Lucas M Luza

Cezar A Rigo

Elder D Tramontin

Victor Martins
email: victor.martins@esa.int

Sara Vega Martínez

Leonardo K Slongo

Laio O Seman
email: laioseman@gmail.com

Luigi Dilillo
email: dilillo@lirmm.fr

Eduardo A Bezerra
email: eduardo.bezerra@ufsc.br

Enabling deep-space CubeSat missions through state-of-the-art radiation-hardened technologies

Keywords: CubeSat, radiation-hardened, reconfiguration, space-packet-protocol, printed-circuit-board

This work presents a radiation-hardened reconfigurable hardware based platform to be used in deep-space cubesat missions. The platform has been designed for the in-orbit validation of two new technologies: a new radiation-hardened Field-Programmable Gate Array (FPGA) developed in France; and a CCSDS/ECSS IP Core for telemetry (TM) and telecommand (TC) designed at UFSC, Brazil. The printed circuit board (PCB) was designed following the European Space Agency (ESA) space product standards. It has a layered structure that mitigates the effects of radiation and electromagnetic interference on the components signals. All signal layers lie between power and ground planes, avoiding tracks on the outer layers. In addition, all components were selected to tolerate wide temperature variation and some even tolerate radiation -as the microcontroller (MCU) (MSP430FR6989) with ferroelectric program memory and the rad-hard FPGA (NX1H35S-BG625PR). An important architecture feature is to allow changing the hardware configuration of the FPGA through remote uplink of its Bitstream. The MCU is responsible for updating the configuration bitstream stored in a flash nonvolatile memory. An aditional bitstream is also stored in the memory, as a fail-safe technique. There are three bitstream copies stored, and a voting scheme is used to ensure the data integrity, as the flash memory is susceptible to Single Event Effects (SEE). The MCU module is responsible for the housekeeping and update management of the rad-hard FPGA. The implementation stored in the FPGA includes not only the TC/TM IP core, but also an abstract execution graph, in the form of a state machine, emulating the basic functionalities of an on-board computer (OBC). The communications module handles TC and TM data and it is an interface between the radio transceiver and the emulated OBC. The emulated OBC is based on the ECSS Telemetry & Telecommand Packet Utilization Standard (PUS), and it performs the validation of the routed telecommand received, and the packaging of the telemetry data acquired by the available sensors. The proposed architecture allows testing all the implementations, exercising its functionalities, and also the module's integration as a payload of the FloripaSat mission.

Introduction

In the last decade there has been a significant increase of interest in small satellites, either by space agencies, industries or academia [START_REF] Tummala | An Overview of Cube-Satellite Propulsion Technologies and Trends[END_REF]. The low cost, possibility of using commercial off-the-shelf components (COTS), validating technologies and doing science are the main factors that lead to this increase in interest [START_REF] Sandau | Small satellites for global coverage: Potential and limits[END_REF].

An emerging technology to be used also in these small satellites is reconfigurable computing and adaptive hardware. The great attraction is the possibility of implementing hardware and system-wide functional changes, transmitted remotely [START_REF] Carmichael | SEU Mitigation Techniques for Virtex FPGAs in Space Applications[END_REF]. That is, reconfiguring the satellite with updates coming from the ground station. Usually, the component underlying this functionality is the Field Programmable Gate Array (FPGA).

At the same time, protons and electrons trapped in Earth's radiation belts, as well as cosmic rays, represent a real hazard to electronics, which must operate reliably in the natural space environment. Single-event effects (SEE) can lead to a sudden failure of the device or system, and the effects of total dose (TID) of radiation can reduce the satellite's life time [START_REF] Fleetwood | An overview of radiation effects on electronics in the space telecommunications environment[END_REF].

The disturbing effect of radiation in electronics [START_REF] Velazco | Radiation effects on embedded systems[END_REF] is well known and it has been widely studied since the loss of the Telestar satellite in 1962, due to a nuclear test at high altitude. The particles of ionizing radiation and electromagnetic radiation can cause a series of sporadic, periodic or permanent damages in circuits, which could result in the loss of the device. When a high-energy particle goes through an integrated circuit junction, extra electrons and holes pairs are created along the path due to the ionization effect, as shown in Figure 1a. These extra carriers can be captured by the sensitive node nearby in two stages, ion drift Figure 1 and ion diffusion (Figure 1c), and if the amount of charge collected exceeds the charge threshold of this node, the state of it can be altered, resulting in a SEE. It is imperative to consider these effects in all the design stages of devices or electronic systems that require robustness and safety in space applications, since this is a naturally radioactive environment. Therefore, FPGAs of high performance, high density and endured to radiation are in great demand, mainly in higher orbit, long time missions, and also for deep space exploration. NanoXplore SAS designed an FPGA, which is implemented using 65nm complementary metal-oxide-semiconductor (CMOS), with radiation protection up to 100,000 Rads and 60 MeV cm 2 mg -1 , multiple voltage level inputs and outputs, and double data rate type 2 (DDR2) memory support [START_REF]NX1H35S Datasheet[END_REF]. However this device has never been tested in orbit (In-orbit Validation, IoV).

The selected case study for the designed rad-hard platform is a telecommand (TC) and telemetry (TM) application for CubeSats, using the recommendations from the Consultative Committee for Space Data Systems (CCSDS). These recommendations have already been used in more than 900 space missions [START_REF]The Consultative Commite for Space Data Systems -The Official Web Site[END_REF]. The standardization of communications protocols for nanosatellites has the aim to remove integration barriers between space missions. On this aspect, the idea behind this case study is to bring standardization for space communications in cubesats.

The architeture, hereinafter referred to as Payload-X, is a hardware architecture implemented in a printed circuit board (PCB), designed for a radioactive environment, having as a main feature the possibility to change the hardware configuration of the FPGA through remote uplink of its Bitstream. Also, the proposed architecture aims to be used as a payload of FloripaSat, a nanosatellite under development at the Federal University of Santa Catarina (UFSC) [START_REF] Martins | The experience of designing and developing the on-board electronics of a Cubesat in Brazil[END_REF][START_REF] Villa | Others, A complete CubeSat mission: the Floripa-Sat experience[END_REF][START_REF] Slongo | The Floripa-Sat experience: mission progress and satellite's development[END_REF]. This payload will perform the IoV of the the rad-hard FPGA, and the CCSDS communications IP core. Additionally, it will use a new strategy for FPGA reconfiguration on-the-fly.

Architecture

An overview of the implemented architecture is presented in this section, and its block diagram is shown in Figure 2. It has a layered structure that mitigates the effects of radiation and electromagnetic interference on the components signals, a microcontroller (MCU) model MSP430FR6989 with ferroelectric program memory, and a radiation-hardened FPGA model NX1H35S-BG625PR.

Its componentes and respective functions are described next.

Reconfiguration and Housekeeping

Payload-X's MCU module is designated by the acronym HUMAN (Housekeeper and Update MANager), as it has 2 main purposes: manage the FPGA reconfiguration; and perform housekeeping tasks. It is a Texas Instruments MSP430FR series MCU and has an FRAM (Ferroelectric Random-Access Memory) memory to store program data. This specific technology was chosen to ensure a better tolerance against bit-flips.

While in orbit, an important feature of Payload-X is to update its operation based on a new FPGA configuration file sent from a ground station. This new configuration file (also called "bitstream") is sent split in multiple packets, where a few bytes per packet are for sequencing and error detection. HUMAN is responsible for receiving, integrity checking and storing the bitstream segments in a nonvolatile memory, as well as waiting for a "commit" telecommand to change the current configuration of the FPGA to the new one.

