Prof El-Ghazali

Talbi

A Unified View of Parallel Multi-objective Evolutionary Algorithms

Keywords: Parallel evolutionary algorithms, metaheuristics, multi-objective optimization

This paper describes a unified view of parallel evolutionary algorithms for multiobjective optimization problems. The parallel optimization algorithms are detailed from both design and implementation aspects. The proposed taxonomy is based on three hierarchical parallel models. Moreover, various parallel architectures are taken into account. The performance assessment issue of parallel multi-objective evolutionary algorithms (MOEA) is also presented. This work can be extended to any population-based metaheuristics such as particle swarm and scatter search.

Introduction

Many multi-objective optimization problems (MOPs), such as in finance, logistics/transportation, engineering design and life science, are complex. Indeed most of the practical and academic MOPs are NP-complete. Moreover they are CPU time and memory consuming. Even if the use of multi-objective evolu-5 tionary algorithms (MOEAs) allows to decrease the computational complexity of the algorithms, this complexity remains important for a great majority of MOPs in multiple domains of applications, in which the constraints and the ✩ This work is part of a project that has received funding from the European UnionH2020 research and innovation programme under grant agreement No 692286.

objective functions associated to the problem are resource intensive and the size of the decision and/or objective space is important.

Additionally, the fast evolution of technology in the development of networks (local networks such as Infiniband or wide area networks such as optical networks), data storage, and processors (e.g. multi-core processors, vector units, GPUs, ARM, FPGAs), make the use of high-performance computers popular.

Such parallel machines represent an interesting opportunity for the development of parallel multi-objective evolutionary algorithms. Indeed, sequential machines are reaching technological limitations. Even workstations and laptops are composed of multi-core processors and GPUs. The ratio between cost and performance is constantly decreasing. The proliferation of puissant processors and networks have shown the apparition of architectures such as many-cores, GPUs, networks of workstations (NOWs), clusters of processors (COWs), Grids and Clouds for high-performance computing.

High-performance computing architectures are used in the development of MOEAs for the enclosed goals:

• Reduce the time to approximate the Pareto front: the objective here is to speedup the search time. For instance this improves the development of interactive optimization algorithms which is an important aspect for multi-criteria decision making. It is an important issue for a given family of MOPs in which there are hard constraints on time such as in dynamic MOPs and operational MOPs such as time-critical control and planning [START_REF] Camara | A single front genetic algorithm for parallel multi-objective optimization in dynamic environments[END_REF].

• Enhance the properties of the Pareto front: parallel models for MOEAs enable to enhance the properties of the Pareto front. Indeed, exchanging knowledge between optimization heuristics will modify their behaviour in exploring the decision and objective spaces associated to the MOP. The main objective in a cooperation between algorithms is to improve the quality of the Pareto front. One can improve both the search time and the convergence/diversification of the Pareto front. A parallel model for MOEAs may be more efficient than a sequential one even on a single machine.

• Resolve large instances of MOPs: parallel MOEAs enable to resolve big instances of MOPs. Those big instances cannot be resolved on a sequential computer. One can also resolve more accurate and then more complex models of MOPs. Enhancing the accuracy of models increases the complexity of the associated problems. Additionally, many MOPs need the handling of big databases such as machine learning of big data.

Parallel MOEAs can be used with systems such as Hadoop and Spark which provide significant computing power in the mining of big databases [START_REF] Barba-Gonzalz | Multi-objective big data optimization with jmetal and spark, in: Evolutionary Multi-Criterion Optimization[END_REF].

• Enhance the robustness: robustness may be measured in terms of solving in an effective manner different MOPs and various instances of a given MOP. It can also represent the sensitivity of the MOEA to its parameters.

In this taxonomy a clear difference is made between the design issue and the implementation issue of parallel MOEAs. A unified description of parallel MOEAs is proposed. In the implementation issue, we will focus on the efficiency of parallel MOEAs on various types of parallel machines. The impact of parallel languages and programming environments, such as message passing and shared memory are analyzed. Several criteria from the architecture point of view are taken into account such as: sharing of memory, homogeneity of resources, multiplicity of users, and network locality. Those considered criteria will influence on the development of efficient load balancing and fault-tolerant approaches.

The organisation of the paper is as follows. In section 2 the main concepts of multi-objective optimization are given. Section 3 details the main parallel models in the design of MOEAs. In section 4 we will focus on the parallel implementation aspects of MOEAs. The most important concepts of parallel machines related to the parallel implementation of MOEAs are underlined. The performance metrics used to assess the performance of parallel MOEAs are also detailed.

Multi-objective optimization

Definition 2.1 (Multi-objective optimization problem). A multi-objective optimization problem (MOP) may be defined as:

(M OP ) =    min F (x, p) = (f 1 (x), f 2 (x), . . . , f n (x)) s.c. x ∈ S (1)
where n (n ≥ 2) is the number of objective functions, x = (x 1 ..., x k ) is the vector representing the decision variables, S represents the set of feasible solutions in the decision space associated with equality and inequality constraints, and explicit bounds.

F (x) = (f 1 (x), f 2 (x)..., f n (x)
) represents the objective space to be optimized

u i ≤ v i ∧ ∃i ∈ {1, . . . , n} : u i < v i . Definition 2.3 (Pareto Optimality). A solution x * ∈ S is Pareto Optimal 2 if
for every x ∈ S, F (x) does not dominate F (x * ), i.e. F (x) ⊀ F (x * ).

A MOP contain a set of solutions known as the Pareto optimal set. The image of this set in the objective space is denoted as the Pareto front. This set of solutions represents the compromise solutions between the different conflicting objectives. The main goal in the resolution of a MOP is to obtain the Pareto optimal set and, consequently, the Pareto front. Notwithstanding, when metaheuristics (e.g. evolutionary algorithms) are applied, the goal becomes to obtain an approximation of the Pareto optimal set having two properties: convergence to the Pareto optimal front and uniform diversity. The first property ensures the generation of near-optimal Pareto solutions, while the second property indicates a good distribution of the obtained solutions around the Pareto optimal front, so that no valuable information is lost.

Design of parallel MOEAs

In the design of parallel MOEAs, three main parallel hierarchical models are identified (Tab. 1):

• Parallel algorithmic-level for MOEAs: in this model, a parallel algorithm is composed of cooperating MOEAs. This model is not dependant on the target MOP to be solved. If the different MOEAs are independent, the search will be similar to the sequential execution of the algorithms.

However, the cooperative model will modify the behaviour of the MOEAs and allow to enhance the quality of the obtained Pareto front.

• Parallel iteration-level for MOEAs: in this parallel model of MOEAs, an iteration of a MOEA is parallelized. This model is not dependant on the target MOP to be solved. This model will not modify the behaviour of the MOEA. The main goal is to speedup the search time of MOEAs manipulating large populations of individuals.

• Parallel solution-level for MOEAs: in this model of MOEAs, the algorithm will handle in parallel a single solution of the decision space.

This model is dependant on the target MOP to be solved. It consists in the parallel evaluation of the different objectives or constraints associated to the MOP. Let us notice that in many MOEAs, the most costly operation is the evaluation of solutions. This model will not modify the behaviour of the algorithm. It deals with improving the search time of the algorithm. The answer relies on the characteristics of the decision and objective spaces of the MOP (e.g. distribution of the Pareto optimal solutions).

Cooperative algorithmic model of MOEAs

In the cooperative algorithmic model of MOEAs, the various MOEAs are cooperating and then exchanging extracted knowledge from the search with the intent to compute a better and more robust Pareto front [START_REF] Yao | Endocrine-based coevolutionary multiswarm for multi-objective workflow scheduling in a cloud system[END_REF]. In most MOEAs an archive is maintained outside the current population. This archive is composed generally of all generated Pareto optimal solutions.

In the development of this parallel model for cooperative MOEAs, the following questions occur:

• The communication criterion (When?): the communication of data between the MOEAs can be carried out in a blind (probabilistic or periodic) manner or using an adaptive criterion. Periodic communication arises in each MOEA after a given number of iterations; this kind of exchange is synchronous. In probabilistic communication, an exchange operation is carried out after each iteration with a given probability. In adaptive communication, the exchange of information is conducted by some knowledge extracted from the multi-objective search. As an example one can use any information about the improvement of the quality of the Pareto front. A traditional criterion can be associated to the update of the Pareto archive when a new Pareto solution is found.

• The communication topology (Where?): the exchange topology denotes for each MOEA node its neighbor(s). It defines the source and the destination of the information exchanged. The most popular topologies are the regular ones such as mesh, hypercube and rings [START_REF] Gómez | A parallel version of SMS-EMOA for many-objective optimization problems[END_REF]. Dynamic and random topologies can also be used [START_REF] Ying | Universal partially evolved parallelization of moea/d for multi-objective optimization on messagepassing clusters[END_REF].

• The exchanged knowledge (What?): here we have to define the knowledge extracted from the search to be exchanged between the MOEAs.

Generally, the exchanged knowledge consists of:

-Non-dominated solutions: the selection strategy of a MOEA can be based on the non-dominated solutions generated during the search.

A given number or percentage of the Pareto set can be selected to be communicated to neighbors.

-Multi-objective search knowledge: except the Pareto solutions, other informations extracted from the multi-objective search can be communicated such as performance indicators of the local Pareto set, or utopian solutions [START_REF] Ying | Universal partially evolved parallelization of moea/d for multi-objective optimization on messagepassing clusters[END_REF].

