Julie Ledoux

Maxim Stolyarchuck

Luba Tchertanov

Luba Tchertanov Human

Vitamin K Epoxide

Redox Ignacio Protein

Olga Rojas

Fernando Valenzuela

Luis Rojas

Javier

Human Vitamin K Epoxide Reductase as a Target of its Redox Protein

Human Vitamin K Epoxide Reductase as a

Target of its Redox Protein Julie Ledoux 1 and Maxim Stolyarchuck 1 Luba Tchertanov 1

Université Paris-Saclay, ENS Paris-Saclay, Centre Borelli, 4 avenue des Sciences, 91190 Gif-sur-Yvette, France julie.ledoux@ens-paris-saclay.fr Abstract. Human Vitamin K epoxide reductase (hVKORC1) is a key enzyme to reduce vitamin K. Such function requires activation of the enzyme by a redox partner delivering reducing equivalents through thioldisulphide exchange reactions. The activation process represents a first and less studied step in hVKORC1 vital cycle, involving the oxidised luminal loop (L-loop) and a reduced thioredoxin protein (Trx), which is yet undefined for hVKORC1. A careful in silico study, based on molecular dynamic (MD) simulations of hVKORC1 in oxidised state, and a comparative analysis of four Trx proteins -protein disulphide isomerase (PDI), endoplasmic reticulum oxidoreductase (ERp18), thioredoxin-related transmembrane protein 1 (Tmx1) and thioredoxin-related transmembrane protein 4 (Tmx4)), viewed as the most probable reducers of hVKORC1 -in their sequence, secondary and tertiary structure, dynamics, intraprotein interactions and composition of the surface exposed to the target -provided the identification of putative recognition/binding sites on each isolated protein. PDI was suggested as the most probable hVKORC1 partner. By probing the alternative orientation of PDI with respect to hVKORC1, two PDI-VKOR models were proposed and one of them considered as precursor for thiol-disulphide exchange reactions.

Keywords: hVKORC1; Trx-fold redox proteins • protein folding; intrinsic disorder • modular protein • molecular recognition • thiol-disulphide exchange • protein-protein interactions • PDI-hVKORC1 complex • 3D modelling • molecular dynamics

The human vitamin K epoxide reductase (hVKOR) hVKORC1 is an endoplasmic reticulum (ER)-resident transmembrane protein reducing vitamin K inside a membrane-embedded cysteine-containing redox centre [START_REF] Tie | Structure and function of vitamin k epoxide reductase[END_REF]. Such activity requires the cooperation of VKOR with a redox partner delivering reducing equivalents through thiol-disulphide exchange reactions, involving a disulphide bridge from the extended luminal loop (L-loop) of VKOR [START_REF] Rishavy | Novel insight into the mechanism of the vitamin k oxidoreductase[END_REF]. The activation process represents a first and less studied step in VKOR vital cycle. The physiological redox partner of hVKORC1 remains uncertain. Four human redoxin proteins (Trx) protein disulphide isomerase (PDI), endoplasmic reticulum oxidoreductase (ERp18), thioredoxin-related transmembrane protein 1 (Tmx1) and thioredoxinrelated transmembrane protein 4 (Tmx4) -were suggested as the most probable H-donors of hVKORC1 [START_REF] Schulman | Vitamin k epoxide reductase prefers ER membrane-anchored thioredoxin-like redox partners 107[END_REF]. In addition, the structure of hVKORC1 L-loop is not credibly characterised. Consequently, deciphering the molecular origins of hVKORC1 recognition by an unknown redox protein is not a trivial task.

We suggested that an accurate in silico study of Trxs and hVKORC1 as isolated proteins would provide useful information for the development of putative Trx-VKOR complexes. Quantitative metrics and qualitative estimations can shed new light on the target (hVKORC1) features and peculiarities of redox proteins (Trx). Such information may help in predicting (i) the protein fragments participating in VKORC1 recognition by a Trx and (ii) the most probable partner of VKORC1. First, conformational features of hVKORC1 and L-loop, the principal platform of hVKORC1 for Trx recognition, scaffolding and intermolecular thioldisulphide exchange reactions, were characterised by extended molecular dynamics simulations (MD) of a de novo model [START_REF] Chatron | Identification of the functional states of human vitamin k epoxide reductase from molecular dynamics simulations[END_REF][START_REF] Stolyarchuk | Identification of the primary factors determining the specificity of human VKORC1 recognition by thioredoxin-fold proteins[END_REF] and crystallographic structures [START_REF] Liu | Structural basis of antagonizing the vitamin k catalytic cycle for anticoagulation 371[END_REF] of the enzyme in oxidized state. This study clearly showed that (i) L-loop is an intrinsically disordered region, and (ii) hVKORC1 is a modular protein composed of the structurally stable transmembrane domain (TMD) crowned by the disordered L-loop [START_REF] Ledoux | Human vitamin k epoxide reductase as a target of its redox protein[END_REF] (Figure 1 a-e). Indeed, the structurally well conserved TM helices, varied slightly only at their ends, show a cooperative drift typical for transmembrane domains rigidified by the stable non-covalent interactions. In contrast, L-loop exhibits an unstable helical fold represented by reversible transient -and 310-helices linked by flexible coils, offering L-loop a great conformational diversity, from compact 'globule-like' shape (closed form) to extended (open form) (Figure 1, b-c).

Such modular architecture of hVKORC1 provides (i) excellent conformational plasticity required for specific adaptation over recognition by redox protein, activation process and catalysis, and (ii) easy and exact reproducibly of hVKORC1 metastable intermediates during repeated enzymatic cycles. Those qualities are strictly required for hVKORC1 activities [START_REF] Ma | Transitionstate ensemble in enzyme catalysis: Possibility, reality, or necessity?[END_REF]. Structure and conformations of the disordered L-loop are better described in terms of free energy than conventional methods such as clustering.

Secondly, focusing on Trx-fold proteins, probable hVKORC1 redox partners, we found that, despite similar architecture, each redox partner has its own sequence-dependent dynamical features. Further analysis identified PDI as the most probable redox partner of hVKORC1 (Figure 1f-h) [START_REF] Stolyarchuk | Identification of the primary factors determining the specificity of human VKORC1 recognition by thioredoxin-fold proteins[END_REF]. By probing PDI alternative orientations with respect to hVKORC1, two models of noncovalent complex were proposed. One of them was considered as functionally related model and postulated as the first precursor to probe thiol-disulphide exchange reaction. This predicted complex, formed by hVKORC1 and PDI, was further reproduced by docking trials (protein-protein docking with HADDOCK) [START_REF] Ledoux | Human vitamin k epoxide reductase as a target of its redox protein[END_REF].

Finally, results obtained for hVKORC1 simulated in different environment (water/membrane) and simulation methods (conventional and accelerated) indicated that, for in silico study of hVKORC1 and its complexes, the membrane is probably not necessary, and the cleaved L-loop, simulated as isolated polypeptide, reflects its properties when fused to the transmembrane domain. Therefore, it may be used to study hVKORC1 recognition by its redox protein. Extension of these conclusions for experimental studies of hVKORC1 requires their empirical validation.

Fig. 1 .

 1 Fig. 1. 3D model of VKORC1 and its complex with redox protein (a) VKORC1 inserted into membrane and surrounded by water molecules. The helically folded L-loop shows structural and conformational disorder in de novo model (left and middle) and in X-ray structures. (b) Clustering of L-loop conformations using RMSD and secondary structures. (d) Projection of MD conformations on the three principal components determined by principal component analysis (PCA). (e) Free energy landscape of L-loop conformations defined on two primary reaction coordinates, RMSD and radius of gyration (Rg). (f) Mechanism of disulphide exchange between Trx and a target. (g) Superimposed 3D structures of Trx-fold proteins with cysteine residue as yellow balls. Regions that are potentially involved in target recognition and/or electron transfer reaction are differentiated by colour. (h) Modelling of human PDI-hVKORC1 complex (left) and reproduced results by protein-protein docking (HADDOCK) (right).


Gérald Umhang
email: gerald.umhang@anses.fr

Céline Richomme

Christophe Caillot

Vanessa Bastid

Jean-Marc Boucher

Jean-Louis Moyen

Corinne Novella

Bruno Richoux

Bernard Davoust

Franck Boué

Jean- Louis Moyen

Towards delimitation of the Echinococcus multilocularis parasite's southernmost range in France

Keywords: Echinococcus multilocularis, surveillance, France, red fox

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

Introduction

Alveolar echinococcosis (AE) is a severe parasitic disease fatal to patients if not appropriately diagnosed and treated [START_REF] Torgerson | The Global Burden of Alveolar Echinococcosis[END_REF]. The infection is due to oral ingestion of eggs of the tapeworm Echinococcus multilocularis, which reaches the liver from the intestines via portal blood flow. The larval stage gradually proliferates and infiltrates the liver parenchyma, thus destroying the surrounding host tissue, and may also affect other organs by infiltration or metastasis [START_REF] Eckert | WHO/OIE Manual on echinococcosis in humans and animals : a public health problem of global concern[END_REF]. After a long asymptomatic period of up to 15 years, human AE may be diagnosed in patients due to a manifestation of symptoms or, increasingly often, coincidentally. The primary lifecycle of the parasite in Europe involves red foxes (Vulpes vulpes) and small rodents mainly from the Arvicolinae sub-family as respectively definitive and intermediate hosts. Worms in fox intestines release the parasite's eggs into the environment through faeces. Rodents develop alveolar echinococcosis after ingesting the eggs. The life cycle is completed when foxes then predate infected rodents. While the parasite was initially identified in only a few western European countries at the end of the 19 th century, its current range now includes 21 European countries [START_REF] Oksanen | The geographical distribution and prevalence of Echinococcus multilocularis in animals in the European Union and adjacent countries: a systematic review and meta-analysis[END_REF] due to expansion through the dispersal movement of foxes from the historical focus [START_REF] Knapp | Genetic diversity of the cestode Echinococcus multilocularis in red foxes at a continental scale in Europe[END_REF]Umhang et al., 2021a).

