Sophie Brana
email: brana@montesquieu.u-bordeaux.fr

Mathilde Maurel
email: maurelm@univ-paris1.fr

Barter in Russia: Liquidity Shortage Versus Lack of Restructuring

Keywords: barter, non-monetary transactions, virtual economy, Russia, transition JEL Classification Number: C22, C23, E5, P2

Barter in Russia can be explained by firms liquidity constraint: it is strongly correlated with financial tightness. However a micro-economic analysis reveals that the rationale behind this liquidity constraint is different according to the firm situation. For firms in a good economic situation, but faced with adverse selection problem and having no access to bank credit, barter acts as a substitute for short term credit. While for indebted firms, barter, in the same way as external finance, is a way of avoiding costly restructuring.

I INTRODUCTION

The rapid growth of barter is one of the most surprising phenomena in Russia: As a percentage of industrial sales it steadily increased from 5% in 1992 to nearly 55% in 1998. Unknown in CEEC's transition countries, barter is only one aspect of the Russian economy's demonetisation process, along with dollarisation, growing arrears, and the widespread use of veksels and offsets. Barter is often seen as the consequence of the lack of restructuring, but some authors argue that it is a mechanism used to avoid shutting down potentially viable firms, in a context of market imperfections. The implications differ depending on the analysis chosen: in the first case, an expansionary monetary policy might not be appropriate, while the contrary is true if the demonetisation process jeopardizes potentially good enterprises.

This paper aims to assess this phenomenon in the Russian economy. The paper's main contribution to work in this field (reviewed and documented in section II) is to highlight two different rationales for barter. Before studying the latter more closely, section III uses official monthly data collected by the central bank of Russia, the Goskomstat, and the Russian Economic Barometer (REB), to emphasize the macro-economic features of barter in Russia, and, more specifically, the link between monetary policy and bartering activity. It appears that macroeconomic policy and macroeconomic indicators are unable to explain the whole process. In section IV, quarterly statistics for 1995 and 1996 taken from the REB survey of roughly 200 firms make it possible to implement a more qualitative survey.

The conclusion is striking: barter is used by potentially viable firms as a way of avoiding closure, while at the same time financing increasing inventories and soft goods in the case of indebted firms who use barter transactions, bank credit and choose to accumulate arrears in order to avoid restructuring.

II BACKGROUND

Two sets of explanations of barter can be drawn (see graph 1 below). The first one, which we call strategic barter, focuses on the inability of money to perform its function [START_REF] Poser | Monetary Disruptions and the Emergence of Barter in FSU Economies[END_REF]. This inability may be due to a process of demonetisation: in the prevailing context of high inflation in Russia, barter could be rational. It can also be the consequence of the growing informal economy: the decision to engage in barter is thus motivated mostly by managers' efforts to seek informal profit, and especially by a desire to avoid taxes (Ickes andal. 1997, Hendlez andal. 1997).

The second set of explanations focuses on liquidity constraints: firms use barter transaction to sustain operations in a cash constrained world (see for example [START_REF] Linz | Enterprise Restructuring in Russia's Transition Economy: Formal and Informal Mechanisms[END_REF]). This cash Cahiers de la MSE -1999.98 constrained world is imposed by the lack of payments at the firm level, and/or growing monetary restraint at the economy-wide level.

Graph 1: survey of barter explanations 2.1 Strategic Barter i) avoiding taxation;

Johnson, Kaufmann and Shleifer (1997) provide a simple model which highlights the incentives leading firms to choose between operating in the official and the unofficial sector. Firms will enter the formal economy if the benefits exceed the costs. In the official sector, the government provides public goods that increase the productivity of firms, but it imposes taxes and regulations on firms. The smaller the potential network effects, the smaller the incentive for a particular firm to operate in the formal sector. An important motive for operating in the unofficial sector is the desire to avoid official taxes. As tax liabilities are due only once the firm receives payment for its deliveries, barter is a useful means of avoiding taxes. For [START_REF] Gaddy | To Restructure or Not to Restructure: Informal Activities and Enterprise Behavior in Transition[END_REF] tax evasion is the first and most obvious motive for barter in Russia.

However, this explanation of barter is not really convincing for at least two reasons. Firstly, the use of barter relies on creation of exchange chains and is very costly [START_REF] Linz | Enterprise Restructuring in Russia's Transition Economy: Formal and Informal Mechanisms[END_REF][START_REF] Hendley | Observations on the Use of Law by Russian Enterprises[END_REF]. Barter requires a «double coincidence of wants» from the two -tight monetary policy transaction agents. This supposes a time consuming search as well as inventory costs. In this context, it is not certain that the benefits of barter, in terms of tax avoidance, exceed the associated costs.

Secondly, payment in cash can be seen as another successful way of tax evasion, as western experience proves. In these countries, cash transactions are the primary means used to avoid taxes. In Russia, the task of collecting taxes is still performed by banks, which have to inform authorities about all payment receipts and to debit the account of a tax debtor. In this context, firms have strong incentives not to effect payments through the banking system. But, this does not apply to cash payment.

The last explanation is based on more empirical grounds. A study carried out by the REB asked firms to give their basic reasons for using barter. If the tax avoidance motive is relevant for 20% of the companies, it is not the dominant factor [START_REF] Aukutsionek | Industrial Barter in Russia[END_REF]. [START_REF] Commander | Understanding Barter in Russia[END_REF] show that most firms believe that barter rather increases their tax bill, partly because the barter prices almost always exceed cash prices.

ii) Demonetization: barter as a monetary substitute;

A second analysis focuses on payments systems failure, with the inability of money to perform its functions as a medium of exchange, a unit of account and a store of value (see [START_REF] Poser | Monetary Disruptions and the Emergence of Barter in FSU Economies[END_REF], for a detailed analysis). Enginer and Bernhardt (1991) consider a theoretical model in which barter competes with money. They show that barter takes place if there is a double coincidence of wants and the cash-in-advance constraint, limiting monetary exchange. In their model, there is a unique inflation rate below which the only means of exchange is money, and over which money has no value. [START_REF] Hayashi | A Model of Fiat Money and Barter[END_REF] found, in a similar analysis, that monetary exchange is costly due to the cash-inadvance constraint, in the case of a positive inflation rate.

In Russia, barter was initially considered a natural response to the high inflation that prevailed in after prices were liberalized. When inflation is high, the opportunity cost of holding money increases, and

barter is used as a monetary substitute. However, if we calculate a simple correlation rate between barter and inflation rate variables, we find that this correlation is negative. Barter increases when inflation decreases. This statistical correlation reflects most notably the fact that barter has substantially increased in Russia as financial stabilization has proceeded. Hence barter cannot be considered a substitute for the depreciating currency, and the negative correlation between inflation and barter suggests rather an explanation in terms of liquidity constraints.

Liquidity constraint

i) Micro-economic explanation: barter expressing an unequal access to liquidity;

The lack of liquidity in good firms is bound to structural reasons. [START_REF] Linz | Enterprise Restructuring in Russia's Transition Economy: Formal and Informal Mechanisms[END_REF] found that barter is used unevenly across firms and is correlated to the particular industry in which the firm operates. Barter should be especially used for purchases which are important compared to the firms' liquidity. For example, intermediate or equipment goods represent large purchases and are more common in barter transactions [START_REF] Marin | Tying Trade Flows: A Theory of Countertrade with Evidence[END_REF]. For [START_REF] Linz | Enterprise Restructuring in Russia's Transition Economy: Formal and Informal Mechanisms[END_REF], firms that have access to cash, such as food industry firms, appear less likely to rely upon barter and pay above average wages. Conversely, machinery industries appear more likely to rely on barter. The explanation is that the latter are removed from the final customer and must deal on a wholesale level.

Non-access to retail customers reduces their ability to develop cash transactions. In the absence of well-functioning capital market which could improve the firms' liquidity position, these firms are obliged to use barter transactions.

Aukutsionek (1998) reinforces this explanation of barter by showing that the sector using barter the most produces intermediate goods (in this sector, the share of barter as an annual average has reached 55% in 1997), followed by the investment goods sector (42%) and finally by the consumer goods (32%) and agricultural (31%) sectors. The regional breakdown (in Table 2) also suggests evidence of an unequal access to liquidity: the level of barter is strongly differentiated depending on the region in which the firm is located: ii) Micro-economic explanation: lack of restructuring versus liquidity shortage;

The worsening of the firms financial situation and the implied increase in barter over time is either linked to poor economic performance or to liquidity shortage, due to credit rationing : for [START_REF] Hendley | Observations on the Use of Law by Russian Enterprises[END_REF], barter is an attempt by firms to sustain socialist production patterns. It can be interpreted as a bankruptcy-delaying tactic for firms and closely reflects the lack of restructuring. On the contrary, for [START_REF] Linz | Enterprise Restructuring in Russia's Transition Economy: Formal and Informal Mechanisms[END_REF] or [START_REF] Aukutsionek | Industrial Barter in Russia[END_REF] barter is a mechanism used to avoid shutting down potentially viable firms.

In this case, barter is connected to liquidity shortage in a context of imperfect financial market conditions and, more precisely, of credit market imperfections [START_REF] Ellingsen | Payments in Kind[END_REF][START_REF] Linz | Enterprise Restructuring in Russia's Transition Economy: Formal and Informal Mechanisms[END_REF].