• The consolidation policy (How?): this question is related to the strategy applied when the communicated knowledge is received. Generally, the local knowledge of a MOEA is renewed with the received one. For instance, when a MOEA receives some non-dominated solutions from its neighbors, an update of its local population or archive is carried out. Many classical replacement approaches (e.g. deterministic, stochastic) can be used. One can use a deterministic elitist approach in which the Pareto solutions from the merging of the local Pareto set and the received Pareto set is selected.

A small number of parallel evolutionary algorithms have been developed for multi-objective optimization compared to single objective optimization [START_REF] Van Veldhuizen | Considerations in engineering parallel multi-objective evolutionary algorithms[END_REF]. The popular parallel model of evolutionary algorithms, the cellular model, may be reduced tho the migration model in which an island consists of a single solution.

The cell of the grid is represented by a single solution. The selection strategy is based on the neighbors of the solution. Consequently, this parallel model supports more diversification than in a sequential search. In [START_REF] Nesmachnow | Parallel multiobjective evolutionary algorithms for batch scheduling in heterogeneous computing and grid systems[END_REF], it has been shown for many practical applications that parallel cellular models for MOEAs are more efficient in the generation of the Pareto front than sequential MOEAs.

Some parallel models of MOEAs may be based on the partitioning of the objective space. Indeed, a given MOEA may be concerned by a subset of the objective functions (Fig. 1). A MOEA can also manage a single objective. Another strategy may be based on using various scalarization strategies of the objectives set such as different weights of a linear aggregation [START_REF] Stanley | A parallel genetic algorithm for multi-objetive microprocessor design[END_REF]. This approach has been used in the MOEA/D algorithm which is based on the decomposition of the objective space [10][7]. Other parallel models can be based on the partitioning of the decision space [11][12]. Hence a given MOEA will focus its search on a partition of the decision space. Another classification criterion may be related to the cenralized or dis-195 tributed ways to generate the whole Pareto front. Two strategies may be developed (Fig. 1):

• Centralized approach: in this approach, the Pareto set is represented in a shared global memory. All MOEAs update this centralized structure in parallel [START_REF] Basseur | Adaptive mechanisms for multiobjective evolutionary algorithms[END_REF] [14][15] [START_REF] Nebro | Parallel multiobjective optimization[END_REF].

Iteration-based model for MOEAs

The . In multi-disciplinary design optimization, complex simulations are handled to evaluate the objective functions associated to the problem [START_REF] Zhang | Multidisciplinary design and multi-objective optimization on guide fins of twin-web disk using kriging surrogate model[END_REF].

In parallel MOEAs the population of solutions may be controled in parallel.

In a classical master/workers model, the master will handle the initialization of the population, the selection and the replacement phases, while the variation phase (e.g. mutation, crossover) and the fitness assignment phases are managed by the workers [START_REF] Rowe | Parallel GAs for multiobjective functions[END_REF] (Fig. 2). In the fitness assignment and the update of the Pareto archive, the Pareto ranking is a costly operation that can also be parallelized [START_REF] Lančinskas | Approaches to parallelize pareto ranking in nsga-ii algorithm[END_REF].

Two different strategies may be developed:

• Synchronous approach: this approach is equivalent to a sequential MOEA. All operations are handled in a synchronous way and then finalised before starting a new iteration. The master has to wait for all results from the whole set of workers. Then a new iteration of the evolution mechanism can be handled.

• Asynchronous approach: in the asynchronous approach, the master process can handle a new iteration before all the workers finalize their process. For instance in asynchronous steady-state MOEAs, the variation and the evaluation phases may be handled in parallel. Two queues of solutions with fixed sizes are managed in parallel: the queue of solutions to be evaluated and the queue of already evaluated solutions. The free workers will handle the solutions of the first queue. Hence the master process handle the selection phase from the second queue without waiting the results from all the workers. This asynchronous model is not equivalent to the sequential one. Indeed, there is no guarantee that the order of selecting and replacing the solutions is the same than in sequential algorithms.

In swarm based multi-objective algorithms, knowledge other than solutions is used to generate new solutions. This knowledge must be shared by all agents of the swarm. As an example, in ant-based optimization, this knowledge is represented by the pheronome matrix. The master process must distribute this matrix to each worker. An agent of the swarm is handled by a worker. Each worker acquires the pheromone matrix, generate and assign a fitness to the new solution and then return the result to the master. The pheromone matrix is updated once all results are collected from the workers [START_REF] Mora | Paretobased multi-colony multi-objective ant colony optimization algorithms: an island model proposal[END_REF][25].

Solution-based model for MOEAs

In this parallel model the main goal is to reduce the search time of a MOEA.

This model focus on the parallelisation of the functions treating a single solution such as the calculation of objective function and constraints. Two different decomposition strategies may be applied [START_REF] Srinivas | Multiobjective optimization using non-dominated sorting in genetic algorithms[END_REF][9][27] (Fig. 1):

• Decomposition of data: many big MOPs can be decomposed according to the data involved in the problem. Hence the objective functions and/or the constraints can be evaluated in parallel for each partition [START_REF] Talbi | Designing cellular networks using a parallel hybrid metaheuristic on the computational grid[END_REF].

Depending on the target MOP, a partition can be a geographical area, a data structure or a database.

• Decomposition of functions: the objectives or the contraints of a MOP can be decomposed in many sub-functions. Those sub-functions can be handled in parallel by a set of workers. The master needs to collect and combine the results from the workers to assign a global fitness to a solution in terms of convergence and diversification. The parallelism degree of such a parallel model is defined by the numer of sub-functions associated to the objectives and constraints.

Models combination for parallel MOEAs

The various parallel models of MOEAs can be associated in a single parallel model using a hierarchical organization [START_REF] Talbi | Designing cellular networks using a parallel hybrid metaheuristic on the computational grid[END_REF]. Hence this combined scalable parallel model will offer a high degree of parallelism k * m * n where k represents the number of independent or cooperating MOEAs, m represents the population size and n represents the number of sub-functions or partitions of the data associated to the MOP.

Implementation issues of parallel MOEAs

This section will focus on the efficient implementation of the proposed parallel models of MOEAs on different types of high-performance machines. In a distributed memory machine, the processors have their local memory.

The processing elements are coupled by a communication network using various topologies such as rings, hypercubes and fat-trees. This type of machines is much more complicated to program but is more scalable. Communication of information must be handled by message passing. The most popular example of distributed memory machines is the clusters of processors (COWs).

Homogeneous/heterogenous machines: the homogeneity of resources (e.g. processors, networks) is an important characteristic that has to be taken into account. One can qualify clusters of processors by the homogenity of the processing elements. Some networks of workstations (NOWs) can be distinguished by the heterogeneity of the processors and the communication networks.

Single/multiple users: many high-performance computing machines such as COWs are non-shared among multiple users. Those machines are dedicated for a single user at a given time. However, some parallel machines such as NOWs can be shared by multiple users.

Local-area network/wide-area network (WAN): local-area networks (LAN) are generally the adopted networks for massively parallel architectures and clusters. Wide-area networks represent loosely coupled networks and are used in grid computing systems and large network of workstations. Those networks are characterized by a highest cost in terms of communication.

A grid is generally composed of a large set of distributed heterogeneous resources which are administrated across multiple domains [START_REF]The grid: Blueprint for a new computing infrastructure[END_REF]. Two different families of Grids may be found:

• High-Performance Grid: in high-performance Grids (HPC Grid) a dedicated high-performance network is used to interconnect the different clusters and supercomputers. HPC Grids are generally non shared by multiple users. At a given time a single application is executed on a subset of processors.

• Desktop Grid: in desktop Grids, many private workstations are connected through a large scale networks (e.g. internet). Desktop Grids are generally shared by many applications and users.

Volatile/non-volatile parallel machines: a volatile machine is a parallel architecture in which there is a dynamic availability of resources. For instance, in a desktop Grid, there is a volatility in terms of processors. Moreover, the probability of failure (e.g. shutdown) of processors is important.

The following table 2 summarizes the properties of the main HPC machines according to the proposed criteria.

Embedded systems, which are small size, reduced complexity and low-power architectures, can be used in the development of parallel efficient MOEAs [START_REF] Moreno | Using low-power platforms for evolutionary multi-objective optimization algorithms[END_REF].

The most popular specific architectures are Graphical Processing Unit (GPU), Field Programmable Gate Arrays (FPGAs) and ARM family of processors. FPGAs are implemented hardware devices by a programming process [START_REF] Zeidman | Designing with FPGAs and CPLDs[END_REF].

We expect that the exploitation of FPGAs (e.g. Xilinx) will be widespread in the implementation of parallel MOEAs especially for some challenging and highly used applications such as in bioinformatics [33][34]. Some parallel implementations of MOEA have been carried out on specific architectures (e.g. microcontrollers) [START_REF] Mamdoohi | Implementation of genetic algorithm in an embedded microcontroller-based polarization control system[END_REF]. Initially GPUs have been dedicated to graphics rendering and then generalized to numerical compuations. GPUs are based on a SIMD (Single Instruction Multiple Data Streams) structure [START_REF] Brodtkorb | Graphics processing unit (gpu) programming strategies and trends in gpu computing[END_REF]. Many efficient implementations of parallel MOEAs on GPUs have been proposed in the literature [START_REF] Li | A fine-grained parallel multi-objective test case prioritization on gpu[END_REF][38][31] [START_REF] Gupta | A scalable parallel implementation of evolutionary algorithms for multi-objective optimization on GPUs[END_REF]. ARM is a family of reduced instruction set computing (RISC) architectures for processors. They are extensively used in consumer electronic devices such as smartphones and tablets. The implementation of parallel evolutionary algorithms on embedded systems based on single-core and multi-core ARM processors starts to be explored [START_REF] Nasrollahzadeh | Implementation of neurofuzzy system with modified high performance genetic algorithm on embedded systems[END_REF].

