Jean-François Rolland

Fabien Castel

Anne Haugommard

Michelle Aubrun

Corneliu Wei Yao

Octavian Dumitru

Mihai Datcu

Michal Bylicki

Ba-Huy Tran

Nathalie Aussenac-Gillles

Catherine Comparot

Cassia Trojahn

CANDELA: A CLOUD PLATFORM FOR COPERNICUS EARTH OBSERVATION DATA ANALYTICS

Keywords: Copernicus, cloud computing, big data, platform-as-a-Service, Earth observation, machine learning, semantic data, data analytics

This article presents the achievements of the Candela project. This project aims to develop a platform and new algorithms for the handling, analysis and interpretation of earth observation data. The platform is hosted on the CREODIAS cloud ensuring the proximity of data and its processing. To ensure good performances the platform can scale up or down its computing resources. New algorithms based on machine learning methods for change detection and classification have been developed in the project. The results of these new algorithms are transformed into semantic data used to enrich earth observation products and provide new ways of exploitation. Finally, an end-to-end use of the platform is presented with a use case study of the impact of intense meteorological events on vineyards.

INTRODUCTION

All the collections of data provided by Copernicus satellites over the past recent years open the way for data scientists to develop hundreds of innovative use cases. This is true if they can manipulate this huge amount of complex data. The Copernicus Data and Information Access Systems (DIAS https://sentinel.esa.int/web/sentinel/sentinel-data-access), provided through an ESA program, are trying to solve the data storage and access issue, but data scientists need other tools to transform data into valuable information. Candela, a research project funded by the European Commission through the H2020 program, intends to provide a generic platform to perform data analytics on Copernicus data with an online development environment providing built-in scalability management features, easy data access, edge-computing, and advanced geoprocessing tools. Candela is implementing a hybrid Artificial Intelligence paradigm, integrating Machine learning, Deep Learning and semantic analysis in advanced data processing architecture for Big Data.

RELATED WORKS

The Candela platform technical foundations have been designed from a previous H2020 project, EO4wildlife [START_REF] Castel | EO4Wildlife: A cloud platform to exploit satellite data for animal protection[END_REF], where the concept of data exploitation cloud platform was experimented in the domain of ecology and wildlife protection. The data mining and data fusion tools presented in section 6.3 have been presented in more details in article [START_REF] Datcu | Data Science Workflows for the CANDELA Project[END_REF] and [START_REF] Dumitru | Artificial Intelligence Data Science Methodology for Earth Observation[END_REF]. Atos expertise on the development of cloud platforms for earth observation comes from the development of the Mundi DIAS (https://mundiwebservices.com/).

ONLINE DEVELOPMENT ENVIRONMENT

The development environment proposed to the user on the platform is based on Jupyter notebooks. This easy to use online development environment allows the user to access to the platform from anywhere. The JupyterLab development environment for Candela is configured with a Python3 kernel and a set of standard libraries for data science and georeferenced data manipulation. Dedicated libraries have been developed to ease the search and access to earth observation products hosted by CREODIAS and to facilitate the access to processing services. The Jupyter environment is the user entry point to the Candela platform: it is used to access earth observation products, to launch the processes developed in this project, to prototype new processing services. When a Candela user launches the online development environment, a new instance of the Candela Jupyter environment is launched in a dedicated Kubernetes pod. The user benefits at the same time from an isolated instance and from the common environment configuration with geoscience libraries, easy access to EO data and processing services. The user has also access to a dedicated storage space, for upload or download.

SMART DATA ACCESS

Candela is hosted on CREODIAS, one of the DIAS platforms, and as such can access Copernicus data locally and perform data processing on the same infrastructure. Data is accessed through S3 protocol on the object storage buckets exposed by CREODIAS, ensuring a high level of performance. In the context of exploiting earth observation data, users have to manipulate large set of data. Having the Candela platform hosted on CREODIAS allows an easy access to this data without the need to download or copy it. Users have the possibility to run their own applications through a platform that uses the functionality of EO Findersearching, ordering and processing through API or GUI (the user has access to this API from its notebook). Users can place an order by submitting a list of images that need processing alongside the required processing workflow. Atos France has developed a Python library for searching, filtering and retrieving earth observation products. As the notebook is run on the CREODIAS platform the retrieving part is straightforward: the description of the product contains the path of the product in CREODIAS architecture. The product is directly accessible from the user's notebook.

FROM INFRASTRUCTURE TO PROCESSING-AS-A-SERVICE

Candela provides a geoprocessing environment for data scientists, on top of a cloud infrastructure with built-in scalability. Instead of an Infrastructure as a service, in which application developers must have an expertise on deployment configuration, Candela provides Processing as a Service, in which the application developer can let the platform orchestrator deploy the service in a transparent way. Candela components are shown in Figure 1, and described in the following sections.

Figure 1 : Candela platform component overview

Infrastructure

The

Platform as a service

On top of these nodes, Docker and Kubernetes technologies are used respectively as containerization and orchestration solutions. The Docker technical foundation allows to standardize the deployment of heterogenous components in terms of technologies used, language or origin (off-the-shelf components, developed in research institute or in an industrial context). The architecture solution based on containers also allows to enrich the platform building blocks easily with a simplified and standardized integration process.

The Kubernetes container orchestrator is the chosen solution to make the most benefit of the processing power provided by the cloud. It allows building a cluster of workers and easily pilot the resources to run dynamic processing tasks on the best available nodes, with built-in scalability.

Computation engine

The computation engine deployed on Candela platform is Geoserver. All processing services are packaged into Docker containers and made available as standard OGC WPS services. From Candela development environment, the user can access to the catalogue of available services and get the description and parameters of each service. The user can then request the execution of a service with required input parameters. When the Geoserver receives the WPS request, the Docker container corresponding to the processing service is launched on a dedicated Kubernetes pod, and the computation benefits from both the containerization offered by Docker, the smart EO data access offered by CREODIAS, the built-in scalability offered by the Platform-as-a-service and the user private storage area offered to Candela user for providing private input data or obtaining private computation g results. If the user works on a large area or a time series, a set of computations can be run in parallel. Geoserver also allows to offer standard OGC access points to the products of the processing services (WMS, WFS, WCS).

Scalability management

Candela platform needs to adapt to an increasing number of parallel users, or to increasing resource consumption. The real-time monitoring of available resources is used to automatically scale up or down the platform. When a threshold is reached, because lot of users are using the platform at the same time for example, a corrective action is triggered: a new node needs to be added to the Kubernetes cluster. The OpenStack API is used to spawn a new virtual machine. When the machine is ready, it is connected to the Kubernetes cluster and new Docker containers can be deployed on this node.

In order to monitor the state of the platform in real-time, a set of components based on influxdata have been deployed on the platform. These components retrieve and store metrics for each computing nodes, Kubernetes pod or service. The availability status of critical services is logged.

For each node, basic metrics including CPU and RAM usage, disk space available and uptime are monitored. For pods, CPU and RAM usage are stored as well as execution duration. This monitoring data is also used to inform Candela users of their resource consumption.

GEOPROCESSING TOOLS

Several geoprocessing building blocks have been integrated into Candela platform, including standard libraries like GDAL, geopandas and dedicated building blocks for change detection, semantic search, data mining and data fusion developed in the frame of the project. Specific libraries have also been integrated to ease EO data access: CreoDIAS data access library developed for the project, but also sentinelhub, eolearn.

Change Detection

Thales Alenia Space France has implemented a change detection building block [START_REF] Aubrun | Unsupervised Learning of Robust Representations for Change Detection on Sentinel-2 Earth Observation Images[END_REF], which is based on an unsupervised approach to detect generic changes and which is designed to run on Sentinel-2 data time series. Using the fine temporal (5 days) and spatial (10 meters per pixel) resolution of these Earth Observation optical satellites, a lot of use cases can be carried out in many diverse sectors. First, the analytic tool defines the different time series thanks to the image metadata (acquisition date and geographic scene coordinates). Then, it transforms each Sentinel-2 image of a time series into a more representative feature space thanks to an encoder model based on a neural network and calculates the distance metric between the Sentinel-2 images in this space to generate the change detection maps. Smart feature spaces allow to be more robust to the lighting and atmospheric condition differences during the data acquisitions that do not represent changes of interest. This analytic tool has been developed in Python using TensorFlow/Keras and GDAL libraries and encapsulated in Docker containers in order to be properly integrated on Candela platform (section 5.2). One of the objectives of this analytic tool is to run on a big amount of data. Thus, the change detection building block requires fast data access, good storage capacity and intensive processing resources.

Semantic module

The Candela platform proposes a semantic search module on the top of a semantic knowledge base. This knowledge base has been constructed from an integration process that relies on a modular ontology for integrating EO and contextual data. The semantic search module is a means to promote the use of EO image data together with their contextual data (weather information, land cover, etc.). There are three categories of datasets of interest:

• Sentinel image metadata: these metadata are available together with the Sentinel images.

• Sentinel image related data: the datasets are provided by partners of the project and are extracted from Sentinel images through image processing tools.