In France, the first focus was described at the end of the 19th century in a few departments (French administrative units corresponding to NUTS3 level in European Union NUTS nomenclature) in northeastern France [START_REF] Vuitton | Clinical epidemiology of human AE in Europe[END_REF], then a second one was identified more recently in the Auvergne region (Figure 1), central France [START_REF] Petavy | Helminths of the common fox (Vulpes vulpes L.) from the massif central (France) (author's transl)][END_REF][START_REF] Petavy | Connaissance du foyer auvergnat d'échinococcose alvéolaire[END_REF]. A westward expansion from the historical eastern focus has since been reported [START_REF] Combes | Westward spread of Echinococcus multilocularis in foxes, France, 2005-2010[END_REF] though assumed to be at least several decades old [START_REF] Umhang | Using the genetics of Echinococcus multilocularis to trace the history of expansion from an endemic area[END_REF]. According to the absence of the parasite in the westernmost department (Morbihan) and detection of infected foxes only in the eastern part of the bordering Brittany (Bretagne administrative region, east of Ille-et-Vilaine department), the northwestern delimitation of the endemic areas to be currently roughly positioned at the east of Brittany [START_REF] Combes | Expansion géographique du parasite Echinococcus multilocularis chez le renard en France[END_REF][START_REF] Combes | Westward spread of Echinococcus multilocularis in foxes, France, 2005-2010[END_REF]. More recently, a southward expansion along the Alps was determined by the detection of the parasite's DNA in three fox faecal samples in the Hautes-Alpes department [START_REF] Umhang | Retrospective analyses of fox feces by real-time PCR to identify new endemic areas of Echinococcus multilocularis in France[END_REF] and later of infected Arvicola terrestris [START_REF] Umhang | Rodent control programmes can integrate Echinococcus multilocularis surveillance by facilitating parasite genotyping: the case of Arvicola terrestris voles screening in France[END_REF]. Furthermore, the parasite's DNA has been identified even further south, near the French-Italian border, in both wolf and dog faeces [START_REF] Massolo | Unexpected Echinococcus multilocularis infections in shepherd dogs and wolves in south-western Italian Alps: A new endemic area?[END_REF]. No surveys have yet investigated southwestern France, and the parasite has not been reported in Spain or Portugal [START_REF] Oksanen | The geographical distribution and prevalence of Echinococcus multilocularis in animals in the European Union and adjacent countries: a systematic review and meta-analysis[END_REF]. However, the parasite's current geographical distribution in southern France is thought to lie further south than the range currently indicated by reported cases. The aim of this study was to use convenience sampling of red fox samples in order to explore the parasite's potential presence far beyond the known endemic areas in southeastern and southwestern France.

Materials and Methods

Samples were collected from 2013 to 2020 in the framework of other transversal epidemiological studies in five sampling areas (Figure 1). Two areas, A and B, are military camps located in the Var and Bouches-du-Rhône departments (southeastern France, 350 km² and 15 km² respectively) where foxes (n=77) were sampled for investigations from 2013 to 2020 on vector-borne pathogens [START_REF] Medkour | MOLECULAR INVESTIGATION OF VECTOR-BORNE PATHOGENS IN RED FOXES (VULPES VULPES) FROM SOUTHERN FRANCE[END_REF]. The three other areas are located in Charente (C: 539 km²), Dordogne (D: 525 km²) and Landes (E: 504 km²) departments (southwestern France) where foxes were sampled for research on Mycobacterium bovis from 2017 to 2020 (n=30, n=147 and n=74 respectively) [START_REF] Richomme | Mycobacterium bovis Infection in Red Foxes in Four Animal Tuberculosis Endemic Areas in France[END_REF].

Foxes were trapped throughout the years for areas A and B and between October and March for areas C, D and E. All fox carcass used in the present study were obtained in agreement with national regulations. As the study did not involve invasive procedures on live animals, no ethical approval was necessary. The fox intestines from areas A, B and C were collected during the necropsy and frozen at -20°C. For foxes from areas D and E, faecal samples were taken from the rectum and frozen at -20°C.

All the intestinal and faecal samples were frozen at -80°C for a week prior to laboratory analyses in order to prevent any risk of zoonotic infection.

The intestines from areas A, B and C were analysed according to the SSCT (Segmental Sedimentation and Counting Technique) method [START_REF] Umhang | Segmental sedimentation and counting technique (SSCT): an adaptable method for qualitative diagnosis of Echinococcus multilocularis in fox intestines[END_REF]. Briefly, intestine of red foxes were divided in five equal parts and the first (from anterior to posterior parts) and fourth were scrapped to remove the intestinal content which is diluted with water to look for the presence of E. multilocularis worms with a binocular. This method is very sensitive (98.4%) regarding the intestinal reference method SCT (Sedimentation and Counting Technique) which is considered the gold standard. For foxes from area D, DNA was extracted from 500 mg of faeces with a KingFisher Flex automated extraction system (Thermo Scientific) according to the manufacturer's instructions after supplemental mechanical lysis using an LSI MagVet Universal Isolation Kit (Life Technologies). Five samples of fox faecal samples previously identified as naturally infected by E. multilocularis were used as a positive control for this automated DNA extraction step. For foxes from area E, the QIAamp Fast DNA stool mini kit (Qiagen) was used, again according to the manufacturer's recommendations. All the copro-DNA samples were submitted for E. multilocularis detection by a real-time PCR based on the amplification of a part of the mitochondrial rrnL gene including an internal control [START_REF] Knapp | Development of a real-time PCR for a sensitive one-step copro-diagnosis allowing both the identification of carnivore feces and the detection of Toxocara spp. and Echinococcus multilocularis[END_REF]. A final qPCR volume of 20µL was used, containing 5µL of DNA, 10µL of Master Mix Maxima Probe, 50 copies of the internal control plasmid, 1.5µM of primers for E. multilocularis and internal control, 0.2µM and 0.1µM of E. multilocularis and internal control probe, respectively. The qPCRs were performed in duplicate and run on a Mx3005P thermocycler (Agilent) was used with a program that consists of 10 min at 95°C and 45 cycles of 15 s at 95°C and 60 s at 60°C. In the event of inhibition, the DNA samples were diluted to 1/10th before being re-tested.

Results and discussion

Previous knowledge on the distribution of E. multilocularis in France was mainly based on the parasite's detection in foxes with a sampling effort ranging from about 1 to 2 foxes per 100 km² in each of the departments investigated [START_REF] Combes | Westward spread of Echinococcus multilocularis in foxes, France, 2005-2010[END_REF][START_REF] Combes | Expansion géographique du parasite Echinococcus multilocularis chez le renard en France[END_REF], Umhang et al. 2016) (Figure 1). In the present study, the sampling areas were smaller due to the use of convenient sampling, but the sampling effort was much higher, ranging from 5 to 400 foxes per 100 km² in the five sampling areas (Table 1). None of the 328 foxes analysed had either E. multilocularis worms or their DNA. Considering the density of collected foxes, this result argues in favour of an absence of the parasite in the studied areas, even if the presence of E. multilocularis cannot be totally excluded from a statistical point of view (upper limit of the confidence interval at 95% of the prevalence: 2.5% in area D in the southwestern, and 4.7% in the southeastern areas). These new data, which show that no parasites were detected, are in accordance with previous knowledge on the endemic situation in France and are helpful in delimiting the southernmost range of the geographical distribution of E. multilocularis in France.

In 2016, E. multilocularis DNA was detected from fox faecal samples in the Hautes-Alpes (Umhang et al., 2016) in southeastern France, approximately 100 kilometres north of area A (Var). According to EmsB microsatellite analyses obtained from infected Arvicola terrestris specimens in the same Alpine area [START_REF] Umhang | Rodent control programmes can integrate Echinococcus multilocularis surveillance by facilitating parasite genotyping: the case of Arvicola terrestris voles screening in France[END_REF], the presence of the parasite there is thought to be the result of an expansion from the northeastern historical focus. Furthermore, the parasite's DNA was also detected in wolf and dog faeces in Italy [START_REF] Massolo | Unexpected Echinococcus multilocularis infections in shepherd dogs and wolves in south-western Italian Alps: A new endemic area?[END_REF], suggesting the cestode's presence in the French-Italian border region (Alpes-Maritimes department). The southernmost positive wolf faecal sample from Italy were from the Province of Imperia (western part of the Liguria region), only 110 km northeast of Area A, found negative for the parasite in the current study. This could be explained by the warm, dry Mediterranean climate of area A, which is less favourable to the transmission of E. multilocularis and especially to the survival of eggs in the environment than the climate of the French Alps or Liguria.

The most southwestern E. multilocularis reports concern the historical focus of the Auvergne region (central France) (Figure 1). The first reports were made in the 1980s [START_REF] Petavy | Helminths of the common fox (Vulpes vulpes L.) from the massif central (France) (author's transl)][END_REF][START_REF] Petavy | Connaissance du foyer auvergnat d'échinococcose alvéolaire[END_REF]. By the early 2000s, the prevalence in foxes was estimated to stand at 9% (95% CI:

Figure 1 :

 1 Figure 1: The five study areas are indicated by blue circles; the sample size in each area is proportional

Table 1 :

 1 Prevalence and confidence interval of E. multilocularis in the five study areas in southern France according to sample type and analysis method.

	Areas	Departments	Nb of samples Type of samples Diagnostic method	Prevalence [95% confidence interval in %]	Density of fox sampled/100 km²
	A	Var	17	intestines	SSCT	0 [0-19.5]	5
	B	Bouches-du-Rhône	60	intestines	SSCT	0 [0-6.0]	400
	C	Charente	30	intestines	SSCT	0 [0-11.6]	6
	D	Dordogne	147	faeces	copro-qPCR	0 [0-2.5]	28
	E	Landes	74	faeces	copro-qPCR	0 [0-4.9)	15

Table 2 :

 2 Helminths found at a macroscopic level during the SSCT analyses (which focus on the first and fourth segments of intestine when divided in five equal parts) and rate of infection in foxes in three areas of the study where this research was implemented. The specific determination of nematodes has not been performed.

					Number of fox found infected (rate of infection)
			Number of fox				Nematoda
	Areas	Departments	analysed	Mesocestoides sp. Taenia sp. Amoebotaenia sp.	(unregards the species)
	A	Var	17	7 (41%)	6 (35%)	0	1 (6%)
	B	Bouches-du-Rhône	60	26 (43%)	26 (43%)	1 (2%)	16 (27%)
	C	Charente	30	20 (67%)	8 (27%)	2 (7%)	3 (10%)
	172
	173

Acknowledgements

The authors would like to thank local hunting federations, trappers and pest control officers for collecting foxes.

Funding

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

5%-17%) in the Cantal department (southern Auvergne) [START_REF] Combes | Westward spread of Echinococcus multilocularis in foxes, France, 2005-2010[END_REF]). An ongoing survey in this region aims to assess the presence of the parasite among foxes and its origin using the EmsB microsatellite approach. The areas of southwestern France investigated in the present study (areas C, D and E) are 150 km west of the westernmost cases reported in Auvergne. This intermediate area will be investigated in the coming years as part of the above-mentioned survey in Auvergne. Moreover, a national surveillance programme on E. multilocularis in foxes is under way and will target departments along the edge of the known endemic area, both in southeastern and western France. The data thus produced will supplement our own study results, thereby advancing efforts to define the actual distribution of E. multilocularis in France today, and to target preventive measures to reduce human exposure.

Declaration of Competing Interests

The authors declare no competing interests in association with this study.