Three features may explain the existence of credit rationing, even for good firms. Firstly, some buyers are liquidity constrained because they are unable to pledge future returns. Furthermore, in the transition process, past performance is an inadequate indicator of future profitability [START_REF] Bevan | Determinants of Enterprise Performance during Transition[END_REF]. Secondly, as in Western countries, buyers have private information about liquidity.

However, the informational asymmetries are stronger in transition economies, where problems of adverse selection and credit rationing are more likely to occur. In Russia, opaque balance sheets foster the barter economy (OECD 1997). Finally, banks suffered from weak protection from creditors' rights.

The dilemma -lack of restructuring versus liquidity shortage -can be assessed at first glance by simply looking at barter, rate of capacity utilization, order books level, and profit variables. If barter is used to sustain the former socialist production patterns, then one can expect barter to be negatively correlated to profit. The reverse should be observed if barter is financing the lack of working capital in a context of credit shortage. As reflected in the following tables, the reality is far from that simple, barter is not clearly associated with an above average indicator of profitability, nor with an above average utilization of capacity rate (or order books level), while it is clearly differentiated by region (see Annex B) and/or sector and/or firms' size (as proxied by the number of employees: labor): Profit is set equal to one when the firm is profit-making, to «2», when the profit is zero, and «3», when the firm is loss-making. The average profit in the branch takes values between 1 and 3: the closer it is to «1» (or «3»), the more profitable (the less profitable) the branch. Averages are weighted averages.

Several interpretations may be drawn:

As far as the opaque balance sheets mentioned above are concerned, the perception by firms of their real situation and profitability is likely to be biased by the overall lack of restructuring in the Russian economy and overall uncertainty. A higher order books level, higher utilization of capacity rate, and higher profit may reflect for instance the maintenance of old ties and old production patterns.

Consequently, the link between barter and profit is weak.

Moreover, the increase in barter over time suggests that increasing returns are at work: certain firms may be drawn to use barter regardless of their real and financial situation simply because the majority of firms in the region or in the branch are operating this way, and it would be costly to do otherwise.

One important consequence of the implied externalities is that the correlation between barter and the other variables, if any, might be not significant by not taking into account the regional, sector, or whatever, component of barter. In section IV, fixed effects are used to cope with that problem.

Finally it is worth mentioning that barter appears positively correlated to firms' size. This result seems to contradict the theoretical reasons highlighted in order to explain the success of barter in market economies: that is the argument that barter eases the squeeze on cash flow that often plagues small business (see [START_REF] Prendergast | Non-monetary Exchange within Firms and Industry[END_REF]). Yet, one of the major problems opposing barter is the challenge of finding a suitable trading partner. Barter, as an informal activity, requires great investment in relational capital [START_REF] Gaddy | To Restructure or Not to Restructure: Informal Activities and Enterprise Behavior in Transition[END_REF]. So, we can expect that the average size of an enterprise governs the potential stock of relational capital. [START_REF] Aukutsionek | Industrial Barter in Russia[END_REF] showed that barter to a large extent replaces already existing trade links between enterprises. The more extensively an enterprise uses barter, the more connections it has maintained with old suppliers.

iii) Macro-economic explanation: tight monetary policy;

This explanation of barter is examined in the following section, where we look at whether tight monetary policy can explain firms' financial situations and the increase in barter over time. The idea is that a rise in refinancing interest rates, or a decrease in money issuing, while bringing inflation under control, may at the same time decrease firms' sales and liquidity.

III BARTER AND MONETARY CONSTRAINTS

In this section we look at the relationships between barter and liquidity constraints at a macroeconomic level. We use two methods: Granger-causality tests and cointegration analysis.

Cahiers de la MSE -1999.98

3.1: Granger-causality tests between barter and a battery of macroeconomic variables

From the negative correlation between barter and inflation mentioned in the previous section, it is tempting to attribute the growth of barter (or of arrears) to a shortage of liquidity linked to stabilization. This point of view relies upon two underlying hypotheses. First, firms are faced with shortage of liquidity and second, this shortage can be explained by macroeconomic policy.

We focused first on the link between barter and the financial situation of firms, as proxied by goodfin.

This variable is set equal to one when the firm perceives its financial situation as good. Averaged over the REB sample each month, we find the share of enterprises perceiving themselves as being in a good financial situation. The barter variable is the share of barter in firms' sales. The correlation between these two variables is negative; barter decreases when the firm's financial situation improves.

We also found a Granger causality relationship: a worsening of the financial situation explains the increasing use of barter (see table 4).

Next, we have to test whether the macroeconomic situation and, more precisely, tight monetary policy explain the evolution of firms' financial situations and the underlying increase in barter over time. A tightening of monetary policy reflected in a rising refinancing interest rate, or in the reduction of money issuing, can bring inflation under control. At the same time, it depresses demand, which decreases firms' sales and liquidity4 . The test is done by computing partial correlation coefficients between a battery of monthly variables and the estimated causality in the sense defined by Granger (1969). These variables are: barter, the inflation rate, the real refinancing interest rate, and the liquidity rate (the liquidity ratio M2/PIB). One Granger causality relationship emerges (see table 4, columns 3 and 4); an increase in the real refinancing rate causes an increase in barter. An increase in the real refinancing rate indeed causes an increase in barter: the decreasing inflation rate over the period raised the real interest rate which became positive in January 1991. In a context of cash-in-advance constraint and liquidity shortage, as the cost of obtaining credit increases, borrowers try to overcome these constraints. They use liquidity from other sources and increase their use of barter. High interest rates make it hard for firms to borrow.

We didn't find the same type of causality with real interest rate on GKO. These results might suggest that firms rely on barter because they do not want to borrow in a context of liquidity shortage and not because they prefer to invest their liquidity in GKO.

The decrease in money supply was not found to cause the increase in barter: this suggests that the shortage of money in the economy (the demonetisation process) does not, in itself, cause the barter phenomenon. We tried to find some other explanations; in terms of the distressed economic situation (causality tests between barter, evolution of production, and evolution of capacity utilization rate in industry are not conclusive) and of share of indebted firms. Results are disappointing (and are not reported here). At the macroeconomic level, barter does not seem strongly correlated with real indicators, but only partially with access to external financing. This suggest that a more careful analysis, at the micro level (see section IV), is needed to understand the exact nature of liquidity constraints.

3.2: Cointegration analysis

We now try to estimate long-run relationships between the different variables highlighted by causality tests. The different variables presented above being non-stationary, we have to rely upon a cointegration analysis. When two series are cointegrated, we can distinguish between a long run relationship between these two series, that is to say the manner in which the two variables drift upward together and the short-run dynamics, that is to say the relationship between deviations from their long run trend. The Johansen maximum likelihood procedure consists in estimating an errorcorrection representation of a vector-autoregressive model of order k. We first estimated the rank of the matrix of the long-run responses using the maximum likelihood method developed by Johansen (1995) (cf. Table 5). The number of lags ( 5) was chosen based on the Hannan-Quinn information criterion. *, ** indicates significance at 95%, 99%.

Table 5 shows that there is only one cointegrating vector. This means that there is only one combination of the variables that produces stationary residuals. The long-run equation for barter is the following:

Barter = -0.52 Goodfin + 0.14 Interest rate Again we find that barter increases together with interest rates, but decreases as the financial situation of firms improves. In the short-run there will be deviations from the long run relations found above.

The short-run barter determination can be explained by a dynamic error correction model, where changes in barter depend on prior deviations from the long-run equilibrium and on prior changes in all variables. with irRF, the real interest rate of refinancing ; crBadfin, the three months moving average increasing rate of firms in bad financial situation ; and crBarter the three months moving average increasing rate of barter.

To summarize, firms seem to use barter transactions in order to sustain production in a cashconstrained economy 7 . Real interest rates have been found to cause fluctuations in barter over time, and the relationships between barter on one hand, and financial situation and interest rates fluctuations on the other hand, prove to be quite strong for the whole period. However, the liquidity ratio, although correlated with barter, does not exhibit any causality relationships with it. Thus, our conclusion is that monetary policy tightness at the macro-economic level only partially explains the increasing use of barter, but we have yet to call upon explanations of the lack of liquidity at the firm level.

IV MICRO-EVIDENCE CONCERNING BARTER

As shown in the previous section, barter is positively linked to the firm's financial situation. In order to better understand the link between these two factors, we distinguish enterprises which have access to credit from those which do not 8 . We show that two different types of behavior can generate barter:

for enterprises which are not provided with credit by banks, it acts as a substitute for short-term credit; for indebted enterprises, barter in the same way as external finance, is a way of avoiding costly restructuring. This approach is slightly different to that followed by Ickes and Gaddy (1998) 9 , who emphasize that barter results from the supply of soft credit by the State to the State sector, and consequently barter should be lower in private firms. Here we look more closely at the microeconomic rationale for barter, by implicitly assuming that soft budget constraints hold only for certain enterprises, which benefit from bank credit, while other firms are obliged to adapt to market discipline.