The target parallel architecture will affect the selection of the suited programming environment for the implementation of a parallel MOEA. Sharedmemory or message passing are the most popular programming paradigms that can be used. For shared-memory HPC machines, there are three main options:

• Multi-threading: a thread is a light process. Multiple threads composing a process share the same memory space. An important issue in multi-threading is the recovery between computation and communication.

Multi-threaded programming may be used within libraries (e.g. Pthreads) [START_REF] Butenhof | Programming with POSIX threads[END_REF] or programming languages (e.g. Java threads) [START_REF] Hyde | Java thread programming[END_REF].

• OpemMP and CUDA: OpenMP (Open Multi-Processing) and CUDA are the most popular programming environment based on shared memory concepts. Various programming langages (e.g. Fortran, C and C++) are interfaced with OpenMP and Cuda [START_REF] Chapman | Using OpenMP: Portable Shared Memory Parallel Programming[END_REF]. CUDA is used for the GPUs and its portability is limited to Nvidia GPUs. The CUDA framework can be accessed by a directive based language such as OpenACC (Open Accelerators). The OpenACC environment has advantages both in efficiency and portability for programming heterogeneous systems composed of GPU and multi-cores.

Message passing is the main paradigm for distributed memory environments.

The tasks composing a program communicate by message exchange using a synchronous or asynchronous communications. The most popular environment is MPI (Message Passing Interface).

Performance assessment of parallel MOEAs

Speedup and efficiency are the most popular performance measures to evaluate the scalability of parallel MOEAs [START_REF] Kumar | Introduction to parallel computing: Design and analysis of algorithms[END_REF]. They define the gain obtained by the parallelization of the program. The speed-up S N is the ratio between the sequential time T 1 on a single processor and the execution time T N on N processors

S N = T 1 T N
The wall-clock time can be used instead of the CPU time. The wall-clock time can be defined as the whole program time which includes the input and output processes. The CPU time is defined as the time which corresponds to the execution of the program. A super-linear (resp. linear) speedup is achieved if S N > N (resp. S N = N ) [START_REF] Talbi | Superlinear speedup of a parallel genetic algorithm on the supernode[END_REF]. In most of the cases a sub-linear speedup S N < N is performed, caused by the overhead of the communications costs.

The efficiency E N with N processors can be formulated as the ratio between the speed-up S N and the number of processors N .

E N = S N N
When all processors are fully exploited the efficiency will be equal to 100%.

The speedup measure may have different formulations. The selection of a given formulation will depend on the goal of the performance assessment process. One can use the absolute speedup, when the sequential time T 1 is defined as the best known sequential time to solve the problem. In multi-objective optimization using MOEAs, it is hard to make out the best sequential program.

Hence this definition is almost never used. One can use the relative speedup when the sequential time T 1 is formulated as the parallel algorithm implemented on a single processor. If we take into account the bottlenecks of the architectures where the MOEAs are going to be run (e.g., maximum bandwidth between memory and CPU on shared memory machines), those metrics represent upper bounds. Other metrics to evaluate the performance of parallel MOEAs can be used. An important issue can be the energy consumption, for example the energy and the power dissipation to find the Pareto front. Another aspect can be related to the financial cost if the implementation of parallel MOEAs is carried out on commercial clouds. Hence the performance evaluation can be itself formulated as a multi-objective optimization problem dealing with speedup, energy consumption and financial aspects.

Various termination criteria may be applied for the algorithms:

• Number of iterations: a given a priori fixed number of iterations can be defined. This is the most popular measure for parallel MOEAs. One can obtain a superlinear speedup (i.e. S N > N ) [START_REF] Dorronsoro | Achieving super-linear performance in parallel multi-objective evolutionary algorithms by means of cooperative coevolution[END_REF]. It is justified by the properties of the parallel machine in which there are more resources than a sequential machine. For instance, when having more cache memory in the parallel architecture, the swapping time will be more important for the sequential program.

• Convergence: a given quality of solution may be fixed as an achievement. One can use this measure to assess the effectiveness of a parallel MOEA. This measure is useful only for algorithmic-level parallel models of MOEAs, in which the behaviour of the parallel algorithm is different from the sequential one. A super-linear speedup may be obtained and is justified by the properties of the parallel search, in which the landscape of the decision space is not visited by a parallel search in the same order as a sequential search. When dealing with stochastic MOEAs, the average speedup

S N = E(T 1 ) E(T N )
must be used.

Main characteristics of parallel MOEAs

The granularity of a parallel MOEA is the most important property of its performance. It can be defined as the ratio between the computation and the communication times. The achieved speedup is better when the granularity is larger. The parallel models of MOEAs have a declining granularity from large grain (algorithmic-level) to fine-grain (solution-level). The maximum amount of parallel processes composing a parallel MOEA represents its degree of concurrency.

An important issue in the implementation of parallel MOEAs is the scheduling of the different processes. Various scheduling techniques may be applied:

• Static: in static scheduling, the number of processes of MOEAs and their placement are identified before the execution (at compilation). It is an effective strategy for homogeneous architectures, non-volatile and nonshared HPC machines. Undeniably, for heterogeneous architectures, there is a difference in load or power among processors. Hence the time for an iteration of MOEAs is deduced from the least powerful processor or the highly loaded, and then many processes are often idle.

• Dynamic: in dynamic scheduling, the placement of processes is defined during their execution but the number of processes is fixed at compile time. It is an effective strategy for shared architectures in which the load of processors cannot be predicted at compile time. It is also an important issue for non-regular parallel MOEAs where the execution time of the different processes cannot be efficiently estimated at compile time. It can happen for instance when the evaluation time of the different objective functions depends on the solution itself.

• Adaptive: in adaptive scheduling, the set of processes is changing dynamically. The number of processes may vary according to the load of the processors. For instance, a process can be created (resp. killed) when a processor becomes idle (resp. overloaded). Adaptive scheduling is essential for highly volatile HPC machines such as desktop Grids.

Fault-tolerance is an important concern for CPU-time intensive MOEAs implemented on loosely tolerant HPC machines such as NOWs and Grids. One has to apply application-level checkpointing and recovery strategies which are more efficient than system-level ones. Minimal information is stored for applicationlevel checkpointing such as the population of solutions and the iteration number.

Parallel algorithmic-level for MOEAs

Granularity: the parallel algorithmic-level model has a relatively big granularity. Communication cost is generally reduced compared to the execution cost. The communication cost will depend on the frequency of communication and the amount of exchanged knowledge (e.g. set of Pareto solutions). This model is the most appropriate for large scale HPC machines and networks such as NOWs and Grids. The frequency of migration (resp. size of communicated knowledge) must be associated to the latency (resp. bandwidth) of the network.

The communication topology between MOEAs can be defined in correlation with the interconnection network.

Degree of concurrency: in terms od scalability, the degree of concurrency of the parallel algorithmic-level MOEA is bounded by the number of involved

MOEAs. This number is generally tuned according to the effectiveness of the parallel MOEAs and the resources of the target HPC machine. In general there is a threshold in which increasing the number of MOEAs will not allow to improve the quality of results.

Asynchronous versus synchronous exchange: the communication exchange in the algorithmic-level parallel model can be synchronous or asynchronous. In the synchronous exchange of knowledge, the MOEAs carry out a synchronization step at a predefined generation. This operation guarantees the same evolution stage for all MOEAs. The synchronous communication is not fault tolerant and then is less efficient on a computational Grid. Indeed a fault of a single MOEA involves the blocking of the global model in a volatile environment.

In the asynchronous approach, a decision criterion for migration is associated to each MOEA [START_REF] Gómez | A parallel version of SMS-EMOA for many-objective optimization problems[END_REF]. At each iteration, if the criterion is satisfied, the MOEA exchanges some knowledge with the neighbors. If the target HPC machine is heterogeneous, the MOEAs may be at various evolution steps leading to the super-solution or non-effect situations, i.e. the reception of bad solutions at an advanced stage will generally not bring any improvements for the local population. In the inverse situation, the exchange will precipitate the convergence. An important advantage of asynchronous exchange is the non-blocking operation.

It will be more critical for shared HPC machines such as desktop Grids and

NOWs (e.g. multiple users). As the load of processors and networks is heterogeneous, the use of synchronous exchange will deteriorate the performances of the parallel MOEA. Indeed, the least powerful processor will arbitrate the performance.

In a volatile HPC machine such as desktop Grids, it is difficult to preserve regular topologies such as torus and rings. The fault of a processor makes necessary a dynamic reconfiguration of the logical topology. This is a costly op-eration which makes the migration of knowledge inefficient. The use of random and adaptive topologies is recommended for highly volatile HPC machines such as desktop Grids.

Scheduling: in the algorithmic-level model of parallel MOEAs, the processes correspond to MOEAs. One can use the following strategies for scheduling MOEAs:

• Static: in static scheduling, the set of MOEAs is fixed and related to the number of processors. Moreover, a static placement of the MOEAs on the processors is carried out. The placement is not modified during the search.

• Dynamic: in dynamic scheduling, the different MOEAs are dynamically placed on the processors. A migration of the MOEAs is carried out during the search according to the load state of the processors.

• Adaptive: in adaptive scheduling, the number of MOEAs implicated in the search can fluctuate dynamically. For instance, a new MOEAs is recovered when a processor becomes idle, and a MOEA is interrupted when a processor becomes busy.

Fault tolerance: in this parallel model of MOEAs, the memory state required to checkpoint a parallel MOEA is represented by the search memory of the MOEA (i.e. population of individuals, Pareto archive, iteration number).

