Julien Boucaron

Anthony Coadou

Robert De Simone

Throughput and FIFO Sizing: an Application to Latency-Insensitive Design

Keywords: Dimensionnement de FIFO, dimensionnement de buffer, débit, Latency-Insensitive Design, Marked Graphs FIFO sizing, Buffer sizing, Throughput, Latency-Insensitive Design, Marked Graphs

On-chip communications are a key concern for high end designs. Since latency issues cannot be avoided in deep-submicron technologies, design methodologies need to cope with it. In such a case, precise FIFO sizings are of high interest, to find the right trade-off in between area, power and throughput. This paper provides means to size optimally FIFOs while reaching maximum achievable throughput. We apply our algorithms to Latency-Insensitive Designs. Such algorithms can also be used to size FIFOs in other application fields, as for instance Networks-on-Chips. We also revisit the equalization process, which introduces as much latencies as possible in the system while preserving global system throughput. This algorithm point out where it is possible to introduce more stage of pipelines while ensuring the maximum throughput of the system. It allows for instance to postpone execution of IP(s) to limit dynamic power peak. We provide a modified algorithm that globally minimizes the number of such introduced latencies.

Introduction

On-chip interconnect is one of the main bottlenecks for high-perfor-mance designs: required bandwidth is growing far away than what standard busses can support. Moreover, interconnect delays exceed the mean clock rate of each IP blocks, and will continue to grow in the future. FIFOs and flow-control (also called back-pressure) are needed for high performance ASICs, multi-clock designs and Networks-on-Chips.

Determining FIFO sizes is a key concern in order to maximize design throughput, and to minimize area footprint while maintaining acceptable power and temperature requirements.

This paper describes how we can determine optimal FIFO sizes in case of single clock IPs, interconnected together with fixed integer latencies. Optimal in our case means to achieve the maximum throughput of the system, while minimizing the sum of FIFO sizes, and take into account the flow-control induced by FIFOs (distributed or atomic ones). We show an application of our results to the specific case of Latency-Insensitive Design. Our results may also apply to different cases, and especially on Networks-on-Chips.

In next section, we briefly describe Latency-Insensitive Design, which is a specific case of synchronous design with non-uniform latencies, re-synchronized through distributed FIFOs (called relay stations) and shell wrappers.

Then, we establish the link that exists between Latency-Insensitive Design and Marked Graphs with finite capacities. We briefly recall some useful results on static scheduling of Marked Graphs. We introduce an algorithm to compute minimum FI-FOs sizes while achieving maximum throughput, and few variants for different set of constraints.

After, we recall the equalization process, which is an algorithm able to push as much as possible latencies on a given design while maintaining its maximum throughput; that is to say, to point out where data flows can be slowed down without affecting the global throughput. This provides hints for re-pipelining a design. We present a revised equalization, which is able to minimize globally the number of such introduced latencies: showing opportunities of re-pipelining giving the smallest area footprint (and still maintain original throughput).

Finally, we discuss results, experiments and implementations.

Latency-Insensitive Design

This section introduces briefly the Latency-Insensitive Design (also known as Latency-Insensitive Systems, Latency-Insensitive Protocols or Synchronous Elastic Flow). Latency-Insensitive Design (LID) [START_REF] Luca | A methodology for correct-by-construction latencyinsensitive design[END_REF] allows to split apart synchronous module functionalities and their communication constraints. It ensures that communication latencies will not interfere with necessary pre-conditions of the synchronous modules. LID is a composition of patient processes: a synchronous process where its functionality only depends on signal values, but not on their reception times. Composition of patient processes is itself patient, as shown in Carloni's seminal paper [START_REF] Luca | Theory of latency-insensitive design[END_REF]. Since most of IPs do not match this requirement, LID has two kind of basic blocks (cf. Figure 1).

A shell wraps each computation block ; the latter is named pearl. Shell function is two-fold: 1) inputs synchronization, the pearl is executed as soon as all input data are present; and 2) outputs propagation, computation results are emitted only if downward receivers are able to store them, in order to avoid over-writings and data losses. Signals cannot go through long wires within a single clock cycle in practice. Such long wires are split up in shorter ones using relay stations; they are patient processes, ensuring data storage from a clock cycle to the next one. Long wires are segmented in a such way that each relay station is only "distant" from its upward emitter and downward receiver of less than a clock cycle. In order to avoid throughput shrinking, the minimum capacity of a relay station is supposed to be two [START_REF] Luca | Theory of latency-insensitive design[END_REF].

Finally, LID relies on two hypotheses: pearls can be stalled within one clock cycle and all latencies are integers.

The design is a composition of modules, communicating through point-to-point channels. This modules are wrapped by shells, used as interfaces between relay stations. Neither blocks placements nor communication latencies are known a priori; they have to be estimated and refined during placement and routing. Channels are iteratively split and relay stations inserted until it reaches a fixed point. Carloni et al. detail this methodology in [START_REF] Luca | A methodology for correct-by-construction latencyinsensitive design[END_REF].

Data flows can be controlled in two ways:

• With dynamic scheduling [START_REF] Boucaron | Formal methods for scheduling of latency-insensitive designs[END_REF][START_REF] Luca | A methodology for correct-by-construction latencyinsensitive design[END_REF][START_REF] Casu | A detailed implementation of latency insensitive protocols[END_REF][START_REF] Cortadella | Synthesis of synchronous elastic architectures[END_REF] using flow-control mechanism (called back-pressure): when a component cannot handle more data, it sustains a stop signal on the upward channel till the register is freed. This solution is flexible enough to prevent data losses, even if a pearl unexpectedly stall. A drawback of the dynamic protocol is that it precisely needs control signals. Such overhead, especially wiring, may be expensive to place and route in an already complex design.

• An alternative is to statically schedule pearls [START_REF] Boucaron | Formal methods for scheduling of latency-insensitive designs[END_REF][START_REF] Casu | A new approach to latency insensitive design[END_REF]. Execution instants can be computed at compile time, and each component knows exactly on its own when it will receive a new data. But it can also take a lot of silicon area to implement such static scheduled pearls: big shift registers may be required, depending on the schedule sequence to store.

Latency-Insensitive Design as Marked Graphs

In the sequel, LID will be modelled as Marked Graphs. We first recall in this section the main definitions and results on Marked Graphs. Then, we show with examples how bounded capacities may shrink the graph throughput.

INRIA

Marked Graphs with Finite Capacities

Marked Graphs (also called Event Graphs) are a quite useful subset of Petri nets, introduced and first studied in [START_REF] Commoner | Marked directed graph[END_REF][START_REF] Hartmann | Einfache Nicht-Sequentielle Prozesse[END_REF]. They were later timed, introducing latencies, in [START_REF] Ramchandani | Analysis of Asynchronous Concurrent Systems by Timed Petri Nets[END_REF].

Definition 1 (Timed marked graph).

A Timed Marked Graph (TMG) is a structure N , P , M 0 , L , such that:

• N is a finite set of vertices, or computation nodes.

• P ⊂ N × N is a finite set of arcs, or places.

• M 0 : P → N is the function that assigns an initial marking (quantity of data abstracted as tokens) to each place1 .

• L : P → N is a function that assigns a weight to each place. In our case, this weight is the latency for a token to go from the input to the output node.

For each place p, we note •p (resp. p•) its tail (resp. its head), such that

•p = {n ∈ N / ∃ n ′ ∈ N , p = (n, n ′ )} (resp. p• = {n ∈ N / ∃ n ′ ∈ N , p = (n ′ , n)}). TMG are bipartite directed graphs, where ∀ p ∈ P , |•p| = |p•| = 1.
In other words, places have a single producer and a single consumer, thus leading to an absence of conflicts. This also means that a TMG is confluent: for all sets of activated nodes, the firing of any of this nodes does not remove another node from this subset than itself. This means that all firing rules define a partial execution order compatible with the as soon as possible (ASAP) firing rule: a node is fired as soon as it is enabled.

We recall some essential results on Marked Graphs given by Commoner et alii. Proofs are deferred to [START_REF] Commoner | Marked directed graph[END_REF].

Lemma 1 (Token count).

The token count of a directed circuit does not change by vertex firing.

Theorem 2 (Liveness).

A marking is live if and only if the token count of every circuit is positive.

Theorem 3 (Firings).

If there exists a firing sequence for a graph whose underlying undirected graph is connected, and this sequence leads back to the initial marking, then all nodes have been fired an equal number of times.

Real-life systems have bounded memory capacities. In order to model this constraints, place capacities may be added to Definition 1. Then, we define the function K : P → N * , assigning to each place the maximum number of tokens that it can contain at a time.