• Contextual datasets: the datasets come from open data sources, such as: administrative units, weather measures or land cover.

The task requires first to perform semantic data integration, based on the spatial and temporal dimensions of these datasets. It involves the design of ontologies needed for integrating the datasets and then integrate the sources through ETL process based on the developed ontologies (data extraction, processing and transformation). We have then developed an interface that helps to query the knowledge base and to display the results in a user-friendly way. Each subtask is encapsulated by a Docker as shown in Figure 2.

Figure 2 : System architecture of the semantic search tool.

Data mining and data fusion

The Data Mining module implements interactive and iterative functions for discovering useful information in collections of the Sentinel-1/Sentinel-2 products and generate semantic annotations. The Earth observation (EO) product is processed and the extracted image features and metadata are structured in a Data Base (DB). The Data Mining is operated in 2 modes. The first is EO Image Mining; the users via an interactive GUI operate a machine learning (ML) module which is using the actionable information. The functions are search, browse, query for image patches of interest for the user and their semantic labelling. This is the actual EO image semantics adapted to the user conjecture and application. It is an Active Learning process achieving: 1) learn the targeted image category as accurately and as exhaustively as possible and 2) minimize the number of iterations in the relevance feedback loop. This is particularly important for EO since labeled data are very expensive and little available and is also increasing the trust in the learning process. The second function is EO Data Mining; this is performed via SQL search, queries, browse extracting the data analytical information from the DB. It uses image features, image semantics, and selected EO product metadata. The Data Fusion module provides functions for land cover classification using jointly the complementary information from the Sentinel-1 and Sentinel-2. It enhances the classification accuracy, extends the use of the Sentinel-2 data in case of atmospheric effects or is enlarging the variety of land cover classes which can be recognized.

USE CASE

Once the change detection building block has been integrated on Candela, it was applied on a region of interest near Bordeaux in France to detect the crops affected by the frost that happened on 27 th April 2017. After such meteorological events, winemaking farmers need to evaluate the level of damage that occurred in their vineyards in order to receive subsidies from the state insurances. Additionally, insurance companies must also estimate the damage levels to check the information provided. Currently, field visits are used to do the estimations, which is non-trivial and requires a huge budget and workforce. Using a notebook from the JupyterLab user interface (section 3), it was easy to execute the following steps: o The first one consists in accessing the Sentinel-2 data of interest via the CREODIAS data access functions (section 4). Thus, two optical Sentinel-2 Level-2 (atmospherically corrected) data products of the T30TYQ tile with low cloud cover on the region of interest have been uploaded on the user workspace. One acquired during 19 th April 2017 (before the frost) and the other during 29 th April 2017 (after the frost). o The second step consist in preprocessing the Sentinel-2 data. In our case, all the bands at 10 and 20 meters of resolution have been extracted, resampled according to the blue band and concatenated into a single image for each data product. To do this, Thales Alenia Space France has also developed and encapsulated a preprocessing tool in a Docker container. o The last step consists in running the change detection building block to generate the change detection map, whose pixel values represent the probability that a change has occurred between the acquisition dates. Several neural network models are available on Candela platform. The entire pipeline has taken less than one hour to run with a consumption of 100% of one virtual CPU and 20% in GPU and has provided results very close to the ones of the operator.

CONCLUSION AND PERSPECTIVES

In this article we have presented the Candela platform which provides an easy-to-use development environment for geoscience. This environment is characterized by a smart data access to earth observation products, a scalable computing platform for performance processing and the publication of results as semantic information. The data access allows to search for earth observation products easily and to retrieve them efficiently. The scalable platform ensures high performances when dealing with processing of large amount of data. The creation of semantic data as a result of the processing algorithms enables the dissemination of earth observation data enriched with semantic information. An illustration of the use of the platform has been presented in section 7. This use case shows how the platform can be used for detection of the effect of high intensity meteorological events. The next steps around Candela project are: o to industrialize this prototype on one or more DIAS platforms and propose it as a value-added service; o to develop furthermore the integration of machine learning and semantic on earth observation data.

  CREODIAS infrastructure is build based on opensource software. The main component is OpenStack (computing resources) and CEPH (highly scalable storage solution) with access to 14.5 PB of EO data. Ceph is a distributed object -based storage system capable of delivering storage services in the form of object repositories, block devices and storage volumes. Ceph is fully integrated with Openstack and can provide persistent block storage for VM-s, storage volume services, object buckets and filesystem services. On top of these resource, CloudFerro provides functionalities to meet the specific requirements of EO Search Engine. Overall infrastructure consists of more than 14 000 virtual Cores (virtual CPUs), GPUs available on demand and 15 TB of RAM. Candela platform is deployed on four virtual machines totalizing 20 virtual CPUS and 72GB of memory. A fifth machine is dedicated to resource consuming algorithms, it has 40 virtual CPUs, 128GB of RAM and is equipped with GPU. The GPU is used for machine learning algorithms based on the Tensorflow library.

ACKNOWLEDGEMENT

This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 776193.


Antoine Robert

Pierre Dechambenoit

Dr Elisabeth A Hillard

Dr Harald Bock

Fabien Durola
email: durola@crpp-bordeaux.cnrs.fr

Dr P A Robert

Dechambenoit

Non-Planar Oligoarylene Macrocycles from Biphenyl

Saddle-and propeller-shaped macrocycles are obtained by fourfold Perkin condensations in transient high dilution of 4,4'-bis(phenylglyoxylic acid) with either 4,4'-bis(phenylacetic acid) or p-phenylenediacetic acid, followed by four-fold oxidative photocyclizations. In the saddle-shaped tetraphenanthrylene, the angle between opposite phenanthrene planes is close to the value of 90º of an ideal saddle. In the two helicene fragments of the propeller-shaped double [5]helicene, the geometry of unsubstituted [5]helicene is preserved without major macrocycle-induced distortions.

 Others consist of a planar macrocycle that includes aromatic moieties that are rigidly orthogonal

to the plane of the macrocycle, such as Herges's picotube, 6 Gleiter's [6.8] 3 cyclacene 7 and Itami's nanobelt. 8 Noncentrosymmetric variations of the latter type are conical macrocycles such as Stępień's chrysaoroles and chrysaorenes. 9 Large aromatic macrocycles where the macrocyclic thread itself is non-planar whilst still being of fixed shape are much rarer. They may be saddle-shaped such as octulene 1 (which has been obtained by Stępień and coworkers in octabutoxy-substituted form), 10 or consist of helicenic fragments, such as Thulin and Wennerström's propellicene 2 11 (Scheme 1). Unfortunately, crystallographic structures have not been reported for either of these two archetypal examples. Related intriguing conjugated macrocycles with non-planar threads are the octaphyrins and other expanded porphyrinoids 12 and the first carbocyclic conjugated Möbius bands. 13 Scheme 1. Non-planar polycyclic aromatic macrocycles: saddle-shaped octulene 1 10 and bis-helicenic propellicene 2. 11 We have recently found that the Perkin reaction of an arylenediacetic acid with an arylenediglyoxylic acid may lead selectively to the tetra-arylenevinylene macrocycle, and thus we obtained the tetrapyrenylene-tetramaleate 3 in a rather satisfying yield of 25%. 14 We also observed that the oxidative photocyclization of p-phenylene-

1 2
bis(phenylmaleate) 4 efficiently leads to [5]helicene-tetracarboxylate 5 in 77% yield 15 (Scheme 2). We thus wondered whether the Perkin condensation of 4,4'-bis(phenylglyoxylic acid) 6 with either 4,4'-bis(phenylacetic acid) 7 or p-phenylenediacetic acid 8 would give the corresponding 2+2 macrocycles 9 and 10 with similar efficiency as in the formation of 3, and whether the resulting macrocycles could be photocyclized to the corresponding octaesters: saddle 11 and propellicene 12 (Scheme 3). The carboxylic substituents not only should ease the intramolecular photocyclization of the macrocyclic Perkin reaction products by sterically shielding the molecule against intermolecular side reactions such as cyclobutane formation, [START_REF] Mallory | 17 Biphenyl can be 4,4[END_REF] but also could improve by their polarity the crystallization behavior of the photocyclized target macrocycles, in view of obtaining the molecular geometries from X-ray diffraction.

Scheme 2. Previous syntheses of tetrameric pyrenophane-octaester 3 14 and [5]helicene-tetraester 5. 15 To obtain the two key biphenyl building blocks 6 and 7, we started from 4,4'-dibromobiphenyl 13, 17 in an analogous approach to the synthesis of the precursors of tetrapyrenophane 3 from 1,6-dibromopyrene: 14 13 was dilithiated with n-butyllithium followed by addition of diethyl oxalate to give diglyoxylic ester 14, which was transformed into 6 and 7 by basic hydrolysis and reduction with hypophosphorous acid and iodide. As both 6 and 7 proved to be soluble in THF at room temperature, it was possible to add an equimolar solution of these substrates from a motor-driven syringe to a refluxing solution of the Perkin reactants acetic anhydride and triethylamine over a period of 20h. Given that Perkin reactions under similar conditions are usually complete after one night, 18 this slow addition ensured near-ideal high dilution conditions that favor macrocycle formation over polymerization, and favor smaller macrocycles over larger ones. After in situ esterification, we thus could obtain the tetrameric (2+2) macrocycle 9 in 52% yield, which could be separated from side products of higher molecular mass by careful chromatography and precipitation. This yield is a significant improvement on the 25% cyclotetramerization yield of pyrenophane 3, whose less soluble diacetic precursor did not allow the same high dilution procedure. Polarized light microscopy revealed that the obtained powder of 9 does not show microcrystals of straight shapes nor significant birefringence, but rather appears to be glassy, showing softening to an isotropic fluid around 190ºC. It is thus not surprising that we were unable to grow single crystals of 9 for Xray structure elucidation.