The non-volatile memory is a flash memory. Although it is more radiation tolerant than SRAM or DRAM memories, some bit-flips are expected [START_REF] Irom | Heavy Ion, Proton and Electron Single-Event Effect Measurements of a Commercial Samsung NAND Flash Memory[END_REF]. To ensure that data is corrected after a bit-flip occurrence, the bitstream is stored in a redundant way. There are 3 copies of the bitstream stored in different regions of the flash memory. Then, a voting scheme is used to check and correct possible errors.

Even after performing several tests, it is impossible to predict every error that could happen in orbit [START_REF] Antunes | Surviving orbit the DIY way: testing the limits your satellite can and must match, O'Reilly[END_REF]. Thus, there is a secure fallback bitstream, so in case of a critical error in the current one, HUMAN will replace the current version, by the secure (fallback) version. Therefore, a total of 6 bitstreams, in 2 versions, are stored in the flash memory: 3 for the current configuration in use; and 3 for the fallback version.

HUMAN is also responsible for managing incoming messages to Payload-X. These messages may be related to reconfiguration, such as new bitstream segments or bitstream status requests, or may be telecommands/telemetry arriving/incoming from the communication module.

When a new bitstream segment is received from the OBDH, HUMAN should check the data integrity using the CRC technique (CRC-16-CCITT). If the segment is correct, it will be stored in the flash memory. When a telecommand is received, it is stored in FRAM memory and sent to the communications module via UART. Likewise, a telemetry sent by the communications module is stored in the FRAM memory and sent to the OBDH via I 2 C.

Since there is a triple redundancy in the stored bitstreams, a HUMAN secondary activity consists of memory scanning, checking and correcting possible errors. This task is performed when nothing else is being done, such as an idle task. The HUMAN states are shown in Figure 3.

Implementation

The FPGA implementation is divided in two main blocks. The first block handles the telecommand and telemetry flow and it is used as an interface between the transceiver and the Finite State Machine (FSM) with OBDH functionalities, denominated as the Unit of Telemetry and Telecommand (UTMC).

The second block is composed of the Payload's OBDH which handles the TM and TC packets using Space Packet Protocol, characterizing the last layer of the CCSDS/ECSS protocol. In addition, it acquires data from sensors and, afterwards, it packages the acquired data. Figure 4 presents the architecture implemented in the FPGA.

The UTMC system is divided in two segments dedicated to telemetry data processing and telecommands handlings. In the TC flow, when a TC is delivered to UTMC from the UART interface, the Command Link Transfer Unity (CLTU) is decoded using a BCH algorithm that performs error detection and correction. When a Direct TC (DTC) is detected, the UTMC delivers it to a Command Pulse Distribution Unit (CPDU) layer that interprets and generates a strictly controlled time pulse in one of the The OBDH system has the architecture presented in Figure 6. All telecommands received from UTCM are verified and a report is generated by the Verify layer, in case the TC is inconsistent. The received TC is routed to its destination by the Route layer and could be delivery to Device Control, Test or Configure. The Device Control layer has two main functions, the first is to receive the sensors data, and to deliver it to the Packing layer. The second fucntion is to execute a direct telecommand. The Configure layer defines the parameters of system execution (e.g. temperature data acquisition interval) and it makes possible to change these parameters by a TC. The test layer executes test functions and generates a report on the test status.

All reports generated by this layers are dispatched to Storage and Retrieval, then, this layer forwards the full telemetry data by request or when the data limit is achieved. The Send layer uses a UART interface to communicate with the UTMC.

Board Implementation

Figure 7 shows a rendering of the developed board, with all the components and interfaces. The board was designed considering that the space environment is much more severe than the terrestrial environment, given high thermal variations coupled with low heat dissipation and high radioactive levels. Therefore, several extra precautions must be taken in the making of space PCBs. In [START_REF] Benfica | Plataforma para Testes e Qualificac ¸ão de Dispositivos Reconfiguráveis e Sistemas em Chip, Submetidos aos Efeitos Combinados da Interferência Eletromagnética e da Radiac ¸ão Ionizante[END_REF], the author developed PCBs to perform radiation effects tests on ICs. For that purpose, it was necessary to implement a PCB structure that isolated from the radioactive effects all circuits except the IC under test. Based on the IEC 62.132-1 standard all layers of the PCB were inserted between layers of VCC and or GND, minimizing routing tracks in the top or bottom layer. Therefore, a similar structure was applied in Payload-X's board layers.

In addition, due to the high thermal variability, great attention was given to the differences in the thermal expansion coefficient of the various components and materials used in the board. Heat dissipation was also considered, as it occurs only by conduction losses and radiation. Also, since electronic space application devices will inevitably be subjected to launch, then soldering, component placement and mechanical fastening points must be properly done to withstand intense vibrations.

Beyond all that, the PCB was designed following the European Space Agency (ESA) design rules for printed circuit boards ECSS-Q-ST-70-12C [START_REF]ECSS-Q-ST-70-12C -Design rules for printed circuit boards[END_REF].

Conclusion

This paper presented a radiation-hardened reconfigurable hardware architecture to implement a telecommand and telemetry module in CubeSats, called Payload-X. The developed architecture consists of a PCB board designed to be radiation-hardened, an MCU to manage the reconfiguration process, and a radiation-hardned FPGA responsible for implementing the telecommand and telemetry module.

The architecture will be used for the in-orbit validation of two new technologies: the new BRAVE FPGA developed in France; and an IP Core for telemetry and telecommand following the CCSDS standard. This process will be handled along the FloripaSat mission of the Federal University of Santa Catarina, in the form of a payload. The FloripaSat-I consists of a 1U CubeSat with five functional modules: EPS; OBDH; TT&C; battery and interface board, besides the payload modules where the Payload-X is integrated. FloripaSat-I will be lunched as a piggyback of the CBERS-4A satellite, using the Chinese Long March 4B rocket.

Before being placed in orbit, the developed PCB board needs to be further tested in order to verify its radiation-hardened capabilities.

Figure 1 :

 1 Figure 1: Radiation effect in transistors structure [6].

Figure 2 :

 2 Figure 2: Interconnection diagram.

Figure 3 :

 3 Figure 3: HUMAN state diagram.

FPGAFigure 4 :

 4 Figure 4: FPGA implementation top level diagram.

Figure 5 Figure 5 :

 55 Figure 5: UTMC top level diagram.

Figure 6 :

 6 Figure 6: Payload-X OBDH top level diagram.

Figure 7 :

 7 Figure 7: PCB 3D rendering.

Acknowledgments

The authors thank for the support of CAPES, -the Brazilian Federal Agency for Support and Evaluation of Graduate Education. This work was partially supported by CNPq/Brazil grant number 151390/2018-5.


Douglas Melo

Cesar Zeferino
email: zeferino@univali.br

Antonio Ramos
email: antonio.ramos@usn.no

Luigi Dilillo

Eduardo Bezerra
email: eduardo.bezerra@eel.ufsc.br

IMPLEMENTATION OF FAULT TOLERANCE TECHNIQUES FOR INTEGRATED NETWORK INTERFACES

Keywords: Networks-on-Chip, Network Interface, Fault Tolerance

The increasing demand for safety and mission-critical computational systems to operate in hostile environments, along with the component miniaturization for such systems, have triggered the need for developing fault tolerance techniques to mitigate the incidence of system failures and increase reliability. Communication architectures used in computers for aerospace applications are made up of a growing number of processing cores. Some approaches that are proposed in the literature do not meet the communication requirements of future on-board computers composed of multiple cores. Networks-on-Chip are the successors of the bus for multicore interconnection, integrating cores by the means of Network Interfaces. This work discusses the implementation and evaluates the performance of the Hamming encoding, the Triple Modular Redundancy (TMR), and temporal redundancy into the eXtensible Interface for Routing Unit (XIRU) Network Interface. Five scenarios are considered based on the combination of these techniques. Results show that the TMR in FIFO buffers is the most costly technique in terms of area usage, the Hamming code has the highest power dissipation, while the temporal redundancy has the lower operation frequency. Finally, a modified version of XIRU to integrate cores into Network-on-Chip systems with reliability requirements is devised. We intend to use the interface to integrate the cores of future cubesats developed in the FloripaSat project.