Dr Laurent Guérin
email: laurent.guerin@univ-rennes1.fr

Dr Takefumi Yoshida
email: takefumi.yoshida@uec.ac.jp

Dr Edoardo Zatterin

Dr Arkadiy Simonov

Dr Dmitry Chernyshov

Dr Hiroaki Iguchi

Dr Bertrand Toudic

Dr Shinya Takaishi

Masahiro Yamashita

Dr A Simonov

Prof M Yamashita

Elucidating 2D Charge-Density-Wave atomic structure in an MXchain by the 3D-∆Pair Distribution Function method

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

Introduction

In the field of molecular-based conductors, investigations of diffuse scattering have played a major role. [START_REF] Pouget | [END_REF]2] Indeed, the first diffuse scattering experiments on TTF-TCNQ [3] paved the way for the discovery of numerous original structural phases in molecular conductors. [4] Due to the so-called Peierls instability that prevails in 1D physics, a resulting periodic modulation of the electron density named Charge-Density-Wave (CDW), can be stabilized, and is associated with a periodic lattice distortion. A very large number of studies in the last 50 years have been conducted in order to understand the different mechanisms of stabilization of the CDW and to control its dimensionality, either using chemical design or via the manipulation of external parameters such as temperature, pressure or light. [5][6][7][8][9][10] Bechgaard salt, Fabre salts or dmit salts compose such a playground. Quasi-one-dimensional halogen-bridged metal complexes, so-called MX-Chains, are also suitable candidates to understand the correlation between the lattice and the electrons responsible for the CDW order. MX-Chains have an isolated onedimensional (1D) electronic system composed of dz 2 orbital of metal ions (M) and pz orbital of bridging halide ions (X) (Figure S1). [START_REF] Yamashita | Material Designs and New Physical Properties in MX-and MMX-Chain Compounds[END_REF] These electronic states are well explained by the extended Peierls-Hubbard model, where the transfer integral (t), the on-site and nearest neighbor-site Coulomb repulsion (U and V, respectively), and the electron-lattice interaction (S) strongly compete with each other. The very large majority of Pd, and Pt complexes, which have a -X•••M II •••X-M IV -X••• Peierls distorted 1D structure, are in a mixed-valence charge-density-wave (MV-CDW) state because of a small U value (S > U) (Figure S2). [START_REF] Nasu | [END_REF] This mixed-valence state is accompanied by a strong dimerization along the chain, with two competing CDW ground states (A and B in Figure 1a) that can be easily characterized using singlecrystal X-ray diffraction. [START_REF] Yamashita | Material Designs and New Physical Properties in MX-and MMX-Chain Compounds[END_REF] However, recently some Pd complexes which show a CDW -to-Mott-Hubbard (MH) phase transition where the decrement of Pd•••Pd distances at low temperature reduce S value (while the U value remains almost constant), thus stabilizing the MH state, have been reported. [13] In such a case, at variance with CDW, the X-M-X bonds are completely symmetric. In particular, [Pd(cptn)2Br]Br2 (cptn = 1R,2R-diaminocyclopentane) was shown to be the only reported system among organic molecular solids, where μm-order CDW and MH domains coexist in a wide temperature range although the stabilization mechanisms were not revealed. [14] Very convincing evidence of the Peierls instability was provided by diffuse scattering since the low-dimensional character of the CDW can be spotted by the diffuse scattering out of the Bragg peaks. [2] However, up to now, most parts of the analysis concerning diffuse scattering originating from CDWs were qualitative, with no quantitative information on the displacement of atoms and therefore on the real structure of the CDW state. Analysis of the local structure requires the Fourier Transform of the intensity of the diffuse scattering, which contains the information on the pair correlation function of the disorder. It should be mentioned that a pioneering handmade approach was made some years ago considering short-range ordering in a Ni-Pd-based MX-Chain compound. [15] These types of studies require single crystals, intense X-rays and a zero-noise detector with ultra-high dynamic range. These experimental conditions are now available thanks to advent of bright synchrotron radiations sources and large area pixel photon-counting detectors. In this study, we characterize the stabilization mechanism of the macroscopic CDW domains measuring X-ray diffuse scattering patterns and interpreting these patterns via three-dimensional difference pair distribution function (3D-ΔPDF) analysis and refinement of disorder models against single-crystal diffuse scattering data (Yell). We extract the effective displacements of the atoms describing the CDW atomic structure quantitatively by this way.

Results and Discussion

Determination of the average structure. Single-crystal [Pd(cptn)2Br]Br2 samples were grown by the electrochemical oxidation method and synthesized from the same cptn enantiomer (1R,2R-diaminocyclopentane). A set of single crystals of [Pd(cptn)2Br]Br2 of plate-like shape, with lateral dimensions of some hundreds of µm, were studied by X-Ray diffraction at 260 K to investigate their crystal structure. X-ray measurements were carried out at the Swiss Norwegian Beamline BM01 at the European Synchrotron Research Facility using monochromatized X-rays with λ = 0.6973 Å. 900 images with 0.4 s exposure times and 0.4° step size were collected with a Pilatus2M detector located 247 mm downstream of the crystal. [16] Structure solution and refinement using the software Jana yielded an orthorhombic structure of space group I222 with the lattice parameters a = 5.249 Å, b = 6.972 Å, c = 22.711 Å. As illustrated in Figure 1b (also Figure S3-4), the structure consists of a body-centered arrangement of [Pd(cptn)2Br]Br2 chains. A single chain is composed of an alternation of Pd(cptn)2 units bridged by Br ions along the a axis; the amine (NH2) groups of the cptn ligand provide cohesion between chains in the b direction through hydrogen bonds formed with the Br -counteranions (H bond length = 2.65 Å). The cptn ligands extend from each chain in the c direction. The space group I222 was discriminated from its crystallographically indistinguishable counterpart Immm on the basis of the chemical reason that the enantiopure ligand violates mmm symmetry. The important observation is that the Pd-Br-Pd distance was symmetric, and no sign of dimerization was observed. There is no evidence of a CDW organization regarding the average structure from this single crystal structural analysis. This appears to be in contradiction with theory and previous STM and Raman measurements. [14] Analysis of the diffuse scattering. A representative (h 0 l) section of the three-dimensional scattering pattern is shown in Figure . 1c. It contains weak but highly structured diffuse scattering, which is the signature of the strongly correlated disorder and is determined by spatial fluctuations in the structure. [17][18][19][20] A set of streaks parallel to the c* axis and perpendicular to the (a*, b*) plane are observed, suggesting the existence of a twodimensional (a, b) ordering in real space with disorder along the c direction. Correlation lengths of 2100 Å (400 unit cells) and 480 Å (70 unit cells) in the a and b crystallographic directions, respectively, were extracted from a Lorentzian fit of the profile of the diffuse streaks along the a* and b* directions. The streaks intersect the H direction at half-integer values, while along the K direction only integer values are met. This means that the ordering phenomenon results in a double periodicity in terms of structural displacements along a with respect to the average structure defined by the Bragg peaks position. On the other hand, the same periodicity between average and real structure occurs in the b direction. Individual (a, b) planes in the crystal are composed of chains with a double periodicity compared to the average structure, with each neighboring chain in the b direction being ordered in phase. Thus, one can say that a long-range order occurs in individual planes. The fundamental question is how this order can be related to a CDW state. A 2D-CDW is evidenced by the 3D-ΔPDF method. The threedimensional difference pair distribution function (3D-ΔPDF) contains information on the self-correlation function of the shortrange ordering as measured away from the Bragg peaks on single crystals. [21][22][23][24][25] To illustrate this method, we introduce a 1Dmodel of dimerization (Figure 2a). We considered a real crystal composed of two different structures A and B generated by antiphase displacement (δ) of nearest atoms, each structure related to the other by a one-half translation along a. Each structure has an equal probability, and no correlation is assumed, so the "real" crystal is highly disordered. Electron density peaks of the average structure are located at the position of the electron density peaks of the two real structures giving rise to a periodicity of half the real periodicity. Model diffraction patterns can be obtained from the autocorrelation function of the electron density known as the PDF and the Patterson calculated from the real structure and the average structure, respectively. The ΔPDF is the difference between the PDF and the Patterson function. In the specific case of dimerization, we observe a distinct repetition of positivenegative-positive and negative-positive-negative peaks, with direct and inverse profiles. The distance 4δ within these profiles is directly related to the displacement of the dimerization. Its periodicity, the same as the real structure, is twice the periodicity of the average structure. The inverse Fourier transform of the normalized diffuse scattering function yields the 3D-ΔPDF, [21] a three-dimensional real space reconstruction consisting of voxels. The position of each voxel with respect to the center of the ΔPDF represents an interatomic vector; the normalized intensity of a voxel corresponds to the probability of that specific interatomic vector being found in the real structure rather than the average one. That is, positive intensities in the 3D-ΔPDF represent interatomic vectors, which are more probable to be found in the real than in the average structure, and vice versa for negative intensities. The quality and the resolution of the ΔPDF are defined by the number of streaks collected and their intensities compared to the background, which is improved drastically with the use of a synchrotron and a pixel detector. [16] The size of the present ΔPDF (26 x 18 x 800 voxels) and the corresponding voxel size (0.40 x 0.58 x 0.03 Å) stems from the data acquisition strategy and the integration procedure. The reciprocal volume of diffuse streaks was merged into 1D pixel arrays to increase the data statistics (Figure 1c), thus implicitly assuming perfect correlation in the a* and b* directions. Figure 2b shows a section of the ΔPDF corresponding to the (u, v, 0) plane. As already discussed for the diffuse scattering, cell doubling along the chain (a direction) is observed in the ΔPDF while the periodicity perpendicular to the chain along the b direction remains unvaried. The typical pattern of dimerization is clearly revealed in the profile along the a direction corresponding to an overall displacement of δ = 0.038 a = 0.2 Å.

