Michael E Ries
email: m.e.ries@leeds.ac.uk

Asanah Radhi

Stephen M Green

Jamie Moffat

Tatiana Budtova

Microscopic and Macroscopic Properties of Carbohydrate Solutions in

Keywords: cellulose, cellobiose, glucose, carbohydrate, ionic liquid, NMR, relaxometry, viscosity, diffusion

come

INTRODUCTION

In 1914 Walden defined an ionic liquid (IL) to be a salt, which has a liquid state below 100 °C at atmospheric pressure. [START_REF] Walden | Molecular magnitude and electrical conductivity of some fused salts[END_REF] Since then, and particularly more recently, there has been much research into using ILs as "green" solvents. [START_REF] Angell | Ionic Liquids: Past, present and future[END_REF][START_REF] Plechkova | Applications of ionic liquids in the chemical industry[END_REF][START_REF] Short | Out of the Ivory tower[END_REF][START_REF] Wang | Ionic liquid processing of cellulose[END_REF][START_REF] Welton | Room-temperature ionic liquids. Solvents for synthesis and catalysis[END_REF][START_REF] Zhu | A Mini-Review on Greenness of Ionic Liquids[END_REF] This is because their properties can include low to negligible vapor pressure, high thermal stability, low flammability and the ability to dissolve natural compounds such as polysaccharides. [START_REF] Zhu | Dissolution of cellulose with ionic liquids and its application: a mini-review[END_REF] In 1934, Graenacher [START_REF] Graenacher | Cellulose solution[END_REF] obtained a patent for, amongst other things, dissolving cellulose with molten N-ethylpyridinium chloride. This salt has a melting point at 118 °C and therefore does not fall under the prior Walden definition of an ionic liquid. Swatloski et al in 2002 published on the use of imidazolium based ionic liquids to dissolve cellulose. [START_REF] Swatloski | Dissolution of cellose with ionic liquids[END_REF] In this work the authors measured the solubility of cellulose in a variety of salts and found that 1butyl-3-methyl-imidazolium chloride [C4mim][Cl] dissolved the greatest amount of cellulose, up to 25 wt % upon microwave heating.

It is often said that cellulose is the world's most abundant biopolymer, and it is indeed one of the most studied with the term "cellulose" dating back to 1839 and the pioneering work of Payen. [START_REF] Klemm | Cellulose: Fascinating biopolymer and sustainable raw material[END_REF] As cellulose does not melt, the processing of cellulose requires dissolution and/or derivatisation, with objects such as fibres and films being formed. Therefore, understanding cellulose dissolution is a very important topic. Despite this and the long history of cellulose research, the dissolution of cellulose is still puzzling and consequently generates much research output. [START_REF] Medronho | Rationalizing cellulose (in)solubility: reviewing basic physicochemical aspects and role of hydrophobic interactions[END_REF] Commonly in the literature [START_REF] Sescousse | Viscosity of Cellulose-Imidazolium-Based Ionic Liquid Solutions[END_REF] the reason given for the insolubility of cellulose in water and typical organic solvents is the many intra-and inter-hydrogen bonds present. [START_REF] French | Glucose, not cellobiose, is the repeating unit of cellulose and why that is important[END_REF] Recently though the "Lindman hypothesis" reminded the community that cellulose is amphiphilic and that the hydrophobic interactions will also be an important aspect of the solubility of cellulose. [START_REF] Glasser | About the structure of cellulose: debating the Lindman hypothesis[END_REF] Understanding the dissolution of cellulose is an active topic, involving various experimental tools and molecular modelling. [START_REF] Sescousse | Viscosity of Cellulose-Imidazolium-Based Ionic Liquid Solutions[END_REF] For example, Gentile and Olsson 17 used pulsed field gradient (PFG) nuclear magnetic resonance (NMR) to measure the self-diffusion coefficients in solutions of microcrystalline cellulose and dissolving pulp in aqueous tetrabutylammonium hydroxide (TBAH). It was demonstrated that the TBA+hydrogen ions and the water molecules had a distinct diffusion dependence on cellulose concentration, indicating quite different molecular interactions with cellulose. One key result was that TBAH binds to cellulose such that there are 1.2 ions associated with each glucose unit, with this number being independent of the cellulose molecular weight. An extensive study was carried out by Zhang et al [START_REF] Zhang | Understanding cellulose dissolution: effect of the cation and anion structure of ionic liquids on the solubility of cellulose[END_REF] in which the solubility of carbohydrates was examined across ionic liquids consisting of eleven different cations and four different anions. The authors used 1 H and [START_REF] Sescousse | Viscosity of Cellulose-Imidazolium-Based Ionic Liquid Solutions[END_REF] C NMR spectroscopy and tracked the change in chemical shift of the various resonances as a function of cellobiose concentration. It was shown that the hydrogen bond interaction between the ions and the hydroxyl groups (OH) on the cellobiose is the dominant process in the dissolution. The anions associated with the hydrogen atoms of the OH groups, whereas the cations associated with the oxygen atoms. Computer simulation work by Bharadwaj et al [START_REF] Bharadwaj | Elucidating the conformational energetics of glucose and cellobiose in ionic liquids[END_REF] examined glucose and cellobiose in water and three imidazolium based ionic liquids. It was found that increasing the alkyl chain length of the cation did not alter the solvation of the OH groups of the cellobiose and glucose by the acetate anion.

Fourier transform infrared spectroscopy (FTIR) and multi nuclear NMR spectroscopy were combined with conductivity measurements by Zhang et al [START_REF] Zhang | Dissolution Mechanism of Cellulose in N,N-Dimethylacetamide/Lithium Chloride: Revisiting through Molecular Interactions[END_REF] to determine the molecular interactions in solutions of cellulose and N,N-dimethylacetamide (DMAc)/LiCl. They showed that Li + -Cl -pairs are broken and the Cl -then forms strong hydrogen bonds with the OH groups of cellulose. Fully atomistic molecular dynamic simulations by Schutt et al [START_REF] Schutt | In silico insights into the solvation characteristics of the ionic liquid 1-methyltriethoxy-3-ethylimidazolium acetate for cellulosic biomass[END_REF] examined the effect of adding oxygen atoms to the tail of an imidazolium cation on cellulose dissolution, using cellobiose and glucose as model cellulose compounds. The modification of the solvent tail was found to lower its viscosity, with the anion's interactions with the OH groups of the glucose or cellobiose playing a key role in determining the bulk solution properties. Zhao et al [START_REF] Zhao | Insight into the Cosolvent Effect of Cellulose Dissolution in Imidazolium-Based Ionic Liquid Systems[END_REF] used molecular dynamic simulations and quantum chemistry calculations to examine the effects of co-solvent on cellulose dissolution in imidazolium based ionic liquids; they showed that the dissolution of cellulose is mainly determined by hydrogen bond interactions between the anion and hydroxyl protons of cellulose. From this very brief overview of articles concerning the solubility of cellulose it is clear that the solventcellulose OH group interactions play a major part in understanding the dissolution of cellulose.

In this work we will examine solutions of cellulose, cellobiose and glucose in the ionic liquid 1ethyl-3-methyl-imidazolium acetate ([C2mim][OAc]), currently [START_REF] Bharadwaj | Elucidating the conformational energetics of glucose and cellobiose in ionic liquids[END_REF] one of the most commonly used ILs in cellulose dissolution. Here we will demonstrate the importance of the molar ratio of carbohydrate hydroxyl groups to ions, showing that this is a key parameter in determining the microscopic dynamics within these systems. The zero shear rate viscosity and low field (20 MHz) NMR relaxometry will be analyzed and then combined through the Stokes-Debye-Einstein relationship. This will enable us to compare and contrast the macroscopic and microscopic properties, showing key differences between the cellulose, cellobiose and glucose solutions. The NMR relaxometry data will be analyzed using Bloembergen-Purcell-Pound (BPP) theory [START_REF] Bloembergen | Relaxation Effects In Nuclear Magnetic Resonance Absorption[END_REF] and it will be argued that the correlation times obtained from this approach correspond to the rotational correlation times of the ions within the solutions. Finally, previous published data [START_REF] Ries | Diffusion of 1-Ethyl-3methyl-imidazolium Acetate in Glucose, Cellobiose, and Cellulose Solutions[END_REF] for the ions' self-diffusion coefficients in the very same solutions will be combined with the relaxometry analysis and viscosity results, in order to explain the difference in activation energy for diffusional and rotational processes. This analysis will also give information on the additional activation energy for ions to bind to each carbohydrate.