Introduction

The demand for real-time embedded computing has been increasing significantly in recent years. The design of such systems is always subject to a specific set of requirements that includes performance, real-time execution capability, response time, with reduced size and costs [START_REF] Vahid | Embedded system design: a unified hardware/software introduction[END_REF]. Modern embedded systems usually require processors with increased performance, while keeping physical dimensions and power dissipation as low as possible.

Recent advances in integrated circuits manufacturing technology allowed the construction of complete computing systems in a single chip, known as Systems-on-Chip (SoCs). The components of a SoC can be designed independently of each other and made available by manufacturers in the form of IP (Intellectual Property) cores. In SoCs with few cores, components are interconnected by shared buses. However, this communication architecture does not meet the requirements of SoCs composed of several dozen cores, which demand parallelism and performance scalability [START_REF] Zeferino | Socin: a parametric and scalable network-on-chip[END_REF].

A solution to overcome the bus limitations is represented by NoCs (Networks-on-Chip), scalable and reusable architectures that provide parallelism in communication. In SoCs based on NoCs, each core of the system is connected to one router, which is connected to neighboring routers. However, a Network Interface (NI) between cores and routers is necessary for an effective communication [START_REF] Micheli | Networks on chips: technology and tools[END_REF].

Miniaturization of the circuits and the increasing operating frequency result in a higher incidence of faults in SoCs [START_REF] Bertozzi ; Micheli | The data-link layer in noc design[END_REF]. The occurrence of faults can be a serious problem, especially in the presence of external interference. For such critical cases, SoC designers have to use fault tolerance techniques to ensure proper operation of these systems.

In general, fault tolerance techniques are based on redundancy and can be classified into spatial, temporal, and information. Spatial redundancy consists of component replication and the insertion of a voter that compares the outputs of these components and chooses the value on a majority principle. In temporal redundancy, a component performs its operation more than once and a voter compares the results of those executions. Information redundancy consists of adding bits to the message to detect and correct possible errors. Therefore, the implementation of fault tolerance mechanisms results in some overhead, whether in performance, silicon area, or dissipated power [START_REF] Sorin | Fault tolerant computer architecture[END_REF].

Several cores for SoCs employ fault tolerance techniques in their design. Examples are the soft-core LEON3 [START_REF] Gaisler | Leon3 multiprocessing cpu core[END_REF], commonly used in space applications, and the works of [START_REF] Veiga | Implementation of techniques for fault tolerance in a network-on-chip[END_REF] and [START_REF] Pereira | Mechanisms to provide fault tolerance to a network-on-chip[END_REF] on System-on-Chip Interconnection Network (SoCIN) [START_REF] Zeferino | Socin: a parametric and scalable network-on-chip[END_REF]. SoCIN uses the XIRU (eXtensible Interface for Routing Unit) [START_REF] Melo | Xiru: Interface de rede extensível para integrac ¸ão de núcleos a uma rede-em-chip[END_REF] to integrate cores based on the Avalon bus. In [START_REF] Gaya | Amba-ahb network interface for core interconnection in a network-on-chip[END_REF], the authors added support for the AMBA-AHB bus to XIRU, without applying any fault tolerance technique.

This work aims at implementing and evaluating the use of fault tolerance techniques on XIRU. We have implemented Hamming encoding, the TMR (Triple Modular Redundancy), and temporal redundancy techniques, as well as combinations of those. We observed a significant area overhead when combining TMR and the Hamming encoding technique. The combination of techniques presents the highest fault coverage. A significant reduction in operating frequency was observed using temporal redundancy, while no significant changes were noticed in terms of power dissipation.

The remainder of this paper is organized as follows. Section 2 presents a brief background on Network Interfaces, Section 3 describes the proposed techniques, while Section 4 discusses the performance evaluation results in various scenarios. Finally, Section 5 presents conclusions and suggestions for future works.

Background

Network Interface (NI) is the component that provides communication services and translates protocols between core and router. An NI comprises a front-end and a back-end [START_REF] Bertozzi ; Micheli | The data-link layer in noc design[END_REF], as shown in Fig. 1. The front-end can be represented by the session layer, whereas the lower layers of the OSI (Open System Interconnection) model represent the back-end. The front-end communicates with the core and it is responsible for facilitating reuse across platforms owing to its standardized point-to-point protocol. Conversely, the back-end communicates with the router and provides high-level communication services (session layer), reliable data transfer (transport layer), packaging and routing (network layer), error detection (link layer), and resolution of physical problems (physical layer) [START_REF] Micheli | Networks on chips: technology and tools[END_REF].

Development

In this work, we implement and add fault tolerance components to the XIRU Network Interface (Fig. 2). We used VHDL for hardware description on the Intel Quartus II (version 13.0sp1), the Mentor Graphics ModelSim (version 10.1d) for simulation, and the Altera DE2 kit with the EP2C35F672C6 FPGA for prototyping. We structured this development into five incremental scenarios, as described below.

Scenario 1: Hamming encoding

The first scenario consists of integrating the Hamming encoder and decoder at the edge of the Network layer, as shown in Fig. 3. Fault tolerance occurs in end-to-end communication, i.e., encoding packets going out to the router, and decoding and correcting packets arriving from the router. The input of the Hamming encoder is 34 bits long, while the output has 41 bits.

The Hamming code detects up to two errors and can correct a single one (SECDED -Single Error Correction, Double Error Detection). In an error-free scenario, the result of the Hamming calculation and the parity calculation is equal to 0. In the case of a single error, both Hamming and parity result in a different value, indicating an error. In the case of a double error, the Hamming calculation results in a value other than zero, while the parity bit is inverted again.

Scenario 2: Triple Modular Redundancy (TMR) on controllers

The second scenario is the application of TMR on the XIRU controllers. We triplicated the Flow Controller (FC) components of the Network layer, and the controllers of the Generic layer, as shown in Fig. 4. We have also added a voter for each replicated component.

Scenario 3: TMR on FIFOs

In this scenario, we applied TMR on the XIRU memorization components (FIFOs), as shown in Fig. 5. These FIFOs are in the Network layer, and are the only components that have been modified for this scenario.

Scenario 4: Hamming and TMR

This scenario applies end-to-end protection using the Hamming encoding and TMR in the controllers and memorization components, as shown in Fig. 6.

Scenario 5: Temporal redundancy on controllers

This scenario applies temporal redundancy on the controllers of the Generic layer. The execution is processed three times and, in the end, a voter compares the results of the executions and sets the output signal. Fig. 7 represents the technique that have been applied to the XIRU network interface.

Results

After synthesis and verification, we have analyzed and compared the different implementations with respect to use of FPGA resources, i.e, look-up tables (LUTs) and flip-flops (FFs), and performance in terms of maximum operation frequency and average power dissipation. Table I shows the obtained results. As can be observed, Scenario 4 is the one with highest resource utilization. This is expected since it implements the Hamming encoding and TMR on the controllers and on the FIFOs. Indeed, there was an increase of 170.82% of LUTs in the master unit against 135.63% in the slave unit in comparison to the original implementation. Concerning the flip-flops, the overhead of this scenario was 143.60% in the master unit against 137.95% in the slave unit. The lowest performance was verified in Scenario 5, with a decrease of 34.40% of the maximum operating frequency in the master unit and 37.30% reduction in the slave unit. Moreover, the addition of new circuits to the system increases the critical path, thereby causing a degradation in the maximum frequency of operation. Finally, no significant variation in terms of dissipated power was observed across the different scenarios, presenting an average consumption of 135 mW.