Parallel iteration-level for MOEAs

Granularity: the parallel iteration-level model for MOEAs has a medium granularity. The granularity will be determined by the ratio between the evaluation of a sub-population (i.e. partition) and its communication cost. The model is effective when the size of the sub-populations is important or the evaluation of the multiple objectives is time-consuming.

Scalability: this model has a degree of concurrency which is bounded by the size of the population. Solving MOPs with many objectives and using large population sizes will enhance the scalability of the parallel iteration-level model of MOEAs.

Asynchronous/synchronous exchange: using asynchronous communications will enhance the effectiveness of the parallel iteration-level model of MOEAs. The evaluation of sub-populations and the generation of solutions must be done in an asynchronous way. For instance, steady-state algorithms may be used in the reproduction phase [START_REF] Depolli | Asynchronous master-slave parallelization of differential evolution for multi-objective optimization[END_REF]. Asynchronism will be more crucial for heterogeneous or volatile and shared HPC machines [START_REF] Mostaghim | Parallel multi-objective optimization using master-slave model on heterogeneous resources[END_REF]. It is also an essential property for MOPs in which the computation time of the objective functions is not deterministic and depends on the carried solution.

The main advantages of the asynchronous model are fault tolerance and robustness. The synchronous model is blocking and therefore less efficient on a heterogeneous grids. The disappearance of an evaluating process needs the redistribution of its solutions to other processes. Then, it is crucial to keep the

solutions not yet evaluated.

Scheduling: in this parallel model, processes correspond to the construction/evaluation of a subset of solutions. Hence, the different scheduling strategies will differ as follows:

• Static: in static scheduling, a partitioning of the population is carried out at compilation time. Is it well adapted for homogeneous non-shared machines in which the population is splitted into equal size partitions related to the number of processors. A static placement of the partitions on the processors is carried out. For heterogeneous non-shared machines, the size of each partition must be initialized in relation to the performance of the nodes. Moreover, the static mapping approach is not efficient for variable computational costs of equal partitions. For instance, it can happen for optimization problems where various CPU-times are associated to the evaluation of different solutions.

• Dynamic: in dynamic scheduling, a migration of tasks can be handled during the execution of MOEAs. The migration decisions depend on the load of processors. In general the number of processes is related to the size of the population and the number of objectives. Many processes may be scheduled on the same processor. The approach based on the masterworkers cycle stealing may be used. To each worker is first assigned a small number of individuals. Once it has performed its iterations the worker requests from the master additional individuals. All the workers are stopped once the final result is returned. Faster and less loaded processors handle more solutions than the others. This approach allows to reduce the execution time compared to the static scheduling approach.

• Adaptive: in adaptive scheduling the number of generated partitions depend on the load of the target HPC machine. This approach is more efficient for shared, volatile and heterogeneous machines such as desktop Grids.

Fault-tolerance: the memory of the parallel iteration-level model needed for checkpointing is collected from the partitions. The partitions are composed of a set of (partial) solutions and their associated fitnesses.

Parallel solution-level for MOEAs

Granularity: the parallel solution-level has the smallest granularity. In the functional decomposition model, the granularity is the ratio between the evaluation cost of the sub-functions and the communication cost of an individual. In the data decomposition model, the granularity is the ratio between the evaluation of a data partition and its communication cost.

This parallel model is less appropriate for large-scale distributed machines in which the communication cost (in terms of bandwidth and/or latency ) is significant, such as in computational Grids. Indeed, its implementation is often restricted to clusters or shared memory machines.

S n = T α + T /n
where α is the communication cost and n is the number of processors.

Scheduling: in the parallel solution-level model, processes correspond to data partitions in the data decomposition model and to sub-functions in the functional decomposition. The different scheduling approaches can be defined as follows:

• Static: in static scheduling, the date or sub-functions are decomposed into equal size partitions. A static placement between the data partitions (or sub-functions) and the processors is carried out. This static scheme is efficient for parallel homogeneous non-shared HPC machines. For a heterogeneous non-shared machine, the size of each partition in terms of sub-functions or data must be tuned according to the performance of the processors.

• Dynamic: dynamic scheduling is crucial for shared parallel machines and MOEAs characterized by variable costs for the sub-functions or data partitions. Dynamic load balancing may be easily achieved by evenly distributing at run-time the sub-functions or the data among the nodes. In MOPs where the computing cost of the sub-functions is unpredictable, dynamic scheduling is necessary.

• Adaptive: in adaptive scheduling, the number of generated data partitions or sub-functions vary in function of the load of the processors. This approach is more appropriate to shared, volatile and heterogeneous parallel machines such as desktop Grids.

Fault-tolerance: the memory of the solution-level parallel model needed for the checkpointing mechanism is straightforward. It is composed of the solution(s) and their partial objective values.

Depending on the target parallel machine, table 3 shows a guideline for the efficient implementation of the various models of parallel MOEAs. For each model (algorithmic-level, iteration-level, solution-level), the table presents its characteristics according to the highlighted criteria (granularity, scalability, asynchronism, scheduling and fault-tolerance).

Conclusions and perspectives

The development of parallel MOEAs allows to improve speedup of the search, the quality of the approximated Pareto front, the robustness, and to solve large scale MOPs. The distinction between parallel design and implementation issues of MOEAs is crucial to analyze parallel MOEAs. The essential conclusions of this paper can be summarized as follows:

• In terms of design of parallel MOEAs, the various parallel models have been unified. Three complementary hierarchical models have been highlighted: algorithmic-level, iteration-level and solution-level parallel models.

• In terms of implementation of parallel MOEAs, we deal with the question of an efficient placement of a parallel MOEA on a given parallel machine.

The focus was made on the main criteria of parallel machines that have an impact on the efficiency of parallel MOEAs.

This paper illustrates the unified parallel models on evolutionary algorithms.

However, the proposed framework can be extended to any population-based metaheuristic such as scatter search, particle swarm, and ant colonies.

In the next years, the main perspective is to attain Exascale performance.

The emanation of heterogeneous and hybrid HPC machines build of multi-cores and many-cores will accelerate the accomplishment of this goal. In terms of parallel programming environments, cloud computing will become an important alternative to traditional high performance computing for the development of MOEAs that harness large scale computational resources. This is an important challenge as nowadays cloud software frameworks for parallel MOEAs are just emerging.

In the future design of high-performance computers, the ratio between power and performance will be important for sustainable supercomputing. The power represents the electrical power consumption of the machine. In the last year, the greenest HPC machines in the world doubled their energy efficiency, thanks to the manycore processors, GPUs and ARM based architectures. Exascale HPC machines operating at less than 20MW will be realizable in two years.

In terms of solving multi-objective optimization problems, parallel MOEAs constitute inevitable strategies for big real-life applications such as engineering design and machine learning. Parallel MOEAs represent an important solution to solve dynamic real-time MOPs [START_REF] Dujardin | A multi-objective interactive system for adaptive traffic control[END_REF], large-scale and many-objective optimization problems [START_REF] Cheng | Test problems for large-scale multiobjective and many-objective optimization[END_REF]. Moreover, parallel models for MOPs with random or epistemic uncertainties have to be developed. The sources of uncertainty in MOPs are due to many factors such as environment parameters, decision variables and objectives functions.

Figure 1 :

 1 Figure 1: A taxonomy of parallel MOEAs for multi-objective problems.

200•

  Distributed approach: here the Pareto set is distributed between the different MOEAs. Each MOEA maintains a local copy of the Pareto set. Then, a global update is carried out at the end of the computation [17][18][19].

  iteration-based parallel model for MOEAs consists in the parallelization of a single iteration of evolutionary algorithms. This model consists generally in handling in parallel the population of individuals. The CPU-time consuming component of any MOEA is the fitness assignment of the solutions composing the population. This parallel model does not depend on the target MOP. Only problem-independant search components are parallelized such as the evaluation of the objective function and the update of the population. Moreover, there is no modification of the behaviour of the algorithm. The goal is only to accelerate the search process. This is a straightforward and popular model for parallelMOEAs. Pratically, many MOPs are characterized by expensive objective functions. As an example, many computational engineering optimization problems are concerned by complex solvers using surrogate models from finite element methods, electromagnetics, fluid dynamics[START_REF] Zavala | A survey of multi-objective metaheuristics applied to structural optimization[END_REF][START_REF] Rangaiah | Multi-objective optimization: techniques and applications in chemical engineering[END_REF]

  Parallel evaluation of the population. (b) Parallel evaluation of the objectives (c) Combined parallel evaluation of the population and the objectives

Figure 2 :

 2 Figure 2: The iteration-based parallel model for MOEAs.

4. 1 .

 1 High-performance computing architectures and programming environmentsHigh-performance computing architectures are emerging rapidly. The classification criteria for parallel machines having a great influence in the efficient implementation of parallel MOEAs are: shared or distributed memory, homogeneity or heterogeneity of machines, multiple users sharing of the machines, and locality of the communication network. All the proposed parallel models of MOEAs will be analyzed according to those criteria.Shared/distributed memory: the set of processors of a shared-memory machine are linked through a global shared memory. Various topologies have been developed for the communication network (e.g. multistage crossbar, shared bus). This kind of parallel machines are comfortable in terms of programming in a way that classical sequential paradigms can be reused. However this kind of architecture has limited scalability and an important cost. A popular example of such high-performance machines are multi-core architectures and symmetric multiprocessors.