TMG with capacities can be transposed in an equivalent without capacities, introducing complementary places [START_REF] André | Use of the behaviour equivalence in place-transition net analysis[END_REF][START_REF] Franc ¸ois Baccelli | Synchronization and Linearity[END_REF]. If p 1 = (a, b) is a place with a capacity K (p 1 ), its equivalent without capacity p 2 = (a, b) and the corresponding complementary place p 2 = (b, a) have initial markings such that M 0 (p 2 ) = M 0 (p 1 ), and M 0 (p 2 ) = K (p 1 ) -M 0 (p 1 ), as shown in Figure 2. In the sequel, for any set of places P , we will note P the set of its complementary places.

This means that, for instance, if it exists a circuit in a capacity-bounded TMG whose initial marking saturates its place capacities (∀ p, M 0 (p) = K (p)), then it is equivalent one to a complementary circuit with a void initial marking, thus violating Theorem 2. In other words, an overflow (or livelock) in a TMG with capacities, is equivalent to a starvation (or deadlock) in its equivalent one without capacities.

It is worth noticing that the property of acyclicity loses its sense when talking about a graph with finite capacities: it behaves the same way as its strongly connected equivalent, where complementary places introduce circuits.

Example-Based Throughput Limitations

A LID can be modeled as a TMG: a shell with its pearl is abstracted as a computation node, and a relay station with its two buffers corresponds to a place of capacity two.

First, we do not take into account place capacities; we consider that places are unbounded channels and recall briefly known results on scheduling of Marked Graphs. Then, we show on two simple examples why finite capacities can slow down throughput of cyclic and acyclic systems.

Infinite-Capacity Places

A lot of interesting scheduling results exists on top of Marked Graphs with unbounded places and ASAP firing rule [START_REF] Franc ¸ois Baccelli | Synchronization and Linearity[END_REF][START_REF] Reiter | Scheduling parallel computations[END_REF].

Definition 2 (Rate).

We denote the rate of a circuit the ratio: #tokens #latencies Theorem 4 (Throughput). The throughput of a Marked Graph is its maximum execution speed. The throughput of a strongly connected graph equals the minimum rate among its circuits. The throughput of an acyclic graph is 1.

Proof. A Marked Graph cannot run faster than such throughput [START_REF] Reiter | Scheduling parallel computations[END_REF]. [START_REF] Franc ¸ois Baccelli | Synchronization and Linearity[END_REF] has shown that Marked Graph executions can reach such throughput.

Definition 3 (Critical circuit).

A circuit is said critical if its rate is equal to the graph throughput.

Finite-Capacity Places

Finite capacities may slow down the graph throughput, compared to a topologically equivalent graph with unbounded buffers. We give an example in Figure 3 places are complementary places. We just show two of them (dashed ones), the most significant ones.

We suppose null places latencies. Initially, the graph has two circuits: the left circuit has a throughput of 5/5 = 1, and the right one has a throughput of 4/5.

However, if we construct its equivalent graph without capacity, we have to introduce complementary places, such that their initial marking equals the capacities minus the markings of original places: this leads to introduce a circuit whose throughput equals 3/4, slowing down the system because of a lack of capacity.

In a graph with infinite capacities, each lock or slowdown is due to (temporary) starvation: a node produces data as long as it receives inputs. It stops only when awaiting tokens to process. Then, as soon as we introduce finite capacities, we introduce new constraints in addition to the previous ones: nodes are not only awaiting inputs, they also need available storage for their outputs. Dynamic LID has back-pressure signals to handle this problem; they have to be modeled while abstracting a LID into a Marked Graph.

At first sight, it seems that the throughput of a directed acyclic graph (DAG) is 1, as stated in [START_REF] Luca | Performance analysis and optimization of latency insensitive systems[END_REF]. However, the introduction of complementary places creates cycles. Then, a DAG may have a throughput lower than 1, according to its initial marking, as illus-trated in Figure 4. In this example, branches do not have a balanced marking, causing a bubble in the left branch to get back in the right one. When we consider the complemented graph, there is a circuit with a throughput 3/4: the one passing through the back-pressure dashed path in the right branch, getting back into the left branch. Only trees with capacities of two or more escape this rule, since introducing complementary arcs do not create more simple circuits than an arc and its complementary.

In both [START_REF] Luca | Performance analysis and optimization of latency insensitive systems[END_REF] and [START_REF] Casu | A new approach to latency insensitive design[END_REF], the authors use the maximum cycle mean problem [START_REF] Franc ¸ois Baccelli | Synchronization and Linearity[END_REF][START_REF] Dasdan | Faster maximum and minimum mean cycle algorithms for system-performance analysis[END_REF] to compute the throughput of LID systems. Authors in [START_REF] Boucaron | Latency-insensitive design and central repetitive scheduling[END_REF] use costly circuits enumeration to obtain its throughput. However, none of these papers discuss the throughput slowdown due to lack of capacity. In [START_REF] Luca | Performance analysis and optimization of latency insensitive systems[END_REF], a DAG is supposed to have a throughput of 1, which is false with our definition of throughput as we shown previously on an instance. We need to clarify what is the throughput of a LID system. If we assume that the throughput is computed without taking into account the back-pressure, then the previous statement about the DAG is true. However, since LID has relay-stations with bounded capacity of 2, such definition of throughput is an overestimation of what will be the real and effective throughput of system. Lack of place capacities (or relaystations in LID case) may cause potential slowdown, as we have explained previously.

Capacities and throughputs

As said above, the maximum achievable throughput is bounded by the ratio #tokens #latencies , but may be slower because of lack of place capacities. In this section, we detail such maximum throughput taking care of place capacities. Next, we provide our algorithm to compute for each place its capacity, in order to achieve maximum throughput while minimizing the global number of capacities introduced.

Maximum Throughput with Given Capacities

Definition 4 introduces necessary notations. Theorem 5 allows to compute the exact system throughput, with respect to its capacities.

Definition 4 (Complemented graph).

If G = N , P , M 0 , L, K is a connected timed marked graph with finite capacities, the complemented graph G ′ = N ′ , P ′ , M ′ 0 , L ′ is its equivalent with complementary arcs and no capacities such that:

N ′ = N P ′ = P ∪ P ∀ p ∈ P , M ′ 0 (p) = M 0 (p) and M ′ 0 (p) = K (p) -M 0 (p) ∀ p ∈ P , L ′ (p) = L ′ (p) = L (p)
In order to shorten notations, we write in the sequel L (C ) or L ′ (C ) of a circuit C

(resp. M 0 (C ) or M ′ 0 (C )) the sum of its place latencies (resp. initial markings). For instance, M 0 (C ) = ∑ p∈C M 0 (p).

Theorem 5 (Maximum throughput).

Let G = N , P , M 0 , L, K be a connected timed marked graph with finite capacities,

INRIA and G ′ = N ′ , P ′ , M ′ 0 , L ′ its complemented graph. The maximum reachable through- put θ (G) of G is: θ (G) = min C ∈G ′ M ′ 0 (C ) |C | + L ′ (C ) , 1
Proof. The rate θ (n) of a node n is usually defined by:

θ (n) = lim i→+∞ i T n (i)
where T n (i) is the elapsed time up to the i th firing of n. For each circuit C , each node cannot be fired more than once per instant; that is to say i ≤ T n (i). So the global throughput is at most 1, and we ignore the case where

M ′ 0 (C ) > |C | + L ′ (C ).
We now consider C with M ′ 0 (C ) ≤ |C | + L ′ (C ). A Marked Graph can be ultimately periodically scheduled with the ASAP firing rule. And as mentioned earlier, all firing rules are compatible with the ASAP one. Then, we can restrict the study on a single period. The minimum time for a token to go round C is |C | + L ′ (C ). This sum of all nodes and places latencies in C is the period length. Over a period, so that each token go round the circuit, each node is fired M ′ 0 (C ) times (cf. Lemma 1 and Theorem 3).

To summarize, the rate of a circuit C is:

θ (C ) = min M ′ 0 (C ) |C | + L ′ (C ) , 1
Since G ′ is the complemented equivalent of G and G is a (possibly acyclic) connected graph, G ′ is strongly connected because of complementary places, and θ (G) = θ (G ′ ).

The throughput of a strongly connected graph equals the rate of its slowest circuit (cf. Theorem 4).

Required Capacities for Optimal Throughput

Additional capacities may be required in order to reach the maximum throughput. Number and positions of such capacities can be computed with the following Integer Linear Program (ILP):

min ∑ p∈P K (p)
with for all circuit C in G ′ such that C contains at least one complementary place:

M ′ 0 (C ) . |C c | + L ′ (C c ) -M ′ 0 (C c ) . |C | + L ′ (C ) ≥ 0
and for all p in P :

K (p) ≥ 2
where C c is the "latency-critical" circuit (without taking capacities into account). M ′ 0 and L ′ are defined in Theorem 5.