Determination of the atomic structure of the CDW and its stabilization mechanism. The software Yell [26] allows for the specification of a disorder model, starting from the average structure of the crystal that we determined previously. A displacive model using 3 parameters corresponding to a displacement along a direction of the Br -bridging anion (Br1), the Br -counteranion (Br2) and the terminal carbon atom of cptn ligand (so-called C atom) is used to generate a ΔPDF (Figure 3a, 4a and Figure S6). This function is refined against the experimentally obtained one. A displacement of Δ = 0.136 Å of the Br bridging atom along the chain is obtained. It has been established that the distortion parameter defined as d = 2Δ/a, bears a linear relationship to a : d = 0.165 a -0.81. [27] The obtained value of d = 2Δ/a = 0.052 for a = 5.25 Å is in perfect agreement with other Pd-based MX chains found in a CDW state, confirming the CDW nature of the electronic state (Figure S7). [27] The analysis of the ΔPDF and width of the diffuse streaks indicate that the (a, b) plane consists of long-range ordered dimerized chains. Because of the observed displacement of the Br bridging atom associated with the Peierls distortion, we conclude that the electronic state of an individual (a, b) plane is a two-dimensional CDW state (figure 3b). In Figure 4a, the (0, v, w) plane shows strong positive peaks corresponding to the interatomic vector between Br1 and Br2 (Figure 3a). It indicates that the Br1 and Br2 atoms are displaced in phase in the a direction. The counteranion Br2 displaces in phase with Br1. The magnitude of the displacement, equal to 0.035 Å is about 4 times less than of the Br bridging atom. Looking at the average structure, one can notice that the Br bridging and counteranions are connected by a hydrogen-bonding network (Figure 3c andS5). In consequence to the Br2 displacement, the hydrogen bond length shows two different value depending on the valence order 2.61 Å for 2+ and 2.69 Å for 4+. Based on those results, both intrachain and interchain correlations can be understood, and the mixed-valence 2D CDW structure discerned, as is sketched in Figure 3c. In the chain, U is affected by the electrostatic / ligand field around the dz 2 orbital. It appears that the influence of the axial ligand of Br anion is dominant, and the in-plane ligand of cptn is irrelevant. The ligand field affects the value of the on-site Coulomb repulsion U on the metal ion and stimulates the formation of the CDW mixed-valence state in the chain via a Peierls distortion. In the interchain, once a dimerization starts occurring locally in the a direction (either A or B type) along the chain axis, it is easily propagated in the b direction due to the presence of the H-bonds (which provides interchain cohesion in the b direction) and mediated by the Br -counteranions. Thus, once one chain has dimerized in a certain way, all the chains contained in the same (a, b) plane dimerize in the same way, and a 2D-CDW state is stabilized (Figure 3b). Characterization of the plane to plane correlation. The (u, 0, w) and (0, v, w) sections shown in Figure 4a further allow the interpretation of the correlated disorder between the two-dimensional CDW (a, b) planes stacked and shuffled along the orthogonal direction. Because of the degenerate ground state of the CDW state (A/B in Figure 1a and3b) and weak plane-to-plane interaction, disorder appears along the c direction. Both the (a, c) and (b, c) section of the ΔPDF show opposite signs of features for adjacent unit cells along c direction, indicating negative correlation between adjacent (a, b) plane. Experimentally, this negative correlation originating from the one-half c* periodicity manifests itself as sharper peaks in the intensity profile of the streaks (Figure 1c). One can then assume a small displacement of the Br1 and Br2 atoms as derived from the first model, apply it to entire (a, b) planes, and derive a substitutional model in order to investigate the correlations along the c direction. The obtained joint probability P(A/B) that planes separated by a given vector in c are ordered in a different way is found to be equal to 0.54. This indicates that there is not a complete disorder along c (which would be characterized by a probability 0.5) (Figure 4d). The 2D-CDW of a given (a, b) plane tends to slightly order in an anti-phase manner, with the CDW being shifted by a/2 between two adjacent planes with a very short correlation length. The value of this length was estimated from the fit of the sharper peaks along c and was found to be equal to 52 Å (2.3 unit cells). This anti-phase process is known as the Coulomb coupling and is illustrated schematically in figure 4c. This mechanism is usually invoked to account for the CDW transverse ordering in TTF-TCNQ and related compounds where these interactions make the diffuse scattering condense in commensurate positions at the phase transition. [2] Very weak and positive correlations between the terminal carbon atom of the cptn ligand (C) and the Br -counteranion (Br2) are also present in the model. Those two atoms tend to displace in phase (as illustrated in Figure 4b), resulting in a small plane to plane correlation, preventing the stabilization of a 3D-CDW order. It is not surprising that the involved chemical bond must be very weak as its bond length is about 3.6 Å. It also seems to act as a chemical press and influence the valence of the metal in the chain.

Temperature dependence. μm-order CDW and MH domains coexist in a wide temperature range with a possible phase transition at 120K. [14] In order to investigate the temperature dependence of the CDW correlation length, we performed several measurements from 100 K to room temperature. The intensity of the diffuse scatterings seems to gradually weaken upon cooling and mostly disappeared at 100 K, indicating that the electronic state is changing from CDW to MH state gradually (Figure S8). The reproducibility was poor due to X-ray damage after few minutes. We observed no temperature dependence of the correlation length. There was no evidence of condensation of diffuse planes to Bragg peaks as observed in other molecular based conductors [2,6,10]. It indicates that the CDW order is 2D for any temperature as the strong hydrogen bonding network anchors the charge order to the chains and the weak plane to plane correlation must prevent the formation of a 3D ordering.

Discussion

The present study has demonstrated the great power of the 3D-ΔPDF method in analyzing diffuse scattering data and provide insights into the disorder presents inside a material. The absence of superstructure Bragg peaks and the wrong assumption that the crystal structure corresponds to the MH state is due to the fact that the information lies within the diffuse scattering. Here the MX-Chain compound [Pd(cptn)2Br]Br2 was studied by analyzing qualitatively and quantitatively the 3D-ΔPDF maps that unambiguously show that 2D sheets in CDW states are formed. It also reveals that the ordering of one given sheet is only slightly correlated with the ordering of the adjacent ones. The apparent discrepancy between different experimental methods pointing in diverse directions, i.e., MH or CDW is explained. The formation of large macroscopic CDW domains, as observed in previous optical measurements [14] is the consequence of the very strong 2D hydrogen-bonding network that is formed between the ligand in the chain and the counteranion that links any two chains. We also showed that the small correlation between two different planes is mediated by the weak bond between the tip of the ligand (CH2 group) and the counteranion (Br -). From a chemistry point of view, this shows the importance of selecting the right ingredients in order to reduce or enhance those interactions and tune the physical properties of the material such as the conductivity. Recently, a multiple hydrogen-bonding network was used to enhance the electrical conductivity or form a conductive zigzag chain. [27][28][29] The CDW dimensionality can be designed based on the strength of those interactions, can be quantitatively measured by refinement of the disorder model. As examples of sophisticated chemical synthesis, the incorporation of aromatic inplane ligands leads to the stabilization of the 1D chain structure in Pt-based MX-Chains, [30] the 2D hydrogen-bonding network gives the 2D-CDW in this study, and the fastener effect acting between alkyl chains leads to a phase transition between 3D CDW and MH state. [31,32] This 2D-CDW can totally be suppressed by synthesizing with a racemic mixture of cptn ligands, as this destabilizes the hydrogen-bonding network. The quantitative analysis using the software Yell showed that the displacement of the in-chain Br -anion is in complete agreement with the empirical formula found for other Pd-based MX-Chains in the CDW state (Figure S7). [27] The advances in noise-free detector technology and highly intense X-ray beams permit the measurement of very high-quality reciprocal space mapping in a few minutes, thus allowing the research on quantitative analysis of diffuse scattering to progress and determine quantitative and meaningful structural parameters. [33][34][35] The 3D-ΔPDF method can be applied to a long list of low dimensional systems, from 1D molecular conductors [START_REF] Pouget | [END_REF][2][3][4][5][6][7][8][9][10]36,37] to 2D metal dichalcogenides [38] to solve their long-range and short-range structure. Experimental Section Data collection. A set of single crystals of [Pd(cptn)2Br]Br2 of plate-like shape, with lateral dimensions of the order of some hundreds of µm were studied by X-Ray diffraction in a temperature range of 100-260 K. The SuperNova diffractometer (Agilent Technologies, UK) was employed to perform the measurements. A Cu anode source with voltage of 50 kV and a current of 50 mA were employed. Each image was 1° rotation and 1 s exposure. The CCD detector was positioned a distance of 60 mm.

Structure determination procedure.

In addition to the structure solution presented in the introduction which was limited due to the use of a single axis diffractometer, conventional diffraction on a SuperNova diffractometer was conducted at 230K in order to increase redundancies and completeness. Structure solution and refinement via SHELXS and SHELXL respectively yielded an Orthorhombic structure of space group I222, with lattice parameters a = 5.247 Å, b = 6.9646 Å, c = 22.702 Å at 230 K The structure consists of a body-centred arrangement of [Pd(cptn)2Br]Br2 chains. A single chain is composed an alternation of Pd(cptn)2 units bridged by Br ions running along the a axis (Figure S3); the amine (NH2) groups of the (cptn) ligand provide cohesion between chains in the b direction through hydrogen bonds formed with the Br -counteranions (Figure S5). The (cptn) ligands extend from each chain in the c direction (Figure S4). The space group I222 was discriminated from its crystallographically indistinguishable counterpart Immm based on chemical reasons; the pentane group present in the ethylenediamine ligand is incompatible with mmm symmetry. The variation of the lattice parameters and Atomic Displacement Parameters (ADPs) with temperature was studied, and showed no evidence of any effect apart from the expected thermal expansion.

Diffuse scattering data collection.

A set of single crystals of [Pd(cptn)2Br]Br2 of plate-like shape, with lateral dimensions of some hundreds of µm, were studied by X-Ray diffraction at 260 K to investigate the diffuse scattering. X-ray measurements were carried out at the Swiss Norwegian Beamline BM01 at the European Synchrotron Research Facility using monochromatized λ = 0.6973 Å X-rays. 900 images with 0.4 s exposure times and 0.4° step sizes were collected with a Pilatus2M detector located 247 mm downstream of the crystal. Short 3min data acquisition were performed every 20 K from 100K to 260K. Crystal were cooled using a Nitrogen gas flow cryosystem.

Data reduction -XDS. The structure solved is used a starting point to perform the already outlined steps of data reduction with the program XDS (MPI for Medical Research, Heidelberg). XDS applies the relevant instrumental corrections to the data, finds and indexes Bragg spots, determines the orientation matrix, integrates and corrects the measured intensities.

Reconstruction of reciprocal space. The orientation matrix as output from XDS is used to reconstruct the probed reciprocal space volume via a custom-made python script. The volume is a 3D array composed of 801 x 801 x 801 pixels. Each pixel corresponds to a step in h; k; l of 0.02, 0.03, and 0.08, respectively. The maximum indexes in the three directions are thus h = 9, k = 12, l = 32.

Extraction of the diffuse scattering. Considering the streak positions, a cubic volume is defined around each streak. The remaining portion of reconstructed space which is not contained in the cubic volume is artificially assigned a value of 0. Integration of the intensity contained in the cubic volume is then performed in the h and k directions; moreover, averaging over the symmetry of the pattern is performed. Taking only the portions of the array which have a finite pixel value, a new array of size of 18 x 24 x 800 is constructed.

Fourier Transform, PDF analysis and modelling. The Fourier transform of this array is computed via the FFT algorithm of the Numpy library (Figure S6). The FT of the diffuse intensity is the 3D-ΔPDF of the probed crystal. The PDF is inspected to acquire insights into the disorder present in the sample, so to prepare a model to be refined with the software Yell. This software allows for the specification of a disorder model, starting from the average structure of the crystal (as determined previously). A set of variables corresponding to the parameters quantifying the different kinds of correlations (represented by the green arrow in Figure S6) is then added to the input file to simulate the effects of disorder on the average structure. The disordered model is then used to generate a ΔPDF which is refined against the experimentally obtained one. The outcome of the refinement is thus a value for the correlation parameters which were included in the disorder model. The outcome of such calculation is shown in Figure S6.