There are some differences among the scenarios related to fault coverage rate. Hamming code (Fig. 3) works as an end-to-end solution, so it can't detect nor correct any fault in the NI infrastructure. The TMR on controllers (Fig. 4) and TMR on FIFOs (Fig. 5) can mask single event and also single permanent faults. The combination of the former techniques (Fig. 6) protects control and memorization structures. In contrast, the temporal redundancy (Fig. 7) protects from transient faults but is ineffective against permanent ones.

Conclusion

This work discusses the application of fault tolerance techniques in a network interface for use in reliable systems based on NoCs. As expected, the use of redundancy techniques resulted in an increase in the utilization of logical resources and in the performance degradation, especially in the scenario combining the Hamming encoding and TMR.

We are currently computing the fault coverage and evaluating the communication latency and energy consumption in each scenario. As future work we intended to adapt the network interface for the next generation of FloripaSat platform [START_REF] Villa | A complete cubesat mission: the floripa-sat experience[END_REF], using a SoC in which all components (processor, network interface, and routers) are protected by reliability techniques.

Figure 1 :

 1 Figure 1: Interface [4].

Figure 2 :

 2 Figure 2: XIRU Network Interface [9].

Figure 3 :

 3 Figure 3: Scenario 1: Hamming encoding.

Figure 4 :

 4 Figure 4: Scenario 2: TMR on controllers.

Figure 5 :

 5 Figure 5: Scenario 3: TMR on FIFOs.

Figure 6 :

 6 Figure 6: Scenario 4: Hamming and TMR.

Figure 7 :

 7 Figure 7: Scenario 5: Temporal redundancy on controllers.

Table 1 :

 1 Synthesis Results

	Scenario Component LUTs FFs Fmax(MHz)
	Original	Master Slave	281 407	422 448	212.04 221.73
	1	Master Slave	287 410	422 448	212.27 216.26
	2	Master Slave	327 517	448 486	178.44 187.06
	3	Master Slave	701 823	994 1020	195.96 202.10
	4	Master Slave	761 959	1028 1066	165.84 192.34
	5	Master Slave	311 503	448 486	139.10 139.02

Acknowledgments

The authors would like to thank the Coordenac ¸ão de Aperfeic ¸oamento de Pessoal de Nível Superior -Brasil (CAPES), the University of Vale do Itajaí (UNIVALI), and the Norwegian Centre for International Cooperation in Education (SIU), for supporting this work.


Yuri Bedjanian
email: yuri.bedjanian@cnrs-orleans.fr

Rate Constants for the Reactions of F Atoms with H 2 and D 2 over the Temperature Range 220-960 K

Keywords: F, hydrogen, rate coefficient, temperature dependence, KIE

The kinetics of the reactions of F atoms with hydrogen and deuterium has been studied in a discharge flow reactor combined with an electron impact ionization quadrupole mass spectrometer at nearly 2 Torr total pressure of helium and in the temperature range 220 -960 K. The rate constant of the reaction F + H 2  HF + H (1) was determined using both relative rate method (using reaction F + Br 2 as a reference) and absolute measurements, monitoring the kinetics of F atom consumption in excess of H 2 : k 1 = (1.24 ± 0.09)10 -10 exp(-(507 ± 23)/T) cm 3 molecule -1 s -1 . The rate constant of the reaction F + D 2  DF + D (2) was measured under pseudo-first order conditions in excess of D 2 over F atoms: k 2 = (8.47± 0.42)10 -11 exp(-(670 ± 16)/T) cm 3 molecule -1 s -1 (the uncertainties on both k 1 and k 2 represent precision at the 2 level, the estimated total uncertainty on the rate constants being 15% at all temperatures). The kinetic isotope effect measured independently, k 1 /k 2 = (1.58 ± 0.05)×exp((131 ± 2)/T), was found to be in excellent agreement (within 7% in the temperature range of the work, T = 220-960 K) with the ratio of k 1 to k 2 calculated with the Arrhenius expressions for k 1 and k 2 determined in the study. The kinetic data from the present work are discussed in comparison with previous measurements and theoretical calculations.

INTRODUCTION

Reaction of F atoms with H 2 F + H 2  HF + H (1) is of practical and theoretical interest and was extensively studied over the past few decades. The kinetics of this reaction was explored in multiple studies, at high temperatures (up to 765 K), [START_REF] Persky | The kinetics of the reaction F + H 2 → HF + H. A cri cal review of literature data[END_REF] in relation with problematic of chemical lasers based on the vibrationally excited HF formed in the reaction, and at very low temperatures (down to 10 K), in relation to the chemistry in interstellar environments where reaction (1) is considered as the only source of HF. [START_REF] Tizniti | The rate of the F + H 2 reaction at very low temperatures[END_REF] In parallel, the F + H 2 reaction has been the subject of numerous dynamic and theoretical investigations (e.g. review 3 and refs therein). Indeed, since 1972, when the first ab initio potential energy surface (PES) was created, [START_REF] Bender | Potential energy surface including electron correlation for the chemical F + H 2 → FH + H I. Preliminary surface[END_REF] about two dozen new or modified PES have appeared. [START_REF] Sun | Development of the potential energy surface and current stage of the quantum dynamics studies of the F + H 2 /HD reaction[END_REF] Theoretical research of the F + H 2 reaction has made a progress, and at present the theory seems to reproduce the experimental kinetic and dynamic observations quite well. [START_REF] Sun | Development of the potential energy surface and current stage of the quantum dynamics studies of the F + H 2 /HD reaction[END_REF] Accurate experimental determination of the Arrhenius parameters for the rate constants of the reactions of F atom with H 2 and its isotope D 2 F + D 2  DF + D (2) in an extended temperature range is of importance for theory, since they carry information on the energetics of the reaction and the extent of the tunneling effect, which are important for further refinement of PES. However, despite the interest to the reactions of F atoms with H 2 and D 2 , and a large number of dedicated studies, kinetic database for these reactions seems incomplete and unsatisfactory compared to the current high level of the theoretical calculations. For the F + H 2 reaction, only two [START_REF] Heidner | Absolute rate coefficients for F+H 2 and F+D 2 at T=295-765 K[END_REF][START_REF] Ioffe | Non-Arrhenius behavior of the F+H 2 reaction rate at 293-700 K[END_REF] of the four most extended temperaturedependent studies [START_REF] Heidner | Absolute rate coefficients for F+H 2 and F+D 2 at T=295-765 K[END_REF][START_REF] Ioffe | Non-Arrhenius behavior of the F+H 2 reaction rate at 293-700 K[END_REF][START_REF] Stevens | Kinetic and mechanistic investigations of F + H 2 O/D 2 O and F + H 2 /D 2 over the temperature range 240-373 K[END_REF][START_REF] Wurzberg | The temperature dependence of absolute rate constants for the F+H 2 and F+D 2 reactions[END_REF] were carried out at temperatures above 376 K, and, in addition, the data on the rate constant from one of them 6 are widely scattered. For reaction F+ D 2 , only one study [START_REF] Heidner | Absolute rate coefficients for F+H 2 and F+D 2 at T=295-765 K[END_REF] was realized at temperatures above 373 K and the results of three available relatively extended temperature-dependent studies differ by a factor of 1.3-1.5 at temperatures between 230 and 360 K. [START_REF] Heidner | Absolute rate coefficients for F+H 2 and F+D 2 at T=295-765 K[END_REF][START_REF] Stevens | Kinetic and mechanistic investigations of F + H 2 O/D 2 O and F + H 2 /D 2 over the temperature range 240-373 K[END_REF][START_REF] Wurzberg | The temperature dependence of absolute rate constants for the F+H 2 and F+D 2 reactions[END_REF] As a result of the uncertainties in the values of the rate constants for reactions (1) and (2) (k 1 and k 2 , respectively), the kinetic isotope effect (KIE) calculated as k 1 /k 2 varies by a factor of up to 1.7 depending on temperature. Above analysis is in line with the conclusion of the most recent critical review of the kinetic data for reactions (1) and ( 2) by Persky and Kornweitz 1 that "additional careful experimental studies of the kinetics of the F + H 2 system would be very useful in order to support our evaluations or to update them."