Data and Methodology

The panel data base we use has been extracted from the REB (see Annex A). The data were collected in June 1995, December 1995, June 1996, and December 1996. There are a total of 736 observations on enterprises in the unbalanced dataset. The variable ncr, equal to 1 when the firm declares that it is not indebted and not going to be, divides the sample into two: those that are not financed through the banking system (484 enterprises), and those that are the main recipients of the banking credit (252, but 263 if we are considering a subset of explanatory variables). As suggested above, the Russian banking system is characterized by severe adverse selection problems. We argue that market discipline is more likely to be observed by non-indebted enterprises: in this sense, the ncr variable is well suited for distinguishing different types of firms.

By contrast, the profit variable, although available in the REB (see Annex A), does not turn out to be a good proxy for firms performance, as emphasized in most papers dealing with the transition process 7 This result confirms the REB survey: barter is primarily, for 61% of enterprises in 1998, a means of maintain production in a context of shortage of working capital. The second motive, for 41% of firms, is the desire to speed up sales of output [START_REF] Aukutsionek | Industrial Barter in Russia[END_REF]. 8 This distinction can also be motivated by the findings in Brana, [START_REF] Maurel | Enterprise adjustment and the role of bank credit in Russia: Evidence from a 420 firm's qualitative survey[END_REF], who showed that credit is mainly allocated towards loss-making firms, while profitable enterprises on the contrary are shut out of the banking system. 9 For those authors, barter allows enterprises in Russia, often monopoly suppliers, to pay taxes in «soft goods».

in the former Soviet Union 10 . We nevertheless tried to estimate barter equations in Table 7 for profit makers and loss makers, using the profit variable, but the results, not reported here, were not satisfactory.

We could also test the assumption that ownership is a key variable in explaining barter. This variable was unfortunately not available in the REB; although [START_REF] Estrin | Enterprise performance and ownership: The case of Ukraine[END_REF] do not find strong links with firm performance, they establish that barter in Ukraine is associated with lower profitability, and is less common in privatised firms11 . However, the rational behind this result is not clear: in particular the assumption that outsider owned firms will perform better in terms of barter than all other ownership types is not supported.

To summarize, both the macro-economic framework in the previous section and the emphasis we place on bank credit towards already indebted enterprises (versus the role of the cash liquidity constraint for non indebted firms) brings out a sharp distinction between indebted and non indebted enterprises. This distinction is not simply a proxy for that between profitable and non-profitable firms.

Our model (see equations 1, 1', 2, 2') of barter simply claims that certain firms, whatever privatised or not and profitable or not, are more subject to market discipline than are others. We suspect that this might be related to access to bank credit, whose allocation is distorted in the Russian context towards already heavily indebted enterprises or/and loss makers. If this model describes the Russian economy correctly, then one important implication is that enterprises excluded from the banking system are victims of the diffusion of barter (in the sense that they would prefer to use money), while other firms, which try to escape from the restructuring effort, are the cause of this diffusion of barter.

The panel structure of the REB allows us to take into account the strong regional and sector components of barter (as suggested in the huge discrepancies in Tables 1 and2), and all other kinds of fixed effects, including the structure of property. The stress is thus put not on the average level of barter by sector, region, ownership, etc., but on the reasons for changes in its level.

Fixed effects are unable to capture all the heterogeneity in the sample. For example, for indebted firms, increased barter is correlated with inventories: it is a way of avoiding costly restructuring. For non-indebted enterprises, barter is used as a substitute for short term credit. We thus expect the determinants of barter to be different between the two sub-samples. Then we estimated two forms:

form 1 contains the fin variable, while form 2 does not.

10 Measurement problem aside, in the transition period profits may yield a distorted picture if active restructuring leads to the writing off of bad debts or accumulated losses. What concerns the REB, this warning has to be moderated: Brana, [START_REF] Maurel | Enterprise adjustment and the role of bank credit in Russia: Evidence from a 420 firm's qualitative survey[END_REF] showed that firms with the worst indicator of profit have poor performances and bad financial positions. For profitable enterprises, on the contrary, profitability, order book level and capacity utilization rate are relatively high.

( )

1 3 2 1 3 2 1 4 3 2 1 it i it it it it it u Q t Q t Q t labor b fin b lma b inv b a br + + + + + + + + + = ν ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ' 1 3 3 2 2 1 1 3 2 1 4 3 2 1 i it i it i it i it i it i it u u Q Q t Q Q t Q Q t labor labor b fin fin b lma lma b inv inv b br br - + - + - + - + - + - + - + - = - ⇔ ( ) 2 3 2 1 3 2 1 4 2 1 it i it it it it u Q t Q t Q t labor b lma b inv b a br + + + + + + + + = ν ( ) ( ) ( ) ( ) ( ) ( ) ( ) ' 2 3 3 2 2 1 1 3 2 1 4 2 1 i it i it i it i it i it u u Q Q t Q Q t Q Q t labor labor b lma lma b inv inv b br br - + - + - + - + - + - + - = - ⇔
where:

• br is the current share of barter in sales (in percent), for each firm at each time (t is successively set equal to Q1= June 1995, Q2 = December 1995, Q3 = June 1996, Q4 = December 1996), and

∑ = t i it i T br br / ;
• inv is inventory stocks, where the usual monthly level is set equal to 100, and

∑ = t i it i T inv inv / .
We assume that this variable is a proxy for the lack of restructuring, inasmuch as an increase in inventories means that the market does not clear supply and demand; • lma is set equal to 1 if the perceived main impediment to production is insufficient demand, and

∑ = t i it i T lma lma
/ . This is a proxy for firm sensitivity to demand conditions on the goods market;

• fin takes values 1 (good financial position), 2 (normal financial position), and 3 (bad financial position), and

∑ = t i it i T fin fin / ;
• labor is the number of employees, and

∑ = t i it i T labor labor / .
As mentioned in Aukutsionek (1998), the more extensively an enterprise uses barter, the more connections it has maintained with old suppliers, while the network of old suppliers depends upon the size of the enterprise;

• it i u + ν
is the residual, i ν being the unit specific residual, and it u the usual residual assumed to be iid; • Q1, Q2, Q3 are dummy variables equal to one when the observation corresponds to the first semester (June 1995), to the second semester (December 1995), to the third (June 1996), and to the fourth (December 1996). They are introduced in the equation to take into account the increase in barter over time.

Assumption 1: Barter allows indebted enterprises, responsible for the adverse-selection problem, to unload excess inventory. There should therefore be a positive correlation between barter and inv.

These firms can continue to produce «soft goods», for which there is no effective demand. We thus expect the correlation between lma and barter to be positive (or not significant): when the lack of demand starts being identified as the main impediment to production, barter either increases or remains stable.

Assumption 2: For enterprises excluded from the banking system, barter is linked to the tightness of external finance. It is expected to decrease (increase), when the main impediment to production ceases to be the lack of demand (becomes the lack of demand). Here barter is seen as a substitute for financial resources, whose shortage acts as an impediment to the supplying of market demand. Under this assumption, the correlation between lma and barter is expected to be negative.

Assumption 3: The coefficient on fin reflects the extent to which a worsening of the financial situation increases barter. If assumptions 1 and 2 are correct, then a worsening financial situation is expected to increase barter, which indeed serves as a substitute for external finance. For non-indebted firms, barter allows the working capital required for production to be financed. For indebted firms, it finances the production of soft goods.

Results

Our findings are reported in Table 7 (columns I, II, III, IV). Each column reports the results of random effects and fixed effects regressions for equations of form 1 (columns I, Ia, Ib, IIIa, IIIb), including the fin variable, and 2 (columns II, IIa, IIb, IVa, IVb), excluding it. The equations are always significant at the usual level (coefficients in italics are not significant). Hausman specification tests prefer the equations without fin. Nevertheless, the coefficients are very similar across the different estimations, which means that the model specification is fairly robust.

Assumptions 1 and 2 are confirmed (see columns Ia to IVa, and Ib to IVb ): in the group of indebted12 firms (and/or going to be indebted), an increase in barter is associated with a positive variation in inventories, but it is insensitive to a jump in lma from 0 to 1, while the contrary is true for nonindebted enterprises. The empirical analysis thus supports the view that barter allows the former to unload excess inventory [START_REF] Prendergast | Non-monetary Exchange within Firms and Industry[END_REF] and to produce «soft goods», for which there is no effective demand. It offers some flexibility to managers and can be seen as the symptom of insufficient restructuring. Non-indebted firms, on the other hand, have hard budget constraints and suffer from a shortage of working capital. This cash constraint is less binding when the main impediment to production is the lack of demand: in this case the enterprise adjusts by decreasing its -22,790 -22,247 -23,094 -22,186 -21,161 -20,502 -21,387 -20,472 Q2 -15,259 -15,706 -15,152 -15,596 -14,691 -14,646 -14,420 -14,472 Q3 -5,012 -5,906 -5,938 -6,068 -4,669 -5,544 -5,401 -5 use of barter. This result has to be put into light with that in [START_REF] Marin | Disorganization and Financial Collapse[END_REF] 13 , for whom the inversely U-shaped relationship between barter and output, that is, the positive effect of barter on output growth for low barter firms and the negative effect for high barter firms, indicates that high growth firms « showed a favorable growth performance because they used their credit constraint and barter activity effectively to avoid an input and financial shortage ». Low growth firms are faced with a « too large credit enforcement costs which makes it worthwhile for the input supplier to participate in the deal », hence barter cannot help to maintain production by getting trade credit from other firms.