Irradiation of a 0.5 mM solution of 9 in the presence of iodine and oxygen for five days with pyrex-filtered irradiation from a medium pressure mercury lamp yielded tetraphenantrylene 11 in 47% yield, of which we obtained crystals suitable for X-ray structure determination by slow diffusion of methanol into a chloroform solution. The simplest aromatic saddle-shaped molecule is o-tetraphenylene 15, and a similarly simple tetrameric macrocycle with four ortho-bridging angular moieties is [2 4 ]paracyclophanetetraene 16 (Figure 1). Of both, crystal structures have been reported. Whereas 16 is essentially planar, 19 with C-C=C bond angles at the olefinic bridges of about 132º, the angle between opposite benzene planes in 15 is 87º, 20 slightly sharper than the ideal value of 90º that would result from 120º bond angles and no o-phenylene torsion. Compared to these two antagonistic prototype molecules, the saddle shape of tetraphenanthrylene 11 is only slightly flattened compared to 15, with angles between opposite phenanthrene planes of around 95º and inner bond angles at the interphenanthrene bonds of around 122º, but exhibits pronounced torsion angles between interphenanthrene bonds of around 18º, which result from the helicenic repulsion between hydrogen atoms in the phenanthrene bay regions. These torsion angles lead to a slightly oval inner cavity of the macrocycle (Figure 2). To obtain ester-substituted propellicene 12 via paracyclophane 10, we reacted 6 with 8 following the same high dilution protocol. To our surprise, the isolated yield of 10 was with 21% significantly lower than the yield of 9, which may indicate that the smaller and less flexible p-phenylene units make macrocycle 10 sterically less favored than the larger tetraphenanthrylene precursor 9 based only on biphenyl blocks. On the other hand, the greater compactness 10 eased its crystallization sufficiently to allow us to collect satisfyingly diffracting crystals by methanol-into-chloroform diffusion. In the crystal, the molecules of 10 adopt a very dissymmetric conformation (Figure 3) in which neither the two opposite biphenyl units are parallel to each other, nor the two p-phenylene units, with the latter adopting near-orthogonally rotated orientations with respect to each other (Figure 3, right).

Thus 10 adopts a twisted conformation that is favorable for the formation of propellicene 12 (compare Figures 3 and4, that show 10 and 12 in similar views). Three orthogonal views of one molecule of propellicene 12 in the monoclinic crystal. The two substituted [5]helicene fragments are respectively colored light and dark gray, with ester substituents thin and aromatic moieties thick. Hydrogen atoms and residual solvent molecules omitted for clarity, and only the predominant configuration is shown in the case of disordered ester substituents. Note that the molecule is chiral, but the crystal is not, with six molecules of each enantiomer per unit cell.

Irradiation of a dilute solution of 10 with iodine and oxygen for two days, followed by eight-fold in situ esterification, gave propellicene 12 in similar yield (54%) to the analogous fourfold photocyclization of 9 to 11, and we obtained crystals suitable for X-ray diffraction by the same method as with 11 and 10, albeit the crystal structure of 12 (six right-and six left-handed molecules per unit cell, disordered ester substituents) testifies of the lower propensity of chiral racemic 12 to pack periodically than nonchiral 11 or 10. The [5]helicene fragments in the crystal of 12 are nearly undistorted with respect to unsubstituted [5]helicene 21 (e.g. the sums of the three inner-rim C-C-C-C torsion angles, as well as the distances between the inner carbon atoms of the terminal rings, differ by less than 3% between 12 and unsubstituted [5]helicene). This notable correspondence, together with the relatively small configurational changes necessary to convert flexible precursor 10 into 12 (e.g. as in 10, the central hexagons of the two helical units in 12 adopt near-orthogonally rotated orientations, see Figure 4, right) may explain why the more condensed propellicene 12 is formed by four-fold photocyclization in similarly satisfactory yield as the saddle 10.

The absorption spectrum of 12, with maxima at 293 and 317 nm, is similar to the corresponding monomer, the Both macrocycles show irreversible first oxidation and first reduction peaks by differential pulse voltammetry (DPV) at very similar values, corresponding to HOMO energies of 5.86 eV (11 and 12) and LUMO energies of 2.79 eV (11) and 2.86 eV (12) that yield electrochemical band gaps of 3.07 eV (11) and 3.00 eV (12) (Table 1). In summary, the four-fold Perkin condensation of soluble arylene-diglyoxylic acid 6 with arylene-diacetic acids 7 or 8 leads to flexible paracyclophanetetraenes 9 and 10 that undergo four-fold oxidative photocyclization in ca. 50% yield to partially condensed, fully aromatic macrocycles, saddle-shaped tetraphenanthrylene-octacarboxylate 11 and propellicene-octacarboxylate 12, whose crystallographic structures testify of the characteristically non-planar geometry of their macrocyclic threads. Non-substituted [5]helicenes quickly racemize at room temperature (with a half-life of ca. 14h). [START_REF] Newman | [END_REF] In the case of propellicene 12, the [5]helicene moieties are not only substituted on hindering positions, but are also linked together in a way that forces them to invert simultaneously their helicity in case of racemization. We currently aim at studying this phenomenon both experimentally and theoretically.

Figure 1 .

 1 Figure 1. Reference materials for comparison with tetraphenanthrylene 11: Saddle-shaped tetra-o-phenylene 15 and essentially planar paracyclophanetetraene 16. Bottom: lateral views of one molecule in the crystal illustrating the nonplanarity/planarity of the macrocycles; 19, 20 hydrogen atoms and residual solvent molecules omitted for clarity; cisoid angular units alternatingly colored light and dark gray.

Figure 2 .

 2 Figure 2. Two orthogonal views of one molecule of tetraphenanthrylene 11 in the triclinic crystal. The four substituted phenanthrene fragments are alternatingly colored light and dark gray, with ester substituents thin and aromatic moieties thick. Hydrogen atoms and residual solvent molecules omitted for clarity.

Figure 3 .

 3 Figure 3. Three orthogonal views of one molecule of flexible propellicene precursor 10 in the triclinic crystal. The two photocyclizable p-phenylenebis(phenylmaleate) fragments are respectively colored light and dark gray, with ester groups thin and the conjugated macrocycle thick. Hydrogen atoms and residual solvent molecules omitted for clarity.

Figure 4 .

 4 Figure 4. Three orthogonal views of one molecule of propellicene 12 in the monoclinic crystal. The two substituted[5]helicene fragments are respectively colored light and dark gray, with ester substituents thin and aromatic moieties thick. Hydrogen atoms and residual solvent molecules omitted for clarity, and only the predominant configuration is shown in the case of disordered ester substituents. Note that the molecule is chiral, but the crystal is not, with six molecules of each enantiomer per unit cell.

[ 5 ]

 5 helicene-tetraester 5, with, as should be expected, roughly doubled intensity, and with only a moderate redshift of the longest-wavelength absorption maximum (5: 310 nm; figure5). The fluorescence spectra of 12 and 5 upon excitation at 280 nm are similar, and the fluorescence intensities peak at the same wavelength (450 nm) and are of similar ratio as the absorption intensities at the excitation wavelength. Optically, 12 behaves thus essentially as a dimer of 5.

Figure 5 .

 5 Figure 5. Absorption (left) and fluorescence spectra (right) of 5, 11 and 12 in 4μM solution in chloroform. Fluorescence spectra are recorded upon excitation at 280 nm (where 11 and 12 absorb with the same intensity) and are in arbitrary units.

  in CHCl3; (b) excitation at 280 nm; (c) vs. N-octyl diphenylmaleimide as standard 22 ; (d) from DPV vs. Fc+/Fc as standard, 1.5mM in DCM.

Table 1 :

 1 Physical properties of macrocycles 11 and 12

	Macrocycle	11	12
	Absorption maxima (nm)	277 [67500],	293 [77500],
	[Extinction coefficients (M -1 cm -1 )] a	317 [52400]	317 [78400]
	Fluorescence maximum (nm) a,b	412	450
	Fluorescence quantum yield a,b,c	0.38	0.09
	HOMO and LUMO energies (eV) d	5.86, 2.79	5.86, 2.86
	Band gap (eV)	3.

Acknowledgements

This research was financed partially by an Agence Nationale de la Recherche (project 13-JS07-0009-01) grant.