As stated previously, the maximal throughput of the graph is the throughput computed on its complemented equivalent. If there is a slowdown in the system, it is caused by a circuit passing through at least one complementary place, that is to say a place where back-pressure shrinks the effective throughput. Intuitively, the ILP states that we want to minimize global capacity count for FIFOs under the following set of constraints: for each circuit C having at least one complementary place, we can add further capacity until we reach the maximal throughput of the graph. We set K (p) greater or equal to two, so that general LIP properties apply [START_REF] Luca | Theory of latency-insensitive design[END_REF].

Previous inequations can be slightly modified if we want to minimize the number of capacities to reach (if possible) a specified throughput θ. Then, M ′ 0 (C c ) and |C c | + L ′ (C c ) can be replaced by M and L respectively, such that θ = M/L.

Such ILP formulation is also interesting to introduce constraints on capacities. Because of blocks placement and routing, it is not always possible to add more capacities to a single place at a given location. One can add constraints of the form K (p) ≤ K max (p), for example.

Algorithm

Now, we provide the algorithm to compute minimum capacities for each place in order to achieve maximum throughput of the system.

Compute maximum throughput on the not-complemented

graph using for instance Bellman-Ford algorithm (or Yen's algorithm [START_REF] Yen | An algorithm for finding shortest routes from all source nodes to a given destination in general network[END_REF] since we do not have any negative circuit).

2. Build complemented graph.

3. Enumerate all directed circuits having at least one complementary arc in the complemented graph. We use a modification of Johnson's algorithm [START_REF] Johnson | Finding all the elementary circuits of a directed graph[END_REF] that saves some memory: to detect circuits this algorithm uses a clever depth-first search algorithm. Once a circuit is found, we check the previous structural criterion. We can optimize this further, in case of LID, we remove simple circuits composed of an arc and its complementary one. LID assumes that there is at most one initial token per place, thus such circuits have a throughput of one. The modification of Johnson's algorithm is straightforward, and remove at least N circuits from potential N ! circuits.

Build and solve previous formulation of the ILP.

The LID optimization is due to the fact that places will have to be expanded to match LID requirements. Relay stations are separated by wire latencies of at most one, so places with latencies of two or more will have to be expanded [START_REF] Ramchandani | Analysis of Asynchronous Concurrent Systems by Timed Petri Nets[END_REF]. A general example of expansion is given in Figure 5.

Thus, a place p of latency L (p) will be synthesized as a row of L (p) relay stations, with a total capacity of 2L (p), plus the inner registers of wrappers (since node latencies are unitary). A cycle C composed of a place p and its complementary p will have a throughput of:

θ (C ) = M ′ 0 (C ) |C | + L ′ (C ) = M 0 (p) + K (p) -M 0 (p) 2 + 2L (p) = 2 + 2L (p) 2 + 2L (p) = 1
That cannot shrink the global throughput which is at most equal to one. Thus, we can remove safely all such simple circuits.

INRIA c L (c) = n a L (a) = 0 b L (b) = m a c n nodes n -1 places b m -1 nodes m places

Equalization

In this section, we recall the equalization process introduced in [START_REF] Boucaron | Latency-insensitive design and central repetitive scheduling[END_REF], and we present a revised one in order to minimize the number of added places. The equalization process is an algorithm that adds as much as possible places in the graph while maintaining the throughput of the system. The addition of such places gives an hint where there is a positive slack, so that the designer can add more pipeline stage(s) while ensuring the same performance of the whole system. Also, such positive slack can be used to postpone an execution, in order to smooth dynamic power and flatten temperature hot-spots that are critical for leakage power (leakage power is exponential with temperature).

Standard Equalization

The equalization process is built using ILP. The algorithm works as follows:

• Compute maximum throughput of the complemented graph.

• Enumerate all circuits (using in our case Johnson's algorithm [START_REF] Johnson | Finding all the elementary circuits of a directed graph[END_REF]): circuits are used to build constraints between places that can be shared by two or more circuits.

• Build and solve the ILP.

The ILP formulation is of the form:

max ∑ p∈P a (p)
with the constraints that for each circuit C in graph G:

(|C c | + L (C c )) .M 0 (C ) -M 0 (C c ) . |C | + L (C ) + ∑ p∈C a (p) ≥ 0
and the following bounds for each place p:

a (p) ≥ 0
where a (p) are latencies added to each place p.

Intuitively, the ILP states that we want to maximize the number of introduced latencies on each place (arc) while ensuring for each circuit that its throughput will be at least as fast as the throughput of the system. Dependency relations exist between circuits through shared places (arcs) that is why we need to enumerate all circuits.

We use ILP for its versatility to introduce new constraints to suit a given need: for instance, a designer run the equalization process and there is a set of arcs he/she does not want any additional latency, such modification is done quickly on the ILP formulation.

Revised Equalization

This revised equalization is a variant of standard equalization that minimizes added latencies, using arcs shared amongst different circuits. The modification is straightforward; it consists in introducing a weight for each arc in the previous formula that we want to maximize.

The function to maximize is:

max ∑ p∈P w(p).a (p)
where w(p), the weight associated to the arc, is simply the number of occurrences of circuits it belongs to. The set of constraints stays unchanged. Correctness criterion: both standard and revised equalization have the same optimum value. The underlying intuition is has follows:

• Let us assume that there is no circuit sharing the same place/arc. Then the weight equals one, we have the same sum to maximize.

• Now, let us assume that there is a set of circuits x sharing a place/arc, and we can add 1 latencies on each circuits. In the standard equalization, we attempt to put at different locations in order to maximize the gain, so we will add x latencies. However, in the revised equalization, if it is possible to add a latency to this shared place/arc, then we will add it. In both cases, we will have the same gain x.

Discussion

Johnson's algorithm One of the building block is Johnson's algorithm, enumerating all elementary circuits. This algorithm and different variants are used for all of our algorithms. This algorithm has been implemented using Boost Graph Library [START_REF] Siek | The Boost Graph Library: User Guide and Reference Manual[END_REF] and C++. As detailed in Johnson's seminal paper [START_REF] Johnson | Finding all the elementary circuits of a directed graph[END_REF], worst case graphs for enumerating all circuits are complete graphs, in such case the number of circuits is huge, up to N !.

But, in real-life such complete graphs are not usual. In Table 1, we provide experiments for complete graphs, run on an Intel Xeon 3Ghz, 8GB RAM, Linux x64, gcc4.3. Memory is of course an issue in a such case. We have implemented a variant of the algorithm just to enumerate circuits on-the-fly. We have been able to enumerate around 10 15 circuits; run time of such experiment is about 5 to 6 days. It is also possible to parallelize the algorithm, using a parallel depth-first search. Equalization Both equalization algorithms have been implemented using previous Johnson's algorithm implementation and the ILP engine lp solve. Table 2 shows results of both algorithms. The worst case for the revised algorithm is when there is no circuits share places. Then both standard and revised algorithm have the same solution. Figure 6 depicts Test4. As shown in the right strongly connected component, we have a hierarchy of circuits with shared paths. In this case, the revised equalization algorithm is much more efficient.

INRIA

Conclusion

This papers introduces an algorithm to compute optimal FIFO sizes while maintaining maximum achievable system throughput, in case of single clock synchronous systems, interconnected with fixed integer latencies. We establish the link between such synchronous systems and Marked Graphs (MG) with bounded-capacity places. After, we briefly recall results about throughput of MGs with unbounded capacity places. Then, we recall a simple structural transformation to convert a MG with bounded capacities into a MG with unbounded capacities: for each place, it introduces a new complementary place in reverse direction, with an appropriate marking. This creates a circuit between the initial place and the complementary one that ensures the capacity constraint of the initial place. This graph transformation enables a simple structural criterion to find out circuits causing throughput degradation, because of bounded FIFO capacities: circuits with at least one complementary place. We provide a variant of Johnson's algorithm using this criterion to enumerate only such circuits. After, using previous algorithm, we provide an algorithm using Integer Linear Programming to compute the optimal size of each FIFO. Hence, we obtain the maximal throughput while minimizing the sum of FIFOs sizes. We also provide an additional simple structural criterion in case of Latency Insensitive Design (a specific case of MG with bounded capacity places). This allows to remove more unneeded circuits: we describe an algorithm using this additional criterion.