EXPERIMENTAL

Materials and sample preparation

Glucose, cellobiose and cellulose (Avicel PH-101, with a degree of polymerization of 180 as given by the manufacturer) were purchased from Sigma Aldrich and prior to dissolution these materials were dried under vacuum at 70 °C for a minimum period of 12 hours. The structures of glucose, cellobiose and cellulose [START_REF] French | Glucose, not cellobiose, is the repeating unit of cellulose and why that is important[END_REF] The sample preparations were made in an MBraun Labmaster 130 atmospheric chamber under nitrogen, providing a dry environment, with the chamber being maintained at a dew point level between -70 and -40 °C, corresponding to less than 0.5 ppm of water. The [C2mim][OAc] and glucose / cellobiose / cellulose were combined and stirred in a container at 50 °C for a minimum of 48 hours. A small quantity of each carbohydrate [C2mim][OAc] solution was then placed in a standard 5 mm NMR tube within the chamber. Each tube was sealed still within the chamber to prevent moisture contamination and when the samples were not in use they were stored in a desiccator. Karl-Fischer titration indicated that all the samples had less than 0.3 wt % water. From our previous work [START_REF] Hall | Macroscopic and Microscopic Study of 1-Ethyl-3-methyl-imidazolium Acetate-Water Mixtures[END_REF] we found that for water concentrations of 0.5 wt % and above, a clearly visible water resonance appears in the high field (Bruker Biospin 400 MHz) spectra. All our samples were checked by high resolution 1 H NMR in a Bruker Avance II 400 MHz spectrometer for impurities and no degradation or decomposition was observed. 41

Low Field NMR Relaxometry

The spin-lattice relaxation time T1 and spin-spin relaxation time T2 were determined for each of our samples in steps of 10 °C between 30 and 70 °C inclusive, using a 20 MHz Maran Benchtop NMR spectrometer. Temperature control was within +/-0.1 C. The inversion recovery method was used to measure T1 and the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence for T2. [START_REF] Carr | Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments[END_REF] At each temperature, the samples were left to equilibrate for 10 min before measurements were recorded. The 90 pulse width was 3.7 s, the signal was averaged across 8 scans, and the repetition time was set to at least 5T1. In the inversion recovery experiment a linear increment time step of ~½ T1 was used with 15 increment steps being recorded. For the CPMG sequence 2000 echoes were used to give a total relaxation time of ~ 5 T2. Single exponential fits were found to model the NMR relaxation curves very closely for all our results. We estimate the uncertainty on our NMR relaxation times to be less than 5%.

Viscosity

A Bohlin Gemini Advanced Rheometer equipped with 4-40 mm cone plate was used to measure the viscosity of the solutions as a function of shear rate. The temperature range was from 10-100 C in 10 C increments. A thin film of low viscosity silicon oil was placed around the borders of the measuring cell in order to prevent moisture uptake.

RESULTS AND DISCUSSION

Viscosity

In the Supplementary Information, Figure SI1 shows the viscosity as a function of shear rate for a selection of glucose and cellobiose-[C2mim][OAc] solutions at 30 °C, demonstrating a Newtonian flow over a wide range of shear rates. This plateau value was then used as the zero shear rate viscosity, simply "viscosity", in all later analyses. Figure SI2 shows that for any given concentration and temperature, cellobiose solution viscosity is very close to that of glucose, well within a 5% difference. This result was expected as far as both glucose and cellobiose are low molecular weight compounds and the volumes occupied by each molecule is comparable, at least on the length scales probed by viscosity. We have previously published [START_REF] Sescousse | Viscosity of Cellulose-Imidazolium-Based Ionic Liquid Solutions[END_REF] the viscosity values for solutions of cellulose-[C2mim][OAc]. Unsurprisingly, due to the polymeric nature of cellulose, its solution viscosity is between one and three orders of magnitudes higher than those of the glucose results presented here, see Figures SI3 andSI4 in the Supplementary Information.

The temperature dependence of the viscosity for the glucose samples is shown in Figure 2, indicating a non-Arrhenius behavior in the large temperature range studied here. Similar non-linear dependence has already been reported for cellulose-

[C2mim][OAc] and cellulose-[C4mim][Cl]
solutions, and it was demonstrated that this is induced by the behaviour of the ionic liquid itself. [START_REF] Sescousse | Viscosity of Cellulose-Imidazolium-Based Ionic Liquid Solutions[END_REF] For further discussions on "fragile" behaviour in liquids, including ionic liquids, the reader is pointed to the seminal work 43 by Angell.

NMR relaxation of ions in glucose, cellobiose and cellulose solutions

In Figure 3a the spin-lattice relaxation times T1 are shown for the pure ionic liquid

[C2mim][OAc], 3 wt % and 15 wt % carbohydrate weight concentrations. Figure 3b shows the spin-spin relaxation times T2 for the same samples. As the majority of protons in these samples belong to the ionic liquid, even at the highest carbohydrate concentrations, it will be assumed that the NMR relaxometry is giving information predominantly about the motion of the ions in these solutions. In the 15 wt % samples 88% of the protons belong to the ionic liquid molecules.

Furthermore, as this is a low field experiment (20 MHz), there is not sufficient chemical resolution to distinguish between cation and anion and so the relaxation times are in effect an average across both ions. The various dynamics or mechanisms that contribute to the NMR relaxation will be discussed in more detail later on. Most of our data has T1 approximately equal to T2, indicating that the results are within the "liquid" [START_REF] Callaghan | Principles of Nuclear Magnetic Resonance Microscopy[END_REF] like NMR response for the majority of our results; only at the highest carbohydrate concentration of 15 wt % and at the lowest temperature 30 C is T1 significantly larger than T2.

This means that with increase in temperature, and corresponding increase in the mobility of the ions, the relaxation times increase. On the other hand, as an increase in carbohydrate concentration is seen to decrease the NMR relaxation times this indicates a corresponding decrease in the mobility of the ions. The interactions between the ions and the carbohydrates are therefore reducing the mobility of the ions. It is interesting to note that, weight for weight, at any given temperature, the glucose NMR relaxation times are shorter than the cellobiose times, which again are shorter than the cellulose times. As these NMR relaxation times are related to the mobility of the ions this result is somewhat surprising, as this goes against what would have been expected

from the viscosity results. The cellulose samples have the highest viscosity, but according to the NMR relaxometry data, the ions in the cellulose solutions have the highest mobility. Additionally, even though the glucose and cellobiose samples have the same viscosity, weight for weight, they are distinguishable in the NMR experiment, with their NMR relaxation times indicating that the mobility of the ions in these systems is significantly different. These results therefore strongly suggest that the local level or "micro" viscosity experienced by the ions is not simply related to the macroscopically determined zero shear rate viscosity.