Conflicts of interest

There are no conflicts to declare.

Notes and references


Narendra Jussien
email: fnarendra.jussien@emn.fr

Olivier Lhomme
email: olivier.lhommeg@emn.fr

The Path-repair algorithm

In this paper, we i n troduce a new solving algorithm for Constraint Satisfaction Problems: the path-repair algorithm. The two m a i n p o i n ts of that algorithm are: it makes use of a repair algorithm (local search) as a basis and it works on a partial instantiation in order to be able to use ltering techniques. Di erent v ersions are presented and rst experiments with both systematic and non systematic versions show promising results.

Introduction

Many industrial and engineering problems can be modeled as constraint satisfaction problems (csps). A csp is de ned as a set of variables each w i t h a n associated domain of possible values and a set of constraints over the variables.

Most of constraint solving algorithms are built upon backtracking mechanisms. Those algorithms usually explore the search space systematically, and thus guarantee to nd a solution if one exists. Backtracking-based search algorithms are usually improved by some ltering techniques which aim at pruning the search space in order to decrease the overall duration of the search.

Another series of constraint solving algorithms are local search algorithms. They perform a probabilistic exploration of the search space and therefore cannot guarantee to nd a solution. The interest of local algorithms (eg. Tabu search 12], GSAT 25]) is that, following local gradients in the search s p a c e , they may be far more e cient ( wrt reponse time) than systematic ones to nd a solution.

Several works have studied cooperation between local and systematic search 6,8,20,22,23,30]. Those hybrid approaches have led to good results on large scale problems. Three categories of hybrid approaches can be found in the literature:

(1) performing a local search before or after a systematic search (2) performing a systematic search i m p r o ved with a local search a t s o m e points of the search ( t ypically for optimisation problems, to try to improve the quality of a solution) (3) performing an overall local search, and using systematic search1 either to select a candidate neighbor or to prune the search space.

The hybrid approach presented in this paper falls in the third category. I t w i l l use ltering methods to both prune the search space and help in choosing the neighbor in a local search. This leads to a new search technique over csps which is called path-repair. Di erents variations of this search t e c hnique are discussed, some of them are shown to be complete. Very promising rst results are presented.

The paper is organized as follow s . S e c t i o n 2 g i v es some notations. Section 3 presents the path-repair algorithm. Section 4 discusses related works andnally section 5 summarizes the rst results obtained in the eld of open shop scheduling problems.

Preliminaries

A csp is a couple < V C > where V is a set of variables and C = fc 1 : : : c m g a set of constraints. Domains of the variables are handled as unary constraints.

For a given constraints set S = fc 1 : : : c k g, Ŝ will be the logical conjunction of the constraints in S: Ŝ = ( c 1 ^: : : ^ck ). By convention: ? = true.

Classical csp solving simultaneously involves a ltering algorithm (to a priori prune the search tree) and an enumeration mechanism (to overcome ltering algorithm incompleteness). For example, for binary csp over nite domains, arc-consistency can be used as ltering technique. After a ltering step, three situations may arise:

(1) the domain of a variable becomes empty: there is no feasible solution (2) all the domains are reduced to a single value: those values assigned to their respective v ariables provide a feasible solution for the considered problem (3) there exists at least one domain which c o n tains at least 2 values: search

has not yet been successful. In a classical approach, it would be time for enumeration through a backtrack-based mechanism.

In a more general way, f o r a n y ltering algorithm 2 applied on the set C of constraints of a given csp (let C 0 = ( C)), there exists a function obviousInference which, when applied on C 0 , a n s w ers: noSolution i it is immediate to infer that no solution can be nd for C (as in situation 1 above). allSolution i the current constraints system 3 can immediately provide a solution that veri es all the constraints in C 0 (as in situation 2 above). ounder in all other situations (as in situation 3 above).

The function obviousInference has typically a low computational cost. Its aim is to make explicit the use of some properties that depends on the used ltering algorithm. The example of arc-consistency ltering with an empty domain or with only singleton domains has already been given, but a function obviousInference can be made explicit in many other ltering or pruning algorithms. For example, in integer linear programming, the aim is to nd an optimal integer solution. This can be done by using the simplex algorithm over the reals. If there is no real solution or if the real optimum has only integer values, then a obviousInference function would respectively return noSolution or allSolution.

Enumerating discrete binary csps is assigning a value 4 a to a variable v k i.e. adding a new constraint v k = a in the system. For other kinds of problems, enumerating may be di erent: for example, for numeric csp, e n umerating is adding a splitting constraint ( eg. v `< a ). When dealing with scheduling problems, enumerating is often adding a precedence constraint b e t ween two tasks of the problem.

In the next section, the path-repair algorithm is presented through an abstraction of the solved problems: they may be discrete binary csp, n umeric csp as well as scheduling problems. This will be possible thanks to:

(1) the parameter which represents the ltering algorithm used (2) the function obviousInference, t i g h tly related to the used ltering algorithm, that is able to examine a set of constraint in order to continue or not the computation (3) the concept of enumerating constraint. An hypothesis holds over the way such constraints are generated: there exists an integer5 N e such t h a t 2 A ltering algorithm applied on a set C of constraints returns a new set C 0 = (C) s u c h that C C 0 (redundant constraints may h a ve been added). [START_REF] Bliek | Generalizing partial order and dynamic backtracking[END_REF] We consider that domain reductions are added as redundant constraints in the constraint system. [START_REF] B R U C Ker | A branch and bound algorithm for the open-shop problem[END_REF] a is an element of the domain of variable v k .

whatever the set E of at least N e di erent e n umerating constraints, the call obviousInference( (C E)) will not answer ounder. This condition is necessary to ensure termination (in the case of the systematic version of the algorithm), and is ful lled by a n y reasonnable search strategy.

3 The path-repair algorithm

The idea of the path-repair algorithm is very simple. First observe that: current local search algorithms mainly work upon a total instantiation of the variables backtracking-based search algorithms work upon a partial instantiation of the variables.

The ability of backtracking-based search algorithms to be combined with ltering techniques only comes from the fact that they work upon a partial instantiation of the variables. Thus, a l o cal search algorithm working upon a partial instantiation of the variables would have the same ability.

Indeed, the path-repair algorithm is such an algorithm. The considered partial instantiation is de ned by a set of enumerating constraints (as de ned above) upon the variables of the problem. Such a constraint set de nes a path in the search tree.

Principles of path-repair

The principle of the path-repair algorithm as shown in gure 1 is the following: let P be a path in the search tree. At e a c h node of that path, an enumerating constraint has been added. Let C P be the set of added enumerating constraints while moving along P.

The path-repair algorithm starts with an initial path (it may range from the empty path, to a path that de nes a complete assignment). The main loop rst checks the conditions of failure [START_REF] Codognet | A metalevel compiler of CLP(FD) and its combination with intelligent backtracking[END_REF] . A ltering algorithm is then applied on C C P giving a new set of constraints C 0 = ( C C P ). The function obviousInference is then called over C 0 . Three cases may occur: desired precision on the result. obviousInference(C 0 ) = flounder: t h e path-repair algorithm tries to extend the current p a t h P by adding an enumerating constraint. That behavior is similar to that of backtracking-based search algorithms. For that purpose, a function extend(P ,;) is assumed to exists that chooses an enumerating constraint to be added and adds it to P. The meaning of parameter ; will be made clear later. obviousInference(C 0 ) = noSolution: C C P is inconsistent. We will say that P is a dead-end, o r P is inconsistent: P cannot be extended. The pathrepair algorithm will thus try to repair the current path by c hoosing a new path through the function neighbor(P ,k,;). P arameters k a n d ; w i l l b e explained later.

The path-repair algorithm appears here as a search method that handles partial instantiations and uses ltering techniques to prune the search space. The key components of this algorithm are the neighboring computation functions (neighbor) and the extension functions (extend).

Properties of the neighborhood o f p ath-repair

In a local search algorithm such a s gsat (on boolean csps), an inconsistent instantiation is replaced by a new one built from the rst one by negating the value of one of its variables. That variable is choosen by a heuristic (for example: the one whose negation will allow the greatest number of clauses to become satis ed). More generally, a local search algorithm uses complete instantiations (called states) and replaces an inconsistent state with another state chosen among its neighbors.

The path-repair algorithm works in the same way except that it uses partial instantiations (paths): as soon as a path becomes inconsistent , o n e o f i t s neighbors needs to be chosen. A path (partial instantiation) synthetizes all the included complete instantiations. Switching paths is like setting aside many irrelevant complete instantiations in one movement.

Like a n y local search algorithm, path-repair may use a heuristic way to select an interesting neighbor. The algorithm can even choose a neighbor in order to implement a systematic search algorithm. Completeness comes from the fact that a path summarizes numerous complete instantiations.

The following sections discuss neighboring path, heuristic choices and speci c techniques leading to a systematic algorithm. We previously introduced a parameter ; in the neighboring computation functions (neighbor) and extension functions (extend). ; can be used to store a context that varies according to the chosen version of the algorithm. In the primitive v ersion that is being presented in this paper, that context is not used.