Next, we briefly recall the equalization process. This algorithm inserts in the system as much latency as possible, while maintaining its maximum achievable throughput. This provides hints where a designer can add further pipeline stages without affecting the system throughput. It also enables to defer execution of some parts of the system, in order to minimize dynamic power peaks. We provide a revised equalization process that globally minimizes the sum of such latencies. It shows best locations where to re-pipeline the design with minimum impact on area.

We apply our results on Latency-Insensitive Design (LID), but such results are not limited to LID and can be used in Network-on-Chips, and other fields.

Figure 1 :

 1 Figure 1: Example of latency-insensitive system.

Figure 2 :

 2 Figure 2: A Marked Graph whose places capacities are 2-bounded (left) and its equivalent without capacities (right).

Figure 3 :

 3 Figure 3: Strongly connected Marked Graph with unitary latencies, whose throughput is limited to 3/4 due to 2-bounded places.

Figure 4 :

 4 Figure 4: Acyclic 2-bounded graph whose capacities shrink the throughput down to 3/4.

Figure 5 :

 5 Figure 5: Latency expansion.

Figure 6 :

 6 Figure 6: Screenshot of example Test4, designed with our tool.

  Graphs with Finite Capacities . . . . . . . . . . . . . . . . . 5 3.2 Example-Based Throughput Limitations . . . . . . . . . . . . . . . . 6 3.2.1 Infinite-Capacity Places . . . . . . . . . . . . . . . . . . . . 6 3.2.2 Finite-Capacity Places . . . . . . . . . . . . . . . . . . . . . 6 INRIA

Table 1 :

 1

	Enumerating circuits of complete graphs
	# circuits # nodes Time (s) Memory (MB)
	125673	9	0.170	20
	1112083	10	1.730	190
	10976184	11	17.0	1600

Table 2 :

 2 Number of added latencies by standard equalization vs revised one

	Examples	Standard	Revised	%
		(latencies) (latencies)
	Simple DAG	9	7	-22
	No Share	14	14	0
	Shared	14	7	-50
	Test4	45	27	-40
	Throughput w.

r.t. capacities

We have structurally characterized the capacity bottleneck, for the maximal theoretical throughput, as circuits containing at least one complementary place. We use this structural hint to implement an efficient variant of Johnson's algorithm that enumerates only circuits having this previous property. As we said, the number of circuits can be huge, up to N !; we reduce memory requirements of N circuits in such a case. This helps the ILP solver (in our case lp solve) to ramp up a bit more. Notice that we used a notation of the form |C | + L (C ) throughout the paper to mention latencies. This is due to the fact that we have supposed that the execution of a pearl takes one clock cycle, in order to match early LID implementations. This can be modified if one suppose combinatorial pearls (null firing latency), or integer latencies as well.

RR n°6919

We recall that N = {0,1,2,... } and N * = N\ {0}.RR n°6919


Ali Tarhini

Juan Aguirre-Araque

Mélanie Guyot

Cyrille Costentin

Guillaume Rogez
email: guillaume.rogez@ipcms.unistra.fr

Sylvie Chardon-Noblat

Vanessa Prevot

Christine Mousty
email: christine.mousty@uca.fr

Behavior of iron tetraphenylsulfonato porphyrin intercalated into LDH and LSH as materials for electrocatalytic applications

Keywords: Electrocatalysis, CO2ERR, Iron porphyrin, Layered double hydroxides, Layered simple hydroxides, Hybrid materials

Organic-inorganic hybrid materials were prepared by intercalation of iron 5,10,15,20 tetrakis(4-sulfonatophenyl)porphyrin complex into layered double hydroxides (ZnCr-FeTSPP LDH) and layered simple hydroxides (Zn-FeTSPP LSH) by coprecipitation. They have been characterized by ancillary techniques to compare their structural characteristics, their morphology and their ability to form films on conductive substrates in view of preparing modified electrodes for CO2 electroreduction reaction (CO2ERR). The electrochemical behavior of intercalated FeTSPP was studied by cyclic voltammetry (CV) showing the role of the nature and pH of aqueous electrolyte solutions on the Fe III/II signal. Evaluation of the CO2ERR of ZnCr-FeTSPP modified electrode was investigated by CV and preparative scale CO2 electrolysis in 0.1 M Na2SO4 aqueous solution. Whereas FeTSPP in the same electrolyte solution exhibits 18% of CO2 conversion to CO, once intercalated into ZnCr-LDH, there is no CO formation, only H2 (FY = 75 %). Using the ZnCr-NO3 modified electrode, without porphyrin, the same FY of H2 was obtained. The study illustrates the problematic and the complexity of an attractive approach for the development of innovative hybrid catalysts for heterogeneous CO2ERR.

Introduction

Electrification of the society requires systems able to efficiently convert electricity to chemical energy and vice-versa. In that endeavour, the development of new electrolysis processes, including search of catalysts to improve selectivity and efficiency towards the desired products is essential. Among the challenges associated with setting-up new electrolysis processes, the development of modified electrodes with catalytic properties is needed. The field of modified electrodes (MEs) is vast ranging from the simple adsorption of molecular catalyst on planar electrodes to nanostructuration in tri-dimensional electrodes [1]. Immobilization of molecular catalysts for a given reaction is an attractive strategy as it offers the possibility to control active sites at the molecular level and thus, redox and catalytic properties. Moreover, incorporation of active molecular catalysts into host matrices to modify electrode surfaces gives access to the advantages of heterogeneous catalysis. On the one hand, developing supported molecular catalysis requires addressing a large number of issues such as: the choice of host material, the method of immobilization of the molecular catalyst, finding ways to transport electrons, ions and substrates within the hybrid structure. On the other hand, the strategy of heterogenization of molecular catalysts may lead to a better control of the environment of the catalytic active centre, to improve catalytic efficiency, to prevent the catalyst deactivation, to facilitate product isolation and catalyst regeneration. It gives also the possibility to perform electrolysis in aqueous electrolytes, and circumvent the limit of use of organic media where molecular catalysts are often soluble.

In the recent years, hybrid organic-inorganic materials, defined as an intimate combination at the nanoscale of organic and inorganic components, have attracted a lot of attention [2]. Some of them have been designed for sensing, separation, and catalytic conversion of CO2 [3]. Among the inorganic host matrices, the layered structures [4], such as layered double hydroxides (LDHs) [5] and layered simple hydroxides (LSHs) [6], constitute an attractive class of materials with advantages for immobilizing molecular catalysts in relatively accessible synthesis methods. They are of increasing interest based on their structural characteristics and their functional applications. In this family of lamellar compounds, LDHs are a versatile class described by the general formula [M 2+ 1-xM 3+ x(OH)2]

x+ (A y- x/y).nH2O where M 2+ and M 3+ are divalent and trivalent metals ions, respectively, and A y-represents an y-valent anion. Regarding the LSHs, they differ from LDHs in the fact that they are composed of only divalent metal ions M 2+ 2(OH)4-xA y-

x/y.nH2O. One of the remarkable characteristics of these latter compounds is that the interlayer anionic species (A y-) is usually coordinated to the inorganic layer metals (M 2+ ), in contrast to LDHs for which the major driving force behind intercalation of guest molecules in the interlayer spaces is related to electrostatic interactions.

Various free bases and metal porphyrins functionalized with anionic groups, i.e. sulfonates or carboxylates, were intercalated into layered hydroxide structures (LDH or LSH) having different compositions by either a conventional anion exchange of pre-formed layered materials or a direct coprecipitation procedure. For instance, the molecular catalyst FeTSPP was associated with CoAl [7], ZnCr [8] and ZnAl [9] LDH. A series of hybrid LSHs (Zn, Cu, and Co) functionalized by tetrasulfonato metal (Cu, Co)-phthalocyanines, was synthesized by an anionic exchange reaction and their electrochemical properties were investigated [10,11].

Demel et al. have intercalated porphyrins (ZnTSPP, PdTSPP and PdTCPP (5,10,15,20-tetrakis(4-carboxyphenyl)porphyrin)) in Zn-LSH by coprecipitation to investigate the photophysical properties of these hybrids materials [12,13]. However, to the best of our knowledge, the intercalation of FeTSPP in LSHs has never been reported so far. Some of the LDH-porphyrin hybrids have been used for their catalytic [14] or photochemical [13] properties and others to build MEs for the catalysis of electroreduction of hydrogen peroxide, dioxygen and nitrites [7,8]. However, although inorganic materials such as LDHs and LSHs are CO2 capture agents and potential materials for structuration at the molecular level, their use as hybrid materials for more demanding reactions, such as hydrogen evolution (HER) or CO2 electroreduction reactions (CO2ERR) is challenging. Indeed, the negative potential required to drive these reactions entails the risk of destabilization of the host structure or competition of the activity of the molecular catalyst with the catalytic activity of the host matrix itself.