This paper presents the results of an experimental study of the reactions of F atom with H 2 and D 2 , including measurements of the rate constants and an independent determination of the kinetic isotope effect (k 1 /k 2 ratio) as a function of temperature in an extended temperature range, T = 220 -960 K.

EXPERIMENTAL

Kinetic measurements have been conducted at nearly 2 Torr total pressure of Helium using a conventional fast-flow reactor combined with a molecular beam sampling electron-impact ionization mass spectrometer operated at 25-30 eV energy. [START_REF] Bedjanian | Temperature-dependent rate constant for the reaction of F atoms with HNO 3[END_REF][START_REF] Bedjanian | Reaction F + C 2 H 4 : rate constant and yields of the reaction products as a function of temperature over 298-950 k[END_REF][START_REF] Bedjanian | Kinetic and mechanistic study of the F atom reaction with nitrous acid[END_REF] Depending on the temperature range two different flow reactors were used. High temperature reactor, used at T = 299 -960 K, consisted of a Quartz tube (45 cm length and 2.5 cm i.d.) with an electrical heater and water-cooled attachments (Figure S1a, Supporting Information (SI)). [START_REF] Morin | Experimental study of the reactions of oh radicals with propane, n-pentane, and n-heptane over a wide temperature range[END_REF] Low temperature reactor (Figure S1b, SI), used at T = 220 -325 K, consisted of a Pyrex tube (45 cm length and 2.4 cm i.d.) surrounded by a jacket through which a thermostated ethanol was circulated. To reduce the heterogeneous loss of F atoms, the inner surface of the low temperature reactor was coated with Halocarbon wax.

Fluorine atoms were generated from the microwave discharge in F 2 /He mixtures in a ceramic (Al 2 O 3 ) tube (Figures S1a -S1c), which was used to avoid potential reactions of F atoms with glass surface inside the microwave cavity. Monitoring of molecular fluorine by mass spectrometry showed that more than 95% of F 2 was dissociated in the microwave discharge. Prior to their sampling to the mass spectrometer, fluorine atoms were converted to FBr by reaction with Br 2 ([Br 2 ] = (4 -6)×10 13 molecule cm -3 , added at the end of the reactor 6 cm upstream of the sampling cone as shown in Figure S1a), F + Br 2  Br + FBr (3) k 3 = (1.28 ± 0.20)  10 -10 cm 3 molecule -1 s -1 (T = 299 -940 K), [START_REF] Bedjanian | Kinetics and products of the reactions of fluorine atoms with ClNO and Br 2 from 295 to 950 K[END_REF] and were finally detected at m/z = 98/100 (FBr + ). Reaction (3)

F + H 2  HF + H (1) F + Br 2  FBr + Br (3)
The fraction of the initial concentration of F atoms, [F] 0 , transformed to FBr in reaction 3, is:

FBr F

Rearrangement of this expression provides:

1 molecule cm -3 , the ranges of concentrations of H 2 are presented in Table 2.

The relative measurements of k 1 were carried out in an uncoated quartz reactor at three temperatures: T = 320, 370 and 575 K. The observed experimental data are shown in Figure 2. In accordance with Equation I, the slopes of the straight lines in Figure 2 provide the values of k 1 /k 3 at respective temperatures. Final values of k 1 (Table 2) were calculated with k 3 = (1.28 ± 0.20)  10 -10 cm 3 molecule -1 s -1 (T = 299 -940 K), determined in a recent study from this group. [START_REF] Bedjanian | Kinetics and products of the reactions of fluorine atoms with ClNO and Br 2 from 295 to 950 K[END_REF]

Rate Constant of Reaction (1): Comparison with Previous Data

Figure 3 summarizes the results of the current measurements of the rate constant of reaction (1) in comparison with those from previous temperature dependence studies. The multiple experimental data for k 1 at room temperature (293-300 K) [START_REF] Zhitneva | Chain interaction in reaction between chlorine monofluoride and hydrogen[END_REF][START_REF] Fasano | The infrared chemiluminescent reaction of Cl atoms with H 2 CO[END_REF][START_REF] Clyne | Reaction kinetics of ground state fluorine, F( 2 P), atoms. I. Measurement of fluorine atom concentrations and the rates of reactions F+CHF 3 and F+Cl 2 using mass spectrometry[END_REF][START_REF] Kompa | Study of some fluorine atom reactions using a chemical laser method[END_REF][START_REF] Pearson | Relative performance of a variety of NF 3+ hydrogen-donor transverse-discharge HF chemical-laser systems[END_REF][START_REF] Dodonov | Mass-spectrometric measurement of rate constant of elementary reaction between fluorine atoms and hydrogen[END_REF][START_REF] Rabideau | A study of the kinetics of the reaction between H 2 and F 2 by EPR methods[END_REF][START_REF] Clyne | Absolute rate constants for the reaction of fluorine atoms with H 2 , CH 2 Cl 2 , CH 2 ClF, CH 2 F 2 and CHCl 2[END_REF][START_REF] Goldberg | Kinetic study of the reaction of F with H 2 and CF 3 H by ESR methods[END_REF][START_REF] Preses | Infrared chemiluminescence from hydrogen halides produced in IR photodissociation[END_REF] were analyzed in previous evaluations. [START_REF] Persky | The kinetics of the reaction F + H 2 → HF + H. A cri cal review of literature data[END_REF][START_REF] Anderson | The Reaction F + H 2 → HF + H[END_REF] Persky and Kornweitz 1 considered that the most accurate results for k 1 available at that moment were those of Clyne and Hodgson, [START_REF] Clyne | Absolute rate constants for the reaction of fluorine atoms with H 2 , CH 2 Cl 2 , CH 2 ClF, CH 2 F 2 and CHCl 2[END_REF] Wurzberg and Houston, [START_REF] Wurzberg | The temperature dependence of absolute rate constants for the F+H 2 and F+D 2 reactions[END_REF] and Stevens et al., [START_REF] Stevens | Kinetic and mechanistic investigations of F + H 2 O/D 2 O and F + H 2 /D 2 over the temperature range 240-373 K[END_REF] measured by Igoshin et al. [START_REF] Igoshin | Determination of the rate constant of the chemical reaction F + H 2 (D 2 ) → HF(DF) + H(D) from the s mulated emission of the HF(DF) molecules[END_REF] at two temperatures (195 and 296 K), although considered in previous reviews as rather uncertain, [START_REF] Persky | The kinetics of the reaction F + H 2 → HF + H. A cri cal review of literature data[END_REF][START_REF] Anderson | The Reaction F + H 2 → HF + H[END_REF] and those reported by Homann et al. [START_REF] Homann | Eine methode zur erzeugung von fluoratomen in inerter atmosphäre[END_REF] (in a rather narrow temperature range 300-400 K) are also in a reasonable agreement with the present measurements. Ioffe et al. [START_REF] Ioffe | Non-Arrhenius behavior of the F+H 2 reaction rate at 293-700 K[END_REF] determined k 1 at T = 293-700 K in a discharge flow system with direct detection of fluorine atom decays in excess of H 2 by Electron Spin Resonance (ESR) method. As one can see in Figure 3, their rather scattered data differ significantly from other studies, especially at T < 500 K. The present measurements are in good agreement (within <20%) with the recommendation from the critical review of Persky and Kornweitz, 1 k 1 = (1.1 ± 0.1)10 -10 exp(-(450 ± 50)/T) cm 3 molecule -1 s -1 for T = 190-376 K (dashed blue line in Figure 3), and with that from the most recent NASA/JPL evaluation, [START_REF] Burkholder | Chemical kinetics and photochemical data for use in atmospheric studies[END_REF] k 1 = 1.410 -10 exp(-500/T) cm 3 molecule -1 s -1 (uncertainty factor of 1.2) for T = 190-765 K (dotted blue line in Figure 3).