Neighboring path

It seems to be a good idea to select a neighboring path P 0 which d o e s n o t h a ve the drawbacks of the current path P (recall that in path-repair, neighbors of path P are computed i P is inconsistent). For example, it would be interesting to get to a consistent n e i g h bor P 0 i.e. such t h a t obviousInference( (C C 0 P 0 )) = allSolution. O b viously, that is not a ordable to compute in the general case.

Therefore, we m a y prefer to get at least to a partially consistent neighbor P 0 i.e. such t h a t obviousInference( (C C 0 P 0 ))6 = noSolution. Unfortunately, the only way to get there (without using computing resources) is to get back to an already explored node but, doing so, we w ould achieve a kind of backtracking mechanism, what is not wanted in the path-repair algorithm.

Nevertheless, what can be done is to avoid the neighbors that can already be known as inconsistent. Such an information can be extracted from an inconsistent path P. Indeed, inconsistency means that Ĉ ^Ĉ P =) false. I t i s possible to compute a subset of C P that is alone inconsistent with C. S u c h a subset will be called a nogood 7].

De nition 1 (Nogood) A n o good k for a set of constraints C and a path P, is a set of constraints such that: k C P and Ĉ ^k =) false.

As long as constraints in a computed nogood k remain altogether in a given path P 0 , that path will remain inconsistent. Therefore, in order to get a path with some hopes to be consistent, we need to remove from the current p a t h P at least one of the constraints in k.

Note that if current path P is inconsistent, C P is a valid nogood. Obviously, a strict subset will be much more interesting and will give a more precise neighborhood. A minimal (for the inclusion) nogood would be the best, but it is very expensive to compute one 28]. Therefore, non minimal nogoods will be computed in practice.

As for now, our neighborhood remains very general. In the following, more interesting neighborhoods are described. Our point here is to show that the concept of nogood is crucial for path-repair: nogoods allow relevant neighborhoods to be considered, nogoods can be used to derive e cient neighbor selecting heuristics for a non-systematic path-repair algorithm, nogoods can be used to derive a complete path-repair algorithm.

Nogoods are provided by the ltering algorithm as soon as it can prove t h a t no solution exists in the subsequent complete paths derived from the current partial path. In ltering based constraint solving algorithms, a contradiction is raised as soon as the domain of a variable v becomes empty. Suppose that, for each v alue (or set of values) a i removed from the domain of v, a set of enumerating constraints k i C P is given. k i is called a removal explanation for a i and is such that: Ĉ ^k i =) v 6 = a i . If so, k = S i k i is a nogood since no value for v is allowed by the union of k i . Therefore, in order to compute nogoods, it is su cient to be able to compute an explanation for each v alue (or set of values) removal for the domain of the failing variable.

Value removals are direct consequences of the ltering algorithms. Therefore, value removal explanations can be easily computed by using a trace mechanism within the ltering algorithm and memorizing the reason why a removal is done 16].

For example, let us consider two v ariables v 1 and v 2 whose domains are both f1 2 3g. Let c 1 be the constraint: v 1 > 3 and let c 2 be the constraint: v 2 > v 1 . Let us assume the used ltering algorithm is arc-consistency ltering. The constraint c 1 explains the fact that f1 2g should be removed from v 1 . Afterwards, c 2 forces to remove f1 2g from v 2 . An explanation of the removal of f1 2g from v 2 will be: c 1 ^c2 because c 2 makes that removal only because previous removals occured in v 1 due to c 1 .

Path-repair instances

Heuristic choice of neighbors

In a local search algorithm, the neighbor selection is very important. Many heuristics may be used. For path-repair it is the same, di erent heuristics can be used.

As for now, we h a ve de ned a neighb o r o f a p a t h P according to a nogood k a s a p a t h t h a t d o e s n o t c o n tain at least one constraint from k. Indeed, a more precise neighborhood can be computed. Let c be a constraint to be removed from C P . As long as all the constraints in knc remain in the active p a t h , c will never be satis able. Thus, the negation of c can be added in the new path.

A possible neighborhood for an inconsistent set of constraints C P , according to a nogood k C P is made from the sets of constraints C P i di erent from C P by the negation of one constraint i n k. Let us take an example. Let P be the path (c 1 c 2 c 3 :c 4 c 5 ). Let the nogood k be the set fc 2 c 3 :c 4 g. The neighborhood so de ned is the set of the three paths (c 1 :c 2 c 3 :c 4 c 5 ), (c 1 c 2 :c 3 :c 4 c 5 ), and(c 1 c 2 c 3 c 4 c 5 ). Now, there remains to specify which neighbor to choose among the above de ned neighbors. That degree of freedom for the choice of the constraint in k to be negated allows the use heuristic techniques. In an initial version, we w anted to try to adapt the min-con ict heuristic 19] that minimizes t h e number of unveri ed constraints. But, when using a ltering algorithm such a mechanism may not be very e cient: the rst unveri ed constraint stops the algorithm.

In our current implementation, an integer (weight) is associated with each constraint counting the number of times that the constraint appeared in a nogood. The heuristic consists in choosing to negate the constraint with the greatest weight. A similar approach counting the number of times that a constraint has not been veri ed has been successfully used for gsat 24].

Tabu path-repair

The tabu version of path-repair u s e s a t a b u l i s t o f a g i v en size s. The s last computed nogoods are kept in a list ;. A valid neighb o r i s d e n e d a s a p a t h that does not completely contain any of the nogoods in ;. In other words, at least one constraint in each nogood of ; is not (or is negated) in the new neighbor. To compute such a neighbor in a reasonable time, a greedy algorithm can be used. Figure 2 shows an implementation of the neighbor function for tabu path-repair that has been used for solving scheduling problems. It chooses function neighbor(P , k, ;) /* precondition: k C P */ add k to the list of nogoods ; if sizeOf(;) > s then remove the oldest element o f ; L := ordered list (by decreasing weight) of constraints in k repeat remove the rst constraint c from L P 0 := P except that :c replaces c if C P 0 covers all nogoods in ; then return P 0 until L empty return stop (or extend the neighborhood) Fig. 2. The neighbor function for tabu path-repair to negate the constraint with the greatest weight that, when negated, makes the new path cover all the nogoods in ;. If such a constraint does not exist, the neighborhood could be extended (for example, we m a y try to negate 2 constraints). In our implementation for open shop problems (see section 5), this case is handled as a stopping criterion.

Note that, in the same way, the function extend(P ,;) should use ; in order to correctly extend the partially consistent current path.

A systematic instance

Backtracking-based approaches are interesting because they provide systematic search algorithms. Filtering techniques are then used for e ciency reasons. Using ltering techniques is even more interesting within local search algorithms: it can make them more e cient but also complete. Let's see how path-repair can become a systematic algorithm.

Nogoods bring that completeness. The easy way i s m e r e l y t o k eep all computed nogoods. If during the resolution no valid neighbor exists, the considered problem does not have a n y feasible solution. Of course, this leads to potentially exponential storage space in order to keep all the nogoods. It is possible to avoid this problem and to keep a polynomial storage space. That is what is done in algorithms such a s dynamic backtracking 10], partial order dynamic backtracking 11] and general partial order backtracking 2].

Those algorithms work on an instantiation of the variables which is locally repaired using nogoods. The used recording mechanism requires only polynomial space. For example, considering dynamic backtracking:

Only nogoods for which at most one constraint is not in the current p a t h are kept in ; the neighbor to be processed is completely deterministic (the chosen enumerating constraint to be undone is the most recent one in the lat encountered nogood).

In path-repair, such a nogood recording mechanism can be used thus providing a systematic search algorithm. Such algorithms can be found in a slightly di erent w ay in 16] for dynamic csps and 17] for numeric csps.

Related works

The path-repair algorithm takes its roots in many other works, among which 9] has probably been the most in uential by highlighting the relationships between local and systematic search, and by the use of nogoods to guide the search and make it systematic.

Two algorithms have been designed that have similarities with the non-systematic path-repair algorithm (see section 3.4.2):

The algorithm proposed by S c haerf 23] can be seen as an instance of the path-repair algorithm where the enumerating contraints are instantiations, there is no propagation and no pruning (the ltering algorithm only consists in checking if the constraints containing only instantiated variables are not violated), it does not make use of nogoods neither in the the neighbor function nor in the extend function. The common idea, which already exists in previous works 15], is essentially to extend a partial instantiation when it is consistent, and to perform a local change when the partial solution appears to be a dead-end. The idea to use a ltering algorithm during the running of a local search has been also used in 26], where an extension to GENET, a local search method based on an arti cial neural network aiming at solving binary CSPs, is introduced. This extension achieves what is called \lazy arc-consistency" during the search. The lazy arc-consistency ltering performs a ltering over the initial domains. The result is at most the one obtained by ltering the domains before any search. In path repair, the ltering is applied over the current domains at every step.