In our approach, although the emphasis is not put on the relative output growth performance, we would explain the negative correlation between output and barter for indebted firms by the lack of market discipline and the persistence of soft budget constraint, which explain the increase in credit enforcement costs.

In light of these results, one can interpret the coefficient of fin (columns Ia, Ib, IIIa, IIIb) in two different ways, depending on which objective is pursued when a particular firm uses barter as a substitute for external finance. If it is to maintain an artificial level of production (assumption 1), then barter reflects liquidity shortage due to the lack of restructuring; if it is to finance production in the context of a hard budget constraint (assumption 2), then barter merely reflects a cash liquidity constraint.

IV. CONCLUSION

The process of transition can be viewed as the transition from a centrally planned economy to a monetary economy, where money imposes hard budget constraints on firms [START_REF] Poser | Monetary Disruptions and the Emergence of Barter in FSU Economies[END_REF]. As the transformation from plan to market proceeds, and profitability becomes the main aim of enterprises, barter should decline. In this context, the growing process of barter in Russia since 1992 can be seen as the sign of a delaying process of transition and restructuring.

We showed, however, that barter is a complex phenomenon, which has different roots from firm to firm. For bad enterprises, barter can be seen as a bankruptcy delaying tactic, while in profitable enterprises it is used as an additional liquidity, in a context of credit rationing by banks. In both cases, the barter phenomenon reveals the importance of bankruptcy procedures. At the micro-economic level, barter lowers the ability of money to harden firms' budgets. It consolidates existing inter-firm relationships, reduces market competition, and tends to create artificial demand. Moreover, relative price changes become less meaningful. Consequently, the pace of economic transition is slowed down, and economic and financial valuation of firms becomes groundless. For good firms, lack of 13 For these authors, barter provides a mechanism to deal with disorganization when credit enforcement is liquidity in a context of low retained earnings and low cash flows makes it impossible for them to invest and restructure effectively. In the presence of capital market imperfections, efficient firms may be forced to exit due to lack of funds 14 . At a macro-economic level, the barterisation process is an obvious impediment to effective macro-economic policy. It is a means of tax evasion (even if tax evasion is more a consequence than a motive of barter) and puts constraints on fiscal policy. At the same time, barter undermines monetary control and thus the stabilization policies. The implication of this paper is that the priority must be given to restructuring at the micro level. Notably, the implementation of efficient bankruptcy procedures appears a prerequisite for coping with barter and with the de-intermediation process. Thus, eventually monetary and fiscal policy could play their role. [START_REF] Johansen | Likelihood-based Inference in Cointegrated Vector Autoregressive Models[END_REF]and 1996[START_REF] Marin | Tying Trade Flows: A Theory of Countertrade with Evidence[END_REF]and 1996 ; ;a: Total sample for ncr=0 (indebted and / or going to be indebted) ; b: Total sample for ncr=1 (not indebted and not going to be).

Cahiers de la MSE -1999.98

Table 1

 1

	below reports the level of barter in our database

Table 2 :

 2 Barter by region

	Codes	Region	Number of	% in the Sample	Barter (%)
			observations
		Siberia	118	14.2	39.2
	2, 32	East Siberia	43	5.2	35
	3, 33, 34	West Siberia	75	9	41.7
		Urals	96	11.6	43.2
	4, 35	South Urals	66	8	41
	5, 36	North Urals	30	3.6	48
		Volga:	182	21.9	32.8
	6, 42	Volga-Vyatka	45	5.4	33.7
	7, 39	Volga	113	13.6	32.6
	8, 40	Volga	24	2.9	32
		West	85	10.3	34.8
	9, 41	Central Black-Soil	62	7.5	34
	10, 43	Central	23	2.8	37
	11, 44	Central	42	5.1	27.2

12, 45, 46 Moscow region 47 5.7 14.8 13, 47 North 114 13.7 30.7 14, 48 St Petersburg region 77 9.3 21.6 16, 38 North Caucasus 68 8.2 27.6

	Total	829	100	32
	Source: quarterly REB survey, June and December 1995 and 1996. See Annexes A and C at the end of the paper.

Table 3 :

 3 Barter, rate of capacity utilization, order book level, and profit.

		%			B a r t e r ( br) %
		Indebted Not indebted Indebted Not indebted	Total	Labor
	Consumer Goods	62.9	37.1	23.4	27.5		25.3	479
	Foodstuffs	69.9	30.1	16	19		17	351
	Textile Goods	67.4	32.6	38	38		38	569
	Paper, Wood	60	40	27	32		29	685
	Others	43.6	56.4	14	26		21	388
	Investment Goods	70	30	32.7	28.8		32.1	910
	Machinery	68.1	31.2	33	32		33	854
	Fuels	81	19	31	11		27	1230
	Intermediate Goods	67.7	32.3	43.6	38		42.3	1087
	Construction Material	67.9	32.1	43	45		44	654
	Chemical (incl. Oil refining)	73.7	26.3	49	16		40	1325
	Energy, Electricity	52	48	35	35		35	1379
	Metallurgy	73.9	26.1	47	44		46	2483
	Total	66.5	33.5	31.5	30.5		31.7	873
		Rate of capacity utilization (utc)%	Order books level (ord) %	Profit
		Indebted Not indebted Total Indebted Not indebted Total
	Consumer Goods	55.9	54.7	55.5	66.3	70.6	67.9	1.78
	Foodstuffs	55	58	56	67	83	72	1.7
	Textile Goods	51	46	50	59	62	60	2
	Paper, Wood	59	54	57	72	63	68	1.8
	Others	62	61	62	69	64	66	1.6
	Investment Goods	56.8	52.9	55.6	69	60.1	66.3	1.9
	Machinery	53	50	52	66	58	64	1.9
	Fuels	78	69	77	86	72	83	2
	Intermediate Goods	55.7	54.5	55.3	62.8	63.5	63.1	1.67
	Construction Material	56	50	54	59	53	57	1.7
	Chemical (incl. Oil refining)	44	55	47	56	72	60	2
	Energy, Electricity	61	84	72	78	95	87	1.2
	Metallurgy	68	43	61	76	66	73	1.5
	Total	56.2	54	55.5	66.4	65.3	66.2	1.8

Source: Quarterly REB survey, June and December 1995 and 1996. See Annex C at the end of the paper.

Table 4 :

 4 Correlation and Granger-causality test between barter and financial tightness

			Granger-causality test
		Correlation with barter	(Fisher statistic with 6 degrees of freedom)
			Over the whole period	Beginning of transition
			1992 (1) -1998(1)	1992(1) -1996(1)
	Goodfin	-59%	2.32*	3.49*
	Inflation rate	-82%	0.71	0.76
	Real refinancing interest rate	41%	1.7	3.47*
	GKO real yield	71%	0.66	0.82
	Liquidity rate	49%	1.04	0.71
	We used stationary variables for Granger-causality tests (variables I(1) are differentiated).
	*, ** indicates significance at 95%, 99%
	Sources of data: Russian Economic Trend and Russian Economic Barometer.

Table 5 :

 5 Johansen maximum likelihood procedure (1993-7; 1998-11)

	H0: rank=p	Maximum	95% critical value	Trace statistics	95% critical value
		eigenvalue statistics
	p=0	37.63**	21	46.51**	29.7
	p<=1	8.32	14.1	8.87	14.4
	p<=2	0.55	3.8	0.55	3.8
		Standardized eigenvectors
	Barter		Goodfin		Interest rate
	1		0.5224		-0.1422
	0.3429		1		1.363
	-0.5096		0.07341		1

Table 6 :

 6 Error correction Engle-Granger equation 5 ∆Barter = 0.13 -0.19 ∆Goodfin t -0.15 ∆Goodfin t-1 + 0.11 ∆txRF t -0.68 ECM t-1 Also in the short run, barter is correlated with indicators of financial tightness: barter increases when current real interest rates increase and decreases as the firm's financial situation improves (see Graph 2). No other variable (as liquidity rate, production, capacity utilization rate or inflation rate) appears significant, as confirmed by the Lagrange-multiplier tests for omitted variables 6 .

		(0.5)	(-3.7)	(-2.7)	(2.7)	(-4.7)
	R 2 = 0.40	DW = 2.13 AR (5, 55) = 1.69 ARCH(5, 50) = 0.30	Normality χ 2 = 2.3

txRF is the refinancing interest rate and ECM t-1 represents the error correction term.

5

All variables, except the error correction term, are differentiated and thus are I(0).