Scalability:

  the degree of concurrency of the model is limited by the number of data partitions or sub-functions. The use of the solution-level parallel model in conjunction with the other parallel models helps to extend the scalability of parallel MOEAs.Asynchronous/synchronous communications: the implementation of this model is always synchronous. In general a master/workers paradigm is implemented. The master must wait for all partial results to compute the global value of the objective functions. The execution time T will be bounded by the maximum time T i of the different tasks. An exception occurs for highlyconstrained MOPs, where feasibility of the solution is first checked. The master terminates as soon as a given process detects that the individual does not satisfy a given constraint. Due to its highly synchronization steps, this parallel model is worth applying to MOPs in which the computations needed at each iteration are CPU-time consuming. The relative speedup may be computed as follows:

Table 1 :

 1 Parallel models of MOEAs in solving MOPs.

	Parallel	MOP	Behaviour	Granularity	Objective
	level	dependent
	Algorithm	No	Modified	MOEA Algorithm Quality & Speedup
	Iteration	No	Non modified	MOEA Iteration	Speedup
	Solution	Yes	Non modified	MOEA Solution	Speedup
	3.1. Algorithmic model of MOEAs
	In the algorithmic parallel model of MOEAs, different evolutionary algo-
	rithms are executed in parallel. They may be independent or cooperative in
	solving MOPs.
	3.1.1. Independent algorithmic model of MOEAs
	In the independent algorithmic model of parallel MOEAs, the various MOEAs
	are executed without any exchange of information. The various MOEAs are
	initialized with different populations. Different parameters are used for the
	MOEAs such as the probability of crossover and mutation. Each component of
	a MOEA may be developed differently: operators (e.g. mutation, crossover),
	representation, objective functions, constraints, diversity preservation, fitness
	assignment, and elitism. Some other parameters will depend on the problem
	formulation. For instance one can use different reference points to generate var-
	ious MOPs problems solved by the same MOEA [3]. The reference points can
	be uniformly distributed within a region that covers the Pareto Frontier.
	This model is straightforward to develop. The master/workers pattern is
	well adapted to this parallel model. A worker implements a MOEA. The mas-
	ter defines the various parameters used by the workers and agregates the best
	found Pareto front from those obtained by the different workers. In addition to
	speedup the MOEA, this parallel model allows to improve its robustness [4].
	This parallel model evokes the question below: is it comparable to launch k
	MOEAs during a given time t and to launch a single MOEA during k * t?

Table 2 :

 2 Propoerties of the main HPC machines.

	Criteria	Shared Memory	Homogeneity	Resource Sharing	Network	Volatility
						No
	Desktop-Grid	No	No	Yes	WAN	Yes

Table 3 :

 3 Efficient implementation of parallel MOEAs.

	Property	Algorithmic-level	Iteration-level	Solution-level
	Granularity	Coarse	Medium	Fine
		(Frequency of exchange,	(Nb. of solutions	(Eval. sub-functions,
		size of information)	per partition)	eval. data partitions)
	Scalability	Number	Neighborhood size,	Nb. of sub-functions,
		of MOEAs	populations size	nb. data partitions
	Asynchronism	High	Moderate	Exceptional
		(Information exchange)	(Eval. of solutions)	(Feasibility test)
	Scheduling and	MOEA	Solution(s)	Partial
	Fault-tolerance			solution(s)

It is assumed, without loss of generality, the minimization of all the objectives.

The Pareto optimal solutions are also known under the name of acceptable solutions, efficient, not-dominated, non-inferior.


Mariam Attoui

Emilie Pouget

Reiko Oda

David Talaga

Thierry Buffeteau

Sylvain Nlate
email: s.nlate@iecb.u-bordeaux.fr

Silica twisted and helical nanoribbons as chiral inducers for peroxophosphotungstate anions

Keywords: chiral silica nanostructures, peroxophosphotungstate, twisted and helical nanoribbons, circular dichroism, chirality induction

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

Introduction

Polyoxometalates (POMs) [1] are an important class of inorganic compounds with highly interesting properties that render them attractive candidates for potential applications in a variety of fields such as catalysis, bio-medicine, optics and nanomaterials [START_REF][END_REF]. Among their diverse functional properties, the chirality of POMs attracts much wider interest, due to the enormous versatility that POMs offer in structural templating, asymmetric catalysis and optics. In this context, assembly of chiral polyoxometalates (POMs)-based materials combines the functionality from both POMs and chiral materials, which can results in improved POM properties [3]. Although POMs exhibit good activity in homogeneous processes, the main disadvantage for practical application lies in their low surface areas and the difficulty to separate them from the reaction mixture. To overcome these drawbacks, the coupling of POMs with soluble supports such as dendrimers [4], or their immobilization onto solid supports [5] to create hybrid materials have attracted particular research interest due to their easy recycling. Among chiral POMs-based materials reported so far, helical selfassembled supramolecular architectures have received more attention in the last few years because of their attractive structural feature and interesting properties. Many approaches are proposed for the preparation of POM-based helical materials generally obtained by chirality induction through attachment of chiral unit as a chirality transfer agent onto the POM [6], or by spontaneous symmetry breaking of POM upon crystallization in the absence of any chiral source, the latter being the most used strategy for the preparation of chiral POM-based materials [7]. The ability to design and fabricate POM-based helical nanostructures with controlled size, in which POM units are organized onto the helical matrix following the helical pitch remains an important challenge in this area of research. Such organization of POMs is expected to bring new optical properties to the whole NANOPOM hybrid material. Thus, a well-defined helicity and strong interactions between POM units and the helical matrix are required for the expression of chiroptical properties of POMs within such POMbased materials. Whereas helically organized Gold Nanoparticles (GNPs) are well developed and show interesting chiroptical properties [8,9], nanomaterials in which POM clusters have been organized on helical structures are rare. Recently, the achiral Keggin anion [PW 12 O 40 ] 3- has been grafted onto silica nanohelices by electrostatic and direct adsorption interactions, and showed the induced chirality from the chiral silica nanohelices [10]. An area of particular interest to us is to investigate how a soluble or solid support may alter the properties of the incorporated POMs. In this context, we have shown few years ago that the incorporation of the Venturello peroxophosphotungstate trianion [PO 4 {WO(O 2 ) 2 } 4 ] 3-[11] into various dendritic cations [4c-h] can resulted in the modification of the POM properties. We found that the nature of the dendritic cation is closely related to the properties (catalytic efficiency, stability, solubility, recyclability and optical activity) of the POM clusters. In the case of chiral dendritic structures, the chirality is manifested in the whole DENDRIPOM hybrid, highlighting the transfer of chirality to POM clusters. These studies indicated that the properties of POM anions can be modulated by varying the nature of the counteranion.

Whereas various POM clusters have been grafted onto solid supports, POM-based materials in which peroxophosphometalate anions have been immobilized onto inorganic solid materials are under represented. Of those reported so far, to the best of our knowledge, no report describes the assembly of peroxophosphometalate with helical structures, and the characteriation of the resulting helical NANOPOM materials as well as their chiroptical properties investigation. In this context, as a continuation of our studies on chiral peroxophosphotungstate based materials, we have investigated the immobilization of peroxophosphotungstate trianion [PO 4 (WO(O 2 ) 2 ) 4 ] 3-onto two chiral silica supports, namely left-and right-handed twisted and helical nanoribbons, and studied the chiroptical properties of the resulting NANOPOM hybrids. Nanostructures obtained by supramolecular organization of organic molecules are known to be very sensitive to chemical, mechanical and thermal perturbation [12]. Thus, much effort has been made to develop more stable inorganic chiral nanostructures [9a,13]. Our approach for the preparation of these chiral peroxophosphotungstate-containing materials is based on the treatment of aminefunctionalized silica twisted and helical nanoribbons with phosphotungstic acid H 3 PW 12 O 40 and excess of H 2 O 2 .

Herein, we described our attempt to prepare NANOPOM hybrids based on the combination of the Venturello peroxophosphotungstate trianion and silica twisted and helical nanoribbons respectively.These NANOPOM hybrids display chiroptical properties, as a result of the chirality transfer from silica nanoribbons to the POM cluster. The morphology and the presence of POM anions within NANOPOM hybrids, as well as the interactions between POMs and silica nanoribbons were investigated by solid 31 P-NMR, UV-Vis, Raman, TEM, HR-TEM, and EDX. Whereas solid 31 P NMR indicates the presence of the Venturello peroxophosphotungstate [PO 4 {WO(O 2 ) 2 } 4 ] 3-within the structures of NANOPOMs, the presence of signals in CD spectroscopy highlights their optical activities, as a result of the chirality induction from chiral nanoribbons to achiral POM clusters. These NANOPOM hybrids were evaluated as recoverable catalysts in the oxidation of methyl phenyl sulfide with H 2 O 2 , as a model reaction. The effects of the nature of the chiral support (twisted ribbons versus helical ribbons) on the properties of POMs are emphasized.

Experimental

Materials

Reagent-grade solvents and all chemicals were used as received. Organic oxidation products were identified by correlation to authentic samples. The 16-2-16 Gemini amphiphile with tartrate counterions (L)-1 and (D)-1 were prepared according to a previously reported procedure [14]. To obtain the organic gel at the concentration of 1mM, 3.6 mg of 16-2-16 L-or D-tartrate powder were dissolved into 5 ml of ultra pure water. The solution is heated up to 60˚C (above the Krafft temperature which is 43˚C for 16-2-16 tartrate) for 20 min to obtain a complete dissolution and incubated at 20˚C. Twisted ribbons (L)-2 and (D)-2 were observed after 2h, whereas helical ribbons (L)-3 and (D)-3 were observed after 2 days. The morphology of self-assembly was monitored by Transmission Electron Microscopy (TEM), after a negative staining with 3 wt% uranyl acetate.