Figure 1 .

 1 Figure 1. X-ray analysis of Pd(cptn)2Br]Br2 MX chains a) Schematic representation in halogen-bridged metal compounds (MX chains) of the Mott Hubbard (left) and the Charge Density Wave states (right)

Figure 2 .

 2 Figure 2. ΔPDF of MX-Chains. a) (left) simple model of a + δ

Figure 3 .

 3 Figure 3. a) Yell Disorder model compared to the experimental 3D-ΔPDF. The normalized experimental ΔPDF of the (u, v, 0) plane and

Figure 4 .

 4 Figure 4. a) Experimental 3D-ΔPDF of (u, 0, w) and (0, v, w). Interatomic vectors corresponding to strong ΔPDF peaks are represented in the ΔPDF and in the average structure. Negative correlation is observed at w = 1 and corresponds to anti-phase ordering along the c direction. b) The mixed-valence 2D CDW schematic structure along the c direction. The interatomic vector between bromide counteranion and terminal carbon atom (black arrow) and the displacement of bromine atoms (yellow glooms) and of terminal carbon atom of cptn ligand (yellow glooms and arrows) are represented. Note the a/2 phase shift of the CDW from plane to plane. c) Schematic structure of stacking of two 2D CDW planes d) Schematic representation of A/B ordering along the c direction. The joint probability PA/B is found to be 0. 54, complete disorder corresponding to 0.5. Alternation of A/B planes is more probable. (PA/B = 0.60 was chosen in this schematic representation to enhance the anti-phase ordering)

Acknowledgements

This project was carried out in the frame of the IM-LED LIA (CNRS) and Université de Rennes 1 -Tohoku University international joint program. This work was also partially supported by JSPS KAKENHI (19H05631). M. Y. thanks the support from the 111 project(B18030) from China. We thank Shun-Ichiro Tanaka, Elzbieta Trzop, Philippe Rabiller and Hervé Cailleau for their support.

Author Contributions

Note

The authors declare no competing financial interest.


Suliman M Alshammari
email: sshamari@kacst.edu.sa

Jean-Luc Le Garrec

J Brian

A Mitchell

Electron Collisions with Dimethylamine and Trimethylamine Molecules and Molecular Ions

Keywords:

Experiments are described in which the dissociative recombination of trimethylamine and dimethylamine ions and related product ions, was studied using a Flowing Afterglow Langmuir Probe-Mass Spectrometer (FALP-MS) apparatus. The technique used in this experiment is based on the measurement of the decay of the electron density as an afterglow plasma flows along a drift tube. The results obtained for the DR for dimethylamine and trimethylamine ions were measured using three different methods. The results for trimethylamine ions are in reasonable accord with those for other polyatomic ions while for dimethylamine ions, are unreasonably high and this was explained by the competition from electron capture by neutral dimethylamine molecules.

INTRODUCTION

Cloud formation is an important factor in climate science since they change the local albedo of the earth and of course are responsible for rainfall and other precipitations. The mechanisms behind the nucleation phenomena leading to cloud formation is an active subject therefore, in aerosol science. It has long been recognized, for example, that sulfuric acid (H2SO4) in the upper atmosphere originating from industrial pollution volcanic activity, plays an important role in the initial nucleation process [START_REF] Sihto | Atmospheric sulphuric acid and aerosol formation: implications from atmospheric measurements for nucleation and early growth mechanisms[END_REF] . This has been demonstrated by both theoretical and experimental studies and the role of negative ions, generated by sunlight driven ionization processes, has been shown to act through the generation of acid/water cluster ions that acts as seeds for the generation of cloud condensation nuclei (CCN) the precursors of droplet formation. Ammonia (generated from agricultural sources amongst others) has also been identified as a partner in this process, enhancing the nucleation rate [START_REF] Erupe | The effect of trimethylamine on atmospheric nucleation involving H2SO4[END_REF][START_REF] Kurtén | Amines are likely to enhance neutral and ion-induced sulfuric acid-water nucleation in the atmosphere more effectively than ammonia[END_REF][START_REF] Almeida | Molecular understanding of sulfuric acid-amine particle nucleation in the atmosphere[END_REF] . In a series of experiments however, performed at the CERN laboratory in Geneva, where a beam of high energy particles is made to enter a large cloud chamber equipped with sophisticated chemical analysis equipment (mass spectrometers), it was found that the presence of dimethylamine [START_REF] Praplan | Dimethylamine and ammonia measurements with ion chromatography during the CLOUD4 campaign[END_REF][START_REF] Kirkby | Role of sulphuric acid, ammonia and galactic cosmic rays in atmospheric aerosol nucleation[END_REF][START_REF] Mckean | The structure of dimethylamine[END_REF] displayed a particularly strong catalytic activity, enhancing the nucleation rate by four orders of magnitude. Dimethylamine and trimethylamine are molecules emitted naturally in agriculture and also from decaying fish products. They can also be produced in the atmosphere through light induced chemical reactions involving ammonia. Because of this interest in dimethylamine (DMA) and trimethylamine (TMA), we decided to study the dissociative recombination of dimethylamine and trimethylamine ions using the Flowing Afterglow Langmuir Probe-Mass Spectrometer apparatus in the University of Rennes I since the rate coefficients for these ions have not been examined previously.

EXPERIMENT

The experimental apparatus has been described in detail before [START_REF] Lehfaoui | The dissociative recombination of hydrocarbon ions: I. Light alkanes[END_REF] and only a brief description is given here. The technique is an extension of the conventional FALP technique (Figure 1) that includes a moveable mass spectrometer which is used to identify ions present in the measurement region of the afterglow and to measure the number density of these ions as a function of distance along the flow. Electron concentration along the flow is measured using a Langmuir probe attached to the nose of the mass spectrometer. In this experiment, helium gas was passed through a Zeolyte trap cooled to liquid nitrogen temperature to remove all impurities (water) and then introduced (inlet P1) at a rate of 24 sl min - 1 , into a 4.2 cm diameter glass tube surrounded by a microwave cavity operating at 2.45 GHz. The helium was then ionized by the microwave discharge. The helium gas flowed out of this tube and into an 8.5 cm diameter, 100 cm long, stainless steel chamber, the flow being established by means of a 4000 m 3 /h Roots pump. Typical operating pressures in the flow were from 0.50 to 0.60 Torr (corresponding to a helium density of 1.6 x 10 16 cm -3 and 1.9 x 10 16 cm -3 respectively) and that means that ions underwent many collisions with the buffer gas during their passage through the apparatus. The upstream region of the afterglow contained He + , He 2 + , neutral metastable atoms He m and electrons.

Due to the helium buffer, the hot electrons in the plasma were cooled within a few µs by collisions and the condition where Tgas= Tion= Te was obtained. Argon gas was introduced at a second entry port (inlet P2), downstream, at a rate of 1 sl min -1 in order to produce an Ar + dominated plasma via the reactions: the argon atom density in the plasma being 0.85 x 10 14 cm -3 for the measurements performed at 0.60 Torr and 0.7 x 10 14 cm -3 for those performed at 0.5 Torr.

The absence of He2 + in the mass spectrum (in the measurement area, about 1 cm after the argon injection) verified that reaction (3) had gone to completion, prior to arriving at the measurement region. Given that He2 + is rapidly formed by reaction of He m with Ar (reaction 2) this is a good indication that the metastables had also been removed. Thus, the helium plasma was converted into an argon plasma. The flow then entered a stainless-steel tube at the exit of which an eight-needle entry port (used to avoid aerodynamic perturbation) allowed us to add reactant gases in order to form the molecular ion under study. The identity of the ions formed was measured using the movable mass spectrometer and the electron number density was measured using a Langmuir Probe method. From these measurements, it is possible to determine the rate coefficients for reactions occurring in the flow and these shall be described in the next section.

The experimental conditions during the experiment were, pressure between 0.50 and 0.60 Torr, room temperature 300 K, electron density (1.5 x 10 9 cm -3 < ne < 7.6 x 10 9 cm -3 ) and plasma velocity (1.85 ± 0.15) x 10 4 cm/s (the central flow velocity of the plasma was determined by modulating the discharge and by measuring the time of flight of the resulting disturbance at the Langmuir probe, located on the central axis). Neutral DMA or TMA vapor phase molecules were injected downstream into the plasma without disturbing the aerodynamics of the flow and reacted with the primary ions (Ar + ) present in the plasma leading to the formation of secondary ions via charge transfer processes [START_REF] Ikezoe | Ion-Molecule Reaction Rate Constants through[END_REF] as seen in reactions (6 and 7).

Ar + + (CH3)2NH → (CH3)2NH + + Ar (6) → CH3 + + CH3NH + Ar and Ar + + (CH3)3N → (CH3)3N + + Ar (7) → CH3NH2 + + C2H4 + Ar → CH3 + + C2H6N + Ar

DATA ANALYSIS

The actual measurement of the recombination coefficient in this apparatus can be performed in one of two ways [START_REF] Rebrion-Rowe | The dissociative recombination of hydrocarbon ions: II Alkene and alkyne derived species[END_REF] . For a pure plasma, containing a single ion that does not react with the neutral gas and in which the electron decay is dominated by recombination only, the decay of the electron density ne with time, t, can be written as

𝑑𝑑𝑑𝑑 𝑒𝑒 𝑑𝑑𝑡𝑡 = -𝛼𝛼 𝑛𝑛 𝑒𝑒 2 (I)
where 𝛼𝛼 is the recombination rate coefficient. Equation I is derived, assuming that the electron density is equal to the ion density (i.e., the plasma is neutral and does not contain negative ions) and that only a single ion is present. In a flowing afterglow, it is easy to measure the electron density at several places downstream of a given origin, using for example, a movable Langmuir probe. One can rewrite Eq. (I) in terms of the downstream distance, z and the plasma velocity, v, thus

𝑣𝑣 𝑑𝑑𝑑𝑑 𝑒𝑒 𝑑𝑑𝑑𝑑 = -𝛼𝛼 𝑛𝑛 𝑒𝑒 2 (II)
Integrating Eq. (II) from some arbitrary origin z = z0 to some downstream position z, yields the following expression for 𝑛𝑛 𝑒𝑒 :

� 1 𝑑𝑑 𝑒𝑒 � 𝑑𝑑 = � 1 𝑑𝑑 𝑒𝑒 � 𝑑𝑑 0 + 𝛼𝛼 𝑣𝑣 (𝑧𝑧 -𝑧𝑧 0 ) (III)
Thus, the plot of 1 𝑛𝑛 𝑒𝑒 ⁄ vs 𝑧𝑧, allows us to determine the recombination rate coefficient 𝛼𝛼 if the plasma velocity v is known.