Nonetheless, iron (III) tetraphenyl porphyrins (FeTPP) have shown high selectivity and efficient transformation of CO2 to CO in both organic and aqueous homogeneous media following a well-known mechanism [15][16][17][18][19]. Heterogenization of such molecular catalyst has been done in organic-inorganic building block Metal-Organic Framework crystalline structures (Fe-porphyrin-based MOFs) [20] and carbon nanotubes (CNTs) [21] for instance, and that immobilizations have a drastic effect on CO2 reduction catalyst efficiency and stability. Thus, inspired by such works and the catalytic properties of ZnCr-FeTSPP LDH with respect to O2 electroreduction, we thought to investigate hybrid FeTSPP-based LDH and LSH materials as electrode modifiers for the catalysis of reductive electrolysis of saturated CO2 aqueous solution.

In the present work, ZnCr-FeTSPP LDH and Zn-FeTSPP LSH were synthesized to compare their structural characteristics, their morphology and their ability to form films on conductive substrates in view of preparing modified electrodes for CO2ERR. The compositions of the host layered structured based on Zn 2+ and Cr 3+ were selected because of their stability at low pH [8].

The electrochemical behavior of FeTSPP-based hybrid LDH was studied by cyclic voltammetry (CV) as a function of the nature and pH of aqueous electrolyte solutions under different atmospheres (Ar and CO2). Evaluation of the CO2ERR was finally done by preparative scale CO2 electrolysis in aqueous solution containing sodium sulfate as electrolyte. between different monomeric and dimeric species according to the nature of axial ligands, H2O, OH -, O 2-, on the metal [22]. In the present work, we will use the notation FeTSPP as a generic name. For comparison purpose ZnCr-NO3 phase was synthesized by coprecipitation following a similar protocol in absence of FeTSPP into the reactor. These synthetic conditions were also used to prepared Mg2Al-LDH intercalated by FeTSPP, in this case the pH was maintained constant at a fixed value of 7.5, the pH of coprecipitation being strongly dependent on the layer metallic composition [START_REF] Forano | Chapter 14.1 -Layered Double Hydroxides (LDH)[END_REF]. were dissolved in 15 mL of water and loaded into an addition funnel. 15 mL of H2O containing 1.9 mmol of NaOH were loaded in another addition funnel and both solutions were added dropwise to the porphyrin solution over the course of six hours at room temperature and strong stirring (1000 rpm). The solid formed was filtered and washed thoroughly with water until the filtrate came out colorless, then washed with ethanol and dried under vacuum.

Experimental section

Preparation of hybrid materials

Synthesis of

Preparation of modified electrodes

For CV analysis, modified electrodes were prepared by solvent casting on glassy carbon electrode (GCE,  = 3 mm, A = 0.07 cm 2 ) following a procedure previously described [8,10].

Before modification, the electrode surface was polished with 1 µm diamond paste (Presi) and washed with acetone and then it was polished again with 0.04 µm alumina slurry (Presi) to be finally rinsed with ethanol and water. Suspensions of hybrid materials (4 mg/mL) were prepared by sonication of ZnCr-FeTSPP LDH or Zn-FeTSPP LSH in water. Aliquots of 10 μL (40 µg) of these suspensions were deposited on the surface of GCE and dried under darkness for at least 2 h to ensure their complete drying before use.

Carbon paper electrodes (CPE-AvCarb MGL190 from FuelCell Store) with a larger surface area (1 cm 2 /side) were used in electrolysis experiments. Hence, the geometrical surface area of all working electrodes used was 2 cm 2 . They were cleaned in ultrasound bath as follow: 15 min acetone, 15 min ethanol, 15 min water and let dry in 40°C oven before the deposition of 125 µL of hybrid material suspension on both sides of the electrodes (2 x 500 µg, 500 µg cm -2 ). The modified CPE were dried at room temperature overnight.

Considering the chemical analysis, the amounts of FeTSPP deposited on the GCE and CPE are 2.00 10 -8 and 5.00 10 -7 mol for ZnCr-FeTSPP|GCE and ZnCr-FeTSPP|CPE, and 1.52 10 -8 and 3.80 10 -7 moles for Zn-FeTSPP|GCE and Zn-FeTSPP|CPE, respectively. The stability of these films was studied using spectrometric method. The ZnCr-FeTSPP|GCE and Zn-FeTSPP|GCE modified electrodes were soaked for 1 h in 3 mL of Na2SO4/CO2 (pH 4.5), then the amount of FeTSPP released from the electrode surface into the electrolyte was determined by UV-vis spectroscopy. The molar extinction coefficient of FeTSPP ( = 10.2 10 4 M -1 cm -1 ) in aqueous acid solution (pH 4.5) was determined from the absorbance of the Soret band at 393 nm as a function of FeTSPP concentrations [START_REF] Fleischer | [END_REF]25]. The same procedure was performed with modified CPE, in this case the volume of electrolyte was 30 mL.

Instrumentation

Powder X-ray diffraction patterns were recorded with a Philips X'Pert automated X-ray diffractometer using CuKα radiation (λ = 0.154051 nm), over the 2-70 • (2θ). FTIR spectra were recorded with a Nicolet 5,700 spectrometer from Thermo Electron Corporation using the KBr pellet technique. The metallic composition of layered materials was determined using inductively coupled plasma-atomic emission spectroscopy (ICP-AES Agilent 5800). Priori analysis, the samples were mineralized by dispersion in 6 mL of HNO3 (69%) and 2 mL of HCl (37%) and heating at 230°C for 1 h using microwave irradiation (Anton-Paar Multiwave 5000). with Ar (20 min) and with CO2 (20 min) until gas saturation, then the bubbling was stopped before starting electrolysis experiments under magnetic stirring (300 rpm) at different applied potentials in the cell hermetically sealed. Nevertheless, in some experiments, we observed a leakage of anolyte in the catholyte. Thus the reduction of O2, produced by oxidation of water at the anode, could explain why the FY is not close to 100% for the electrolysis process in these particularly cases. Gaseous products were sampled from the atmosphere of the cell. CO and H2

CHNS contents in

gases were quantitatively analysed respectively with a Perkin Elmer Clarus 500 gas chromatograph (GC) and a Perkin Elmer AutosystemXL GCs, both equipped with a 30 m molecular sieve 5 Å column and a TCD detector. For both GCs, helium was used as the carrier gas and quantification of products was insured by calibrating the gas chromatogram using a standard mixture of gases of known concentrations (5/5/5/85 v/v H2/CH4/CO/sCO2 from Air Liquide). It should be underlined that no additional gas and liquid products to CO and H2 were detected by GCMS and HPLC. The faraday efficiency (FY, %) was calculated as a ratio between the number of mole of product (n exp ) determined by GC and the theoretical number of mole of product formed (n th ), calculated from the experimentally measured charge (n th = Q/Fx2), knowing that the number of electrons required to form a molecule of CO or H2 is 2 and F is the Faraday constant (96485 C mol -1 ).

Results and Discussion

Structural and morphological characterization of hybrid compounds

Layered hybrid materials, ZnCr-FeTSPP and Zn-FeTSPP, were prepared by the direct coprecipitation method to facilitate the effective intercalation of the bulky macrocycles. The PXRD patterns of the obtained materials (Fig. 1) evidenced a layered structure with a series of harmonic reflection lines corresponding to similar interlayered distances of 2.41 nm and 2.45 nm for ZnCr-FeTSPP and Zn-FeTSPP phases, respectively. All the diffraction lines can be assigned to pure layered phases with no impurities. The formation of hybrid layered hydroxide structures is confirmed by the limited number of (hkl) reflections above 30°. The interlayered values are in good agreement with the values previously reported for ZnCr-FeTSPP (2.326 nm) [8] and ZnAl-FeTSPP (2.295 nm) [9], which are consistent with the porphyrin intercalation with a perpendicular orientation of the porphyrin plane with respect to the LDH layers, the sulfonate groups interacting with adjacent positively charged sheets. Similar values have also been reported in the case of the intercalation of ZnTSPP (2.28 nm) and PdTSPP (2.22 nm) [12] within Zn-LSH, highlighting that the FeTSPP adopts a similar orientation, the nature of the metalation having no significant effect. Despite the presence of the tetrahedral Zn atoms on the hydroxide octahedral layers pointing into the interlayer domain in the case of LSH, the interlayer distances for the LSH and LDH hybrids are similar. Chemical analysis of the materials (see Supporting Information (SI)) confirmed the presence of the different elements in the materials. For the LDH a Zn/Cr ratio of 2.02 and an excess of porphyrin were evaluated, the latter suggesting that a part of the macrocycles is adsorbed at the surface of the LDH particles. For the LSH, the analysis led to a Fe/Zn ratio of 0.078, close to the maximum theoretical loading (Fe/Znth-max = 0.1). The presence of the FeTSPP within the layered structures was confirmed by FTIR (Fig. S1) and UV-Vis spectroscopies (Fig. 2). The fundamental stretching vibrations as (SO3) and s(SO3)

were observed at 1182 and 1037 cm -1 for ZnCr-FeTSPP and 1180 and 1037 cm -1 for Zn-FeTSPP, respectively. Interestingly, the position of these two bands are practically the same as that reported for the ZnAl-FeTSPP (1184 and 1039 cm -1 ) [9] or for the non-intercalated FeTSPP (1187 and 1033 cm -1 ), suggesting that -SO3 -groups of intercalated porphyrins interact with the LDH or LSH layers in a similar way that is via weak interactions, i.e. hydrogen bonding.