In a recent publication [START_REF] Ries | Diffusion of 1-Ethyl-3methyl-imidazolium Acetate in Glucose, Cellobiose, and Cellulose Solutions[END_REF] we measured the self-diffusion coefficients of ions in the very same systems on which we report here. In that previous work, it was found that glucose was the most effective at slowing down the diffusion of the ions and cellulose the least effective, with this perfectly reflecting the change in mobility indicated by the results obtained here on low field NMR relaxometry. The dependence of T1 on concentration of solute is displayed in Figure 4, showing glucose to be the most effective and cellulose the least effective at reducing T1. Similar results are found for the spin-spin relaxation times and can be found in the supporting information, see Figure SI5. In our recent article on diffusion [START_REF] Ries | Diffusion of 1-Ethyl-3methyl-imidazolium Acetate in Glucose, Cellobiose, and Cellulose Solutions[END_REF] we introduced a parameter α, termed the "associated fraction" of ions bound to the carbohydrate. Cellulose consists of D-anhydroglucopyranose units (AGU) joined together by β(1→4) glycosidic bonds, each AGU unit within cellulose has three OH groups (Figure 1). Cellobiose is a disaccharide consisting of two D-Glucopyranoses linked by a β(1→4)

   -   = 100 GU IL M M N ( 1
)
where N is the number of OH groups per "glucose unit" (5, 4, 3 respectively for glucose, cellobiose and cellulose), MIL is the molar mass of the ionic liquid (170 g/mol), MGU is the molar mass of a "glucose unit" (180 g/mol, 171 g/mol, 162 g/mol respectively for glucose, cellobiose and cellulose)

and  the weight percent of the carbohydrate in solution. We argued [START_REF] Ries | Diffusion of 1-Ethyl-3methyl-imidazolium Acetate in Glucose, Cellobiose, and Cellulose Solutions[END_REF] that the molar ratio  is the fraction of IL molecules involved in dissolving "glucose units" and therefore can be considered as an associated fraction of the ionic liquid. When the diffusion data was plotted as a function of α, instead of carbohydrate weight fraction, then all the data from the different systems (glucose / cellobiose / cellulose) fell onto one master curve. In Figure 5 both T1 and T2 are plotted against α for two temperatures, 30 C and 70 C, showing that master curves are obtained for the NMR relaxation times, as with the published 37 diffusion data, and this works both in the limit that T1=T2

(liquid like regime) and when T1>T2 (solid like regime). NMR relaxation times depend on the dynamics within the system being measured. Rotational and translational motions cause the magnetic fields at the protons to fluctuate. The benchtop analyzer used here operates at a Larmor frequency of 20 MHz, making both the T1 and T2 sensitive to molecular motion and consequent fluctuations at and around this frequency. For ionic liquids this corresponds to predominantly rotational motion; [START_REF] Daniel | H-1 NMR Relaxometry, Viscometry, and PFG NMR Studies of Magnetic and Nonmagnetic Ionic Liquids[END_REF] for Larmor frequencies above 10 MHz the contribution to the NMR relaxation mechanisms from translational motion becomes less significant as the Larmor frequency is further increased. [START_REF] Daniel | H-1 NMR Relaxometry, Viscometry, and PFG NMR Studies of Magnetic and Nonmagnetic Ionic Liquids[END_REF][START_REF] Daniel | H-1 NMR Relaxation Study of a Magnetic Ionic Liquid as a Potential Contrast Agent[END_REF][START_REF] Driver | Correlated/non-correlated ion dynamics of charge-neutral ion couples: the origin of ionicity in ionic liquids[END_REF][START_REF] Neves | Proton NMR Relaxometry Study of Nafion Membranes Modified with Ionic Liquid Cations[END_REF][START_REF] Seyedlar | Dynamics of the ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethylsulphonyl)imide studied by nuclear magnetic resonance dispersion and diffusion[END_REF] In this article we will therefore make the working assumption that rotational motion of the ions is the dominant mechanism for the NMR relaxation and assume a single rotational correlation time R is responsible for determining both T1

and T2 for any given temperature and sample. This assumption can later be assessed by judging how successful it was in: i) modelling both spin-lattice and spin-spin relaxation times simultaneously across all samples and temperatures measured; ii) following quantitatively the Stokes-Debye-Einstein relationships; and iii) explaining the difference in activation energies from this analysis and those determined in our prior publication on the ions' self-diffusion coefficients.

According to Bloembergen, Purcell and Pound approach the NMR relaxation times can be related to a fluctuation correlation time, here assumed to be a rotational correlation time R for two protons at fixed distance r apart, as [START_REF] Bloembergen | Relaxation Effects In Nuclear Magnetic Resonance Absorption[END_REF][START_REF] Blicharska | Hydration water dynamics in biopolymers from NMR relaxation in the rotating frame[END_REF]  

    + + + = 2 2 0 2 2 0 1 4 1 4 1 1 R R R R K T       (2a)       + + + + = 2 2 0 2 2 0 2 4 1 2 1 5 3 2 1 R R R R R K T        (2b) 6 2 0 2 4 1 4 10 3 r K       =     ( 2c
)
where 0 is the Larmor frequency,  the gyromagnetic ratio for protons, ħ the reduced Planck constant, o the permeability of free space and r a system average or effective distance between protons. For each sample it will be assumed that there is an activation energy ER for the rotation correlation time given by

      = RT E R R exp 0   ( 3
)
where 0 is a constant sometimes referred to as the high temperature or zero activation energy rotational correlation time, R the gas constant and T the temperature in kelvin. When fitting the data, 0 and K will be taken as a global fitting parameters as they are related to the moment of inertia of the ions and the distance between protons respectively, [START_REF] Carper | C-13 NMR relaxation and H-1 diffusion (DOSY) studies of an acidic chloroaluminate melt[END_REF] which should not change significantly with solute type (glucose / cellobiose / cellulose), concentration and temperature. For each sample there will thus be one free parameter, the rotational activation energy ER, and this will have to correctly model both the T1 and T2 full temperature dependences simultaneously.

In Figure 3 the dashed lines are the resultant fits of equation ( 2) to the pure ionic liquid and glucose samples. Fits to all the carbohydrates were equally good as the selection for glucose shown in Figure 3. The global fitting parameters found are 0 equal to 2.4±0.1 × 10 -15 s and K equal to 1.7±0.1 × 10 9 s -2 . The value of 0 will be discussed later on. From equation (2c) the parameter K gives a very reasonable value for the effective distance between protons r of 2.16±0.02 × 10 -10 m.

Comparatively, a rough estimation gives the distance, or lattice spacing, between protons of 2.64 × 10 -10 m (taking the molecular weight of [C2mim][OAc] at 170 g/mol, the density of the ionic liquid as 1.1 g/cm 3 , 33 the number of protons per molecule 14 and assuming that the protons are on a cubic lattice). This is remarkably close to the value determined through the NMR relaxometry analysis, especially given such a simple calculation, and thus supports the quantitative validity of the BPP analysis applied here.

In our recent article [START_REF] Ries | Diffusion of 1-Ethyl-3methyl-imidazolium Acetate in Glucose, Cellobiose, and Cellulose Solutions[END_REF] we argued that the ions in these carbohydrate systems behaved as an "ideal mixture" of free and associated ions. It was shown theoretically that for this ideal mixture rule to correctly describe the diffusion of the ions, the activation energy for their translational diffusion needed to be linear with respect to the associated fraction . This was verified experimentally for diffusion of [C2mim][OAc] in glucose / cellobiose / cellulose solutions. In Figure 6 we likewise plot the rotational activation energy as determined from the BPP analysis of the low field relaxometry data. The activation energy results all follow a linear dependence as a function of associated fraction of ions, suggesting that the rotational motion also obeys an ideal mixture rule.

Since both rotational and translational motions are governed by , then the effective local microscopic viscosity experienced by the ions must also be determined by this parameter. In other words, the number of carbohydrate OH groups within these solutions dictates the dynamics of the ions. The extra "cost" in terms of additional activation energy for rotation of an ion due to its association with an OH group from a carbohydrate molecule is given directly by the gradient of the solid line in Figure 6 as 6.2±0.5 kJ/mol, which is reasonably close to the values found previously [START_REF] Ries | Diffusion of 1-Ethyl-3methyl-imidazolium Acetate in Glucose, Cellobiose, and Cellulose Solutions[END_REF] for the increase in diffusional activation energy for being associated with an OH group of a carbohydrate molecule of 8.2±0.4 kJ/mol and 7.6±0.4 kJ/mol for the anion and cation respectively. Therefore, there is across the full range of associated fractions  an approximately constant difference between the rotational activation energy and the corresponding diffusional activation energy of 14±2 kJ/mol, [START_REF] Ries | Diffusion of 1-Ethyl-3methyl-imidazolium Acetate in Glucose, Cellobiose, and Cellulose Solutions[END_REF] with the diffusional motion having the higher energy barrier.