Table 7 :

 7 Estimation of Equations 1' and 2'.

				Total Sample
	column			I			II
	Barter	Random effects	Fixed Effects	Random effects	Fixed Effects
	inv		0,036		0,037		0,040		0,038
	lma		-1,600		-0,922		-1,850		-0,962
	fin		3,517		0,527
	labor		0,00203		0,00152		0,00211	0,00155
	Q1		-18,368		-18,034		-18,729	-18,093
	Q2		-13,331		-13,284		-13,442	-13,289
	Q3		-3,206		-2,986		-3,482		-3,029
	intercept		26,728				36,215
	R 2		0,1488				0,1294
	number of observations				736
	number of groups				403
				Hausman Specification Test
	Chi( )		Chi(7) = 14,56			Chi(6) = 2,07
	Prob>Chi2			0,042			0,9128
				Indebted Firms
					ncr = 0
	column		Ia		IIa		IIIa		IVa
	Barter	Random	Fixed Effects Random	Fixed Effects Random	Fixed Effects Random	Fixed Effects
		effects		effects		effects		effects
	inv	0,052	0,077	0,059	0,079	0,053	0,077	0,060	0,079
	lma	0,991	0,823	0,441	0,648
	fin	4,674	1,536			4,567	1,454
	labor	0,00215	0,00050	0,00222	0,00053	0,00211	0,00047	0,00220	0,00051
	Q1	-17,079	-17,330	-17,613	-17,528	-17,221	-17,448	-17,672	-17,614
	Q2	-12,308	-12,398	-12,617	-12,452	-12,375	-12,473	-12,644	-12,509
	Q3	-2,320	-2,709	-2,587	-2,795	-2,369	-2,736	-2,606	-2,813
	intercept	19,368		32,166		20,179		32,400
	R 2	0,1544		0,1345		0,1538		0,1345
	number of observations				484
	number of groups				310
				Hausman Specification Test
	Chi( )	Chi(7) = 5,34	Chi(6) = 1,83	Chi(6) = 5,34	Chi(5) = 1,82
	Prob>Chi2		0,618	0,9346	0,5011	0,8736

Non Indebted Firms (and not going to be); ncr

					= 1
	column		Ib		IIb		IIIb		IVb
	Barter	Random	Fixed Effects Random	Fixed Effects Random	Fixed Effects Random	Fixed Effects
		effects		effects		effects		effects
	inv	0,013	-0,010	0,015	-0,009
	lma	-8,022	-6,575	-7,364	-6,174	-6,889	-6,498	-6,308	-6,112
	fin	6,043	1,533			4,629	1,454
	labor	0,00413	0,01105	0,00434	0,01067	0,00457	0,00395	0,00470	0,00372
	Q1

  Percentage of firms which identify demand, shortage of financial resources, availability of inputs, as the main impediment to production, by Region Total Sample: survey of June 1995 and 1996, December 1995 and 1996 ; a: Total sample for ncr=0 (indebted and / or going to be indebted) ; b: Total sample for ncr=1 (non-indebted and not going to be). of firms which identify demand, shortage of financial resources, availability of inputs, as the main impediment to production, by branch

														ANNEX B ANNEX B (followed)
						Breakdown of barter, inventories, order books level, and rate of capacity of utilisation by Region
	Region Region Number of observations Number of observations share of barter (br) in sales % Limit to production : demand (lma) Limit to production : inputs (lmb) Inventories (inv) % order books level (ord) % Limit to production : financial (lmc) rate of capacity utilisation (utc)
		Code	Total	Indebted	Non-indebted	Total	Indebted	(usual monthly level =100) Non-indebted Total	(usual monthly level =100) Indebted Non-indebted Total (%, usual monthly level =100) Indebted Non-indebted
	Code Total sample 0	Indebted firms a sample 11	Non-indebted firms b firms a 10	Total sample firms b Indebted firms a sample Non-indebted firms b firms a sample Total 1 0,45 0,50	Indebted firms a firms b 0,00	Non-indebted firms b sample 0,09	Total sample firms a 0,10	Indebted firms a firms b Non-indebted firms b sample Total sample firms a Indebted firms a 0,00 0,82 0,80	Non-indebted firms b firms b 1,00
	0	2	11	10 43	1 27			17 16	13	0,40	55	0,52	98		97 0,19			110 0,28			53 0,22	55	0,38	35	0,70	38	39 0,67	25 0,75
	2	3	4 3	2 7 66	1 6 46			3 5 20	3 8	0,38	3 2	0,39	8 7		9 4 0,35			7 7 0,26			6 3 0,28	6 8	0,20	5 6	0,85	5 4	5 1 0,83	5 9 0,90
	3	4	6 6	4 6 56	2 0 35			4 1 21	4 1	0,38	4 1	0,43	7 2		7 3 0,29			6 9 0,21			7 1 0,17	7 1	0,29	7 2	0,79	6 6	6 8 0,77	6 0 0,81
	4	5	56	35 30	21 22			41	8	40	0,50	42	0,50	98		94 0,50			105 0,17			77 0,14	77	0,25	78	0,80	60	60 0,86	60 0,63
	5	6	30	22 31	8 19			48 12	50	0,65	43	0,74	93		93 0,50			94 0,23			63 0,26	59	0,17	72	0,71	48	46 0,63	54 0,83
	6	7	3 1	1 9 99	1 2 68			2 9 31	3 0	0,67	2 9	0,65	8 1		8 1 0,71			8 1 0,22			5 7 0,28	5 6	0,10	5 9	0,57	5 2	5 0 0,54	5 4 0,61
	7 8 9 10	9 9 24 6 2 41 Paper, Wood 6 8 19 4 5 29 8 24 9 62 10 41 Energy, Electricity 11 23 Metallurgy	3 1 5 1 7 12 19 45 70 29 25 16 23	42 13 17	3 0 32 3 4 27 17 5 12 7	2 8 33 3 4 23 28 12 6	0,46 0,48 29 0,66 35 0,35 46	3 3 27 3 5 35	0,47 0,47 27 0,72 35 0,38 47	9 7 70 8 2 85	9 9 64 8 5 108 0,40 0,53 32 0,50 35 0,29 44	92 26 88	9 3 99 7 6 35 0,25 0,23 101 0,15 57 0,13 83			5 7 60 6 7 66 0,21 0,16 79 0,10 18 0,13 100	5 9 57 6 9 64	0,40 0,41 68 0,25 87 0,14 73	5 2 72 6 3 72 72 78 76	0,79 0,61 0,61 0,57	4 9 48 5 5 56 63 95 66	5 1 44 5 9 53 0,84 0,62 57 0,59 72 0,44 61	4 5 63 4 4 64 0,60 59 0,59 61 0,67 0,86 68	54 84 43
	11	12	23	16 42	7 18			37 24	36	0,40	40	0,39	62		80 0,42			21 0,07			68 0,06	67	0,08	72	0,57	54	54 0,67	55 0,50
	12 13 14 16 33 34 37 39 42 43 45 47 48	42 100 61 48 8 1 20 14 14 1 5 Construction Material 18 68 13 100 Branches 44 14 61 32 16 48 4 33 8 1 34 1 12 37 20 Foodstuffs 11 39 14 Machinery 6 42 14 Fuels 1 43 1 Others 1 45 5 14 11 47 14 Consumer Goods 16 10 48 16 Chemical (incl. Oil refining) 24 32 68 17 44 16 32 4 4 1 8 12 3 11 8 6 1 4 1 3 11 6 10 Paper, Wood	14 29 32 Limit to production : demand (lma) Limit to production : inputs (lmb) 14 13 90 67 106 27 32 98 97 99 0,59 0,62 0,53 0,24 22 24 18 99 118 48 17 0,62 0,68 0,47 0,13 27 27 27 83 84 82 16 0,75 0,72 0,81 0,25 Total Indebted Non-Total Indebted Non-45 58 33 126 121 131 4 0,75 0,75 0,75 0,13 sample firms a indebted sample firms a indebted 65 65 35 35 0,00 0,00 0,00 firms b firms b 29 39 15 98 98 98 8 0,70 0,75 0,63 0,20 0,70 0,74 0,60 0,30 0,29 0,33 51 56 34 111 111 112 3 0,57 0,64 0,33 0,21 0,50 0,51 0,48 0,16 0,16 0,17 44 45 44 115 127 107 8 0,57 0,33 0,75 0,21 0,29 0,24 0,50 0,14 0,18 0,00 35 35 215 215 1,00 1,00 0,00 0,56 0,67 0,48 0,24 0,13 0,32 22 3 28 68 65 70 4 0,60 0,00 0,75 0,40 0,80 0,83 0,75 0,14 0,11 0,22 43 37 65 61 66 45 3 0,64 0,55 1,00 0,14 0,53 0,48 0,64 0,27 0,26 0,29 20 25 12 102 115 82 6 0,31 0,30 0,33 0,13 0,53 0,57 0,40 0,21 0,18 0,30 0,27 0,29 0,25 0,19 0,14 0,25	60 71 0,19 Limit to production : financial 70 51 64 74 67 62 0,34 0,63 71 70 71 55 0,09 0,24 0,64 (lmc) 67 65 71 58 0,25 0,25 0,52 Total Indebted Non-62 74 50 53 0,00 0,25 0,63 sample firms a indebted 65 65 15 0,00 1,00 firms b 59 49 75 49 0,00 0,50 0,55 0,46 0,48 0,40 68 62 85 47 0,18 0,33 0,71 0,71 0,73 0,68 85 78 91 53 0,17 0,25 0,57 0,71 0,71 0,75 65 65 35 0,00 0,00 0,69 0,71 0,68 77 65 80 65 1,00 0,25 0,60 0,67 0,64 0,72 63 68 35 46 0,09 0,33 0,86 0,71 0,71 0,71 59 61 55 56 0,20 0,00 0,88 0,68 0,71 0,60 0,70 0,74 0,64	69 63 0,63 58 0,68 59 0,47 Total 65 0,75 sample 1,00 15 46 0,58 404 49 0,82 858 53 0,83 2140 0,00 371 35 65 1,00 576 49 0,82 672 61 0,90 1457 641	60 0,63 Labor 60 0,53 48 0,63 Indebted 57 0,50 firms a 40 0,50 432 53 0,33 1071 42 0,38 2262 53 439 0,50 591 65 1,00 684 38 0,83 1616 47 829	Non-indebted firms b 339 381 1649 317 547 647 1014 348
	Total Sample: survey of June 1995 and 1996, December 1995 and 1996 ; Energy, Electricity 0,36 0,62 0,08 0,20			0,23	0,17			0,76	0,62	0,92	1358	1657	1005
	a: Total sample for ncr=0 (indebted and / or going to be indebted) ; Metallurgy 0,35 0,41 0,17 b: Total sample for ncr=1 (non-indebted and not going to be). Total Sample: survey of June	0,22			0,12	0,50			0,78	0,82	0,67	2167	2155	2204
														Cahiers de la MSE -1999.98 Cahiers de la MSE -1999.98