Previously, Demel et al. suggested that metallic TSPP were not covalently link to zinc atoms of the LSH layers [12,13].

Aqueous solutions of FeTSPP are characterized by a pH-dependent equilibrium of monomers and dimers [22,[START_REF] Fleischer | [END_REF]25]. This equilibrium depends also on the medium ionic strength and on the porphyrin concentration. The UV-Vis absorption spectrum of the monomer Fe(H2O)nTSPP dissolved in acidic solution (pH 4.0) exhibits a Soret band at 394 nm and Q bands at 503 and 531 nm; whereas at pH 9.0, bands attributed to µ-oxo dimer are situated at 410 nm (Soret band), 565 and 610 nm (Q bands) [22,25]. For comparison, a thin film of FeTSPP deposited on a quartz plate exhibits bands located at 408, 578 and 621 nm, respectively [8]. The same band positions are reported for an ultrathin film built by the layer-by-layer self-assembled technique of FeTSPP and CoAl-LDH nanosheets [7]. The red shift is consistent with strong interactions between the molecular complexes in the films. Figure 2 The morphology of LDH and LSH powders (Fig. 3a andb) and the texture of the as-made thin films on glassy carbon electrode (GCE, Fig. 3c andd) and on carbon paper electrode (CPE, Fig. 3e andf) were analysed by SEM. The particles of the two hybrid materials display a similar platelet like morphology with for LSH however larger platelets and a more pronounced interparticle growth. Surprisingly, the morphology of the films obtained by solvent casting differs radically whether using GCE or CPE. The ZnCr-FeTSPP dispersed in suspension led to the formation of regular and homogenous films on GCE in which the particles are well distributed (Fig. 3c), while in the film obtained from Zn-FeTSPP, large particle aggregates (Fig. 3d) are observed at the surface of the electrode indicating a low dispersion of the LSH platelets during the film formation. Using CPE, the LDH suspension successfully infiltrates into the carbon fibres and interacts with the surface as highlighted in the inset (Fig. 3e). In the case, of Zn-FeTSPP, even if a similar protocol was followed involving aqueous suspension, the material forms large plates at the surface (Fig. 3f) and does not penetrate within the carbon paper which suggest in this case a low wettability. The carbon fibres observed at high magnification in the Zn-FeTSPP modified CPE (Fig. 3e) are unmodified compared to the pristine CPE (Fig. S2).

The stability of these as-prepared films was analyzed after soaking the modified electrodes in the electrolyte (0.1 M Na2SO4/CO2, pH 4.5) for 1 h. The quantification of released species was performed by an UV-Vis absorption spectrometric method. The variation of absorbance was measured at 393 nm that corresponds to the Soret band of FeTSPP in acidic solution (Fig. S3).

The percentages of leaching were 17 and 12 % for ZnCr-FeTSPP|GCE or ZnCr-FeTSPP|CPE, respectively, which could be linked to a part of adsorbed FeTSPP, rather than intercalated, as evidenced by the chemical analysis (see SI). However, this percentage increased significantly for the modified electrodes prepared with Zn-FeTSPP LSH, with more than 60 % of leaching whatever the electrode used. The quality and the stability of the Zn-FeTSPP LSH thin films, prepared in the present conditions, are limited and clearly necessitate further optimization to limit the release of FeTSPP in electrolyte to be used as MEs. Therefore, Zn-FeTSPP LSH was not further studied in detail in the following and we focused only on ZnCr-FeTSPP LDH.

This study aimed at describing the potential electrocatalytic properties of FeTSPP intercalated into LDH towards CO2ERR. The ZnCr-LDH host structure was chosen since it is reported to be stable in acid conditions [8]. The electrochemical behavior of the free FeTSPP was first investigated in aqueous solution under CO2 atmosphere, then the electrochemical response of ZnCr-FeTSPP was investigated by CV as a thin film deposited on the surface of GCE.

Evaluation of the CO2ERR was finally done by preparative scale CO2 electrolysis in aqueous electrolytes using modified CPE.

Electrochemical characterization of FeTSPP in aqueous electrolytes.

The electrochemical behavior of water soluble FeTSPP is known to be pH dependent according to the nature of axial ligands (H2O, OH -, O 2-) on the metal centre [26][27][28]. In acidic media the FeTSPP monomer is favored but a µ-oxo-bridged dimer is detected in basic solutions [22,[START_REF] Fleischer | [END_REF]25]. This latter species shows a slow heterogeneous charge transfer without any well-defined electrochemical signal in CV [26]. As shown in figure 4, in 0.1 M KHCO3 at pH 8.6 (curve a and inset), an irreversible wave is observed at -1.2 V vs. SCE which may correspond to the irreversible reduction of Fe II/I [26] . A well-defined Fe III/II signal is not observable in these pH conditions in line with a chemically slow µ-oxo-dimer dissociation prior to reduction thus leading to a chemically limited CE mechanism [START_REF] Savéant | Elements of Molecular and Biomolecular Electrochemistry: An Electrochemical Approach to Electron Transfer Chemistry[END_REF]. The Fe I/0 redox process is also hardly discernible since it is concomitant to the hydrogen evolution reaction (HER). However, this third wave is the wave of interest for CO2 electrocatalytic activation [START_REF] Costentin | [END_REF]. In the presence of CO2, the pH of the electrolyte solution (H2O + 0.1 M KHCO3) decreases to 6.4 and the features of the successive reduction of the initial µ-oxo dimer are modified. An increase of the catalytic cathodic current at -1.60 V is observed (Fig. 4, curve b). However, the catalytic wave shows a crossing of the forward and backward CV traces, indicating an increase of the catalytic current as time is passing by. This behavior is often due to an evolution of the initial catalyst toward a more efficient catalytic species that might be deposited on the electrode surface [31]. In 0.1 M Na 2 SO 4 upon CO 2 saturation atmosphere (pH 4.5), the well-defined reversible redox couple Fe III/II of the monomeric form of FeTSPP is recovered at E1/2 = -0.28 V and an intense cathodic peak appears at -1.49 V which may probably be due to the catalytic reduction of CO2 (Fig. 4,curve c). We again note a trace crossing in the CV presumably indicating an evolution of the iron porphyrin catalyst at highly negative potentials. In order to verify the ability of the electrogenerated Fe 0 TSPP to catalyse the CO2ERR, a controlled potential electrolysis was performed in an aqueous solution of 0.45 mM FeTSPP in 0.1 M Na2SO4 under CO2 atmosphere at an applied potential -1.45 V (negative enough to observe catalysis but positive enough to prevent catalyst evolution). After the passage of Q = 22 C, analysis of the headspace gas led to a faradaic yield (FY) of 18 % of CO2-to-CO conversion and 60 % of hydrogen production.