In the seminal work by Powell, Roseveare, and Eyring, a theory of viscosity, diffusion, thermal, and ionic conductivities in terms of a statistical mechanical theory for reaction rate was developed. [START_REF] Powell | Diffusion, thermal conductivity, and viscous flow of liquids[END_REF] For flow to take place a single molecule moves past its neighbor and falls into a vacant equilibrium position, termed a hole or vacancy. An activation energy is required for a molecule to jump over its neighbor. The authors showed that there was a close link between viscous flow and vaporization, because the same bonds that need to be broken for flow to take place are required to be broken for vaporization. [START_REF] Powell | Diffusion, thermal conductivity, and viscous flow of liquids[END_REF] In mixtures the ease of molecular flow is not determined predominantly by its own properties, but by the "solvent" or surrounding molecules that must contribute holes for it to flow into. In 1968, O'Reilly investigated the diffusion coefficients and rotational correlation times of several polar liquids. [START_REF] Oreilly | SELF-DIFFUSION COEFFICIENTS AND ROTATIONAL CORRELATION TIMES IN POLAR LIQUIDS[END_REF] In his work he argued that the difference between the activation energy for rotational motion and that for diffusional motion was due to the additional cost of creating the vacancy (or hole) for the diffusing molecule to move into. For both rotational and diffusional motion to occur all the close neighboring bonds must be broken, but for the diffusional translation there is the extra cost of creating the hole. This can be written mathematically as, [START_REF] Oreilly | SELF-DIFFUSION COEFFICIENTS AND ROTATIONAL CORRELATION TIMES IN POLAR LIQUIDS[END_REF]  

    + - = RT E E D D hole R exp 0 (4)
where Ehole is the additional activation energy needed to create a vacancy into which the diffusing molecule can move into and, as argued above, has a value of 14 ± 2 kJ/mol.

If we now continue to assume that the fluctuation correlation times R found from the BPP analysis are due to the rotational motion of the ions, it is then possible to theoretically predict value for Ehole through the Stokes-Debye-Einstein relationship, [START_REF] Carper | C-13 NMR relaxation and H-1 diffusion (DOSY) studies of an acidic chloroaluminate melt[END_REF][START_REF] Antony | C-13 NMR relaxation rates in the ionic liquid 1-methyl-3-nonylimidazolium hexafluorophosphate[END_REF] kT

R H R 3 4 3    = ( 5
)
where RH is the effective hydrodynamic radius of the molecule and k the Boltzmann constant.

The ratio of the viscosity to the temperature in equation ( 5) can be eliminated in favour of the diffusion coefficient through the Stokes-Einstein formula, [START_REF] Carper | C-13 NMR relaxation and H-1 diffusion (DOSY) studies of an acidic chloroaluminate melt[END_REF][START_REF] Antony | C-13 NMR relaxation rates in the ionic liquid 1-methyl-3-nonylimidazolium hexafluorophosphate[END_REF]

  H R kT D 6 = (6)
This gives,

D R H 9 2 2 =  (7)
Then combining this result with equations ( 3) and (4) obtains,

        = 2 0 0 2 9 ln H hole R D RT E  (8)
In the BPP analysis we obtain only one correlation time R and this is an effective average rotational time scale for the cations and anions in our system. To use equation (8) to estimate Ehole we take: i) the average value of D0 of 1.5 10 -3 m 2 s -1 for the cation and anion (1.40.2 10 -3 m 2 s -1 and 1.60.2 10 -3 m 2 s -1 , respectively [START_REF] Ries | Diffusion of 1-Ethyl-3methyl-imidazolium Acetate in Glucose, Cellobiose, and Cellulose Solutions[END_REF] ; and ii) the average value of hydrodynamic radii RH, 2.510 - 10 m, of the cation and anion (2.810 -10 m and 2.210 -10 m, respectively [START_REF] Ries | Diffusion of 1-Ethyl-3methyl-imidazolium Acetate in Glucose, Cellobiose, and Cellulose Solutions[END_REF] ) and o = 2.4±0.1 ×10 -15 s from the above BPP analysis. Since our measurements span from 30 C to 70 C, we set T in equation ( 8) to an average value of 320 K (50 C); all the temperatures in this study are within 6% of this middle value. Finally, combining all these parameters into equation (8) gives a prediction for Ehole of 15 kJ/mol, which is remarkably close to the measured value of 14±2 kJ/mol. This is strong support for taking the correlations time found from the relaxometry measurements through the BPP analysis as rotational correlation times; it also indicates that the parameters found from this approach are quantitatively correct.

When R and D are compared, as in the above analysis, then one microscopic term is being compared with another microscopic term. The quantitative agreement found above indicates that there is one effective microscopic viscosity that determines both the rotational and translational motion of the ions. This local microscopic viscosity can be altered by either varying the temperature and/or changing the number of solute OH groups for the ions to interact with, and it makes no difference whether those OH groups come from glucose, or cellobiose or indeed cellulose molecules. But what is interesting now is to compare the microscopic environment with the macroscopic one. This can be done by plotting T1, which as we have shown is determined by microscopic rotational motion, against T/, as is done in Figure 7. The zero shear rate viscosity  is a macroscopic term, measured using a rheometer, and thus here large scale effects relative to the size of ions, such as polymer entanglements, play a significant role in determining the resultant macroscopic viscosity. However, they play an almost insignificant role in determining the microscopic viscosity that determines the rotational and translational motions of the ions: for glucose and cellobiose all data at various concentrations fall on one master plot (Figures 7 a and b, respectively), which is not the case for cellulose (Figure 7c).

For the glucose and cellobiose solutions the macroscopic and microscopic viscosities are proportional to each other, both being affected in a similar manner by changes in temperature and solute concentration. This is not the case for the cellulose solutions, with macroscopic viscosity dramatically increasing when macromolecules [START_REF] Staudinger | Highly polymerized compounds. XCIV. An insoluble polystyrene[END_REF] are added into a solvent, especially above the overlap concentration (here, around [START_REF] Gericke | Rheological Properties of Cellulose/Ionic Liquid Solutions: From Dilute to Concentrated States[END_REF] 1 wt%), as expected. On the length scale of the ions the local microviscosity within the cellulose samples is similar to that of the glucose and cellobiose samples;

the key determining factor on these local length scales is the density of OH groups that the ions interact with.

CONCLUSIONS

In this work we analysed carbohydrate solutions in ionic liquid [C2mim][OAc] by measuring: i) the relaxation times of protons of ionic liquid probed by NMR relaxometry at 20 MHz and ii) viscosity of these solutions. The carbohydrates were glucose, cellobiose and cellulose, and each set of solutions was of five concentrations (1, 3, 5, 10, and 15 wt %). Each solution was measured at temperatures from 30 and 70 °C. Cellulose is found to be the most effective in increasing the solution viscosity as compared to glucose and cellobiose. In contrast, glucose was found to be the most effective in reducing the NMR relaxation times and cellulose the least effective. As the NMR relaxation times can be related to the mobility of the ions, this indicates that the ions in the most viscous set of samples have, counterintuitively, the highest mobility. A similar surprising result was found when these samples were investigated previously 37 using pulsed field gradient NMR to determine the self-diffusion coefficients of the ions.

We demonstrated that it is the number of carbohydrate OH groups per repeating "glucose" unit that determines the mobility of the ions. We introduced 37 the parameter α, which quantifies the molar ratio of OH groups per ionic liquid molecule. As glucose has more OH groups per repeat unit, then for any corresponding weight concentrations these samples will have a higher number of OH groups for the ions to interact with. It is these interactions that slow down the rotational and translational motion of the ions and, as a consequence, this loss of mobility reduces the NMR relaxation times. When the NMR relaxation times are plotted not as a function of weight concentration, but instead against α, then all data fall on master curves independent of particular carbohydrate. This is strong evidence that the molar density of OH groups is the most important factor in determining the microscopic environment of the ions.