In Figure 4, the experimental data for k 1 are shown in comparison with some theoretical calculations [START_REF] Aquilanti | Benchmark rate constants by the hyperquantization algorithm. The F+H 2 reaction for various potential energy surfaces: features of the entrance channel and of the transition state, and low temperature reactivity[END_REF][START_REF] Chen | An accurate potential energy surface for the F + H 2 → HF + H reaction by the coupled-cluster method[END_REF][START_REF] Wang | Direct" Calculation of Thermal Rate Constants for the F + H 2 → HF + F Reac on[END_REF] of the rate constant in the relevant temperature range. Looking at Figure 4

Rate Constant of Reaction (2)

The rate constant of the reaction of F atoms with D 2 was determined in an absolute way, similar to the measurements of k 1 , from the kinetics of F atom consumption ([F] 0 = (2.0 -4.0)×10 11 molecule cm -3 ) monitored in excess of D 2 (see Table 3 3.

The available for k 2 experimental data are summarized in Figure 6. The solid line in the assumption of Stevens et al. [START_REF] Stevens | Kinetic and mechanistic investigations of F + H 2 O/D 2 O and F + H 2 /D 2 over the temperature range 240-373 K[END_REF] on the possible systematic error between their data and those of both Heidner et al. [START_REF] Heidner | Absolute rate coefficients for F+H 2 and F+D 2 at T=295-765 K[END_REF] and Wurzberg and Houston. [START_REF] Wurzberg | The temperature dependence of absolute rate constants for the F+H 2 and F+D 2 reactions[END_REF] The values of k 2 reported by Igoshin et al. [START_REF] Igoshin | Determination of the rate constant of the chemical reaction F + H 2 (D 2 ) → HF(DF) + H(D) from the s mulated emission of the HF(DF) molecules[END_REF] at two temperatures, 195 and 295 K, which are significantly higher than all other data, were analyzed in the reviews of Anderson [START_REF] Anderson | The Reaction F + H 2 → HF + H[END_REF] and Persky and Kornweitz 1 and estimated to be highly uncertain. The Arrhenius expression k 2 = (1.06± 0.12) × 10 -10 exp(-635± 55/T) cm 3 molecule -1 s -1 (dashed line in Figure 6), recommended by Persky and Kornweitz 1 in a critical evaluation of the available kinetic data for reaction of fluorine atoms with D 2 for T = 190-376 K, provides the values of k 2 by a factor of 1.4-1.5 higher than those measured in the present work. The above recommendation was based on the expression for k 1 = 1.1×10 -10 exp(-450/T) cm 3 molecule -1 s -1 1 and that for the kinetic isotope effect, k 1 /k 2 = 1.04×10 -10 exp(186/T). [START_REF] Persky | Kinetic isotope effects in the reaction of fluorine atoms with molecular hydrogen. I H 2 /D 2 kinetic isotope effect[END_REF] It can be noted that k 1 /k 2 = 1.46 × 10 -10 exp(163/T), based on the Arrhenius expressions for k 1 and k 2 determined in the present work, provides the values of KIE by nearly 30% higher (at T = 220-376 K) compared with those used in the critical evaluation. To determine the kinetic isotope effect more accurately, we have carried out independent relative measurements of the k 1 to k 2 ratio described in the next section.

Kinetic Isotope Effect

In addition to the direct measurements of the rate constants k 1 and k 2 , their ratio was measured using a relative rate method. The applied procedure was similar to that employed in the relative measurements of the rate constant of the F + H 2 reaction. F atoms were titrated with a mixture of H 2 and D 2 (Figure S1c, SI) and the yield of DF was measured as a function of the [H 2 ]/[D 2 ] ratio:

F + H 2  HF + H (1) F + D 2  DF + D (2)
The fraction of the initial concentration of F atoms, [F] 0 , transformed to DF, is: 4. with conservative independent of temperature uncertainty of 15%. For the kinetic isotope effect both expression resulting from the ratio of the recommended k 1 and k 2 ,

k 1 /k 2 = 1.46×exp(163/T),
and that directly measured (leading to similar within 7% results),

k 1 /k 2 = 1.58×exp(131/T),
can be used with conservative uncertainty of 10% at all temperatures of the study.

The self-consistent kinetic data set for the reaction of F atom with H 2 and its isotope analog F + D 2 , reported in this paper, seems to represent a good experimental basis for further refinement of the theoretical models.

CONCLUSIONS

The rate constants of the reactions of F atoms with H

TABLES

  concentration of Br 2 , the second term in equation (I) is constant and k 1 /k 3 can be determined as a slope of the linear dependence of ([F] 0 /[FBr] -1) on the [H 2 ]/[Br 2 ]ratio. In the experiments, FBr was monitored in the presence of Br 2 in both H 2 -free system, corresponding to [F] 0 , and in the presence of H 2 in the reactor, corresponding to the fraction of [F] 0 reacted with Br 2 . Reaction time was around 0.02 s, [F] 0 = (0.5-1.0)×10 11 , [Br 2 ]  9×10[START_REF] Morin | Experimental study of the reactions of oh radicals with propane, n-pentane, and n-heptane over a wide temperature range[END_REF]

  and recommended k 1 = (2.43± 0.15) × 10 -11 cm 3 molecule -1 s -1 at T = 298 K, the mean value from the three studies. Concerning the results from this study, one can note an excellent agreement between absolute and relative measurements of the rate constant. Least-squares analysis of the present temperature dependent data for k 1 yields the following Arrhenius expression in the temperature range T = 220-960 K:k 1 = (1.24 ± 0.09)10 -10 exp(-(507 ± 23)/T) cm 3 molecule -1 s -1with 2 uncertainties representing the precision of the fit. Our data are in very good agreement with the previous studies of Wurzberg and Houston,[START_REF] Wurzberg | The temperature dependence of absolute rate constants for the F+H 2 and F+D 2 reactions[END_REF] and Stevens et al.,[START_REF] Stevens | Kinetic and mechanistic investigations of F + H 2 O/D 2 O and F + H 2 /D 2 over the temperature range 240-373 K[END_REF] reporting k 1 = 1.010 -10 exp(-(433 ± 50)/T) at T = 190-373 K and (1.2 ± 0.1)10 -10 exp(-(470 ± 30)/T) cm 3 molecule -1 s -1 at T = 221-376 K, respectively. In the work of Stevens et al.,[START_REF] Stevens | Kinetic and mechanistic investigations of F + H 2 O/D 2 O and F + H 2 /D 2 over the temperature range 240-373 K[END_REF] the rate constant of reaction (1) was measured in a discharge flow system under experimental conditions close to those of the present work. F atoms were detected through their chemical conversion to D atoms in reaction with D 2 , followed by D-atom detection by atomic resonance scattering. In the study of Wurzberg and Houston, 8 the reaction rate constant was derived by monitoring the chemiluminescence of the reaction product, HF, formed upon dissociation of SF 6 in the presence of H 2 . Similar method was applied in the study of Heidner et al.[START_REF] Heidner | Absolute rate coefficients for F+H 2 and F+D 2 at T=295-765 K[END_REF] who reported k 1 = (2.16 ± 0.42)10 -10 exp(-(595 ± 50)/T) cm 3 molecule -1 s -1 at T = 295-765 K. The absolute values of k 1 measured by Heidner et al.[START_REF] Heidner | Absolute rate coefficients for F+H 2 and F+D 2 at T=295-765 K[END_REF] are by a factor of 1.4-1.7 higher than the current data, and the difference increases with temperature. The values of k 1