%

Alfanderi and Schaffer (1996), who focused on payment arrears in the Russian enterprise sector, found a similar negative relationship between the consumer price index (CPI) lagged one month and the ratio of overdue commercial receivables in industry to mid 1995. They found a strong negative correlation; when inflation is high (rising) in Russia, trade credit arrears are low (falling). For these authors, this close inverse relationship can be explained by the fact that tightening liquidity conditions drive these two variables.

This allows tests for the significance of complete lag functions of excluded variables. Results are not conclusive and therefore are not presented here.

This result is compatible with the model developed by[START_REF] Gaddy | To Restructure or Not to Restructure: Informal Activities and Enterprise Behavior in Transition[END_REF], as privatised firms are less likely to receive soft credit from the State, therefore less likely to engage in bartering activity.

In Brana,[START_REF] Maurel | Enterprise adjustment and the role of bank credit in Russia: Evidence from a 420 firm's qualitative survey[END_REF] again, these enterprises have been shown to be in serious financial difficulties: being chronic loss-makers, they are unable to pay in cash.

Program n° T95-4152-R. It has been presented at the Second

ANNEX A Russian Economic Barometer (REB) survey

The REB is a survey which has been conducted since 1992, on a monthly and quarterly basis. It is sent to between 170 to 210 enterprises considered representative in terms of geographic as well as sector localization. An important bias is the predominance of privatized firms, as opposed to new private firms. In the 1996 sample, 18% were State-owned, 26% had a mixed property structure, and 56% were privatized former State-ownedenterprises.

The econometric part of this paper focuses on the panel dimension of the database, while aggregated indicators, like monthly barter averaged over the whole sample or the percentage of firms which are in a good financial situation for a given month, are used for the macroeconomic analysis. The variables we used are either expressed in per cent of a monthly usual current level (br, inv, ord, utc), or are dummy variables: br is the current share of barter in sales (in percent), for each individual at each time (t varies from t= first quarter of 1995 to t= last quarter of 1996). inv is the stock of inventories, where the usual monthly level is set equal to 100. ord is the order books' level, where the usual monthly level is set equal to 100. utc: is the rate of capacity utilization, where the usual monthly level is set equal to 100.

ncr is set equal to 1 when the firm is not indebted and not going to be. lma is set equal to «1» when the firm identifies insufficient demand as the main impediment to production. lmb is set equal to «1» when the firm identifies a shortage of raw materials as the main impediment to production. lmc is set equal to «1» when the firm identifies a shortage of financial resources as the main impediment to production. fin takes values 1 (good financial position), 2 (normal financial position), and 3 (bad financial position). goodfin is set equal to 1 when the answer to fin is 1, and 0 elsewhere, in per cent it represents the share of enterprises in a good financial situation.

By averaging over the whole sample, or sub-samples, one gets the percentage of firms which identify insufficient demand (respectively the shortage of raw materials, the shortage of financial resources) as the main impediment to production, as well as the percentage of firms which are in a good, bad, or normal financial situation.

REGIONS CODES


Amel Kort

F-X Ouf

Riadh Lakhmi

T Gelain

J Malet

Philippe Breuil

Jean-Paul Viricelle

J-P Viricelle

An innovative method for soot deposit quantification using a CO2 sensor: application to fire studies in research facilities

Keywords: Gas sensor, soot, quantification, fire

est destinée au dépôt

INTRODUCTION

In industrial facilities handling or manufacturing hazardous materials (biological, chemical, nuclear, nanoscale…), fires are one of the major hazards when considering particles emission and dispersion in an airborne phase. Therefore, it is important to develop experimental and modeling tools to better understand the transport and deposition phenomenon of emitted particles in order to predict the consequences of such accidental situations and to implement relevant containment devices (high efficiency particulate air filters HEPA, physical barriers such as fire dampers or butterfly valves…) and strategies (pressure cascade, in depth defense…). For this purpose, development of simulation tools are currently in progress [START_REF] Mensch | Measurements and predictions of thermophoretic soot deposition[END_REF][START_REF] Plagge | An alternative method for thermal plume-induced aerosol release and deposition calculations in large geometries using fireFoam[END_REF] associated with specific prediction models of aerosol release/emission [START_REF] Zepper | Contaminated Fuel Fires : Parametric Sensitivity of Resuspension and Boiling Particle Evolution[END_REF], their transport [START_REF] Gelain | Development and validation of an agglomeration model for CFD simulations of aerosol dispersion in the frame of Fukushima fuel debris retrieval[END_REF] and their deposition within industrial facilities or ventilation network [START_REF] Overholt | Computational Modeling and Validation of Aerosol Deposition in Ventilation Ducts[END_REF]. Beyond the question of aerosol fate during conventional industrial fires, special care is an absolute requirement for fires involving radioactive materials due to potential release of these materials in airborne phase. In such situations, assessment of radiation exposure/contamination of workers and release of radioactive materials in the environment must be carried out by predicting fire emitted particles inhalation in the human respiratory pathway and developing clogging models of HEPA filters since it is generally assumed as the last barrier of containment within a nuclear basic installation (NBI) before potential release in the atmosphere. To support such developments, experimental data on soot deposition quantities and main mechanisms are crucial. Nevertheless, the lack of development and validation of measurement devices could be noticed, limiting the availability of relevant and quantitative information regarding mass per surface area of soot deposit formed under realistic fire conditions. Beyond limited technology readiness level of measurement devices, available soot deposition data are also limited to analytical combustion experiments [START_REF] Riahi | Faculty of The School of Engineering and Applied Science of The George Washington University in partial satisfaction of the requirements for the The George[END_REF], medium scale fires performed in a marine container [START_REF] Decoster | Contribution à l'étude et à la modélisation du dépôt des suies lors d'un incendie[END_REF] or in an office [START_REF] Decoster | Measurements on Smoke Generated from an Office Fire: Soot Mass Concentration, Wall Deposition and Particle Characterization[END_REF]. [START_REF] Mensch | A Soot Deposition Gauge for Fire Measurements[END_REF] used resistive sensors for a first attempt to quantify soot deposits formed by thermophoresis within a temperature gradient imposed between thermally regulated rectangular flow chanel. According to this literature review, corresponding soot deposited mass per surface area are ranging from 20 to nearly 350 mg.m -2 , values confirming the relevance of the quantification method introduced by [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF]. Nevertheless, additional measurements, carried out during real-scale and confined fire experiments [START_REF] Kort | Quantification spatiale du dépôt de suies dans un local lors d'un incendie[END_REF] have demonstrated that significantly higher mass deposit (up to 25 g.m -2 ) could be obtained under realistic conditions, limiting the range of application of the quantification method introduced by [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF]. Thus, the aim of this work is to develop an additional measurement devices able to quantify such high soot deposit contamination levels in a direct, non-invasive, representative and complementary way to the quantification method proposed by [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF]. This first experimental approach for an in situ quantification of soot deposition on walls during fires [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF]) is based on a resistive sensor previously developed in our consortium [START_REF] Grondin | Development of a particulate matter sensor for diesel engine[END_REF]. The principle of this sensor is based on the conductance increase induced by the soot deposit formed between interdigitated electrodes when a polarization voltage is applied [START_REF] Grondin | Influence of Electrodes Polarization on the Response of Resistive Soot Sensor[END_REF]. In their study, [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF] adapted this technology for quantification of the soot particles' deposit and demonstrated its non-invasive behavior, regarding soot deposition mechanism for a defined range of polarization voltages. They also qualified a methodology to correlate the soot mass deposited onto the sensitive surface and the corresponding sensor's conductance value, opening the way to nearly real-time quantification of deposited mass of soot per surface area. For convenience, this method will be called "Electrical conductance" and will be particularly useful for predicting effects of soot deposit on safety elements such as electrical devices [START_REF] Peacock | A Literature Review of the Effects of Smoke from a Fire on Electrical Equipment[END_REF]. The sensitive surface of the resistive sensor must be therefore frequently regenerated by burning the soot deposit at 650°C thanks to the heating resistance screen-printed on its back side to avoid conductance saturation reported by [START_REF] Grondin | Influence of Electrodes Polarization on the Response of Resistive Soot Sensor[END_REF]. Similar asymptotic behaviour was also reported during tests carried out after the publication of [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF] considering realistic soot emitted by burning organic solvents used for nuclear waste reprocessing (Tributylphosphate (TBP) / Hydrogenated Tetrapropylene (HTP) mixture) but for significantly lower deposited mass of soot on the resistive sensor sensitive surface. To overcome these limitations and enhance the mass detection range to higher mass per surface area, an innovative quantification method is proposed in this study using gases emitted during the burn-off of soot deposit during the regeneration of the resistive sensor sensitive surface. The advantages of measuring the CO2 during resistive sensor regeneration over using a gravimetric sensor after an exposure is that it provides information during the exposure (electrical measurement of resistive sensor) and then a quantification into the hermetically isolated cell by using a suitable sampling system. Moreover, with such a system, rapid cycles of sensor exposure/generation with CO2 measurements could be applied, allowing a quasi-real time analysis with time frequency of a few minutes depending of the miniaturization level of the final sampling system. The principle of the protocol proposed in this study is to correlate emitted gases concentration during soot oxidation with the corresponding mass of soot particles deposited on the sensing surface. Thus, the chemical reactivity of soot and specifically its potential to be oxidized at a specific temperature will be discussed in the present study since it intervenes during the regeneration process. Several authors have studied and proposed suitable range of temperatures associated to the maximum loss of soot mass during their oxidation. According to [START_REF] Müller | Morphology-controlled reactivity of carbonaceous materials towards oxidation[END_REF], a reasonable assumption of temperatures range between 600 °C and 700 °C could be considered for a large variety of soot particles. In agreement with [START_REF] Müller | Morphology-controlled reactivity of carbonaceous materials towards oxidation[END_REF], we will then consider a regeneration temperature of our resistive sensor of 650 °C. Beyond the question of identifying the most relevant temperature for soot burn-off, oxidation of soot is a complex process due to their heterogeneous and versatile structure. Indeed, the chemical composition of soot emitted during fires can vary from organic to elemental carbon and the soot particle themselves can adsorb at their surface different kinds of complex organic molecules and even water ones [START_REF] Lintis | Quantification and prediction of water uptake by soot deposited on ventilation filters during fire events[END_REF]. Despite their complex nature, soot particles oxidation is generally assumed to produce mostly CO2, CO and H2O. Since the method proposed in the present study is based on gases analysis during soot oxidation, thermogravimetric analyses coupled with mass spectroscopy analyses were performed on the two types of soot considered in the study: soot produced by a Mini-cast burner and soot produced by the combustion of TBP/HTP. These thermogravimetric analyses were carried out in order to determine the nature of the gases emitted during regeneration and to choose the most suitable technologies of gas sensors needed for this quantification method. Then, a specific transparent glass cell, coupling the resistive sensor with a regeneration tool and gas sensors to analyze the quantities of gas produced during the regeneration, was developed, qualified and validated for mass quantification purpose. A comparison between the present new method called "CO2 emission" and the previous "Electrical conductance" method is finally proposed and discussed according to the level of mass deposition generally encountered during industrial fires, studied in research experimental facilities.