The way nogoods are computed by the ltering algorithm is a well-known technique that has already been used for di erent c o m binations of ltering algorithm with systematic search algorithms (forward checking + intelligent b a c k-tracking 21], forward checking + dynamic backtracking 29], arc-consistency + i n telligent backtracking 5], arc-consistency + dynamic backtracking 16], 2B-consistency + dynamic backtracking 17]. Nevertheless, as far as we k n o w, the tabu version of path-repair is the rst time such a technique is used in combination with a local search algorithm.

5 Solving scheduling problems Classical scheduling shop problems for which a s e t J of n jobs consisting each in m tasks (operations) must be scheduled on a set M of m machines can be considered as csps u p o n i n tervals [START_REF] David | A constraint-based approach for examination timetabling using local repair techniques[END_REF] . One of those problems is called the Open Shop problem 13]. For that problem, operations for a given job may be sequenced as wanted but only one at a time. We will consider here the building of non preemptive s c hedules of minimal makespan [START_REF] Doyle | A truth maintenance system[END_REF] . That problem is NP-hard as soon as min(n m) 3.

Constraints on resources (machines and jobs) are propagated thanks to immediate selections from 4]. The consistency level achieved by that technique does not ensure the computation of a feasible solution. An enumeration step is therefore needed. For shop problems, enumeration is classically performed on the relative order on which tasks are scheduled on the resources. When every possible precedence has been posted, setting the starting date of the variable to their smallest value provides a feasible solution. Such a precedence constraint is therefore an enumerating constraint as de ned in section 2.

One of the best systematic search algorithms developed for the Open Shop problem is the branch and bound algorithm presented in 3]. It consists in adding precedence constraints along the critical path of a heuristic solution in each node. As far as we k n o w, although this is one of the best methods ever, some problems of size 7 7 remain unsolved.

Enumerating techniques used for the Open Shop problem are interesting for path-repair because they dynamically build independent sub-problems (by adding precedence constraints). We can suppose that path-repair will be able to make pro t of that situation. We also tested a tabu version of path-repair. T able 1 presents the results obtained on a series of 30 problems from Taillard 27]. In order to put in perspective our results, we recall results presented in 1,18]. Those papers present tabu searches speci cally developed for the Open Shop problem. Those methods both use carefully chosen complex parameter values. Results presented in table 1 show that our simple approach w h i c h merely applies principles presented in this paper already gives very good results.

Our implementation uses a tabu list of size 15. The neighbor function is the one given in gure 2. The conditions of failure specifying the exit of the main loop ( gure 1) are either \stop"returned by t h e neihgbor function or 1500 iterations reached.

Taillard's problems are optimization problems. This requires a main loop that calls the function path-repair until improvement is no longer possible (see gure 3). Improvements are generated by adding a constraint that speci es that the makespan is less than the current best solution found. The initial path for each call of the function path-repair is the latest path (which describes the last solution found).

Conclusion and future works

In this paper, we i n troduced a new solving algorithm for csp: t h e path-repair algorithm. The two main points of that algorithm are: it makes use of a repair algorithm (local search) as a basis and it works on a partial instantiation in order to be able to use ltering techniques. We s h o wed that the most useful tool to implement that algorithm was the use of nogoods.

Fig. 1 .

 1 Fig.1. The path-repair algorithm obviousInference(C 0 ) = allSolution: a solution has been found. The algorithm terminates and returns C 0 . obviousInference(C 0 ) = flounder: t h e path-repair algorithm tries to extend the current p a t h P by adding an enumerating constraint. That behavior is similar to that of backtracking-based search algorithms. For that purpose, a function extend(P ,;) is assumed to exists that chooses an enumerating constraint to be added and adds it to P. The meaning of parameter ; will be made clear later. obviousInference(C 0 ) = noSolution: C C P is inconsistent. We will say that P is a dead-end, o r P is inconsistent: P cannot be extended. The pathrepair algorithm will thus try to repair the current path by c hoosing a new path through the function neighbor(P ,k,;). P arameters k a n d ; w i l l b e explained later.

  We rst tested systematic versions of path-repair on the Open Shop problem. We obtained a very high improvement in terms of numb e r o f e x p l o r e d n o d e s comparing with the results of 3]. Moreover, a problem of size 10 10 has been solved for the rst time. Those results have been presented in 14].

Fig. 3 .

 3 Fig. 3. Algorithm used to solve T aillard's problems

Note that ltering techniques can be considered as a limited form of systematic search.

For discrete csps where enumerating constraint a r e v alue assignments N e is clearly the number of involved variables. For numeric csps N e strongly depends on the

These conditions depend on the instance of the algorithm examples are given in the following sections.

Variables are starting date of the tasks. Bounds thus represent the least feasible starting time and the least feasible ending time.

Ending time of the last task.

First experiments with both systematic versions (based upon a managing of the nogoods inspired from dynamic backtracking) and non systematic versions (using a tabu list) of path-repair have shown promising results.


Petru Apostol

Juliana Eccher

Marta Elisa

Rosso Dotto

Cassiano Batesttin Costa

Thiago Cazati

Elisabeth A Hillard

Harald Bock

Ivan H Bechtold

Elizabeth A Hillard

High rectification in organic diodes based on liquid crystalline phthalocyanines

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Phthalocyanines (PCs) have found widespread use as charge transport materials in organic electronics research due to their good chemical stability and their large flat π-electron system that allows good π-orbital contact between neighboring molecules. [1][2][3][4] Metal PCs have been used as dyes or pigments for various different applications, they are very promising materials for modern optoelectronic devices due to high chemical and thermal stability. 5 Whilst unsubstituted PCs are insoluble in common organic solvents, four-or eightfold alkyl or alkoxy substitution leads to highly soluble PCs that can be solution-processed. [START_REF] Mckeown | Phthalocyanine materials : synthesis, structure, and function[END_REF] The nature of the ligand substituent and of the metal ion in the core of the ligand influences strongly the PCs properties. In polar solvents a large red shift of the Q absorption band has been observed. [START_REF] Rauf | [END_REF] The addition of large solubilizing substituents might worsen the charge transport properties due to the dilution of the electronically active molecular cores by a large amount of electronically inert alkyl groups, but the introduction of suitably shaped flexible substituents might also lead to improved intermolecular π-electron contacts via the formation of columns of closely stacked aromatic disks surrounded by a nanosegregated alkyl periphery in a columnar liquid crystal (LC) or plastic crystal state. 8,9 Such organized macroscopic structures merit special attention due to the self organizing characteristics that allow to modify and to control the optoelectronic properties. 10- 12 One of the main advantages of liquid crystalline PCs in relation to the other discotic macrocycles is their strong absorption in the visible and NIR regions. [START_REF] Laschat | [END_REF] Columnar LC PCs have been promising candidates for photovoltaic applications 14,15 and a columnar LC CuPC was efficiently applied as an organic active layer in thin film transistors, where the device performance was shown to strongly depend on the annealing procedure. 16 We have recently reported that racemic 3-(2-butyloctyloxy)phthalonitrile can be tetramerized to a regiosymmetrically tetrasubstituted PC and its transition metal(II) complexes, where the four branched alkoxy substituents lead to the formation of columnar mesophases with moderate phase transition temperatures. 17 Here we present the electronic behavior in solution-processed organic diodes of the metal-free (H 2 -) and metalated (Cu-and Ni-) tetraalkoxy-PCs in order to correlate the optoelectronic properties with the molecular organization and film structure.

Experimental

X-ray diffraction (XRD) experiments were performed with an X'Pert PRO (PANalytical) diffractometer using CuKα beam ( = 1.5405Å) and using the X'Celerator detector to collect the diffracted radiation. Films were prepared by depositing an amount of powder on a glass plate, where the temperature was controlled with a TCU2000-Temperature Control Unit (Anton Paar). The diffractograms were collected in continuous mode (2 to 30 degrees) at room temperature after cooling from the isotropic phase.

Cyclic Voltammetry (CV) was performed in a three electrode cell, utilizing an Autolab PGStat20 potentiostat, driven by GPES software (General Purpose Electrochemical System, Version 4.4, EcoChemie B.V., Utrecht, the Netherlands), a platinum wire counter electrode, a 1.6 mm platinum disc working electrode, and a non-aqueous reference electrode comprised of a silver wire in a 0.01 M solution of AgNO 3 and 0.1 M tetrabutylammonium perchlorate in acetonitrile; the analytes (approximately 1 mM) were dissolved in DCM supplemented with 0.1 M tetrabutylammonium hexafluorophosphate and degassed by bubbling argon prior to measurement.

A SpectroVision UV-vis spectrophotometer, model DB-1880S, was used to record the absorption spectra of the PCs in solution and spin-coated films, whereas, for the emission measurements, a Hitachi fluorescence spectrophotometer, model F-7000, was used, with the samples excited at a wavelength of 636 nm. Time-resolved fluorescence decays were recorded using the technique of time-correlated single photon counting [START_REF] O'connor | Time-correlated single photon counting[END_REF] with a FluoTime 200 (PicoQuant). Excitation was provided using a pulsed diode laser (instrument response function around 100 ps, 20 MHz repetition rate) at a wavelength of 636 nm. Fluorescence was collected perpendicular to excitation and passed through a polarizer set at the magic angle.