The NMR relaxation times were analyzed in terms of the theoretical 40 work of Bloembergen, Purcell and Pound. For each sample at each temperature a correlation time R was found. The activation energies for this correlation time were shown to be linearly dependent on α and this reveals that these solutions can be considered as ideal mixtures of associated and non-associated ions.

For an associated ion there is the additional cost for rotation, 6.20.5 kJ/mol, compared to that for a free ion. From previous work on the diffusion of ions in these same systems, 37 translational motion involves a higher activation energy, an extra 142 kJ/mol, than that for rotational motion obtained in this work. We interpreted this additional barrier stemming from the need of a hole or vacancy to form in translational motion. [START_REF] Powell | Diffusion, thermal conductivity, and viscous flow of liquids[END_REF] By using Stokes-Debye-Einstein equations linking viscosity to rotation and diffusion, combined with the fitting parameters from the NMR relaxometry analysis, it was possible to predict this additional cost quite accurately (15 kJ/mol). This supports our interpretation that the correlation times R found are predominantly arising from rotational motion. The success of equation ( 8) is quite remarkable, in that it uses two parameters D0 and 0 that are not usually the subjects of Arrhenius-type analysis, which when coupled with the average hydrodynamic radius of the ions calculates the activation energy in forming a vacancy for translational motion. This then predicts the difference between how diffusion and rotation change as a function of temperature. This is strong evidence for the quantitative nature of our analysis and supports our interpretation that the NMR relaxometry can be related to the rotational motion of the ions.

  are shown below, in Figure 1. The ionic liquid 1-ethyl-3methyl-imidazolium [C2mim][OAc] (97% purity) was purchased from Sigma Aldrich and used without any further purification. Neat [C2mim][OAc] and three sets of samples (glucose / cellobiose / cellulose) each with five concentrations of the corresponding carbohydrate (1, 3, 5, 10, and 15 wt %) in [C2mim][OAc] were prepared. Diffusion data from our previous publication 37 on the same systems is also included in this work.

Figure 1 .

 1 Figure 1. Structure of a) glucose b) cellobiose and c) cellulose.

Figure 2 .

 2 Figure 2. Viscosity of glucose-[C2mim][OAc] solutions as a function of inverse temperature

Figure 3 .

 3 Figure 3. NMR relaxation times a) T1 and b) T2 of [C2mim][OAc] in glucose, cellobiose and

Figure 4 .

 4 Figure 4. NMR spin-lattice relaxation times T1 for glucose, cellobiose and cellulose as a

Figure 5 .

 5 Figure 5. NMR spin-lattice relaxation times T1 and T2 for [C2mim][OAc] solutions with

Figure 6 .

 6 Figure 6.

Figure 7 .

 7 Figure 7. Spin-lattice relaxation time T1 against temperature over viscosity for a) glucose, b)

Finally

  , this work highlights important differences between what is occurring microscopically and macroscopically in a carbohydrate ionic liquid mixture. Macroscopically, the viscosity depends on the volume occupied by the solute. Microscopically, the dominant factor is the number of OH groups on a carbohydrate molecule, the effect of which can be quantified by the associated fraction . ACKNOWLEDGEMENT S.M.G. is funded by an EPSRC CASE Award (EP/I501495/1) with Innovia Films (Wigton, Cumbria, CA7 9BG, UK). M.E.R. is a Royal Society Industry Fellow (IF120090). The data for this article can be found at doi: https://doi.org/10.5518/369 ForTable of Contents Use Only Microscopic and macroscopic properties of carbohydrate solutions in the ionic liquid 1-ethyl-3methyl-imidazolium acetate Michael E. Ries, Asanah Radhi, Stephen M Green, Jamie Moffat and Tatiana Budtova Keywords: cellulose, cellobiose, glucose, carbohydrate, ionic liquid, NMR, relaxometry, viscosity, diffusion.

Figure SI1 .

 SI1 Figure SI1. Viscosity against shear rate of carbohydrate-[C2mim][OAc] solutions at different

Figure SI2 .

 SI2 Figure SI2. Viscosity at 10 °C, 60 °C and 100 °C for the glucose and cellobiose in

Figure SI3 .

 SI3 Figure SI3. Viscosity of cellulose [C2mim][OAc] solutions against cellulose concentration.

Figure SI4 .

 SI4 Figure SI4. Viscosity ratio of cellulose to glucose in [C2mim][OAc] solutions (at the same

Figure SI5 .

 SI5 Figure SI5. NMR spin-lattice relaxation times T2 for glucose, cellobiose and cellulose as a

  bond, each D-Glucopyranose in cellobiose has four OH groups. Finally, glucose is a monosaccharide with five OH groups. The term α corresponds to a molar weight fraction, weighted

	to	the	number	of	OH	groups	from	the	"glucose	units"	(D-
	anhydroglucopyranose/Dglucopyranose/D-glucose unit) per [C2mim][OAc] molecule, and is
	given by 37

Supporting Information

Microscopic and macroscopic properties of carbohydrate solutions in the ionic liquid 1-ethyl-3methyl-imidazolium acetate m.e.ries@leeds.ac.uk Data for this publication can be found at doi: https://doi.org/10.5518/369


Giada Iacono-Marziano

Fabrice Gaillard

Bruno Scaillet

Michel Pichavant

Giovanni Chiodini

Role of non-mantle CO 2 in the dynamics of volcano degassing: The Mount Vesuvius example

Mount Vesuvius, quiescent since 1944, is a dangerous volcano currently characterized by elevated CO 2 emissions of debated origin. We show that such emissions are most likely the surface manifestation of the deep intrusion of alkali-basaltic magma into the sedimentary carbonate basement, accompanied by sidewall assimilation and CO 2 volatilization. During the last eruptive period , the carbonate-sourced CO 2 made up 4.7-5.3 wt% of the vented magma. On a yearly basis, the resulting CO 2 production rate is comparable to CO 2 emissions currently measured in the volcanic area. The chemical and isotopic composition of the fumaroles supports the predominance of this crust-derived CO 2 in volatile emissions at Mount Vesuvius.

INTRODUCTION

Volatile abundances in magmas are widely considered to be inherited from melting conditions in the mantle and subsequently modified by degassing processes during magma rising. However, crustal assimilation may dramatically affect volatiles dissolved in magma at a low concentration level (<1wt%), such as C-S-Cl [START_REF] Behrens | Geochemical aspects of melts: volatiles and redox behaviour: Elements[END_REF], whenever small Publisher: GSA Journal: GEOL: Geology Article ID: G25446

Page 2 of 18 amount of carbonates, sulfates, or salt rich-sediments are assimilated. Nevertheless, in the recent literature the addition of volatiles of crustal origin during magma transfer toward the surface has been suggested only in a few instances [START_REF] Goff | Passive infrared remote sensing evidence for large, intermittent CO2 emissions at[END_REF][START_REF] Obenholzner | Particles from the plume of Popocatépetl volcano, Mexico -the FESEM/EDS approach[END_REF][START_REF] Werner | CO2 emissions from the Yellowstone volcanic system[END_REF]. In this paper, we present a novel approach to quantify the contribution of carbonate assimilation to CO 2 degassing at Mount Vesuvius, Italy. Our estimates are based on petrological constraints and are in agreement with geochemical data about current fluxes and isotopic composition of Mount Vesuvius volcanic gases.