MATERIALS AND METHOD

Soot particles generation

The generated soot particles that will be quantified are representative, in terms of structure, size distribution and organic content (OC), of those produced during a fire involving fuels commonly encountered in the nuclear industry [START_REF] Ouf | Physicochemical properties of aerosol released in the case of a fire involving materials used in the nuclear industry[END_REF]. The first type of soot particles was generated using a Mini-CAST burner (Jing 5201). In this case, the production of soot is based on a propane-air diffusion flame quenched by a nitrogen flow. The air, nitrogen and propane flowrates values define an operating point that can be modified to produce aerosols with different soot size distributions and chemical natures (Moore et al., 2014;[START_REF] Ouf | Physicochemical properties of aerosol released in the case of a fire involving materials used in the nuclear industry[END_REF]. The chosen operating point allowed generating soot with a small organic part, this latter being less conductive (Grondin et al., 2019). In the present study, the selected point is QC3H8 =3.6 L.h -1 , Qoxidation air =90 L.h -1 , and Qdilution air =1200 L.h -1 . The median mobility diameter has been measured using a SMPS (Scanning Mobility Particle Sizer Spectrometer 3082 TSI). The median electrical mobility diameter of the particles is equal to 197 ± 6 nm with an average for the standard geometric deviation 1.6 ± 0.1, for the chosen working conditions of the Mini-Cast burner. A second type of tested soot particles was produced by the combustion of the TBP (30%) /HTP (70 %) mixture. The test bench used for this production is described by [START_REF] Lintis | Quantification and prediction of water uptake by soot deposited on ventilation filters during fire events[END_REF]. The flow of oxidizing gas routed into the combustion chamber (0.03 m 3 in volume) is equal to 180 NL.min -1 . The residence time is about 10 seconds, which corresponds to a renewal rate of 400 h -1 . We begin the test by introducing the sample into the combustion chamber. The sample is therefore placed on the sample holder specified on a tared weighing cell. Data recording is synchronized with ignition. We recorded the size distribution using an SMPS (3082 TSI). We reported a median electrical mobility diameter of 216 ± 15 nm and a standard geometric deviation of 1.5 ± 0.1. These particles present a size distribution similar to the one reported for the Mini-CAST soot but with a more complex chemical composition [START_REF] Ouf | Physicochemical properties of aerosol released in the case of a fire involving materials used in the nuclear industry[END_REF] as illustrated in transmission electronic microscopy images reported in figures 1 and 2 with a clear evidence of nanodroplets located around TBP/HTP soot particles.

Choice of gas sensors

As previously mentioned, the proposed quantification method is based on the measurement of gases concentration emitted by the combustion of soot deposited on the sensor surface during the regeneration phase using the heating resistance of the sensor. Prior to such analyses, identification of gases to be quantified is needed to identify the most suitable gas sensors to be implemented. For this purpose, and in order to characterize the thermal behavior of the soot produced by the Mini-CAST and of the combustion of TBP/HTP, thermogravimetric analyses (TGA) coupled with mass spectroscopy analyses (MS) were performed.

This type of analysis allows first to confirm the temperature of maximum oxidation proposed according to our literature analysis (650°C) and second, to identify the gaseous compounds emitted during the degradation of the studied soot particles. The used device is a TGA/DSC 1 thermobalance from Mettler coupled to a Omnistar GSD301 mass spectrometer. The soot samples produced by the Mini-CAST and the combustion of TBP/HTP are steamed at 150 ° C for 1 hour. 6 mg of this sample are heated in synthetic air (air flow rate equal to 5 L. h -1 ) up to 1200°C with a ramp of 10°C.min -1 . In order to assess repeatability, 3 identical tests were achieved. Figure 3 shows the thermogram obtained under air (left) and the mass spectrum (right) as a function of temperature for soot produced by the Mini-CAST. A single loss of mass occurs between 500 and 700°C, with a maximum rate of oxidation (97% of cumulative mass loss of the sample) associated with a temperature of about 620 ° C. This temperature appears in accordance with the one considered for the sensor's regeneration phase (650°C), making it possible to ensure the efficiency of this process. The main species produced in this temperature range is CO2 (m / z = 44), resulting from the oxidation of carbon species composing the soot. The cumulative mass loss of 2 % can be attributed to the desorption of physisorbed water (m / z = 18) since TBP/HTP soot particles present significant amount of phosphor [START_REF] Ouf | Physicochemical properties of aerosol released in the case of a fire involving materials used in the nuclear industry[END_REF] known to be active site for water molecules. Water has been re-absorbed after soot pretreatment. The second mass loss occurs between 120 and 230°C (maximum at 168°C) corresponding to a cumulative mass loss of 5% and which can be attributed to the production of "VOC" type species (volatile organic compounds, m / z = 39, 41, 56) difficult to identify from present MS analysis. The third mass loss cannot be dissociated from the fourth and the main one that occurs between 500 and 800°C with a maximum mass loss at 670°C (in accordance with the regeneration temperature of 650°C of the sensor) and corresponds to a cumulative loss of mass total of 93%. In agreement with Mini-CAST soot particles, the species produced in this temperature range is mainly CO2 (m / z = 44) that could be associated with the degradation of carbon contained in soot for quantification purpose.

From the thermogravimetric analyses and mass spectroscopy analyses, we can conclude that the temperature of maximum mass loss due to the oxidation of studied soot can be assumed to be close to 650°C. Furthermore, at this temperature, soot oxidation mainly produces CO2. Following thermogravimetric analyses coupled with mass spectroscopy analyses, the main gas emitted during the combustion of CAST and TBP/HTP soot is CO2. Consequently, a CO2 sensor can be used as described by the protocol in part 2.3 to propose a correlation between the mass of soot present on the soot sensor sensitive surface and the mass of carbon calculated from the difference in CO2 concentration before and after regeneration of the soot sensor. Therefore, we have selected a Sensirion SCD30 CO2 sensor which also includes a temperature sensor and a humidity sensor. This CO2 sensor is an optical one (NDIR for "Non-Dispersive Infrared Sensor") which uses an infrared source whose radiation passes through a gas-filled chamber, and the infrared detector retrieves the wavelengths corresponding to a CO2 absorption band at the output thanks to an interference filter.