The detection system consisted of a monochromator and a MCP-PMT photomultiplier (Hamamatsu R3809U-50). FluoFit Software was used to analyze the decay curves and the plots of weighted residuals and reduced chi-square (χ2) were used to accurate the quality of the fittings during the analysis procedure. The measurements were done on tetrahydrofuran (THF) solutions at a concentration of 12 mg/mL and spin-coated films produced by solutions of 30 mg/mL in THF with 2000 rpm during 30 seconds.

Optical textures of the films were obtained from an Olympus BX50 polarizing optical microscope (POM) in transmission mode, equipped with a Mettler Toledo FP-82 hot stage to control the temperature. The images were recorded with a CCD camera coupled to the optical microscope. The thickness and roughness of the spin-coated films was probed with an atomic force microscope (AFM), using a Nanosurf EasyScan2 apparatus in tapping mode with a scanning rate of 1.0 Hz covering a size of 20 µm × 20 µm with (512 × 512) pixels.

For the electrical characterization of phthalocyanines 1-3, diodes were fabricated by solution processing of the compounds in THF at a concentration of 30 mg/mL. Indium tinoxide (ITO) coated glass plates with a sheet resistance of about

Results and discussion

We investigated three PCs: Metal-free 1, copper derivative 2 and nickel homolog 3, (Fig. 1).

As reported previously, all three exhibit a plastic crystalline columnar mesophase of rectangular symmetry at room temperature that forms upon cooling (1: below 40°C, 2: below 70°C, 3: below 45°C) from a higher-temperature LC mesophase of hexagonal (1) or rectangular (2, 3) symmetry, the transition enthalpies between the liquid crystalline and plastic crystalline states being barely noticeable by calorimetry. 17 1 and 3 can be obtained in a conventional crystalline state (with a strong melting enthalpy to the LC state of ca. 40 kJ/mol in both cases) by slow crystallization from a bad solvent, whereas in the case of 2, the plastic crystalline state is directly obtained by slow precipitation from solution. Fig. 2 shows the XRD patterns of solid films of compounds 1-3, measured at room temperature after cooling from the isotropic state. Inset of Fig. 2 displays the low angle region, where the peaks could be identically indexed as in the powder XRD experiments presented previously, where a detailed discussion about the molecular organization is presented. 17 Despite the fact that all the three compounds present a rectangular tilted columnar plastic crystalline phase at room temperature, compound 1 is the only one to show a hexagonal mesophase upon cooling from the isotropic liquid, indicating that delocalized π-π intermolecular interactions are more pronounced in 1, whereas tilt-inducing metal-nitrogen interactions play a dominant role for the intermolecular interactions in 2 and 3. In all three cases, it is to be presumed that spincoating leads to the same plastic crystalline state at room temperature that is observed after cooling down the pure material from elevated temperatures. The electrochemical behavior of 1-3 is characterized by three quasi-reversible oxidation waves and two reversible reduction waves in the cyclic voltammograms between -2.2 and 1.4 V vs. Fc/Fc + (CVs, Fig. 3). The potential of the first oxidation wave depends on the presence of a metal; it is found at significantly lower potential (ca. 0.021 V) for the metalcontaining compounds than for the free ligand (0.098 V). The second oxidation wave is less sensitive with potentials of 0.292 (0.006), 0.287 (0.003) and 0.280 (0.001) V for 1, 2 and 3, respectively. A third, larger peak, occurs at potentials between 0.854 (0.003) and 0.765

(0.005) V.
Differences between the free ligand and metal-containing compounds are more marked in the reduction chemistry, with a significant shift to more negative potentials for the coordination compounds. Two reversible waves are observed at -1.339 (0.001) and -1.734 (0.006) V for the free ligand, while 2 and 3 are very similar, with potentials of -1.446 (0.003) and -1.855 (0.01) V and -1.457 (0.003) and -1.895 (0.01) V, respectively. The absorbance spectrum of 1 (Fig. 4) is characteristic of phthalocyanines with two kinds of energy bands, 21 a so-called B (or Soret) band between 280-400 nm in the UV region and a Q band between 600-720 nm. The Q band is attributed to the π-π * transitions from the HOMO to the LUMO. In the spin-coated thin film the Soret band is relatively more intense, whereas the Q band is broader and less defined than in solution, being associated to the aggregation of molecules via intermolecular interactions between the aromatic planes. 4 The vibronic structure clearly seen in the solution spectrum reflects the different coupling patterns in solution and solid state. Fig. 4 UV-vis absorption spectra of 1 in THF and in film.

I (A) E (V) vs Fc + /Fc
The band gap energies of the Q band were determined from the analysis of the absorption edges in solid films 23 and were estimated to be 1.48, 1.55 and 1.57 eV for 1, 2 and The fluorescence decays of the PCs 1-3 spin-coated films were bi-exponential showing two distinct excited-state lifetimes that are both shorter than the lifetimes observed in THF solution. Moreover, the relative amplitude of the second short-living exponential component (A 2 ) becomes predominant over the first one (A 1 ), suggesting that the second might be due to co-planar π-stacking. The formation of aggregates due to π-π intermolecular interactions in solid thin films was also observed by Bertoncello and co-workers for sulfonated CuPc films deposited by a layer-by-layer technique. 27 At Fig. S2 of the Supporting Information it is possible to compare the mono-exponential fitting for PC 1 in solution with the bi-exponential fitting in spin-coated film.

The shorter excited state lifetimes in the condensed film, and especially, the fact that the second time is dominant, agrees with the evidence from the absorption measurements where a broader Q band is observed in the film. These effects indicate a strong aggregation of the molecules in the spin-coated films driven by π-π interactions. On comparing the film absorption spectra of the free-metal and the metalated PCs it is evident that the Q band broadening of the metal-free PC 1 is larger (see Fig. S1 at the Supporting Information). In addition, the highest A 2 value is also observed for 1. Both results suggest that the π-π interactions are more pronounced for the free-metal PC. This can be explained by the fact that metal-nitrogen interactions between adjacent molecules may constrain the establishment of maximal π-π interactions in 2 and 3. We found that rather smooth homogeneous PC layers of uniform thickness are obtained with thickness of 300 nm for 1-3. AFM images obtained before and after annealing for PC 3 are shown in Fig. 5(a) and (b), respectively. The R rms (Root Mean Square Roughness) of the film as-spun was 9.0 nm. After annealing, the R rms value increased to 25.0 nm and the morphology of the film surface is quite different, where domains corresponding to birefringent textures typical of planar surface alignment are clearly seen (also observed by POM in Fig. 6). (column axes parallel to substrate plane) (Fig. 6(b)). As such a planar surface orientation is unfavorable to good electrode-to-electrode charge transport in diodes (which in columnar LCs is found to be better within columns than from column to column, 28,29 and as indeed diodes made with annealed films tended to be short-circuited (probably due to partial dewetting during annealing, 30,31 we explored diodes with as-spun PC layers, whose birefringence also suggests predominantly planar alignment (in line with previous studies of unannealed open columnar LC films 32 ), but which did not tend to short-circuits. The scale on the pictures is 20 µm.

To conform with well-established procedures, 33 we used poly(ethylenedioxythiophene): poly(styrenesulfonic acid) (PEDOT:PSS)-coated indium-tinoxide (ITO) as glass-supported anode, onto which the PC layer was spun, and an aluminum cathode that was vacuum-deposited on top. The device structure used for electrical characterization of the PCs was ITO/PEDOT:PSS (80 nm)/PC 1, 2 or 3 (300 nm)/Al (80 nm).

The electrical measurements were performed at room temperature and under ambient conditions. The current density-voltage (J-V) characteristics are presented in Fig. 7. The energy levels of the PCs determined by cyclic voltammetry match well with the work functions of the PEDOT:PSS ( 5.2 eV) and the Al electrode ( 4.3 eV), leading a good charge carrier injection.