MOUNT VESUVIUS PLUMBING SYSTEM AND GAS EMISSIONS

Mount Vesuvius is located on the southern margin of the Campanian Plain and is emplaced on a carbonate sedimentary sequence several kilometers thick. No sedimentary rocks are exposed in the plain; however, it is bordered by structural highs (e.g., Mount Massico, the Sorrento Peninsula) where Mesozoic carbonate rocks crop out. The sedimentary sequence comprises Upper Triassic dolomitic limestones and dolostones, Jurassic limestones, and Cretaceous-Paleogene limestones and dolostones [START_REF] D'argenio | Stratigraphic evidence for crustal thickness changes on the Southern Tethyan margin during the Alpine cycle[END_REF]. The Trecase 1 geothermal well, on the southeast slopes of Mount Vesuvius, encountered dolomitic deposits at ~1890 m (1665 m below sea level [bsl]; [START_REF] Brocchini | Quaternary evolution of the southern sector of the Campanian Plain and early Somma-Vesuvius activity: insights from the Trecase 1 well[END_REF]. Figure 1 summarizes the information, from geophysical surveys, about the Mount Vesuvius basement and magmatic system. Seismic tomographic studies have imaged an extended low velocity layer, with a flat top at ~8-10 km b.s.l. beneath the volcano, interpreted as the top of the present-day magma reservoir (Auger et al., 2001, and references therein). No evidence exists of any reflectors between the top of the limestone basement (2-3 km b.s.l.) and the 8-10 km discontinuity [START_REF] Auger | Seismic evidence of an extended magmatic sill under Mt[END_REF], suggesting that the magma is probably hosted within or at the base of the carbonate sequence.

The seismic data are consistent with a sill-shaped zone constituted by magma interspersed in a densely fractured rock, favoring exchanges between magma and host-rock [START_REF] Auger | Seismic evidence of an extended magmatic sill under Mt[END_REF].

Since the last eruption in 1944, Mount Vesuvius has been quiescent; only seismicity [START_REF] De Natale | The Somma-Vesuvius volcano (Southern Italy): Structure, dynamics and hazard evaluation[END_REF] and low temperature fumarolic emissions [START_REF] Chiodini | Geochemical evidence for the existence of hightemperature hydrothermal brines at Vesuvio volcano, Italy[END_REF] suggest that it is still active.

CO 2 PRODUCTION BY SEDIMENTARY CARBONATE ASSIMILATION AT MOUNT

VESUVIUS

The importance of limestone assimilation in the plumbing system of Mount Vesuvius has long been recognized [START_REF] Rittmann | Evolution and differentiation des Somma-Vesuv-magmas: Zeitsch[END_REF]. However, recent geochemical and experimental studies suggest that Mount Vesuvius magmas underwent increasing carbonate assimilation in the past 25 k.y. [START_REF] Iacono-Marziano | Limestone assimilation by basaltic magmas: an experimental re-assessment and application to Italian volcanoes[END_REF], with as much as 10-15 wt% carbonate assimilation for recent volcanic rocks [START_REF] Di Renzo | Magmatic History of Somma-Vesuvius on the Basis of New Geochemical and Isotopic Data from a Deep Borehole[END_REF]. Laboratory work [START_REF] Iacono-Marziano | Limestone assimilation by basaltic magmas: an experimental re-assessment and application to Italian volcanoes[END_REF] has shown that magmatic assimilation of carbonates liberates CO 2 following the reactions:

2 CaCO 3 + Mg 2 SiO 4 olivine + 3 SiO 2 melt →2 CaMgSi 2 O 6 cpx + 2 CO 2 , ( 1
) (CaMg) (CO 3 ) 2 + 2 SiO 2 melt → CaMgSi 2 O 6 cpx + 2 CO 2 , ( 2
)
where cpx is clinopyroxene. More details about the petrological implications of carbonate assimilation (after [START_REF] Iacono-Marziano | Limestone assimilation by basaltic magmas: an experimental re-assessment and application to Italian volcanoes[END_REF] are in the GSA Data Repository. Figure 2 shows the variations in composition of primitive melt inclusions in olivine and clinopyroxene from the 1794-1944 Mount Vesuvius eruptive period [START_REF] Fulignati | Towards a reconstruction of the magmatic feeding system of the 1944 eruption of Mt Vesuvius[END_REF][START_REF] Marianelli | The deep feeding system of Vesuvius involved in recent violent strombolian eruptions[END_REF], and of melt inclusions in clinopyroxene of high temperature skarn xenoliths of the 1944 eruption [START_REF] Fulignati | Towards a reconstruction of the magmatic feeding system of the 1944 eruption of Mt Vesuvius[END_REF]. The experimental results (Fig. 2; after [START_REF] Iacono-Marziano | Limestone assimilation by basaltic magmas: an experimental re-assessment and application to Italian volcanoes[END_REF] show that such variations are consistent with the effect of carbonate assimilation by basaltic magmas in the upper crust (see the Data Repository). We provide quantitative constraints on the assimilation process by means of mass-balance calculations considering variable degrees of dolomite +/-calcite assimilation and clinopyroxene +/-olivine crystallization (see the Data Repository for explanation). These calculations permit an accurate estimation of the amount of assimilated carbonates, because (1) they use the most suited composition of the uncontaminated magma, and (2) the compositions of the assimilated rocks can be fitted together with the mineral and fluid proportions (see the Data Repository). A shoshonite with SiO 2 ~51 wt% and MgO ~8.5 wt% (Fig. 2) has been assumed as the noncontaminated, or at least less contaminated, composition. Di Renzo et al. ( 2007) came to the same conclusions on the basis of the shoshonite Sr isotopic ratio, which is one of the lowest measured at Mount Vesuvius. The best-fit of melt inclusion array (curves in Fig. 2) is obtained by computing progressing carbonate assimilation from 0 to ~22 wt% of which dolomite composed 60%-85% (Table DR1). Melt inclusions record variable degrees of carbonate assimilation probably because they sample melt aliquots at variable distances from the carbonate host rock. Field evidence show that carbonate assimilation affects the magma composition in an inhomogeneous way [START_REF] Barnes | Pervasive assimilation of carbonate and silicate rocks in the Hortavaer igneous complex, north-central Norway[END_REF], as also suggested by the strongly heterogeneous Sr isotopic composition of Mount Vesuvius eruptive products belonging to a single eruptive period (Di Renzo et al., 2007 and references therein). However, the average amount of assimilation can be estimated for the most recent eruptive period, on the basis of the bulk rock composition of the erupted lavas and pyroclasts. Between 1631 and 1944, tephritic to tephriphonolitic magmas have been erupted [START_REF] Joron | Chemistry and petrography[END_REF]; we restrict our calculations to the more mafic terms because the assimilation process is significantly more efficient in hotter and Mg-rich magmas [START_REF] Barnes | Pervasive assimilation of carbonate and silicate rocks in the Hortavaer igneous complex, north-central Norway[END_REF][START_REF] Iacono-Marziano | Limestone assimilation by basaltic magmas: an experimental re-assessment and application to Italian volcanoes[END_REF]. The compositions of the most primitive tephritic-phonotephritic rocks (gray square in Fig. 2; after [START_REF] Joron | Chemistry and petrography[END_REF] require 9.8-11.2 wt% of assimilation, of which dolomite composed 82-84% (tephrite average in Table DR1).

Figure 1 illustrates the role of carbonate assimilation in the dynamic of magma degassing at Mount Vesuvius. The rising basaltic magma batches are likely to be horizontally channeled at the carbonate-crystalline basement discontinuity [START_REF] De Natale | The Somma-Vesuvius volcano (Southern Italy): Structure, dynamics and hazard evaluation[END_REF]. The Upper Triassic dolomitic formations (>1200m) at the base of the Mesozoic sedimentary series (D'Argenio and Alvarez, 1980) represent the first layers in which the magma most extensively assimilates carbonate rocks, upon which clinopyroxene crystallizes and CO 2 is liberated, according to reactions 1 and 2. An average of 9.8-11.2 wt% of carbonate assimilation liberates 4.7-5.3 wt% CO 2 (Fig. 2). Under the relatively low crustal pressure conditions at which carbonate assimilation is likely to occur (<300 MPa), CO 2 solubility does not exceed 0.3-0.4 wt% CO 2 [START_REF] Blank | Experimental studies of carbon dioxide in silicate melts: solubility, speciation, and stable carbon isotope behavior[END_REF]. CO 2 contents dissolved in primitive melt inclusions of the last Mount Vesuvius eruption (1944) range between 0.09 and 0.30 wt% (Fig. 2; after [START_REF] Marianelli | The deep feeding system of Vesuvius involved in recent violent strombolian eruptions[END_REF]. Most of the 4.7-5.3 wt% CO 2 deriving from carbonate assimilation is therefore likely to be present as a separate gas phase, with only minor CO 2 dissolved in the melt. At 200 MPa and 1150-1200°C, considering a density of CO 2 of ~0.5 g/cm 3 [START_REF] Bottinga | High pressure and temperature equation of state and calculation of the thermodynamic properties of gaseous carbon dioxide[END_REF] and an average magma density of 2.7 g/cm 3 , we calculate that the mafic Mount Vesuvius magma is likely to contain ca. 25-30 vol.% of bubbles following 9.8-11.2 wt% of carbonate assimilation at a depth of ~7.5 km. CO 2 -rich bubbles tend to escape from the system because the magma and the surrounding rocks are significantly more dense. Provided that the host rocks are sufficiently permeable, most of the CO 2 produced at depth will therefore ascend toward the surface.