In DMA + and TMA + plasma case, several ions were found to be present in the plasma where the secondary ions reacted with other neutral DMA or TMA molecules to form other ion fragments such as clusters ions. The set of formation reactions for these ions is summarized in Table 2. Therefore, an alternative (and less restrictive) method used for determining the recombination rate from an afterglow measurement was as follows. One can write down the equation for the change in the density [AB + ] of the ions under study as a function of time, t, and therefore of distance, z, along the flow tube, thus

𝑑𝑑[𝐴𝐴𝐴𝐴 + ] 𝑑𝑑𝑡𝑡 = 𝑣𝑣 𝑑𝑑[𝐴𝐴𝐴𝐴 + ] 𝑑𝑑𝑑𝑑 = -𝛼𝛼[𝐴𝐴𝐴𝐴 + ]𝑛𝑛 𝑒𝑒 -𝑘𝑘 [𝐴𝐴𝐴𝐴 + ][𝑋𝑋] - 𝐷𝐷 𝐴𝐴 ⩘ 2 [𝐴𝐴𝐴𝐴 + ], (IV)
where v is the plasma velocity, measured at the centerline of the flow, [X] the density of a reagent, such as an impurity with which the ion can undergo an ion-molecule reaction, ne is the electron density, DA is the coefficient of ambipolar diffusion and ⩘ is the characteristic diffusion length. By integrating Eq. (IV) from some initial starting point, z0 to some position, z, one obtains the following solution:

𝑣𝑣 ln

[𝐴𝐴𝐴𝐴 + ] 𝑧𝑧 [𝐴𝐴𝐴𝐴 + ] 𝑧𝑧 0 = -𝛼𝛼 ∫ 𝑛𝑛 𝑒𝑒 𝑑𝑑𝑧𝑧 - 𝑑𝑑 𝑑𝑑 0 �𝑘𝑘[𝑋𝑋] + 𝐷𝐷 𝐴𝐴 Λ 2 � (𝑧𝑧 -𝑧𝑧 0 ) , (V)
where [𝐴𝐴𝐴𝐴 + ] 𝑑𝑑 and [𝐴𝐴𝐴𝐴 + ] 𝑑𝑑 0 are the ion number densities at position 𝑧𝑧 and 𝑧𝑧 0 , respectively.

It can be seen from this equation that if the ion-molecule reaction and diffusion losses are small compared to those due to recombination, the change in the number density of [AB + ] with distance is proportional to the integral of the electron density over z, from the starting point z0 to the point where the measurement is made. The constant of proportionality is 𝛼𝛼/𝑣𝑣 where v is the velocity of the plasma. The crucial thing to notice about this method is that since the effects of ion-molecule reactions due to interaction with impurity species (or with one of the secondary plasma components), are independent of the electron density, they should not interfere with the determination of α, provided one sees a decrease in the ion density as a function of distance along the flow. Even if diffusion losses are not small, as long as Eq. (V) is a good description of the ion decay process, the term due to diffusion remains constant and thus does not interfere with the determination of 𝛼𝛼.

In this case, it is still possible to use Eq. (V) to determine α, by measuring the ratio on the Left-Hand Side (LHS) but at a fixed value of z for different electron densities. Indeed, ion molecule reactions do not depend on the electron density but only on the density of the reactant gas and time, i.e. the position z in the reaction zone. Variation of the electron density in the flow can be achieved, in practice, by varying the position of the microwave cavity with respect to the helium inlet port (P1). In this method, the second term on the RHS is now constant (being independent of electron density) and only reactions involving electrons are taken into consideration. Therefore, assuming that electron attachment does not occur in these chemical reaction networks, only dissociative electron recombination plays a role in the evolution of both the ions and electron density.

This analysis is well suited to the study of ions which are not terminal and that are being produced and destroyed along the flow. Fixing a z position and varying the electron density allow the dissociative recombination rate coefficient to be determined, electron density being the only variable parameter. In fact, the rate coefficient for recombination was determined in most of the experiments, described in this report by measuring [AB + ] at a fixed z position for several different electron densities as well as at variable z positions for a given electron density, for a known plasma velocity. 9

(CH 3 ) 2 NH + + (CH 3 ) 2 NH + He → ((CH 3 ) 2 NH) 2 + + He - - TMA + formation 10 CH 3 + + (CH 3 ) 3 N → (CH 3 ) 3 NH + + CH 2 6.30 x 10 -10 [15]
11

CH 3 NH 2 + + (CH 3 ) 3 N → (CH 3 ) 3 N + + CH 3 NH 2 → (CH 3 ) 3 NH + + CH 2 NH 2 1.60 x 10 -9 [16]
12

(CH 3 ) 3 N + + (CH 3 ) 3 N → (CH 3 ) 3 NH + + (CH 3 ) 2 NCH 2
1.50 x 10 -9 [16] 13

(CH 3 ) 3 N + + (CH 3 ) 3 N → products 8.20 x 10 -10 [17]
14

(CH 3 ) 3 NH + + (CH 3 ) 3 N → ((CH 3 ) 3 N) 2 ). H + - [18]

RESULTS AND DISCUSSION

Measurements of the DR Rate Coefficient for TMA Molecular Ions

The reactant gas was mixed with helium in the required ratio (TMA gas diluted with He gas at a ratio of about 1:50) before injection into the flow tube with flow rates such as to obtain densities of TMA molecules in the range ~1.4 -4 x 10 12 cm -3 .

In our plasma, and for a TMA gas density of 1.4 x 10 12 cm -3 , it was found that ion-molecule reactions of the Ar + dominated plasma with neutral TMA molecules, generated (CH3)3N + (m/q=59), protonated trimethylamine (CH3)3NH + (m/q =60) and other fragments ions such as

CH 3 + (m/q=15), CH3NH + (m/q=30), methylamine CH3NH 2 + (m/q=31
) and (CH2)3NH + (m/q =57). as shown in Figure 2.

The formation of some of the major ion products of the reaction of Ar + with (CH3)3N via charge transfer reactions can be explained by reaction (7). Ion products such as CH 3 + and methylamine CH 3 NH 2 + reacting with neutral TMA molecules, lead to the production of more TMA molecular ions and protonated TMA ions as can be seen in reaction (10 and 11). The mass spectrum thus obtained is shown in Figure 2. In order to remove all the precursor ions in the reaction zone, the number density of TMA molecules was increased to 4.0 x 10 12 cm -3 and, the ion peaks then found in the mass spectrum measured at z0 = 30 mm are attributed to TMA + (m/q = 59) ion, protonated TMA (m/q = 60) ion and to the cluster ions ((CH3)3N)2 + (m/q = 118), ((CH3)3N)2.H + (m/q = 119). We found that the signal peaks of TMA + and protonated ions were reduced when moving the mass spectrometer further downstream from the injection port of TMA mixture and this loss, due to the reaction with neutral TMA molecules and electrons and indeed further clustering, can be seen in Figure 3.

It should be noted that in this experiment, there are many ions present in the measurement region and that these ions react with other molecules to form cluster ions. Given that several ions were seen to be present in the mass spectra, the measurement protocol was applied for multiple ions present in the plasma as described in equation V. In the FALP-MS at room temperature and at a relatively high pressure of He and TMA, the formation of cluster ions via a three-body association reactions and their destruction by ion-molecule reactions with neutral TMA molecules and recombination with electrons can play an essential role. In such cases, we have to consider the reactions (10-14).

The balance equation for the studied ion (i.e. TMA + ) can be written as:

ln( [TMA + ] 𝑧𝑧 [TMA + ] 𝑧𝑧 0 ) = - 𝛼𝛼 𝑣𝑣 ∫ 𝑛𝑛 𝑒𝑒 𝑑𝑑𝑧𝑧 - 𝑑𝑑 𝑑𝑑 0 1 𝑣𝑣 �𝑘𝑘[TMA] + 𝐷𝐷 𝐴𝐴 Λ 2 � (𝑧𝑧 -𝑧𝑧 0 ) (VI)
Values for the recombination rate coefficient were determined in several measurements where ln ( [TMA + ] 𝑧𝑧

[TMA + ] 𝑧𝑧 0
) was plotted as a function of ∫ 𝑛𝑛 𝑒𝑒 𝑑𝑑𝑧𝑧 𝑑𝑑 𝑑𝑑 0 measured for multiple z positions. Figure 4 shows an example such a plot [START_REF] Sihto | Atmospheric sulphuric acid and aerosol formation: implications from atmospheric measurements for nucleation and early growth mechanisms[END_REF] . Knowing the plasma velocity, the recombination rate coefficient α is obtained from the slope of this plot. These measurements however, do not take into account the influence of ion-molecule reactions (in this case clustering) which also lead to a change of [TMA + ] as a function of z. Hence the multiple ion/fixed z method was employed to yield the recombination rate coefficient. In this case the only variable is the electron number density which is independent of ion-molecule reactions and so the latter can be ignored. As described above, the upstream electron number density was varied while monitoring the ion number density of TMA + or TMA.H + at fixed z. The plots of ln([TMA + ]z /[ TMA + ]z0) and ln([TMA.H + ]z /[ TMA.H + ]z0) versus integrated electron density yield α/v as the slope. The measurement was performed with several initial electron densities (4.5, 5.9 and 7.6 x 10 9 cm -3 ) at fixed z, and the results obtained were found to yield linear plots as shown (for TMA + ) in Figure 5. Within the accuracy of the FALP-MS measurements, the recombination rate coefficient for TMA + ion and TMA.H + were measured several times and the mean values are presented in Table 3. The values quoted include combined statistical and systematic uncertainties. The values of DR rates obtained by both methods were consistent for these two ions and so it would seem that the effects of diffusion or ion-molecule reactions do not have a major effect on the measurements in this case. Our measured rates coefficients for TMA + and TMA.H + are in reasonable accord with those for other polyatomic ions [START_REF] Adams | Measurements of the dissociative recombination coefficients for several polyatomic ion species at 300 K[END_REF] (e.g. 1.4 x 10 -6 cm 3 s -1 for CH3NH3 + ). Equation I, does not take into account, any electron loss effects due to electron attachment. To check if this was justified, the voltages on the mass spectrometer were inverted and a search was made for negative ions. No negative ions were found in the TMA plasma. Therefore, we can say that there was no electron attachment to the neutral TMA molecule found in our measurements and in fact this observation is borne out by measurements made by other workers [START_REF] Culbertson | Fates of the molecular anions of SF6 and C7F14 upon recombination with positive ions[END_REF] .