Replacing the Na2SO4 electrolyte by a phosphate buffer (PBS, pH 4.5, E app -1.60 V) leads to the exclusive formation of H2. This is in line with previously reported results for CO2ERR with a water soluble iron porphyrin catalyst showing that addition of phosphate buffer promotes the catalytic HER over the competing CO2-to-CO conversion [START_REF] Costentin | [END_REF]. These CO2 electrolysis results, obtained with homogeneous FeTSPP aqueous solutions, show that this molecular catalyst can be used for the conversion of CO2, but with some limitations regarding its selectivity, the nature

Electrochemical characterization of Fe III in ZnCr-FeTSPP

To assess the electroactivity of the metallic centres in ZnCr-FeTSPP, CV measurements were conducted in different aqueous electrolytes (LiClO4, NaClO4, KClO4, and Na2SO4, 0.1 M in H2O) in a potential range between 0 and -0.50 V vs. SCE. From XDR, UV-Vis and FTIR data, we can assume that µ-oxo dimers are present within the interlayer space of ZnCr-LDH host matrix [8]. We studied the evolution of UV-Vis spectra of ZnCr-FeTSPP|ITO thin films dried and when they were soaked in aqueous electrolyte solutions saturated under Ar or CO2 and/or as a function of pH (Fig. S4). The UV-Vis spectra were recorded directly in the cuvette. When the ZnCr-FeTSPP film is hydrated, a shift of the Soret band towards the lower wavelength is observed. In LiClO4 under Ar or CO2 (pH fixed at 4.5) or in Na2SO4/Ar (pH 8.6) it is located at 412 nm. This band shifts to 394 nm with a shoulder at 412 nm in the latter electrolyte saturated with CO2, which induces the pH decrease to pH 4.5. This illustrates the evolution of the species present in the film as a function of the pH of the medium. The position of the Soret bands depending on the conditions are summarized in Table S1.

As observed for the FeTSPP in aqueous solution, this immobilized µ-oxo-dimer species gives an ill-defined electrochemical signal in neutral pH in line with a reduction of the Fe III centres preceded by a chemically slow µ-oxo-dimer dissociation [8]. Since the monomer is favored in acidic medium, the pH of the electrolyte solutions was fixed at 4.5. In 0.1 M LiClO4 under Ar, a small reduction signal is observed around -0.30 V (Fig. 5A,curve a). In the presence of CO 2 , an increase of the signal reversibility was systematically observed whatever the electrolyte used (i.e. in LiClO4 Fig. 5A curve b). The presence of carbonate might favor the monomer species over the µ-oxo-dimer. Moreover, the peak intensity depends on the cation (Li + < Na + < K + ) and also the anion (ClO4 -or SO4 2-) of the electrolyte (Fig. 5B). The best response was obtained in Na2SO4 under CO2 with a one-electron Fe III/II reversible signal at E1/2 = -0.27 V vs. SCE with a Ep = 55 mV, close to the observed potential value of the of Fe III/II redox system of the FeTSPP in solution (E1/2 = -0.28 V), measured in the same electrolyte condition (see above). It should be noted that the current intensity of this Fe III/II signal is particularly small compared to the electrochemical signals previously reported for other electroactive anions intercalated in LDH, such as anthraquinone sulfonates [32], ferrocene sulfonates [33] or 2,2'-azino-bis(3ethylbenzthiazoline-6-sulfonate [34]. Due to a charge balancing effect, the amount of intercalated FeTSPP, bearing four sulfonate groups, is at least two or four times lower than disulfonate or monosulfonate anions. Moreover, this iron complex must be in a specific coordination to be electroactive. In Na2SO4 electrolyte under CO2, the peak intensities (Ipa and Ipc) varied as a function of v 1/2 in the 10-100 mV s -1 range (Fig. 6), indicating that the reduction process of immobilized FeTSPP, inside the LDH, is under diffusion control. Knowing the amount of FeTSPP immobilized on the electrode surface (2 10 -8 moles) and the thickness of the film (~ 2 µm) estimated from SEM image, an apparent diffusion coefficient (D app ) in the range of 10 -14 cm 2 s - 1 is obtained. The observed effect of the electrolyte composition is indicative that the diffusive behavior of the charge transport within the film is certainly limited by ion displacement for charge compensation within the film. This very low value for D app appears to be in line with the observation of regular and dense homogenous films on GCE (Fig. 3c). It is certainly a limitation for the catalytic application since only a small amount of immobilized FeTSPP is expected to be electrocatalytically active as only a thin diffusion-reaction layer will develop, which size is

√ 𝐷𝑎𝑝𝑝 𝑘𝑐𝑎𝑡
(kcat is the apparent catalytic rate in s -1 ) and therefore proportional to the square root of D app . Nonetheless, the aspect of LDH on CPE (Fig. 3e) showing a less dense deposit seems to indicate that the expected limitation might be much less severe on CPE (used as catalyst support for electrolysis) than on GCE (used for CV).

Electrocatalytic response in the presence of CO2

As shown in figure 4 for the FeTSPP in aqueous solution, the CO2 electrocatalysis process occurs at a cathodic potential corresponding to the reduction of Fe I . Therefore, the electrochemical response of ZnCr-FeTSPP was studied in 0.1 M Na2SO4 over a wider potential range (Fig. 7). A significant increase of the electrochemical signal is observed in the presence of CO2 (curve b) compared to the signal obtained under Ar (curve a). However, the new peak observed at -1.50 V is associated on the reverse scan with an irreversible anodic wave at -1.00

V. This irreversible redox system was observed in all investigated electrolytes. Comparing the CV of ZnCr-FeTSPP with a reference LDH containing no porphyrin (ZnCr-NO3, Inset Fig. 7), one can assume that these peaks can be associated with the presence of Zn 2+ in the LDH matrix [35][36][37]. It should be noted that the position and intensity of the anodic peak depend strongly on the presence of CO2, and then on the pH of the solution. what was performed for porphyrin in solution. Unfortunately, at these applied potentials the catalytic currents were too low and do not provide an efficient catalytic process. At a more cathodic potential (E app = -1.60 V) with a ZnCr-FeTSPPCPE electrode, there is no CO formation and only H 2 is detected (FY = 75%; Table 1). Using a LDH containing no Feporphyrin (ZnCr-NO3), we obtain the same faradaic yield of H2, with low efficiency (Table 1), in line with the CVs shown in figure 7 indicating that at -1.6 V the current is dominated by the redox activity of the LDH matrix. These results show that the catalytic electrochemical process takes place mainly on the ZnCr-based LDH part of the hybrid material. Indeed, the very slow apparent diffusion coefficient (D app ) of the charge transport required for activation of FeTSPP would only make a very tiny amount of CO2ERR catalyst available. In order to prevent the role of Zn that we thought was harmful in the LDH hybrid material for catalysis of the CO2ERR (see above), MgAl-FeTSPP was prepared and its electrochemical behavior was studied in Na2SO4 (Fig. 8). In this case, the MgAl-based LDH matrix appears electrochemically inactive but it is likely to be more unstable under CO2 due to the acidic pH conditions [START_REF] Forano | Chapter 14.1 -Layered Double Hydroxides (LDH)[END_REF]. With MgAl-FeTSPP|GCE under Ar (curve a), two reversible redox couples appear at E1/2 = -0.46 and -1.14V vs. SCE that could correspond to the Fe III/II and Fe II/I redox systems. However contrary to what has been observed for FeTSPP in ZnCr-LDH, these peaks appear even under a basic condition (pH 8.6) and their potentials are shifted towards more cathodic values. This suggests that the Fe-porphyrin environment is different in both types of hybrid LDH materials, as confirmed with the position of the Soret band (Fig. S5 and Table S1).

FeTSPP is more favorable to aggregate when it is intercalated in ZnCr-LDH (Fig. S4) than in Mg2Al-LDH host structure. These results may be related to the highly ordered ZnCr hydroxide layer leading to structural constraint accompanying FeTSPP intercalation [8,38]. Under CO2 saturated atmosphere (Fig. 8, curve b), these two reversible peaks disappear to give way to two reduction waves that start at -1.30 V and -1.40 V/SCE. The cathodic currents are in the same range than those observed with ZnCr-LDH and significantly higher than that obtained with Mg2Al-NO3|GCE (Fig. 8, curve c). During the return scan, an anodic peak appears at a potential of -0.32 V.

In order to know the activity of this new Zn free hybrid material deposited on CPE, an electrolysis was conducted in the same experimental conditions than with ZnCr-FeTSPP at -1.60 V (Table 1). With a MgAl-FeTSPP|CPE electrode the major product detected is also H2

(FY = 97%), confirming the poor catalytic behavior for CO2ERR of immobilized FeTSPP when it is intercalated in the LDH materials, and also the non-innocent role of the LDH matrices and/or FeTSPP towards HER, the competitive CO2ERR reaction in aqueous electrolytes.