Currently, at least 301 t/day of deep CO 2 are degassed in the Mount Vesuvius volcanic area: 151 t/day are diffusely degassed from the crater area and 150 t/day are dissolved in the groundwaters of the volcano flank [START_REF] Frondini | Diffuse CO 2 soil degassing at Vesuvio, Italy[END_REF][START_REF] Caliro | Volcanic degassing at Somma-Vesuvio (Italy) inferred by chemical and isotopic signatures of groundwater[END_REF]. The tensile faults in the Mesozoic basement, typically oriented northwest-southeast and northeast-southwest, act as tectonic controls on CO 2 emissions, facilitating and to channelling the rising CO 2 [START_REF] Federico | Magma-derived gas influx and water-rock interactions in the volcanic aquifer of Mt. Vesuvius, Italy[END_REF].

QUANTIFICATION OF NONMANTLE CO 2 EMISSIONS AT MOUNT VESUVIUS

We first use helium and carbon abundances and isotopic compositions in the gases of the fumaroles to infer the proportion of mantle CO 2 at Mount Vesuvius. The He ( 3 He/ 4 He = 2.51-3.98 Ra, where Ra is the atmospheric ratio = 1.38 x 10 -6 ; [START_REF] Tedesco | Noble gas isotopic ratios from historical lavas and fumaroles at Mount Vesuvius (southern Italy): constraints for current and future volcanic activity[END_REF] and C (δ 13 C = 0.06-0.34‰ Vienna Peedee belemnite, VPDB; [START_REF] Chiodini | Geochemical evidence for the existence of hightemperature hydrothermal brines at Vesuvio volcano, Italy[END_REF] isotopic compositions of the CO 2 -rich gas emitted by the crater fumaroles are similar to those of groundwaters and magmatic volatiles analyzed in CO 2 -rich inclusions of recent volcanic products [START_REF] Tedesco | Noble gas isotopic ratios from historical lavas and fumaroles at Mount Vesuvius (southern Italy): constraints for current and future volcanic activity[END_REF][START_REF] Federico | Magma-derived gas influx and water-rock interactions in the volcanic aquifer of Mt. Vesuvius, Italy[END_REF][START_REF] Martelli | Helium-stronzium isotope constraints on mantle evolution beneath the Roman Comagmatic Province[END_REF], indicating a common source. The carbon isotopic composition clearly deviates from the typical mantle range (δ 13 C = -4 to -7 ‰; [START_REF] Pineau | Deep-sea explosive activity on the Mid-Atlantic Ridge near 34°50′N: a stable isotope[END_REF] and from the mantle volatile end member of Pantelleria Island, southern Italy (δ 13 C = -4.2 to -5.8 ‰; [START_REF] Parello | Isotope geochemistry of Pantelleria volcanic fluids, Sicily Channel rift: a mantle volatile end-member for volcanism in southern Europe[END_REF], and most likely indicates a dominant contribution from marine carbonate [START_REF] Chiodini | Geochemical evidence for the existence of hightemperature hydrothermal brines at Vesuvio volcano, Italy[END_REF]. The He isotopic composition also strongly deviates from characteristic mantle signatures (~7-9 Ra; Tedesco et al., 1998 and references therein) and suggests a "dilution" by more radiogenic materials. The C isotopic composition of Mount Vesuvius fumaroles can be used to estimate the contribution of sedimentary sources to volcanic emissions, using an approach similar to that of [START_REF] Werner | CO2 emissions from the Yellowstone volcanic system[END_REF], who calculated between 40 and 50% of crustal contribution at the Yellowstone area, western United States. The carbonate contribution (% carb) is here estimated as:

% carb = 100*(δ 13 C fumarole -δ 13 C mantle)/(δ 13 C carbonate -δ 13 C mantle),

where δ 13 C mantle is the isotopic compositions of the mantle end member reported above, and δ 13 C carbonate is the C isotopic composition of the carbonate rocks of the Campanian platform (between -2 and +4 ‰ VPDB; [START_REF] Parente | Carbon-isotope stratigraphy of Cenomanian-Turonian platform carbonates from the southern Apennines (Italy): a chemostratigraphic approach to the problem of correlation between shallow-water and deep-water successions[END_REF]. The resulting carbonate contribution is between 52 and 100%. A more accurate estimation of the sedimentary contribution is possible using the [START_REF] Sano | Origin of carbon in fumarolic gas from island arcs[END_REF] approach. CO 2 concentrations in the fumaroles of Mount Vesuvius crater are 75,900-156,800 μmol/mol, and He concentrations are 0.22-0.64 μmol/mol [START_REF] Chiodini | Geochemical evidence for the existence of hightemperature hydrothermal brines at Vesuvio volcano, Italy[END_REF]. The CO 2 / 3 He ratio is therefore 4.5-9.9 x 10 10 (using He isotopic ratios of [START_REF] Tedesco | Noble gas isotopic ratios from historical lavas and fumaroles at Mount Vesuvius (southern Italy): constraints for current and future volcanic activity[END_REF]. Considering CO 2 / 3 He ratios of ~2 x 10 9 for the mantle source [START_REF] Sano | Origin of carbon in fumarolic gas from island arcs[END_REF] and 1 x 10 12 -10 13 for the carbonate rocks (the variations of this parameter being insignificant in the calculations), we estimate carbonate contributions to volcanic emissions of 96-98%. Although these calculations lack precision, due to the uncertainties in the concentration and isotopic composition of the source and, to a lesser extent, of the contaminant, they strongly suggest that carbonate assimilation plays a major role in volcanic emissions at Mount Vesuvius.

Although the estimation of the amount of CO 2 currently produced at Mount Vesuvius by carbonate assimilation is unfeasible on the basis of the petrological constraints detailed above (due to the lack of lava emissions since 1944), present day measured emissions can be compared to carbonate-derived CO 2 estimated for the last eruptive period. During this period (1631-1944),

Mount Vesuvius was characterized by semipersistent activity in open conduit conditions: 20 cycles of mainly effusive activity were distinguished, separated by short rest periods (generally not exceeding a few years) and closed by powerful explosive eruptions [START_REF] Civetta | Steady state magma supply in the last 3400 years of Vesuvius activity[END_REF][START_REF] Scandone | Persistent activity and violent strombolian eruptions at Vesuvius between 1631 and 1944[END_REF]. Erupted lavas and pyroclasts are characterized by relatively primitive compositions and are supposed to have been erupted after a nearly direct ascent from Publisher: GSA Journal: GEOL: Geology Article ID: G25446

Page 8 of 18 the deep part of the magma plumbing system (Scaillet et al., 2008). The magma feeding rate is therefore assumed to equal the eruption rate [START_REF] Rosi | (ed) Somma-Vesuvius[END_REF], which has been estimated at 1.05-4.31 x 10 6 m 3 /yr [START_REF] Rosi | (ed) Somma-Vesuvius[END_REF][START_REF] Civetta | Steady state magma supply in the last 3400 years of Vesuvius activity[END_REF]after Scandone et al., 2008). Combining this magma feeding rate (MFR) with the estimated amounts of carbonate assimilation (wt% carb), following the equation:

CO 2 (t/day)= MFR(m 3 /yr) x magma density (kg/m 3 ) x wt% carb x MW CO 2 (4)

10 5 * 365 * MW CaCO 3
where MW is molecular weight, we calculate a rate of CO 2 production of 335-1566 t/day for the recent eruptive period. This estimation is comparable to present-day measured emissions in the Mount Vesuvius area (301 t/day; [START_REF] Frondini | Diffuse CO 2 soil degassing at Vesuvio, Italy[END_REF][START_REF] Caliro | Volcanic degassing at Somma-Vesuvio (Italy) inferred by chemical and isotopic signatures of groundwater[END_REF], which represent a minimum estimation of the current CO 2 production rate at depth.