  for the range of D 2 concentrations). Examples of F atom decays observed at different concentrations of D 2 at T = 440 K are shown in Figure S4 (SI). Typical plots of the pseudo-first-order rate constant, k 2 ' = k 2 ×[D 2 ]+k w , versus concentration of D 2 are shown in Figures 5 and S5 (SI). Diffusion corrections on k 2 ' were usually less than 10% being up to 15% in a few kinetic runs at highest temperatures of the study. All the results obtained for k 2 in the current work are shown in Table

Figure 6

 6 Figure 6 results from a least-squares analysis of the present experimental data and provides the following Arrhenius expression for k 2 : k 2 = (8.47± 0.42)10 -11 exp(-(670 ± 16)/T) cm 3 molecule -1 s -1 ,

  observed experimental data are shown in Figures 7 and S6 (SI). The final values of k 1 /k 2 at different temperatures, determined, in accordance with equation II, from the slopes of the linear dependencies in Figures 7 and S6, are given in Table

Figure 8 2 = 1 .

 821 Figure 8 summarizes the results of the previous and current temperature dependent measurements of the kinetic isotope effect for the F atom reactions with H 2 and D 2 . One can note that the experimental data from the present study obtained with two different methods, direct measurements of k 1 and k 2 (dashed black line, k 1 /k 2 = 1.46×exp(163/T) with estimated total uncertainty of 20% at all temperatures) and relative measurements of KIE (filled circles, fitted with a solid black line, k 1 /k 2 = (1.58±0.05)×exp((131±2)/T) (with 2 statistical uncertainties, total estimated uncertainty being of nearly 10%), are in excellent agreement (within 7%) in the temperature range used, T = 220 -960 K. Although KIE derived from the rate constant data of Heidner et al. (k 1 /k 2 = 2.1×exp(9/T)) 5 and Stevens et al. (k 1 /k 2 = 1.29×exp(210/T)) 7 exhibit different temperature dependence, the absolute values of k 1 /k 2from these studies deviate by less than 15% from the present results. KIE reported in the relative measurements of Grant and Root, k 1 /k 2 = (1.04±0.06)×exp((192±18)/T),[START_REF] Grant | Hydrogen abstraction reactions by atomic fluorine. III. Temperature dependence of the intermolecular kinetic isotope effect for the thermal F+H 2 reaction[END_REF] and Persky (k 1 /k 2 = (1.04±0.02)×exp((186±5)/T),[START_REF] Persky | Kinetic isotope effects in the reaction of fluorine atoms with molecular hydrogen. I H 2 /D 2 kinetic isotope effect[END_REF] are very close to each other and are by approximately 20% lower compared to the current data. Grant and Root 35 used a reactive competition between H 2 (D 2 ) and C 3 F 6 for F atoms, measuring HF(DF) yield as a function of the composition of the H 2 (D 2 ) + C 3 F 6 mixtures. In the study of Persky,[START_REF] Persky | Kinetic isotope effects in the reaction of fluorine atoms with molecular hydrogen. I H 2 /D 2 kinetic isotope effect[END_REF] carried out in a discharge flow system, KIE was determined through mass spectrometric detection of [HF] to [DF] ratio upon consumption of F atoms in competitive reactions with H 2 and D 2 . Similar approach, except for a few details, was used in the present relative measurements of KIE. Firstly, in the current work only DF was monitored and, as a result, there was no need to apply the corrections on HF signal due to formation of this compound in the microwave discharge and on the walls of the reactor and movable injector, and due to contribution of D 2 O at m/z = 20.[START_REF] Persky | Kinetic isotope effects in the reaction of fluorine atoms with molecular hydrogen. I H 2 /D 2 kinetic isotope effect[END_REF] Secondly, there was no need to measure the absolute concentrations of HF and DF (in ref.34 the sensitivities for the detection of these species by mass spectrometry were

  2 and D 2 have been measured using a discharge flow reactor combined with an electron impact ionization mass spectrometer at T = 220 -960 K: k 1 = (1.24 ± 0.09)10 -10 exp(-(507 ± 23)/T) cm 3 molecule -1 s -1 and k 2 = (8.47± 0.42)10 -11 exp(-(670 ± 16)/T) cm 3 molecule -1 s -1 . The Arrhenius expressions for k 1 and k 2 and independently measured kinetic isotope effect, k 1 /k 2 = (1.58±0.05)×exp((131±2)/T), provide a self-consistent data set for the F + H 2 reaction and its isotope analog F + D 2 over an extended temperature range and represent a good experimental basis to further refine the theoretical calculations.

FIGURE 5

 5 FIGURE 5 Reaction F + D 2 : plots of pseudo-first-order rate constant k 2 ′ versus concentration of D 2 at different temperatures.

FIGURE 6

 6 FIGURE 6Reaction F + D 2 : summary of the available data on the temperature dependence of the reaction rate constant.

FIGURE 7

 7 FIGURE 7 Yield of DF from F atom titration with D 2 + H 2 mixtures at different temperatures. Partially shown error bars represent typical uncertainties of the measurements ( 5%).

FIGURE 8

 8 FIGURE 8Temperature dependence of the kinetic isotope effect k 1 /k 2 . AM: k 1 /k 2 calculated from the reported values of k 1 and k 2 ; RM: relative measurements of the k 1 to k 2 ratio. Partially shown error bars represent estimated total uncertainty of 10% on the present measurements.

Figure 1 .

 1 Figure 1.

Figure 2 .

 2 Figure 2.

  Figure 3.

Figure 4 .

 4 Figure 4.

  Figure 5.

Figure 6 .

 6 Figure 6.

  Figure 7.

Figure 8 .

 8 Figure 8.

3 RESULTS AND DISCUSSION 3.1 Rate Constant of Reaction (1): Absolute Measurements

  In this series of experiments, the rate constant of the reaction of F atoms with H 2 was measured relative to that of F atoms with Br 2 . The experiments consisted in a fast titration of F atoms in reaction with a mixture of H 2 and Br 2 and the measurements of FBr yield as a function of the [H 2 ]/[Br 2 ] ratio:

	in excess of Br 2 was also used
	for the determination of the absolute concentrations of F atoms by linking the concentration
	of F atoms to the consumed fraction of [Br 2 ]: [F] = [FBr] = [Br 2 ]. The absolute
	concentrations of all stable species (H 2 , D 2 , Br 2 , F 2 ) in the reactor were calculated from their
	flow rates obtained from the measurements of the pressure drop of their mixtures in He
	stored in calibrated volume flasks. All species were detected by mass spectrometry at their
	parent peaks: m/z= 160 (Br 2 + ), 98/100 (BrF + ), 38 (F 2 + ), 21 (DF + ).
	The purities of the gases used were as follows: He >99.9995% (Alphagaz), passed
	through liquid nitrogen trap; D 2 >99.7% (Alphagaz); H 2 >99.998% (Alphagaz); Br 2 >99.99%
	(Aldrich); F 2 , 5% in helium (Alphagaz).
	The absolute measurements of k 1 were carried out under pseudo-first order conditions
	monitoring consumption of F atoms ([F] 0 = (2 -4)×10 11 molecule cm -3 ) in excess of H 2 (the
	ranges of the initial concentrations of H 2 used are shown in Table 1). The flow velocity in the
	reactor was in the range (1750-2920) cm s -1 . The F atom decays were treated with an
	exponential function, [F] = [F] 0 ×exp(-k 1 '×t), where k 1 ' = k 1 ×[H 2 ]+k w is the pseudo-first-order
	rate constant and k w corresponds to F atom loss rate in the absence of H 2 in the reactor.
	Examples of the kinetic runs observed at T = 400 K are shown in Figure S2 (SI). To take into
	account the consumption of the excess reactant, H 2 , the average concentration of H 2 in the
	reaction zone, calculated as [H 2 ]=[H 2 ] 0 -[F]×(k 1 '-k w )/k 1 ', was used in the treatment of the
	experimental data. As one could expect, the corrections on [H 2 ]