Preparation of peroxophosphotungstate

Preparation of silica twisted nanoribbons (L)-4 and (D)-4 as well as helical nanoribbons (L)-5 and (D)-5.

After the preparation of organic gels, the later were used as template to prepare silica nanofibers through a sol-gel transcription method. In a typical procedure, 500 μL of tetraethoxysilane (TEOS) were added to the 10 mL of 0.1 mM aqueous solution of (L)-tartaric acid (pH 3.8) and prehydrolyzed at 20°C by stirring on the roller-mixer for 7 h. In parallel, a solution of 1 mM 16-2-16 gemini surfactant with (L)-tartrate counterion is aged between 2 h and 2 days for the formation of twisted nanoribbons (L)-4 and (D)-4 as well as helical nanoribbons (L)-5 and (D)-5, respectively. Equal volume of prehydrolyzed TEOS (5 mL) in 0.1 mM aqueous solution of (L)-tartaric acid and organic gel (5 mL) are mixed and stirred at 20˚C with a roller-mixer overnight. Once the transcription is completed, the mixture thoroughly is washed five times with isopropanol in order to eliminate the excess of TEOS and the organic template. Finally, the suspension of silica fibers is stored in pure ethanol. The morphology of the later was checked by TEM. Basically, we obtained 5 mg of silica nanoribbons from 1 mM of organic gel. Generally, 20 mol of APTES in absolute ethanol was added per 1 mg of silica nanohelices in ethanol. The reaction mixture was sonicated in ultrasonic bath for 5 min and heated for 15 h at 70˚C. After completion, the modified silica nanostructure was washed 3 times with absolute ethanol and then 2 times with water. This procedure can be repeated once to improve the coverage of silica surface with amine groups. The quantity of amine groups at the surface of silica nanohelice was estimated as reported in ref. [9a].

Silica NANOPOM twisted ribbons (L)-8 and (D)-8 as well as helical nanoribbons (L)-9 and (D)-9 built by electrostatic coupling of POM clusters with amine functionalized silica nanoribbons.

For the preparation of peroxophosphotungstate anion, phosphotungstic acid H 3 PW 12 O 40 (10 -5 mol, 28.8 mg) was dissolved in water (0.1 mL), and 587 equiv of hydrogen peroxide 35% (0.5 mL, 5.87 mmol) was added to the mixture. The latter was stirred for 30 min at room temperature, and this mixture was added to a water suspension of 5 mg of amine functionalized silica twisted nanoribbons (L)-6 and (D)-6 or helical nanoribbons (L)-7 and (D)-7. The mixture was stirred at 20˚C with a roller-mixer for 4 h. The corresponding silica NANOPOM twisted ribbons (L)-8 and (D)-8 as well as helical nanoribbons (L)-9 and (D)-9 were washed at least 10 times by centrifugation with ultrapure water to remove water soluble unreacted phosphotungstate species, then freeze-dried for 1 day. The final samples were kept at 20°C before any characterization and measurements.

Characterization of POM-based silica twisted nanoribbons (L)-8 and (D)-8 as well as

helical nanoribbons (L)-9 and (D)-9. Data processing was performed with Bruker TOPSPIN 3.5 software. All NMR experiments were recorded at 298K at the spinning speed of 11 kHz, by means of a single pulse sequence with the following parameters : 15° flip angle, sweep width of 59.5 kHz, a recycling delay of 2 s, number of scans were adapted depending on the signal to noise ratio (between 642 and 88800 scans).

Solid

UV-Vis Measurements

The UV-Vis spectra were recorded with a Jasco J-815 CD spectrometer between 180 and 400 nm, with 0.5 nm data interval and 200 nm/min scan rate for the Venturello POM-Arquad and 20 nm/min for the silica NANOPOM twisted ribbons (L)-8 and (D)-8 as well as helical nanoribbons (L)-9 and (D)-9 with a concentration of 0.2 mg/ml. Quartz cuvette with optical path length 1 cm was used for the measurements.

Raman measurements

Raman spectra were recorded with a LabRam HR800 confocal spectrometer (HORIBA), using for excitation 514.5 nm radiation from an argon ion laser and equipped with an aircooled CCD detector (ANDOR) cooled to -85°C. The laser power at the samples was 10 mW and the spectra were accumulated 4 times during 900 s. The spectral resolution given by the entrance slit of 100 μm and the 600 lines/mm grating was 6.8 cm -1 . A DuoScan device composed of two mirrors was activated in order to prevent any sample degradation. Using this device, the excitation beam scan a 10x10µm sized area with a 50x objective (NA 0.75) in the confocal regime. The Raman spectra were recorded between 200 and 1600 cm -1 .

Transmission electron microscopy (TEM) measurements

TEM measurements were performed at room temperature on a Philips EM 120 electron microscope operating at 120 kV, and the images were collected by 2k × 2k Gatan ssCCD camera. Drops of diluted dispersion of the hybrids were deposited on a carbon-coated 200/400-mesh copper grids. Hydrophilic grids were prepared for the observation of samples dispersed in water by treating the carbon-coated copper grids in BioForce Nanosciences UV/Ozone ProCleaner 220 for 20 min. For the sample preparation, 5µL of silica suspension were drop-casted onto the grid and blotted after 1 min. Samples were dried in air.

HR-TEM measurements

POM clusters grafted on the silica nanohelices were observed by a JEOL 2200FS high resolution transmission electron microscope operating at 200 kV and several images was taken using the STEM mode with probe size: spot 1.5 nm. EDX (Energy Dispersive X-ray Spectrometry) and element mapping were performed on the JEOL 2200FS using STEM mode.

Elemental energy dispersive X-ray analysis (EDX)

The EDX was used to estimate the quantity of POM grafted on the silica nanohelices. The atomic percentage of the tungsten W (L) and silicon Si (K), in the different samples was estimated by EDX. For each sample several areas of the sample were studied and the average of percentage of tungsten and silicon was calculated. % [PW 4 O 24 ] 3-= % W/4; %Silica = % Si.

To obtain the % of POM in weight, the molar percentage of POM cluster was multiplied by its molar mass.

Circular Dichroism measurements

Electronic circular dichroism (ECD) measurements were performed on a Jasco J-815 CD spectrometer. The scan rate was 20 nm/min and 50 scans were applied to each sample. The concentration of hybrids applied for these experiments was 0.2 mg/ml. All CD experiments were carried out in acetonitrile with a quartz cuvette (1 cm path length) at 25˚C and with stirring. The baseline corrections of the ECD spectra were performed by subtracting the two opposite-enantiomers ECD spectra and divided by two in case of APTES functionalized silica twisted nanoribbons (L)-6 and (D)-6 as well as helical nanoribbons (L)-7 and (D)-7

respectively. This baseline procedure removes the experimental artefacts coming from the ECD spectrometer. For the NANOPOM ribbons (L)-8 and (D)-8 as well as (L)-9 and (D)-9, the ECD spectra were subtracted from the ECD spectra of the APTES functionalized silica nanoribbons.

General procedure for catalytic oxidation reactions with POM-based silica twisted nanoribbons (L)-8 and (D)-8 and helical nanoribbons (L)-9 and (D)-9.

Silica NANOPOM catalyst was dispersed in 1 mL of solvent and the sulfide (250 equiv) was added to the mixture. An aqueous solution of H 2 O 2 (35% in water, 375 equiv) was added to the reaction mixture at the appropriate temperature. The latter was stirred and monitored by 1 H NMR spectroscopy. Upon completion of the reaction, the catalyst was separated from the medium by centrifugation. The enantiomeric excess were evaluated by chiral HPLC using

Chiracel ASH column and UV detector (254 nm), eluting with hexane/2-propanol (1:1) at a flow of 0.5 mL.min -1 . Retention time: (R)-11: 22.5 min ; (S)-11: 30.9 min.

Results and discussion

Synthesis of peroxophosphotungstate-based silica twisted and helical nanoribbons.

As as well as helical nanoribbons (L)-7 and (D)-7, respectively. To build the peroxophosphotungstate salts of silica nanoribbons 6 and 7, we have used the procedure involving peroxide-mediated decomposition of the heteropolyacid H 3 PW 12 O 40 [18].

According to this procedure, H 3 PW

Solid 31 P NMR measurements

As shown in Figure SI1a in the supporting information, the 31 P NMR spectrum of NANOPOM twisted ribbons (L)-8 showed three broad peaks at 3.5, -6.1 and -14.7 ppm indicating a mixture of phosphorus-containing POM species. We were unable to obtain a better 31 P NMR spectrum with a sufficiently higher signal-to-noise ratio, probably because of the low amount of phosphorus-containing POM species within NANOPOM hybrids.

However, according to the 31 P NMR spectrum, the presence of the peroxophosphotungstate ) 4 ] 3-is protected against the acidic attacks by the dendritic structure around the POM species, as well as its transfer to the organic phase which prevents its transformation to new phosphotungstate species. In the system described herein, the presence of a mixture of phosphorus-containing species within the structure of NANOPOM hybrids can be explained by the slow transformation of the peroxophosphotungstate trianion to new phosphorus-containing species in acidic reaction medium, due to acidic attacks. Thus, according to the litterature, the broad peaks obtained in the 31 P NMR spectrum, at 3.5, -6.1 and -14.7 ppm should be assigned to [PO 4 (WO(O 2 ) 2 ) 4 ] 3- Venturello anion, an undefined lacunary Keggin-type structure and the [PW 12 O 40 ] 3-Keggin species, respectively.

