC, while providing further evidence for a monoprotic H + -DMPC interaction at low aqueous pH. It is difficult to compare the experimentally determined pK a values as there is, to the best of our knowledge, no other experimental evaluation of such values. A recent molecular dynamics simulation has however proposed that in an hydrophobic environment the pK a of the phosphate group of DMPC would shift by several units toward values more alkaline than that of methylphosphate (of pK a = 2.5). [START_REF] Teixeira | Protonation of DMPC in a Bilayer Environment Using a Linear Response Approximation[END_REF] These calculations were performed at the level of a lipid bilayer and do not compare to our system even though it might explain the observed increased basicity of DMPC in the organic CHCl 3 solvent and its facilitated protonation at w|CHCl 3 interface.

The large β for the H-DMPC + complex suggests that proton transfer in this system proceeds with minimal energetic expense and one can envision DMPC use in biphasic systems such as droplet-based microfluidics or for the generation of solar fuels at a liquid|liquid interface. It is illustrated here through O 2 reduction (Figure 4C and equations S1 in SI), but could operate equivalently through H 2 evolution reactions (equation S2 in SI). [START_REF] Smirnov | Gold Metal Liquid-Like Droplets[END_REF][START_REF] Rivier | Decamethylruthenocene Hydride and Hydrogen Formation at Liquid|Liquid Interfaces[END_REF][START_REF] Su | H2O2 generation by decamethylferrocene at a liquid vertical bar liquid interface[END_REF] In either case, protons activate the sacrificial electron donor, e.g.

* 2
Cp Fe(II) , forming a metallocene-hydride that reacts further with dissolved O 2 or H + . Not only would DMPC facilitate proton transfer, but also support the formation of vesicles/micelles that would decrease interfacial surface tension, while enhancing reaction rates for batch reactors. To demonstrate this utility, shake-flask experiments were performed with * 2

Cp Fe(II) and tetramethylammonium tetraphenylborate (TMATPB) was used as a phase transfer catalyst, forming the weakly coordinating HTPB in acidic conditions, which transfers favourably to the organic phase, as described recently. [START_REF] Rivier | Decamethylruthenocene Hydride and Hydrogen Formation at Liquid|Liquid Interfaces[END_REF][START_REF] Ge | Biphasic water splitting by osmocene[END_REF] Figures 3A andB show photos of the shake-flasks at time 0 and after 24 h, respectively; all vials contained an organic phase with 5 mM * 2

Cp Fe(II) , 10 mM DMPC, and 5 mM P 8888 TB, with vial 1 containing an aqueous phase of 50 mM H 2 SO 4 and ~10 mM TMATPB, while vial 2 had no aqueous phase.

One can qualitatively assess the green colour change between the vials such that 1>>2. Furthermore, similar conclusions can be drawn from a w|DCE interfacial system with only a catalytic amount of DMPC (~4 µM). Figure 5 shows a similar system, at a w|DCE interface, this time with only ~4 µM of DMPC added to the DCE phase. Vials B1 and B2 both contained an aqueous phase: either with or without acid, respectively. The vibrant green colour in B1 demonstrates that even with such a small amount of DMPC, a significant enhancement in O 2 reduction can be achieved despite using a weak proton phase transfer catalyst such as TMATPB. This is supported by the regeneration of unbound DMPC (Figure 4C). DMPC is unlikely to react with * 2

Cp Fe(II) as it is neither an acid nor an oxidant.

UV/Vis spectra could not be obtained for vials 1, 2, B1, or B2 as the emulsion interfered with the signal measurement.

CONCLUSIONS

The thermodynamic quantification and mechanistic elucidation of proton-lipid interaction provides a critical insight into the molecular interactions of DMPC towards protons and metal ions using a w|CHCl 3 interface. Analysis was made possible by employing an inert IL as supporting electrolyte in the organic phase. In this way, the study highlights the usefulness of ionic liquids as supporting electrolytes, which permit one to work with unusual solvents with low permittivity (e.g. CHCl 3 ), which can in turn be useful in the dissolution of particular chemical reagents.

Two 1:1, proton:DMPC stoichiometries with distinct complexation constant values equal to 1.3 × 10 13 and 3.3 × 10 8 L mol -1 were estimated, indicating the independent coordination of protons to two sites on the DMPC molecule (e.g. the phosphine oxide and carbonyl moieties).

These results provide evidence that DMPC is a powerful vector for Lewis acid (e.g. H + and Li + ) transfer into organic solutions and they show how it plays crucial roles in biological/biomimetic applications, including chemical communication. This also demonstrates how DMPC can convert the w|CHCl 3 interface from one that repels to one that attracts H + and may further illuminate the proton/membrane concentration/surface diffusion phenomena.

Meanwhile, shake-flask experiments illustrate the feasibility of DMPC supported emulsion systems towards solar fuel energy applications based on the liquid|liquid platform. These data have further implications towards micro-emulsions and synthetic reactor systems.

ASSOCIATED CONTENT

Supporting Information. Experimental Details, additional CV Experiments, Comsol simulation of the facilitated ion transfer, shake-flask Experiments.

Scheme 1 :

 1 Scheme 1: Schematic representations of the electrolytic cells employed where the [DMPC, 1,2-

Figure 1 :

 1 Figure 1: A: Cyclic voltammograms at a w|CHCl 3 micro-interface (25 µm diameter), using

Figure 2 :

 2 Figure 2: Cyclic voltammograms using Cell 1 where H 2 SO 4 has been replaced by 5 mM Li 2 SO 4 ,

  of the SI) while varying [H 2 SO 4 ] were treated using (3) and plotted in Figure 3 (red traces) versus ln[ * H c  ]; the results of the linear regression analysis are given in Table

3 .

 3 )borate (TDATPBCl) as the CHCl 3 phase supporting electrolyte, while [H 2SO 4 ] was varied (Cell 3, Scheme 1); the CVs are plotted in FigureS5(SI). Two DMPC facilitated proton transfer waves were again observed and the values for The predicted variation provided in(2) shows that for excess [H + ] the slope should be 1 whatever the extent of protonation of the ligand. However, a slope larger than 1

Figure 3

 3 Figure 3: Plots of

  Figure S7A in the SI depicts the simulated CVs obtained a low pH (1.6-0.8) and demonstrates

Figure 4 :

 4 Figure 4: Photographs of shake-flask experiments performed at time 0 (A) and after 24 h (B)

Figure 5 : 2 Cp

 52 Figure 5: Photographs of shake-flask experiments performed at time 0 (A) and after 24 h (B)

ACKNOWLEDGMENT

The authors acknowledge support from Labex MICHEM, CNRS, Paris Diderot University, and UPMC.