0 were insignificant (within a few percent) in the most kinetic runs, however reached up to 20% in a few experiments with the lowest concentrations of H 2 . Examples of the dependencies of the pseudo-first order rate constant, k 1 ' = k 1 ×[H 2 ]+k w , on concentration of H 2 at different temperatures are shown in Figures 1 and S3(SI). All measured values of k 1 ' were corrected for the effects of axial and radial diffusion of fluorine atoms. 14 Corrections were <10 % in the vast majority of the experiments and up to 18% in a few kinetic runs. The slopes of the straight lines in Figures 1 and S3 provide the values of k 1 at respective temperatures. All the results of the absolute measurements of k 1 at different temperatures are shown in Table

1

. The combined uncertainty on the measurements of the rate constants was estimated to be ≤ 15 %, including (in quadrature) statistical error (within a few percent, Table

1

) and those on the measurements of the flows (5%), pressure (3%), temperature (1%) and absolute concentration of H 2 (< 10%).

3.2. Rate Constant of Reaction (1): Relative Measurements

  , one can state that the current level of theoretical understanding of the F + H 2 system makes it possible to reproduce the kinetic data with very good accuracy. It is interesting to note the almost perfect agreement (most likely, accidental) between experimental data from the present work and those calculated by Wang et al.[START_REF] Wang | Direct" Calculation of Thermal Rate Constants for the F + H 2 → HF + F Reac on[END_REF] and Chen et al. with CSZ (Chen, Sun and Zhang) PES.[START_REF] Chen | An accurate potential energy surface for the F + H 2 → HF + H reaction by the coupled-cluster method[END_REF]

TABLE 1

 1 Reaction F + H 2 : summary of the absolute measurements of the rate constant

	T (K) a	[H 2 ] (10 13 molecule cm -3 )	k 1 (± 2) (10 -11 cm 3 molecule -1 s -1 )	Reactor surface b
	220	0.18-2.98	1.39±0.03	HW
	235	0.22-3.31	1.47±0.02	HW
	250	0.17-3.09	1.66±0.02	HW
	265	0.18-2.98	1.84±0.03	HW
	285	0.12-2.44	1.97±0.03	HW
	298	0.13-2.97	2.26±0.04	HW
	299	0.16-2.26	2.24±0.04	Q
	320	0.15-2.51	2.40±0.03	HW
	340	0.20-1.85	2.59±0.05	Q
	400	0.17-1.87	3.51±0.07	Q
	445	0.21-1.82	3.83±0.04	Q
	540	0.12-1.51	4.92±0.07	Q
	660	0.12-1.14	5.77±0.03	Q
	780	0.11-1.14	6.44±0.11	Q
	960	0.08-0.97	7.90±0.11	Q

a 8-13 kinetic runs at each temperature. b HW: halocarbon wax; Q: quartz.

TABLE 2

 2 Experimental conditions and results of the relative measurements of k 1 Units of 10 -11 cm 3 molecule -1 s -1 , estimated total uncertainty on k 1 is nearly 20% and includes the uncertainty on the rate constant of the reference reaction.

	T (K)	[H 2 ] a	[H 2 ]/[Br 2 ]	k 1 /k 3 (± 2)	k 1	b
	320	0.64-26.5	0.58-25.9	0.187±0.002	2.39
	370	0.49-16.3	0.51-17.2	0.238±0.002	3.05
	575	0.45-14.0	0.54-16.7	0.414±0.004	5.30

a Units of 10 13 molecule cm -3 . b

TABLE 3

 3 Reaction F + D 2 : summary of the measurements of the rate constant

	T (K) a	[D 2 ] (10 13 molecule cm -3 )	k 2 (± 2) b (10 -11 cm 3 molecule -1 s -1 )	Reactor surface c
	220	0.64-7.77	0.416±0.034	HW
	235	0.57-7.06	0.494±0.007	HW

a 9-11 kinetic runs at each temperature. b estimated total uncertainty on k 2 is ≤ 15%. c HW: halocarbon wax; Q: quartz.

TABLE 4

 4 Experimental conditions and results of the relative measurements of k 1 /k 2 Units of 10 13 molecule cm -3 . Reaction F + H 2 : plots of pseudo-first-order rate constant k 1 ′ versus concentration of H 2 at different temperatures. Partially shown error bars represent typical uncertainties (≤5%) on the determination of k 1 ′.FIGURE 2 Yield of FBr from F atom titration by the reaction with Br 2 + H 2 mixtures at different temperatures. Partially shown error bars represent typical uncertainties of the measurements ( 5%).FIGURE 3 Reaction F + H 2 : summary of the data on the temperature dependence of the reaction rate constant.FIGURE 4 Reaction F + H 2 : comparison of the experimental data with theoretical calculations of the reaction rate constant. Potential energy surface (PES) used in calculations: SW (Stark and Werner),[START_REF] Stark | An accurate multireference configuration interaction calculation of the potential energy surface for the F+H 2 →HF+H reac on[END_REF] FXZ (Fu, Xu and Zhang),[START_REF] Fu | A hierarchical construction scheme for accurate potential energy surface generation: An application to the F+H 2 reaction[END_REF] CSZ (Chen, Sun and Zhang).[START_REF] Chen | An accurate potential energy surface for the F + H 2 → HF + H reaction by the coupled-cluster method[END_REF]

	T (K) a	[H 2 ] b	[D 2 ] b	k 1 /k 2 (± 2)	Reactor surface c
	220	0.21-6.0	8.2	2.98±0.04	HW
	235	0.32-6.4	6.6	2.74±0.03	HW
	250	0.19-7.2	5.9	2.62±0.02	HW
	265	0.21-6.7	5.4	2.54±0.04	HW
	285	0.27-6.1	4.9	2.44±0.02	HW
	298	0.17-6.7	5.8	2.38±0.03	HW
	301	0.19-5.5	4.2	2.45±0.02	Q
	320	0.30-6.0	5.2	2.36±0.04	HW
	365	0.11-4.7	4.6	2.31±0.02	Q
	440	0.18-4.6	3.9	2.12±0.01	Q
	535	0.12-4.9	4.0	2.08±0.02	Q
	650	0.18-4.7	3.2	1.90±0.02	Q
	790	0.08-3.6	2.5	1.85±0.04	Q
	960	0.06-3.1	2.0	1.81±0.02	Q

a 10-13 runs at each temperature. b c HW: halocarbon wax; Q: quartz.

FIGURE LEGENDS

FIGURE 1

ACKNOWLEDGEMENT

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

SUPPORTING INFORMATION

Additional supporting information may be found online in the Supporting Information section at the end of the article.

TABLES LEGENDS