[PO 4 (WO(O 2 ) 2 ) 4 ]

TEM, HR-TEM, STEM and EDX analyses measurements

Transmission Electron Microscopy (TEM) measurements were performed for all the silica nanoribbons summarized in scheme 1. The twisted and helical morphologies are evidenced for POM-based nanoribbons (L)-8 and (L)-9 as shown in Fig. 1a and Fig. 1b, respectively. No discernible change was observed by the TEM images in the morphology, size and periodicity of POM-based nanoribbons (L)-8 and (L)-9, with respect to those obtained for APTES functionalized silica twisted (L)-6 and helical (L)-7 nanoribbons, as stated in Supporting Information (Fig. SI2a andSI2b). Indeed, well defined NANOPOM hybrids with the diameter of 18±2 nm for twisted ribbons and the diameter of 29±4 nm for helical ribbons and pitches of 95±3 nm for twisted ribbons and 64±5 nm for helical ribbons were obtained.

All these are in good agreement with the silica twisted or helical ribbons before the POM grafting, indicating a high stability of these silica nanoribbons during the POM grafting.

Interestingly, the high-resolution HR-TEM images of silica POM-based twisted ribbons (L)-8 (Figure 1c) and POM-based helical ribbons (L)-9 (Figure 1d) as well as their scanning transmission electron microscopy (STEM) shown in Fig. 1e and1f, confirm the uniformity of these NANOPOM hybrids. Black dots attributed to phosphotungstate anions are observed within the nanoribbons. The diameter sizes of POM clusters in the range of 0.7 to 1.3 nm are consistent with that of the peroxophosphotungstate trianion alone or as small aggregates. HR-TEM and STEM images of NANOPOM ribbons revealed that for both nanoribbons, POMs are organized on the silica surface, without strong aggregation, as already observed in our previous work, for electrostatic grafting of the Keggin anion [10]. Interestingly, compared to helical ribbons (L)-9, the surface of silica twisted ribbons (L)-8 showed more black dots, indicating higher concentration of POM clusters.

In order to confirm the presence of POM clusters within silica nanoribbons, NANOPOM hybrids were characterized by elemental energy dispersive X-ray analysis (EDX). The EDX analysis at several locations on the surface of nanoribbons showed comparable results. The spectra of silica twisted nanoribbons (L)-8 (Fig. 2a) and helical nanoribbons (L)-9 (Fig. 2b) reveal the presence of tungsten element, indicating a successful incorporation of phosphotungstate anions within the structure of silica twisted and helical nanoribbons, respectively.

Fig.2. (HERE)

EDX spectra of silica NANOPOM: a) twisted ribbons (L)-8 and b) helical ribbons (L)-9.

Even if silicon was the dominant element, tungsten was also detected as shown in Figure 3.

Based on these results, it is demonstrated that phosphotungstate clusters were successfully immobilized onto the surface of silica nanoribbons, without altering their morphologies. The average of atomic percentage of tungsten was found as 4.75% % and 3.24% for twisted ribbons (L)-8 and helical nanoribbons (L)-9, respectively. These results are in agreement with the HR-TEM images (Figure 1), that showed a higher concentration of POM clusters on twisted ribbon hybrids. As shown in Fig. 3a to 3d, the elemental mappings patterns of silica helical nanoribbons (L)-9 confirm that the black dots correspond to phosphotungstate anions. We have estimated the amount of POM within silica nanoribbons and found average values of 20w% and 14w% for silica twisted ribbons 8 and helical ribbons 9, respectively.

Raman spectroscopy of NANOPOM hybrids.

The grafting of POM clusters onto silica nanoribbons was also investigated using Raman spectroscopy. The Raman spectrum of NANOPOM twisted ribbons 8 (Fig. 4) exhibits the two most intense bands characteristic of the peroxophosphotungstate [PO 4 (WO(O 2 ) 2 ) 4 ] 3-trianion at 958 cm -1 and 220 cm -1 , attributed to the stretching W=O and bending WOW vibrations,respectively [11d,20]. The band observed at 490 cm -1 can be assigned to bending vibration of Si-O-Si groups [21], whereas the small bands in the 1460-1410 cm -1 spectral range are related to APTES. The Raman spectrum of NANOPOM helical ribbons 9 reveals comparable bands to those of twisted ribbons 8. Nevertheless, the W=O band is observed at higher wavenumbers (ca 970 cm -1 ) whereas the shoulder at 1040 cm -1 is slightly more intense than for twisted ribbons. The positions of the W=O band for (L)-8 and (L)-9 are different to the one observed for the Keggin heteropolyacid H 3 PW 12 O 40 grafted onto the silica nanohelices (ca 980 cm -1 ) [10]. This slight shift observed in the case of NANOPOMs 8 and 9 as well as the presence of a shoulder at 1040 cm -1 may resulted on the presence of a phosphotungstate mixture, instead of the Keggin or the peroxophosphotungstate species alone. Finally, the ratio of the intensity of the W=O and Si-O-Si bands is clearly higher for (L)-8 than for (L)-9, confirming the higher concentration of POM clusters on twisted ribbon hybrids.

Fig.4. (HERE)

Raman spectra of silica twisted ribbons (L)-8 (black spectrum), silica helical ribbons (L)-9 (red spectrum), and Keggin heteropolyacid immobilized onto (L)-7 (blue spectrum).

UV-Vis measurements and chiroptical properties of NANOPOM twisted ribbons (L)-8, (D)-8 and helical ribbons (L)-9, (D)-9..

The UV-Vis measurement of twisted ribbons (L)-8, (D)-8 and helical ribbons (L)-9, (D)-9 have been performed in acetonitrile. The spectra of twisted nanoribbons (L)-8 (or (D)-8) (Fig. 5a) shows an intense absorption band around 200 nm and a weak band around 260 nm, which correspond to the O  W charge-transfer band of phosphotungstate [4f, 19b, 22]. As expected, a UV signal characteristic to phosphotungstate absorption was observed, indicating the presence of phosphotungstate species within silica nanoribbons. Interestingly, these signals are comparable to those obtained for the UV-Vis measurement of peroxophosphotungstate-Arquad salts ([{n-C 18 H 37 Information (Fig. SI4b). These results may be explained by the higher amount of POM units within twisted NANOPOMs, and their organization within these structures, as indicated by EDX analyses and TEM images. These images showed a well arrangement of POM units following the pitch of the silica twisted ribbons. On the other hand, the weaker CD obtained for NANOPOM hybrids 8 and 9 with respect to silica NANOPOM built from direct adsorption of Keggin anion may result to the presence of the amino propyl spacer between POM units and nanoribbons (chiral sources), that increases the distance between the two components. In addition, the small size of peroxophosphotungstate anions ca 0.7 nm may also contribute to the decrease of the chirality induction. To support this point, it has been reported for helical gold nanoparticle superstructures that increasing the diameter of nanoparticles decrease the interparticle distance, resulting to the increase of the CD signals of the corresponding hybrid material [9a] . Even if the induced chirality is not as intensive as for silica NANOPOM built from more stable Keggin anion, to the best of our knowledge, the systems described herein represent the first report in which achiral peroxophosphotungstate anions have been immobilized onto twisted and helical nanoribbons and display chiroptical effects, as a result of the chirality induction. We tested the catalytic performance of NANOPOM twisted (L)-8 and helical ribbons (L)-9 in the oxidation of methyl phenyl sulfide 10 in CH 3 CN and acetone, using H 2 O 2 (35%) as primary oxidant. The reaction was monitored over time by plotting the ratio between the intensity of the disappearing 1 H signals of sulfide 10 and the new peaks of the product. The results summarized in Table 1 showed that the NANOPOM hybrids (L)-8 and (L)-9 catalyzed the oxidation of methyl phenyl sulfide to the corresponding methyl phenyl sulfoxide 11 in a racemic form and methyl phenyl sulfone 12.

(75%) + n-(C 16 H 33 (25%)} 2 NMe 2 ] + 3 [PO 4 {WO(O 2 ) 2 } 4 ] 3-), in which Arquad = ([{n-C 18 H 37 (75%) + n-(C 16 H 33 (25%)} 2 NMe 2 ] (Figure SI3 in Supporting Information) [18c].

Table 1 (HERE)

Oxidation of methyl phenyl sulfide 10 catalyzed by silica NANOPOM hybrids 8 and 9, using

H 2 O 2 . a
The selectivity to sulfoxide increased with decreasing reaction temperature. As shown in Table 1, in the presence of NANOPOM twisted ribbon (L)-8, methyl phenyl sulfone 10 is oxidized in CH 3 CN with 100% conversion after 30 min, giving 89% sulfoxide 11 and 11% of sulfone 12, at -30°C (Table 1, entry 1), whereas 68% of sulfoxide 11 and 32% of sulfone 12 were obtained after 15 min at 0°C (entry 3). In similar condition, NANOPOM helical ribbon (L)-9 oxidize methyl phenyl sulfide 10 with 100% conversion after 30 min at 0°C (entry 6), indicating that NANOPOM twisted ribbon (L)-8 is the more efficient catalytic system in the conditions used. This result may be due to the higher concentration of phosphotungstate anions within twisted ribbons than their helical ribbons analogues.