A pure magmatic contribution to CO 2 degassing is barely quantifiable at Mount Vesuvius, because good estimations of CO 2 concentration in the mantle source are not available.

The CO 2 contents in primitive melt inclusions that did not undergo assimilation represent the contribution of magmatic CO 2 dissolved in the magma. The maximum CO 2 content in the most primitive melt inclusions of the period 1794-1944 (considered representative of the uncontaminated or less contaminated magma) is ~0.3 wt% [START_REF] Marianelli | The deep feeding system of Vesuvius involved in recent violent strombolian eruptions[END_REF], which represents 6-7% of what we estimate to be produced by carbonate assimilation. Primitive magmas may have been volatile saturated at the depth at which these inclusions were trapped (~8 km; [START_REF] Marianelli | The deep feeding system of Vesuvius involved in recent violent strombolian eruptions[END_REF]; however, there are no constraints on the amount of the mantle CO 2 that could have been in the gas phase. Available data on fluid inclusions identified in Mount Vesuvius products concern metamorphic and metasomatized sedimentary nodules and cumulate Publisher: GSA Journal: GEOL: Geology Article ID: G25446

Page 9 of 18 ejecta (Gilg et al., 2001, and references therein), which most likely derive from the interaction between the magma and the carbonate rocks [START_REF] Gilg | Isotope geochemistry and fluid inclusion study of skarns from Vesuvius[END_REF].

Several lines of evidence hence suggest that carbonate assimilation, which is thought to be responsible for the secular chemical variations of Mount Vesuvius eruptive product since 25 ka, may currently account for the elevated CO 2 emissions measured in Mount Vesuvius volcanic area, prevailing over the contribution of mantle-derived CO 2 .

CONCLUSIONS

The carbonate assimilation process presented in this study represents a CO 2 degassing mechanism alternative to those classically considered to drive magmatic degassing, i.e., crystallization at depth and decompression related to magma ascent.

Like Mount Vesuvius, several other volcanic centers, either quiescent or active, recognized to be emplaced over carbonate sedimentary successions and showing skarn xenoliths in their eruptive products, are characterized by elevated rates of CO 2 degassing (high ratios of emitted gas to emitted magma), e.g., Alban Hills and Mount Etna in central-southern Italy [START_REF] Michaud | Crustal xenoliths in recent hawaiites from Mount Etna, Italy: evidence for alkali exchanges during magma-wall rock interaction[END_REF][START_REF] Iacono-Marziano | Limestone assimilation and the origin of CO 2 emissions at the Alban Hills (Central Italy): constraints from experimental petrology[END_REF], Popocatépetl in Mexico, Yellowstone in the United States, Merapi in Indonesia, and Mount Erebus in Antarctica [START_REF] Goff | Passive infrared remote sensing evidence for large, intermittent CO2 emissions at[END_REF][START_REF] Werner | CO2 emissions from the Yellowstone volcanic system[END_REF][START_REF] Chadwick | Carbonate Assimilation at Merapi Volcano, Java, Indonesia: insights from crystal isotope stratigraphy[END_REF]. For some of these volcanoes, magma-carbonate interactions have been proposed to contribute to their degassing dynamics to some extent [START_REF] Goff | Passive infrared remote sensing evidence for large, intermittent CO2 emissions at[END_REF][START_REF] Obenholzner | Particles from the plume of Popocatépetl volcano, Mexico -the FESEM/EDS approach[END_REF][START_REF] Werner | CO2 emissions from the Yellowstone volcanic system[END_REF]. Further studies are therefore needed to assess the total contribution of CO 2 of nonmantle origin to global magmatic degassing.

FIGURE CAPTIONS

Figure 1 Simplified (not to scale) mechanism of carbonate assimilation and CO 2 release at Mount Vesuvius. Rising primary magma (magma feeding rates from [START_REF] Rosi | (ed) Somma-Vesuvius[END_REF][START_REF] Civetta | Steady state magma supply in the last 3400 years of Vesuvius activity[END_REF][START_REF] Scandone | Persistent activity and violent strombolian eruptions at Vesuvius between 1631 and 1944[END_REF]) is channeled at the metamorphic basementcarbonate rocks discontinuity, forming sill-shaped body [START_REF] Auger | Seismic evidence of an extended magmatic sill under Mt[END_REF][START_REF] De Natale | The Somma-Vesuvius volcano (Southern Italy): Structure, dynamics and hazard evaluation[END_REF]. Primary magma reacts with carbonate rocks, crystallizing clinopyroxene (cpx) and liberating CO 2 according to the reactions 1 and 2 in text. Arrows indicate CO 2 migration through rock's most permeable zones, dissolving in the aquifer [START_REF] Caliro | Volcanic degassing at Somma-Vesuvio (Italy) inferred by chemical and isotopic signatures of groundwater[END_REF], and finally generating diffuse degassing at the surface concentrated above the tensile faults of the sedimentary basement [START_REF] Federico | Magma-derived gas influx and water-rock interactions in the volcanic aquifer of Mt. Vesuvius, Italy[END_REF]. Geometry of sedimentary and metamorphic basement is from geophysical surveys. Top of carbonate sequence is dissected by series of regional normal faults and generally deepens toward Bay of Naples and center of Campanian

  Figure 2

ACKNOWLEDGMENTS

Publisher: GSA Journal: GEOL: Geology Article ID: G25446 Page 10 of 18 This work was funded by the French National Research Agency (ANR grant JC 05-42707 to Gaillard) and the Marie Curie Intra European fellowship (grant PIEF-GA-2008-220926 to Iacono-Marziano). Iacono-Marziano also acknowledges the postdoctoral grant of the Istituto Nazionale di geofisica e Vulcanolgia, sezione di Palermo. The comments of Cynthia Werner, Jake Lowenstern and an anonymous reviewer greatly improved the manuscript. We thank Andrew Barth for the careful editorial handling.

Plain [START_REF] Berrino | Sea gravity data in the Gulf of Naples: a contribution to delineating the structural pattern of the Vesuvian area[END_REF]. Inversion of gravity data suggests that the thickness of the carbonate basement is ~11 km (Berrino et al., 1998 and references therein). .D. 1794-1944eruptive period (MgO>5wt%, Marianelli et al., 2005;[START_REF] Fulignati | Towards a reconstruction of the magmatic feeding system of the 1944 eruption of Mt Vesuvius[END_REF]. Open diamonds: MI compositions in high-temperature skarn xenoliths from 1944 eruption (MgO>3wt%, [START_REF] Fulignati | Towards a reconstruction of the magmatic feeding system of the 1944 eruption of Mt Vesuvius[END_REF].

Open circles: residual liquids of interaction experiments at 1150 °C and 200 MPa (Iacono-Marziano et al., 2008). Thick lines: mass balance calculations (this study) simulating chemical changes in the melt composition in response to carbonate assimilation + crystallization following reactions 1 and 2 in text; crosses show calculated melt compositions (Table DR1; see footnote 1 for explanation) for 0, 6, 14 and 22 wt% carbonate assimilation. As much as 22 wt% of carbonate assimilation is required to reproduce composition of the MI found in high-temperature skarn minerals (SiO 2 ~43.3 wt%), while ~14 wt% of assimilation is needed for most extreme compositions of MI trapped in phenocrysts (SiO 2 ~46.2 wt%). Gray field represents average whole-rock composition of 1631-1944 lavas [START_REF] Joron | Chemistry and petrography[END_REF]