Conclusion

An anionic iron-porphyrin (FeTSPP) was intercalated between ZnCr-LDH and Zn-LSH layers using a coprecipitation method at constant pH. Structural and UV-Vis spectrometric characterizations show the intercalation of the guest molecule as an oxo-bridged diron(III) complex with a perpendicular arrangement of the porphyrin ring with respect to the hydroxide layers. While a small contribution of monomers (<1%) can be taken into account in the electrochemical responses of ZnCr-FeTSPP at pH 4.5 (0.1 M Na2SO4), the electrocatalytic properties of this hybrid material for CO2 electroreduction reaction was investigated for the first time, showing that the major product detected was H2 which results from the competitive HER. This study of hybrid catalytic materials illustrates the problematic and the complexity of an attractive approach for the development of innovative solid hybrid catalysts based on LDH and LSH for CO2ERR which is challenging due to the negative potential required to drive this reaction. It reveals the main drawbacks of the iron porphyrin immobilization in various LDH on its catalytic activity towards CO2ERR. In conclusion, it appears essential to immobilise molecular catalysts that are very efficient for CO2ERR, to choose a host matrix with an open structure that is favourable to the diffusion of ions and electrons and does not have competitive catalytic properties such as HER. This is the challenge we will face and we want to address by continuing this project, by developing other materials in that direction.

platforms of ICCF and IPCMS are acknowledged for access to the SEM and X-Ray diffractometers.

  the hybrid materials were measured using a Thermo Scientific CHNS/O FlashSmart. Intercalated FeTSPP was characterized by UV-Vis using Shimadzu v-2400 spectrophotometer. Thin films of ZnCr-FeTSPP and Zn-FeTSPP, prepared on ITO glass plates following the same procedure as used to prepare thin films on GCE and CPE, were analysed by transmittance under dried condition and in the presence of electrolyte solutions. The morphologies of the powders mounted on conductive carbon adhesive tabs and the films deposited on GCE or CPE were investigated with scanning electron microscopy (SEM) using a Zeiss Supra 55 FEG-VP Field-Emission Scanning Electron Microscope operating at 3 kV.Cyclic voltammetry experiments were carried out with a BioLogic (SP-150) potentiostat using a single-compartment three-electrode cell (30 mL). Electrode potentials were reported with respect to a saturated calomel electrode reference electrode (SCE); a Pt wire was used as counter electrode. The working electrode was the ZnCr-FeTSPPGCE. Each sample electrode was prepared in duplicate and analysed in CV for 5 cycles to obtain a stable signal. Various electrolytes, namely KHCO3, LiClO4, NaClO4, KClO4, H3PO4/KH2PO4 buffer (PBS) and Na2SO4, under controlled atmospheres (Ar or CO2) and controlled pH were used. Controlled potential electrolyses were performed in a homemade three electrode glass electrochemical cell using a potentiostat/galvanostat ModulLab XM equipped with an external HV 100 power booster (Solartron Analytical from Ametek Scientific Instruments). Aqueous solution of 0.1 M Na2SO4 was used as electrolyte (volume of catholyte: 30 mL; volume of gas: 158 mL). The ZnCr-FeTSPPCPE were used as the working electrode, only the modified surface (A = 2 cm 2 ) was immersed in the electrolyte. An Ag/AgCl in 3 M KCl reference electrode (Metrohm), connected to the catholyte by a Luggin capillary filled with electrolyte, was used. To convert a potential vs. Ag/AgCl to a potential vs. SCE 20 mV must be added. The counter electrode was a platinum plate connected to the solution by a frit-bridge containing the electrolyte. The aqueous electrolyte solution was bubbled at room temperature successively

Figure 1 .

 1 Figure 1. XRD patterns a) ZnCr-FeTSPP and b) Zn-FeTSPP

  shows the absorption spectra of ZnCr-FeTSPP, Zn-FeTSPP and ZnCr-NO3, prepared as thin films on ITO plates. The absorption band at 335 nm corresponds to the absorption of the LDH host matrix. For ZnCr-FeTSPP|ITO, the Soret band is centred at 422 nm and Q bands are situated at 578 and 622 nm. For Zn-FeTSPP|ITO the Soret band is situated at 414 nm. Owing to the coprecipitation pH values used in the present study, namely pH 6.25 for ZnCr-FeTSPP and 7.30 for Zn-FeTSPP, we can assume that the predominant intercalated FeTSPP species are oxo-bridged dimers O(FeTSPP)2, corresponding to a Soret band red shift. This hypothesis is confirmed by the presence of a vibration band at 874 cm -1 on the FTIR spectrum corresponding to the Fe-O-Fe antisymmetric stretching[START_REF] Fleischer | [END_REF] (Fig.S1).

Figure 2 .

 2 Figure 2. UV-Vis spectra of dried thin films of (a) ZnCr-FeTSPP|ITO, (b) Zn-FeTSPP|/ITO, (c) ZnCr-NO3|ITO, (d) bare ITO.

Figure 3 .

 3 Figure 3. SEM images of hybrid powders of ZnCr-FeTSPP (a) and Zn-FeTSPP (b), and of the thin films coated on GCE (c and d) and on CPE (e and f) for ZnCr-FeTSPP and Zn-FeTSPP, respectively.

  of electrolyte and hence the catalyst environment. In the context of the present work, the questions are: (i) what is the catalytic behavior of FeTSPP when it is intercalated in the LDH material and (ii) what is the role of the ZnCr-LDH matrix in the hybrid catalyst material on the electrochemical reaction?

Figure 4 .

 4 Figure 4. Cyclic voltammograms of 0.5 mM FeTSPP (GCE, v = 50 mV s -1 ) in different aqueous electrolytes a) 0.1 M KHCO3 under Ar at pH 8.6 (black curve), b) 0.1 M KHCO3 under CO2 at pH 6.8 (red curve) and c) 0.1 M Na2SO4 under CO2 at pH 4.5 (blue curve). Inset shows a zoom of a and c curves between -1.60 and 0 V.

Figure 5 .

 5 Figure 5. Cyclic voltammograms of ZnCr-FeTSPP|GCE (5 th cycle) A) in 0.1 M LiClO4 a) under Ar, b) under CO2; B) under CO2 in a) 0.1 M LiClO4, b) NaClO4, c) KClO4, d) Na2SO4 (pH 4.5, v = 50 mV s -1 ).

Figure 6 . 5 ( 10 ≤

 6510 Figure 6. Cyclic voltammograms of ZnCr-FeTSPP|GCE in 0.1 M Na2SO4 under CO2 at pH 4.5 (10 ≤ v ≤ 100 mV s -1 ). Insert shows the evolution of Ipa and Ipc as function of v 1/2 .

Figure 7 .

 7 Figure 7. Cyclic voltammograms of ZnCr-FeTSPPGCE, in 0.1 M Na2SO4 under a) Ar pH 8.6, b) CO2 pH 4.5 (5 th cycle, v = 50 mV s -1 ). Inset: ZnCr-NO3GCE in the same condition

Figure 8 .

 8 Figure 8. Cyclic voltammograms of MgAl-FeTSPP|GCE in 0.1 M Na2SO4 under a) Ar pH 8.6, b) CO2 pH 4.5 and c) MgAl-NO3|GCE in 0.1 M Na2SO4 under CO2 (v = 50 mV s -1 ). Inset shows a zoom of a and b curves between -1.40 and 0 V.

Table 1 .

 1 Electrolysis

	data obtained with LDH|CPE modified electrodes in 0.1 M Na2SO4 under
	CO2 atmosphere (pH 4.5), E app =-1.60 V.
	LDH	ZnCr-FeTSPP	ZnCr-NO3	MgAl-FeTSPP
	Current (mA)	6.2	2	3
	FY CO (%)	<1	<1	3
	FY H2 (%)	<75	<73	97

Acknowledgements

The authors would like to thank the French ANR (CALHYCO2 -ANR-19-C05-0015) for their financial support, in particular AT, MG and JA-A for their doctoral fellowship or post-doctoral grant. We would like to thank also Pr. Claude Forano (ICCF) for his help in chemical analysis and Florian Molton (DCM) for his technical assistance. Technical

Funding This work was supported by the French National Research Agency (CALHYCO2 -ANR-19-C05-0015)

Availability of supporting data: All data generated or analyzed during this study are included in this article and in the supplementary material.

Supplementary Information

The online version contains supplementary material available at….

Declarations

Ethical Approval and Consent to participate not applicable

Human Ethics not applicable

Consent for publication not applicable

Competing interests The authors declare no competing interests

Author's Contributions All authors contributed equally to the study conception, design and data analysis. Material preparation and data collection were performed by Ali Tarhini, Juan Aguirre-Araque and Mélanie Guyot. The first draft of the manuscript was written by Christine Mousty and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript submitted to this journal.

Authors' information Juan Aguirre-Araque (ORCID 0000-0002-3442-5248); Cyrille Costentin (ORCID 0000-0002-7098-3132); Guillaume Rogez (ORCID 0000-0001-9006-7273); Sylvie Chardon-Noblat (ORCID 0000-0003-0273-1571); Vanessa Prevot (ORCID 0000-0001-6250-7550); Christine Mousty (ORCID 000-0002-3003-2092).