Compare to silica nanohelices based on the Keggin trianion [PW 12 O 40 ] reported recently [10], the oxidation of methyl phenyl sulfide 10 with peroxophosphotungstate-based nanoribbons 8 and 9 indicate a significant increase in the reaction kinetic, whereas the selectivity to the sulfoxide product decreases. These results are in agreement with those reported for peroxophosphotungstate catalysts and highlight the transformation of the under similar conditions, the peroxophosphotungstate anion is a more active oxidation catalyst than the Keggin species, but can be quickly disable depending on the counter ion and the microenvironment around. Thus, this catalytic system can be defined as a mixture of phosphotungstate anions which also contains the peroxophosphotungstate species. It is interesting to note that without POM, less than 4% conversion of sulfide to sulfoxide was generally after 6 h under similar conditions. Reactions in acetone (entries 4-5) are less efficient that those in CH 3 CN. The evaluation of the optical properties of twisted ribbons and helical ribbons in the oxidation of sulfide 10 indicates no significant enantioselectivity (ee) even at low temperature. Even if a CD signal which reflects a chirality induction on the POM is obtained for twisted nanoribbons 8, this property is not expressed at the level of the oxidation reaction of methyl phenyl sulfide 10. We believe that new approaches for the preparation of helical NANOPOM hybrids with greater potential for chiral induction, such as a covalent coupling of POM units with nanohelices, should be interesting in promoting the enantioselectivity. The development of catalytic systems for this purpose is in progress.

Conclusions

In the quest for new chiral POM-based nanomaterials, we have developed a simple way to prepare peroxophosphotungstate-based silica twisted and helical nanoribbons by coupling achiral peroxophosphotungstate anions with well defined amine-funtionalized twisted and helical nanoribbons in acidic medium. The structures of these silica NANOPOM hybrids were determined by 31 P NMR, TEM and HR-TEM as well as UV-Vis and Raman spectroscopy.

The induced chirality of POM was demonstrated by electronic circular dichroism measurements which showed a higher CD signal for silica twisted ribbons with respect to silica helical ribbons, due to the higher amount of POM clusters and their arrangement onto the chiral source. Compared to silica NANOPOM helices based on the Keggin anion previously reported, the amount of phosphotungstate grafted onto the silica matrix is lower, probably due to the difference in stability between the two POM species, the Keggin anion being the most stable. However, as expected, under comparable conditions, silica NANOPOM hybrids based on the peroxophosphotungstate are more active catalysts in the oxidation of mehyl phenyl sulfide. We expect to improve the stability and the chiroptical properties of these new systems by isolating the peroxophosphotungstate anion before its grafting on the silica matrix and its direct adsorption on the chiral sources. We believe that an increase in the stability of the peroxophosphotungstate cluster added to its proximity to the chiral source should improve the chiroptical properties of resulting NANOPOMs. Further studies with this approach are in progress.

  -based silica twisted (L)-8 and (D)-8, as well as helical (L)-9 and (D)-9 nanoribbons 2.2.1. Synthesis of gemini tartrate (L)-1 and (D)-1, organic twisted ribbons (L)-2 and (D)-2, as well as organic helical ribbons (L)-3 and (D)-3

2. 2

 2 .3. Preparation of amine functionalized silica twisted nanoribbons (L)-6 and (D)-6 as well as helical nanoribbons (L)-7 and (D)-7. For electrostatic grafting of POM clusters at the surface of silica nanohelices, the silica nanohelices were functionalized with (3-aminopropyl)triethoxysilane (APTES) [9b].

  Scheme 1. (HERE)Schematic representation of the synthesis of right-handed POM-based silica twisted (L)-8 and helical (L)-9 nanoribbons.

3. 2 .

 2 Characterization of silica NANOPOM hybrids.The morphology and the structure of the resulting NANOPOM twisted ribbons (L)-8 and (D)-8 as well as helical ribbons (L)-9 and (D)-9 were characterized by TEM, HR-TEM, STEM, EDX, UV-Vis and Raman. Particular focus was devoted to solid state 31 P NMR and circular dichroism (CD) spectroscopy, as the 31 P NMR offers evidence for the presence of the peroxophosphotungstate species within NANOPOM hybrids, whereas the CD highlights the chirality induction to POM species.

Fig. 1 .

 1 Fig.1. (HERE) TEM images of silica NANOPOM: a) POM with silica twisted ribbons (L)-8 and b) POM with silica helical ribbons (L)-9; HR-TEM images of silica NANOPOM: c) Silica twisted ribbons (L)-8 and d) Silica helical ribbons (L)-9; STEM images of silica NANOPOM: e) Silica twisted ribbons (L)-8 and f) Silica helical ribbons (L)-9.

Fig. 3 .

 3 Fig.3. (HERE) a) STEM images of silica helical nanoribbons (L)-9; b) Elemental mappings of tungsten (W) and silicon (Si); c) Elemental mapping of Si; d) Elemental mapping of W.

Fig. 5 .

 5 Fig.5. (HERE) (a) UV-Vis spectra of silica NANOPOM twisted ribbons (L)-8 or ((D)-8) in acetonitrile; (b) CD spectra of APTES functionalized silica twisted ribbons before (L)-6, (D)-6, and after mixing with POM (L)-8, (D)-8 in acetonitrile.

3. 3 .

 3 Catalytic tests of phosphotungstate-based silica twisted ribbons 8 and helical ribbons 9 in the oxidation of methyl phenyl sulfide 10.

Fig. 1 .

 1 Fig.1. TEM images of silica NANOPOM: a) POM with silica twisted ribbons (L)-8 and b) POM with silica helical ribbons (L)-9; HR-TEM images of silica NANOPOM: c) Silica twisted ribbons (L)-8 and d) Silica helical ribbons (L)-9; STEM images of silica NANOPOM: e) Silica twisted ribbons (L)-8 and f) Silica helical ribbons (L)-9.

Fig. 2 .

 2 Fig.2. EDX spectra of silica NANOPOM: a) twisted ribbons (L)-8 and b) helical ribbons (L)-9.

Fig. 3 .

 3 Fig.3. a) STEM images of silica helical nanoribbons (L)-9; b) Elemental mappings of tungsten (W) and silicon (Si); c) Elemental mapping of Si; d) Elemental mapping of W.

Fig. 4 .

 4 Fig.4.Raman spectra of silica twisted ribbons (L)-8 (black spectrum), silica helical ribbons (L)-9 (red spectrum), and Keggin heteropolyacid immobilized onto (L)-7 (blue spectrum) .

Fig. 5 .

 5 Fig.5. a) UV-Vis spectra of silica NANOPOM twisted ribbons (L)-8 or (D)-8 in acetonitrile; b) CD spectra of APTES functionalized silica twisted ribbons before (L)-6, (D)-6, and after mixing with POM (L)-8, (D)-8 in acetonitrile

  Solid 31 P NMR spectra were recorded on an Avance III NMR spectrometer (Bruker Biospin) with a vertical 11,74T wide bore magnet operating at 202.47 MHz for 31 P observation by means of a CP-MAS 4-mm H/X probe. 31 P chemical shifts are reported relative to the external reference of ammonium dihydrogen phosphate (ADP) whose phosphorus group was set at 0 ppm. Samples were packed in 4 mm ZrO 2 CP-MAS rotors.

31 P NMR measurements. 1 H NMR spectra were recorded at 25˚C with a Bruker Avance 300 FT spectrometer ( 1 H: 300 MHz) at IECB (Bordeaux, France). All proton chemical shifts are referenced to Me 4 Si (TMS).

  12 O 40 was decomposed in the presence of excess H 2 O 2 to form the trianionic peroxophosphotungstate [PO 4 (WO(O 2 ) 2 ) 4 ] 3-and the dinuclear peroxotungstate [{WO(O 2 ) 2 (H 2 O)} 2 O] 2-. It is well known that in a biphasic medium of water and organic solvant, the trianion [PO 4 (WO(O 2 ) 2 ) 4 ] 3-reacts selectively with the ammonium moieties and transfered to the organic phase (phase-transfer agents), whereas [{WO(O 2 ) 2 (H 2 O)} 2 O] 2-remains in the aqueous phase. In the work described herein, the trianionic peroxophosphotungstate [PO 4 (WO(O 2 ) 2 ) 4 ] 3-is expected to react with ammonium groups of silica nanoribbons 6 and 7 to give silica twisted and helical nanoribbons 8 and 9, which contain the peroxophosphotungstate within their structures. The dinuclear [{WO(O 2 ) 2 (H 2 O)} 2 O] 2-and others non identified POM species were removed from water supernatant by several washing and centrifugation steps.

  water and dichlorometane, only one signal was obtained in the 31 P NMR of [PO 4 (WO(O 2 ) 2 ) 4 ] 3-containing POM-cored dendrimers [4c-h]. In this case, the peroxophosphotungstate [PO 4 (WO(O 2 ) 2

	3-is confirmed by the signal at  = 3.5 ppm. Interestingly, this value is
	comparable to that obtained at  = 2.2 ppm for the solid 31 P NMR measurement of
	peroxophosphotungstate-Arquad salts ([{n-C 18 H 37 (75%) + n-(C 16 H 33 (25%)} 2 NMe 2 ] + 3
	[PO 4 {WO(O 2 ) 2 } 4 ] 3-), in which Arquad = ([{n-C 18 H 37 (75%) + n-(C 16 H 33 (25%)} 2 NMe 2 ]

(Figure

SI1b

in Supporting Information).In addition, Hill [18c] and other groups

[19]

have shown that [PO 4 (WO(O 2 ) 2 ) 4 ] 3-can evolve to a mixture of phosphorus-contaning species in acidic mediums, depending on the system and the experimental conditions. For example in a biphasic medium of

Acknowledgements

Financial support from the University of Bordeaux and CNRS is gratefully knowledged.

We thank IECB technology platforms and S. Tan, M. Decossas and E. Morvan, A. Grelard (CBMN) for TEM and 31 P NMR experiments, S. Buffière (ICMCB, CNRS) and Placamat platform for HR-TEM and EDX measurements.