To our surprise, diodes made from any of the three homologs 1-3 show a degree of rectification higher than three orders of magnitude, see Fig. 6(a). These rectification ratios are much higher than those reported for a less regularly substituted PC, a hexagonal columnar liquid crystalline zinc PC derivative with a considerably larger electronically inert alkyl periphery, 21 giving rectification ratios of less than 10:1 in a very similar device configuration with ITO/PEDOT:PSS and Ca/Al electrodes. The strong rectification might result from close and regular molecular packing in the well ordered plastic rectangular columnar mesophases present in the materials 1-3, 17 which provides intimate intermolecular π-orbital and metalnitrogen interactions and therewith an efficient charge transport through the PC columns even in planar alignment, and thus leads to efficient charge evacuation after injection, avoiding the build-up of a counter-field that would outplay the built-in rectifier geometry. A rectification of 3 orders of magnitude was also obtained for a perylene-based columnar LC in a diode

(a) (b)

structure in a similar edge-on configuration. Such effect results from a compact molecular packing induced to the organic film by thermal evaporation of the molecules. 34 Substrate-PC interactions were investigated by structural analysis in Chang-Hyun Kim et al. 35 They showed that in CuPC films deposited on ITO/PEDOT:PSS the molecules crystallized in an edge-on orientation whereas the deposition on graphene led to face-on orientation, providing higher rectification ratios. For CuPC films deposited in the device structure ITO/PEDOT:PSS/CuPC/Al, they obtained a ratio of rectification lower than 2 orders of magnitude. Mativetsky et al. 36 also used graphene to induce face-on stacking of CuPC thus improving the out-of-plane hole mobility. the electrodes becomes dominant) at higher voltages. As the measurements do not obey the Mott-Gurney law (J  V 2 ), the charge mobilities were obtained directly from the J-V curves by fitting the trap-limited SCLC regimes with a theoretical model presented previously. 37 This model considers an electric field dependent mobility, given by , where µ 0 is the carrier mobility at zero field and γ the field dependence of the mobility, with µ 0 and γ being the parameters extracted from the fitting. Values for µ 0 and γ were extracted for 1-3 and the respective fits are displayed as red solid lines in Fig. 7(b)-(d). The fits agree well with the experimental data obtained at the trap-limited SCLC regime. The µ 0 and γ values found for 1-3 are listed in Table 2, where the mobility values calculated from are presented for an applied voltage of +4.6 V. The voltage dependence of the mobility is shown in Fig. S5 at the Supporting Information. At the same given voltage, mobility of 1 is the lowest and of 3 is highest. These mobilities of the order of 10 -5 to 10 -4 cm 2 /Vs perpendicular to the column direction are low compared to the mobilities typically of 10 -3 to 1.0 in the column direction reported for columnar liquid or plastic crystals, in agreement with the known anisotropy of mobility in columnar mesophases. [38][39][40] The higher Poole-Frenkel coefficients γ indicate that the hopping transport is easier for 3 and 2 than for 1.

From the XRD patterns collected at room temperature cooling from the isotropic and the singlet excited-state lifetime measurements, where the exponential component (A 2 ) is higher, it is to be inferred that the free-metal PC 1 presents a higher contribution coming from the π-π intermolecular interactions, as is also corroborated by its broader absorption spectrum in the film compared to the metal derivatives 2 and 3. On the other hand, the mobility obtained for the metalated PCs 2 and 3 is higher, which is consistent with the fact that the metallic center plays an important role for the charge conduction inside these organic layers.

In the metal PCs, the electrons from nitrogens of neighboring molecules interact with the metallic center, which thus acts as a bridge between the nitrogen atoms of the stacking molecules, contributing to the enhancement of the π-electron delocalization in comparison to the corresponding metal-free PC. Thus, the higher mobility for Ni and Cu PCs is due to an increased interaction of the molecular orbitals between parallely aligned molecules. Nonmesogenic Ni and Cu PCs exhibit in general a higher mobility than H 2 PCs. 41

Conclusions

In summary, regioregularly all-endo tetrasubstituted PCs exhibiting a highly ordered plastic crystalline columnar phase at room temperature give rise to pronounced current rectification in simple ITO/PEDOT:PSS/PC/Al diode structures. These good diode characteristics are obtained despite the preponderantly in-plane alignment of the columns and thus of the axis of preferred charge migration within the PC layer. The field dependent charge carrier mobilities across the devices were obtained in the trap-limited SCLC regimes from the current-voltage curves to be of the order of 10 -5 cm 2 /Vs for the metal-free PC homologue, and of the order of 10 -4 cm 2 /Vs for the metalated Cu and Ni derivatives at +4.6 V. This mobility could still be improved by obtaining a homeotropic alignment of the molecular columns, as previously demonstrated for a perylene based molecule, where an increase of 5 orders of magnitude was obtained. 37 The planar alignment is disadvantageous in diode-type devices since in this way the charges have to be transported perpendicular to the π-stacking direction. On the other hand such orientation is beneficial for thin film transistors. The XRD, excited-state lifetime and optical absorption characterizations suggest that the π-π intermolecular interactions are stronger for metal-free PC 1, whereas CuPC 2 and NiPC 3 presented better electrical response. This demonstrates that for phtalocyanines the intermolecular ligand-ligand π-π interactions do not dominate the electrical conduction, confirming that the metallic centre plays an important role for the charge transport inside these materials.

Associated Content

Supporting Information

Absorption spectra of H 2 PC and CuPC in solution and film, comparison between the monoexponential fitting for H 2 PC in solution and bi-exponential in spin-coated film, fluorescence spectra of 1-3 excited at 636 nm in solution and thin film, AFM analysis of PCs 1 and 2 before annealing and after annealing for 2, and mobility of the PCs at the SCLC regime as a function of the applied voltage.

Fig. 1 Fig. 2

 12 Fig. 1 Chemical structure of the investigated PCs 1-3.

Fig. 3

 3 Fig. 3 Cyclic voltammograms of 1-3 in CH 2 Cl 2 supplemented with 0.1 M Bu 4 NPF 6 . 1.6 mm Pt working electrode: (a) reduction processes and (b) oxidation processes. Current intensities were normalized for concentration using the factor 1.15 for 1 and 1.06 for 3.

22

 22

3 , 2 and 3

 323 Fig. S1.The singlet excited-state lifetimes of 1-3 in THF solvent and spin-coated thin films were investigated by time-resolved fluorescence spectroscopy. The lifetimes of the PCs in solution and spin-coated films are shown in Table1. The PCs 1-3 in solution exhibited monoexponential decays with a singlet excited-state lifetime in the nanoseconds range. The lifetimes found for all PCs in THF are similar to long-lived excited states observed for monomeric PCs in solution.24,25 Bi-exponential decays are usually for aggregated PC species in solution where their lifetimes are characterized by intermediate and fast fluorescence lifetimes, and where the fastest component becomes dominant upon increasing the concentration.26

Fig. 5 ( 2 and 3

 523 b) also suggest partial dewetting, which can result in short-circuit after metallization. Films of metal-free 1 are somewhat less smooth in comparison with samples before annealing. Before annealing the R rms values for 1 and 2 are 17.5 nm and 7.4 nm, respectively. After annealing the R rms for PC 2 increased to 18.4 nm. With metal-free 1, annealing lead to large separated domains and feature sizes that exceeded the range of our AFM images. AFM images of 1 and 2 can be seen in Fig.S4at the Supporting Information.

Fig. 5 183°C, 2 :

 52 Fig. 5 AFM images of spin-coated film of 3: as-spun (a) after annealing (b).

Fig. 6 :

 6 Fig. 6: POM textures of 3 as-spun film (a) and after fast cooling from the isotropic phase (b).

Fig. 7

 7 Fig. 7 Electrical characterization of the PC spin-coated films in the device configuration ITO -PEDOT:PSS (80nm) -PC (300nm) -Al (80nm). (a) Current density versus voltage. (b), (c) and (d) log-log plots of the J-V curves for compounds 1, 2 and 3. The red solid lines indicate the fitting at the trap-limited SCLC regimes.

Table 1

 1 Emission

		 max * /nm	 1 / ns	A 1 (%)	 2 / ps	A 2 (%)	 2
	Solution in
	THF
	1	730.0	5.7 ± 0.1	100.0	-	-	1.019
	2	728.0	4.1 ± 0.2	100.0	-	-	0,997
	3	727.0	4.9 ± 0.1	100.0	-	-	0.978
	Spin-coated
	film
	1	692.0	1.4 ± 0.3	10.3	281 ± 20	89.7	0.995
	2	692.0	1.6 ± 0.7	16.1	320 ± 55	83.9	0.990
	3	692.0	1.8 ± 0.2	27.6	359 ± 80	72.4	1.005
	Excited state lifetimes were measured at maxima of the emission intensities. The
	fluorescence spectra of 1-3 excited at 636 nm in solution and thin film are presented in Fig.
	S3 at the Supporting Information.

wavelength maxima, lifetimes and relative amplitudes of 1-3 in THF solutions and spin-coated films after excitation at 636 nm. *

Table 2

 2 Fitting values obtained for µ 0 and γ.

	Parameter	1	2	3
	(cm 2 /Vs)	8.97×10 -10	1.08×10 -9	2.88×10 -9
	(cm/V) 1/2	2.23×10 -2	2.93×10 -2	2.94×10 -2
	at applied +4.6 V	1.28×10 -5	5.53×10 -5	2.46×10 -4
	(cm 2 /Vs)

Acknowledgements

This research was financed partially by a Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Comité Français d'Evaluation de la Coopération Universitaire et Scientifique avec le Brésil (CAPES-COFECUB, project Ph-C 803-14) grantand by CNPq, Capes, FAPEMIG and INCT/INEO funds. The XRD experiments were carried out in the aborat rio de Difraç o de Raios-X (LDRX-CFM/UFSC).

Author information

Corresponding Author E-mail: juh_19@yahoo.com.br *Phone: +55 48 37212304. Fax: +55 48 37219946. E-mail: ivan.bechtold@ufsc.br *Phone: +55 48 37212304. Fax: +55 48 37219946.

Notes

The authors declare no competing financial interest.