Measurements of DR Rate Coefficient for DMA Molecular Ions

It was found that dimethylamine vapor, when introduced at a density of 1.7 x 10 12 cm -3 via the eight-needle entry port into the sampling region of the apparatus, reacted with argon ions, producing several ions including CH 3 + (m/q = 15) and (CH 3 ) 2 NH + (m/q = 45) which went on to react with the parent dimethylamine vapor to produce species such as CH 3 NH + (m/q = 30), (CH 3 ) 2 NH 2 + (m/q = 46) and dimer ((CH 3 ) 2 NH) 2 + ion (m/q = 90 ), and these could be described by reactions (7, 10 and 11), and the mass spectra for these ion masses shown in Figure 6.

It is seen that the parent molecule (CH 3 ) 2 NH + and the dimer ((CH 3 ) 2 NH) 2 + ions are the majority ions and all other fragment ions are much less abundant. The main purpose for introducing the low density of DMA was to explore the formation of source ions (such as CH 3 + ) which react very fast to form the major product ions. Figure 6 is plotted for several different z positions and it is seen that the peaks with mass less than or equal to 40, disappear downstream, the DMA + peak decreases regularly and the dimer ion peak increases. The trimer ions peak is also seen to grow. By increasing the density of dimethylamine to 4.5 x 10 12 cm -3 , a spectrum was found with, (CH3)2NH + , (m/q = 45) (CH 3 ) 3 NH + (m/q = 60) and the cluster ions ((CH3)2NH)2 + (m/q = 90), ((CH 3 ) 2 NH) 3 + (m/q = 135) and the source of most these ions disappeared as shown in Figure 7. It can be seen that when the dimethylamine concentration was increased, the mass 45 amu and 90 amu peaks due to the DMA + ion and the dimer (DMA)2 + were seen to decrease (the dimer peaks much less rapidly than the monomer peak) while the mass 135 amu due to the (DMA)3 + ion, was seen to increase. This is because the dimer (DMA)2 + ion is present in large abundance and reacted continually with neutral DMA molecules to form the (DMA)3 + .

The decrease of the (DMA)3 + ion signal could be seen at higher density of DMA and it also could possibly be undergoing further reactions with neutral DMA molecules to produce further clustering beyond our measurable mass range. The mass 60 amu due to (CH 3 ) 3 NH + increases slightly downstream.

The experiment was performed with a dimethylamine density of 4.5 x 10 12 cm -3 and at initial electron number density of 1.5 x 10 9 cm -3 . Using the multiple ion/ z variable method , from several measurements we found the average value for the apparent recombination rate coefficient for the (CH 3 ) 2 NH + ion was 5 x 10 -5 cm 3 s -1 , for ((CH 3 ) 2 NH) 2 + , 6.5 x 10 -5 cm 3 s -1 and for ((CH 3 ) 2 NH) 3 + 5.4 x 10 -5 cm 3 s -1 . An example of these measurements is shown (for DMA + ) in Figure 8. In fact, these rates are considered to be unreasonably high as such values have never been seen for ground state monomer ions. Indeed, never even for highly clustered ions [START_REF] Smith | Attachment coefficients for the reactions of electrons with CCl4, CCl3F, CCl2F2, CHCl3, Cl2 and SF6 determined between 200 and 600 K using the FALP technique[END_REF] . As a check, the multiple ions/ fixed z method was applied and the results for both methods (illustrated for DMA + in Figure 9) are summarized in Table 4. Table 4: Measured values of apparent recombination rates determined using the methods of multiple ions present in the plasma. Fitting errors are quoted to allow a comparison to be made between the individual measurements. Note that these values are just given as apparent output from the method and should in no way be considered as real as the method has yielded values which are abnormally high.

Ion

Number of data points

Apparent recombination rate coefficient [10 -5 cm 3 s -1 ] Multiple ions/z variable method Multiple ions/fixed z method It is seen that unlike the case for TMA ions, the values obtained are quite different, being between 2 and 4 times smaller. This still leaves unreasonably large apparent rate coefficients for the DMA monomer, dimer and trimer ions examined. For this reason, it was decided to check to see if there could be interference due to electron attachment which would compete with DR for electron removal and hence yield over-determined values.

(CH 3 ) 2 NH + ((CH 3 ) 2 NH) 2 + ((CH 3 ) 2 NH) 3 +
The polarity of the quadrupole mass analyser was inverted (from negative to positive ion mode). In this case, it was found that a negative ion was present in the plasma, namely HCNH -at m/q = 28 amu as shown in Figure 10, indicating the presence of the electron attachment processes in the plasmas, forming negative ions. It was indeed observed that the negative ion counting rate increased regularly as the mass spectrometer was moved from the needle entry port position to the downstream part of the flow. Given this observation it was decided to examine the electron attachment process in more detail and to obtain its rate coefficient.

Electron Attachment to Neutral DMA Molecule

Although our FALP-MS apparatus is essentially dedicated to studying the dissociative recombination process, it is also possible to measure the rate coefficient for electron attachment reactions. The coefficient rate β for electron attachment with neutral DMA molecule was obtained by introducing into the plasma flow (dominated by Ar + ions), a mixture composed of dimethylamine (CH 3 ) 2 NH and helium gas (the ratio of DMA/He mixture was about 1:50).

Since [DMA] >> [DMA + ], as a first crude approximation, one can ignore the influence of recombination in the plasma compared to that of electron attachment [START_REF] Smith | Attachment coefficients for the reactions of electrons with CCl4, CCl3F, CCl2F2, CHCl3, Cl2 and SF6 determined between 200 and 600 K using the FALP technique[END_REF][START_REF] Carles | Electron and ion reactions with hexamethyldisiloxane and pentamethyldisiloxane[END_REF] , and in this case, the electron density, ne would vary as a function of neutral DMA density [DMA], as

𝑑𝑑𝑑𝑑 𝑒𝑒 𝑑𝑑𝑡𝑡 = 𝑣𝑣 𝑑𝑑𝑑𝑑 𝑒𝑒 𝑑𝑑𝑑𝑑 ~ -β [DMA]𝑛𝑛 𝑒𝑒 (VII)
where β is the attachment rate coefficient and it is assumed that diffusion is negligible. After integration, equation VII is reduced to:

ln(𝑛𝑛 𝑒𝑒 ) 𝑑𝑑 = ln(𝑛𝑛 𝑒𝑒 ) 𝑑𝑑 0 -� 𝛽𝛽 [𝐷𝐷𝐷𝐷𝐴𝐴] 𝑑𝑑 𝑣𝑣 � , (VIII)
where 𝑧𝑧 0 is the position where the first measurement is performed. The plot of ln(ne)z versus z would therefore yield a straight line whose slope is -β [DMA] 𝑣𝑣 ⁄ . Performing measurements of electron density decay for different DMA densities in the flow would give a series of lines with negative slopes. Figure 11 shows these series of lines at different DMA densities in the flow. The slopes of these lines yield the first order electron attachment rate coefficient 𝑘𝑘 1𝑠𝑠𝑡𝑡 . By plotting these negative slopes which are obtained from equation IX as a function of neutral DMA density, we obtained a straight line as expected (see Figure 12) for which its slope is -𝛽𝛽 /𝑣𝑣 Then, by multiplying it by the plasma velocity v (in our measurements, v = 1.85 x 10 4 cm/s), we get the electron attachment rate coefficient (𝛽𝛽). We performed two such measurements and the mean value of 𝛽𝛽 was found to be (5.0 ± 1.5) x 10 -10 cm 3 s -1 taking into account an uncertainty of about 30%. The value of 𝛽𝛽 obtained with an initial electron density of 7.5 x 10 9 cm -3 can be considered to be an upper limit of the electron attachment value. This is because we have neglected recombination which also reduces the measured electron density.

𝑘𝑘 1𝑠𝑠𝑡𝑡 = -𝛽𝛽 [𝐷𝐷𝐷𝐷𝐴𝐴]/𝑣𝑣 (IX)

Calculation of the Actual Recombination Rate for DMA Molecular Ions

In this section we shall examine the possibility of extracting the actual recombination coefficient for DMA ions assuming that it is not so large as to render the attachment rate determination uncertain. To perform this modelling we can consider the change of electron density with time (

d𝑑𝑑 𝑒𝑒 dt
) as a function of both the recombination of electrons with the DMA ions and electron attachment with neutral DMA:

d𝑑𝑑 𝑒𝑒 dt = -[∑ 𝛼𝛼 𝑖𝑖 𝐷𝐷 𝑖𝑖 + 𝑖𝑖 ]𝑛𝑛 𝑒𝑒 -𝛽𝛽 [M]𝑛𝑛 𝑒𝑒 , (X)
where the [∑ 𝐷𝐷 𝑖𝑖

+ 𝑖𝑖

] is the sum of the ion densities in the plasma and [M] is the neutral density. We can take equation X and re-write it in the form:

-[∑ 𝛼𝛼 𝑖𝑖 𝑚𝑚𝑒𝑒𝑚𝑚𝑠𝑠𝑚𝑚𝑚𝑚𝑒𝑒𝑑𝑑 𝐷𝐷 𝑖𝑖 + 𝑖𝑖 ]𝑛𝑛 𝑒𝑒 = -[∑ 𝛼𝛼 𝑖𝑖 𝑚𝑚𝑒𝑒𝑚𝑚𝑟𝑟 𝐷𝐷 𝑖𝑖 + 𝑖𝑖 ]𝑛𝑛 𝑒𝑒 -𝛽𝛽 𝑚𝑚𝑒𝑒𝑚𝑚𝑠𝑠𝑚𝑚𝑚𝑚𝑒𝑒𝑑𝑑 [M]ne (XI)
We can insert the values from Table 3, for example →∑ 𝛼𝛼 𝑖𝑖 𝑚𝑚𝑒𝑒𝑚𝑚𝑠𝑠𝑚𝑚𝑚𝑚𝑒𝑒𝑑𝑑 𝑖𝑖 ~ 5.7 x 10 -5 cm 3 s -1 , β = 5 x 10 -10 cm 3 s -1 and [M] = 4.5 x 10 12 cm -3 , and let us say that the actual rate coefficient for the recombination of DMA + is 1 x 10 -6 cm 3 s -1 , in line with that for TMA + with those for the dimer and trimer ions being 2 x 10 -6 . Thus: However, the typical initial electron density in these experiments was 1.5 x 10 9 cm -3 , i.e. a factor of 30 greater. One possibility is that there are other heavier cluster ions which are beyond the mass range of our mass spectrometer but these would contribute to both sides of equation XI and so it is unlikely, though impossible to verify, that this would compensate for this discrepancy. Equations X and XI of course neglect the fact that when there is an attaching gas in the plasma, some of the negative charge resides with the negative ions formed, thus:

𝑛𝑛 𝑒𝑒 + ∑ �𝐷𝐷 𝑗𝑗 -� = ∑ [𝐷𝐷 𝑖𝑖 + ] 𝑖𝑖 𝑗𝑗

Negative ion products

As mentioned above, when searching for negative ions with DMA, only HCNH -was found. In fact, the formation of HCNH -is endothermic by about 4 eV. How then could such an endothermic channel appear? Firstly, it should be noticed that the observed signal for HCNH - (Figure 10) is very much weaker than typical positive ion signals routinely measured in this apparatus (Figures 6,7). This suggests that this is very much a minority process. More important however, is the fact that the FALP-MS apparatus operates with a movable mass spectrometer which is used not only to identify the ions in the plasma but also as a means of determining rate coefficients. This mass spectrometer is illustrated schematically in Figure 13. The ions in the plasma enter the instrument, contained in a differentially pumped, movable vacuum chamber, via the grounded inlet cone. During operation, various voltages are applied to the electrodes L1-L5. In these experiments, ± 2 volts were applied to the electrode L1 in order to draw in the negative/positive ions and then ± 50 volts to the aperture L2 (and to L3) so that the ions would have sufficiently velocity to be analysed by the radiofrequency quadrupole analyser2 . Hence ions entering the instrument are accelerated and if they collide with an aperture, and are thus dissociated by ion-surface collisions, it is possible that an endothermic channel can be accessed. Positive ions and cluster ions are robust structures and such a dissociation is less likely to occur than for negative ions where the binding energy of the attached electron is typically less than a few electron volts at most. In particular, negative clusters are expected to be fragile and we believe that this acceleration necessary for the operation of the mass spectrometer, is responsible for the disintegration of these clusters, entering the instrument, (by both surface and buffer gas collisions) so that we were not able to observed them. This is a known problem in mass spectrometer-based studies of cluster ions and particularly of negative cluster ions [START_REF] Hayhurst | The effects of applying electric fields on the mass spectrometric sampling of positive and negative ions from a flame at atmospheric pressure[END_REF] . Hence, given this addition of kinetic energy to the ions (and in particular for the case of negative ions), it is possible for the dissociation to an endothermic channel to be observed. This suggests that the formation of HCNH -is a rather rare reaction path and that other products are formed in the electon attachment, which are not seen. Although positive cluster ions are seen in the mass spectrum shown in Figure 7, negative cluster ions are not seen in the mass spectrum for negative ions shown in Figure 10. This could be because these ions would be destroyed by field induced electron detachment and collisions during the ion sampling process. Positive cluster ions are much more stable than negative cluster ions. A lightly bound electron could be stripped off during the ion sampling processes, and the resulting neutral cluster would dissociate. Thus we were able to see positive cluster ions though not negative ions. This is clearly a subject of speculation at this stage and will eventually be the subject of further study.

DISCUSSION AND CONCLUSION

In this study, we have measured the absolute rate coefficients for the dissociative recombination of trimethylamine and protonated trimethylamine cations with electrons. They are respectively, α1 = (1.3 ± 0.4) x 10 -6 cm 3 s -1 and α2 = (1.5 ± 0.5) x 10 -6 cm 3 s -1 taking into account the total measurement uncertainty of 30%. The measurements were performed using two techniques as discussed in the text (method B and C) and the obtained values for recombination rate were consistent for a given ion (see Table 2). A search was made for electron attachment to neutral TMA was made but no evidence for this was found indicating that this process is negligible in the Ar/TMA plasma chemistry.

On the other hand, the electron attachment to the neutral dimethylamine molecule was studied and we found that the parent molecule does undergo electron attachment, and this produces electron loss and so interferes with the recombination measurement. The measured rate for electron attachment was (5.0 ± 1.5) x 10 -10 cm 3 s -1 . Rate coefficients for the dissociative recombination of dimethylamine and cluster ions with electrons were measured using methods B and C but the values obtained were anomalously high (several x 10 -5 cm 3 s -1 ) even for polyatomic ions and so we should ignore these. A possible explanation has been presented for this involving the mutual neutralisation of negative and positive cluster ions, the effect of which would not be eliminated by method C. Thus, although we have been able to measure the rate coefficient for electron attachment and we have not been able to give a rate coefficient for the DR of DMA ions.

What is clear from our measurements is that DMA is a molecule which clusters very easily, and in the upper atmosphere it can be ionized, for example by cosmic rays or other ionization processes or attach electrons to form negative ions which then form negative clusters though we have only been able to speculate on this. This fact is perhaps the reason that the influence of DMA in the upper atmosphere is to increase the rate of nucleation of water droplets and thus the formation of clouds [START_REF] Kurtén | Amines are likely to enhance neutral and ion-induced sulfuric acid-water nucleation in the atmosphere more effectively than ammonia[END_REF][START_REF] Praplan | Dimethylamine and ammonia measurements with ion chromatography during the CLOUD4 campaign[END_REF] . This is a phenomenon which deserves further study of the underlying chemical processes and will be the subject of follow-on research to be conducted in the new accelerator laboratory in the KACST laboratory in Riyadh, Saudi Arabia.

Fig. 1 :

 1 Fig. 1: Sketch of FALP-MS apparatus at University of Rennes 8

Fig. 2 :

 2 Fig. 2: Mass spectrum in the reaction chamber for a trimethylamine density of 1.4 x 10 12 cm -3 taken at 30 mm downstream from the injection port of the TMA/He mixture into an Ar + dominated plasma.

Fig. 3 :

 3 Fig. 3: Mass spectrum in the reaction chamber for a trimethylamine density of 4.0 x 10 12 cm -3 taken at 30 mm downstream from the injection port of the TMA/He mixture into an Ar + dominated plasma.

Fig. 4 :

 4 Fig. 4: Plot of the logarithm of [(CH3)3N + ] at position z over [(CH3)3N + ] at position z0 as a function of the electron density integral divided by the plasma velocity (v =1.85 .10 4 cm/ s). The slope gives the rate coefficient for dissociative recombination of (CH3)3N + .

Fig. 5 :

 5 Fig. 5:The ratio of the density of [(CH3)3N + ] at a single value of z = 90 mm downstream from the origin to the density at z0 vs the integral of the electron density from z0 to z, for three different initial electron densities, 4.5, 5.9 and 7.6 x 10 9 cm -3 .

Fig. 6 :

 6 Fig. 6: Mass spectrum in the reaction chamber for a dimethylamine density of 1.7 x 10 12 cm -3 taken at different z positions downstream from the injection port of the DMA/He mixture into an Ar + dominated plasma.

Fig. 7 :

 7 Fig. 7: Mass spectrum in the reaction chamber for a dimethylamine density of 4.5 x 10 12 cm -3 taken at different z positions downstream from the injection port of the DMA/He mixture into an Ar + dominated plasma.

Fig. 8 :

 8 Fig. 8: Plot of the logarithm of [(CH 3 ) 2 NH + ] at position z over [(CH 3 ) 2 NH + ] at position z0 as a function of the electron density integral divided by the plasma velocity (v=1.85 x 10 4 cm/s). The slope gives the rate coefficient for dissociative recombination of (CH 3 ) 2 NH + .

Fig. 9 :

 9 Fig. 9:The ratio of the density of [(CH3)2NH + ] at a single value of z = 70 mm downstream from the origin to the density at z0 vs the integral of the electron density from z0 to z, for three different initial electrons densities.

Fig. 10 :

 10 Fig. 10: Evolution of the HCNH -ion at two different z position downstream from the injection port of DMA mixture with a neutral DMA density of 4.5 x 10 12 cm -3 .

Fig. 11 :

 11 Fig. 11: Plots of the logarithm of different electron densities for different DMA concentrations as a function of different z positions along Langmuir probe distance.

Fig. 12 :

 12 Fig. 12: Plot of the k1st = -𝛽𝛽 [DMA] v as a function of the different DMA densities. The slope (𝛽𝛽 /𝑣𝑣) of this plot multiplied by plasma velocity (v = 1.85 x 10 4 cm/s) gives us the electron attachment rate. In this example (𝛽𝛽 = 4.8 x 10 -10 cm 3 s -1 ).

Fig. 13 :

 13 Fig. 13: Schematic of the lens structure of the quadrupole mass analyser in the FALP-MS apparatus.

Table 1 :

 1 Main reactions occur in conversion of the helium plasma to Ar + dominated plasma.

	No	Reaction	Rate Coefficient	References
			(cm 3 s -1 )
		He
	1	He + + He + He → He2 + + He	1 x 10 -31	[9]
	2	He m + He m → He + + He + e -	5 x 10 -9	[10]
		→ He + 2 + e -	5 x 10 -9	[11]
		Ar
	3	He m + Ar→ He + Ar + + e	7 x 10 -11	[9]
	4	He + + Ar → Ar + + He	1 x 10 -13	[12]
	5	He2 + + Ar → He + He + Ar +	2 x 10 -10	[9]

Table 2 :

 2 Main reactions taking place in the formation of DMA + and TMA + ions.

	No	Reaction	Rate Coefficient	Ref
			(cm 3 s -1 )
		DMA + formation
	8	CH 3 + + (CH 3 ) 2 NH → (CH 3 ) 2 NH 2 + + CH 2	2.10 x 10 -9	[14]

Table 3 :

 3 Measured recombination rate coefficient for TMA + and TMA.H + ions at T= 300 K. In this case, statistical errors of 30% are quoted.

			Recombination rate coefficient
	Ion	Number of		[10 -6 cm 3 s -1 ]
		data points	Multiple ions/z	Multiple ions/fixed z
			variable method	method
	(CH3)3N +
	(CH3)3NH +

Similar plots were obtained ln ([TMA. H + ] z /[TMA. H + ] z 0 ) versus ∫ 𝑛𝑛 𝑒𝑒 𝑑𝑑𝑧𝑧. In the following, only plots for the primary ions are presented, those for other ions studied being similar.

(L4 is used to deflect ions exiting from the quadrupole analyser into the multi-channel plate detector (MCP) and a voltage of about ± 2.5 kV is applied to L5 to accelerate them so that they can be efficiently detected).

ACCEPTED MANUSCRIPT -CLEAN COPY

With regard to the actual measurements, again we see that the recombination of a polyatomic molecule (TMA) has a recombination rate little different from that of other polyatomic ions. The attachment behavior on the other hand is completely different for TMA and DMA. This is the striking difference between recombination and attachment processes, where in the latter case, rate coefficients for molecules of the same families such as halocarbons can differ by as much as 5 orders of magnitude [START_REF] Christophorou | Electron-Molecule Interactions and Their Application[END_REF] while DR rates fall within a narrow range [START_REF] Florescu-Mitchell | Dissociative recombination[END_REF] . This may be because in DR, the process passes via a myriad of Rydberg states which take part in the electron capture process while for DEA, it must involve a direct transition from the neutral to the final ionic state, and the availability of such as state will determine the likelihood of the process.

Notes

The authors declare no competing financial interest.

 ACKNOWLEDGMENTS S. Alshammari thanks the King Abdulaziz City for Science and Technology (KACST) for funding this work under grant no: 162-28 which underlies this manuscript. Valuable discussions with Dr. Bertrand Rowe are also gratefully acknowledged.