Principles and assumptions associated with the method

After identifying and choosing the most relevant gas sensor to correlate soot deposited mass with gas concentration encountered in a closed system during soot oxidation, a quantification protocol and a measurement cell were introduced. In order to draw a calibration curve for the proposed method, the following quantification protocol was used according to the four stages described in figure 5: Then, the non-sensitive surface of the sensor is protected by a parafilm to avoid any deposition of soot on the nonsensitive surface of the soot sensor. A mass of soot is set in a petri dish and the resistive surface of the sensor is manually contaminated. The parafilm is then removed and the non-sensitive surface of the sensor was additionally cleaned using a Chemtronics© micropoint cotton tip swab with a constant volume of 0.1 mL of ethanol (ethanol absolute anhydrous 99.9% from Carlo ERBA) to be totally sure that it is free of any soot deposit. Manually contaminated sensor was then weighed (Sartorius MC210P) to determine the mass of the system prior to regeneration in the measuring cell.

2 °) the contaminated sensor is introduced into the measuring cell for quantifying the mass of deposited soot. The deposited soot is brought to a temperature of 650°C thanks to the heater on the back face of the substrate and are thus oxidized. Since the cell is hermetically isolated, the CO2 gas concentration in the cell reaches a steady state which is a function of the quantity of oxidized soot and cell volume. This concentration is continuously measured by the CO2 sensor. As demonstrated in our previous studies [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF][START_REF] Ouf | Physicochemical properties of aerosol released in the case of a fire involving materials used in the nuclear industry[END_REF], soot produced by the Mini-CAST or by the combustion of TBP/HTP consist mainly of carbon in an elemental form.

We also know, based on coupled TGA / MS analyses (figures 3 and 4), that the gas produced during regeneration is overwhelmingly CO2. Knowing the volume of the sensor cell (V = 0.4 ± 0.004 L), we calculate the number of moles of CO2 (mol) 𝛥𝑛𝐶𝑂2 generated by the combustion of soot:

∆n CO 2 = ∆C 𝐶𝑂 2 . 10 -6 V V M (1)
where VM is the molar volume of an ideal gas (24.5 L.mol -1 at 20°C and 1013 bar) and ∆CCO2 the CO2 concentrations variation measured (in ppm) in the cell consecutively to sensor's regeneration.

During the oxidation of soot, 1 mole of carbon reacts with 1 mole of O2 to give 1 mole of CO2. Therefore, the mass of carbon "mC" having served, after combustion, to vary the CO2 concentration of a ΔCCO2 value in the sensor cell can be expressed as follows:

m c = ∆C 𝐶𝑂 2 . 10 -6 V V m M 𝐶 (2)
with MC the molar mass of carbon equal to 12 g.mol -1 .

The in pressure and temperature being neglected, we can then connect linearly the mass of carbon mC and the variation of CO2 concentration in the cell ∆C 𝐶𝑂 2 so that:

m c = a ∆C 𝐶𝑂 2 (3)
with factor "a" being defined by:

a = V V m 10 -6 M 𝐶 = 0.196 ± 0.004 µg. ppm -1 (4)
The uncertainty on the mass determined can, then, be expressed by:

𝑢(𝑚 𝑐 ) = √ (𝑢 ∆𝐶 𝐶𝑂 2 ) 2 + (𝑢 𝑎 ) 2 (5)
With 𝑢 ∆𝐶 𝐶𝑂 2 the uncertainty on ∆C 𝐶𝑂 2 and 𝑢 𝑎 on the factor "a".

3 °) the last step of this protocol consists in weighing the resistive sensor after regeneration using the microbalance (Sartorius MC210P). Difference between sensor mass before and after regeneration could then be used to determine the mass of soot mC oxidized during the regeneration step.

RESULTS AND DISCUSSIONS

Experimental data and analysis of the measurement of the CO2 variation

In order to determine whether there is a bias in the concentration measured by the CO2 sensor, regeneration of the soot-free sensor is carried out. The protocol illustrated on figure 6 in the case of a soot-free sensor has been applied and will be used also for sensors loaded with soot (with t0 considered as the time at the beginning of the CO2 sensor's signal acquisition): a) Continuous flow by purified and filtered dry compressed air, in the sensor cell at 1 L.min -1 , is injected in the measuring cell using critical orifices and a pump. The pump is triggered 120 s after the start of the acquisition (t0). This sequence lasts long enough to renew the air in the cell. Taking into account the volume of the cell (0.4 L) and the flow rate, the renewal time is of the order of 40 s. Then, an air sweep time of the network of 240 s is considered sufficient to retrieve an air free of combustion gases. The signal from the humidity sensor integrated within the CO2 sensor allows the renewal step to be checked since relative humidity is almost zero at the end of the airsweeping phase of the dry network.

The pump is stopped at t0 + 360 s and the system is isolated with the upstream and downstream 2-way valves, and the cell is then stabilized during 360 s. b) Regeneration is triggered at t0 + 720 s under static air conditions (no air flow). c) Regeneration is stopped at t0 + 860 s. d) Data acquisition is stopped after 1800 s.

The analysis of these data makes it possible to estimate the difference in CO2 concentration marked by two phases during measurement:  The mean CO2 concentration in the measuring cell is determined before the regeneration phase between 500 and 600 s (horizontal red arrow in figure 6),  The mean CO2 concentration in the measuring cell is determined after the regeneration phase, waiting for the signal stabilization (horizontal blue line in figure 7 and 8, around 1500-1600 s),  The concentration difference (ΔCCO2) from the averages obtained during these two phases as well as the uncertainty on this difference 𝑢 (ΔCCO2) expressed by:

𝑢(∆𝐶 𝐶𝑂2 ) = √ (𝑢 𝑟𝑒𝑝𝑒𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ) 2 + ((√2 𝑢 𝑔𝑎𝑖𝑛 ∆𝐶 𝐶𝑂2 )) 2 (6)
with 𝑢 𝑟epetability the repeatability uncertainty = 10 ppm and 𝑢 𝑔𝑎𝑖𝑛 the uncertainty of gain= 0.01. The repeatability uncertainty (static error) corresponds to the noise amplitude of 10 ppm reported by the CO2 sensor for a soot free resistive sensor after several measurements. The gain uncertainty was determined thanks to the CO2 sensor calibration curve performed for CO2 concentrations ranging from 0 to 1000 ppm at a relative humidity between 3% and 5% and at room temperature (24°C). It corresponds to 2 times the standard deviation of the calibration curve's slope. Both uncertainties are determined in a confidence level of 95%.

Figure 6 shows the signals provided by the CO2 sensor during the regeneration of a soot-free sensor. At the end of regeneration, a rapid decrease followed by an abrupt increase in the CO2 concentration could be noticed. Finally, the signal regained its state before the regeneration.

In the absence of soot, we do not notice any significant difference between the CO2 concentration signal before and after regeneration with a ΔCCO2 = 0 ppm (horizontal red and blue lines at the same value of 1005 ppm taking into account the uncertainty of 10 ppm). The same protocol is used to study the response of the measuring cell during the regeneration of the soot sensor contaminated by TBP/HTP soot. Figure 8.a shows the signal delivered by the CO2 sensor for low quantities of soot produced by TBP/HTP, approximately 15 µg of weighed mass (3.74 µg of calculated mass), still deposited on the sensitive face of the resistive sensor before regeneration. We find the same form for the CO2 concentration signal: a stable signal at first, followed by a decrease when regeneration begins and then an increase and finally stabilization of the concentration at the end of the regeneration. The difference in CO2 concentrations (ΔCCO2) is then estimated at 19 ± 10 ppm. Figure 8.b shows the signal delivered by the CO2 sensor for larger quantities of soot produced by the combustion of TBP/HTP. We notice similar evolution of the CO2 concentration signal with stable steps before and after regeneration of the soot sensor corresponding to a concentration difference of 861 ± 21 ppm for a weighed mass of approximately 160 µg (169.58 µg of calculated mass), confirming the ability of this system to quantify soot deposit.

Prediction curve: instrumental approach

Regenerations and CO2 quantifications of sensors contaminated by several masses have been conducted and corresponding results are summarized in figure 9 for soot produced with Mini-CAST and from the combustion of TBP/HTP. Three tests were performed for each type of soot.

Figure 9 shows the evolution of the mass of carbon calculated from the difference of CO2 concentrations (see equation 3) according to the weighed sensor mass variation before and after regeneration of sensor contaminated with these two types of soot. The carbon calculated mass is globally underestimated (in regard to linear proportional hypothesis), especially for Mini-CAST soot. The errors regarding the linear relationship vary between:

 18 and 84 % for masses under 100 µg;  4 and 57 % for masses above 100 µg.

This underestimation can be explained by three assumptions:

• The first hypothesis is the presence of other species than CO2. In fact, soot particles from Mini-CAST and TBP/HTP do not exclusively generate CO2 during their oxidation. In fact, on the x-axis are represented differences in weighed soot while on the y-axis, we exclusively calculate the mass of carbon. Referring to the TGA curves (figure 3 and figure 4) and results obtained in figure 9, this assumption is not preponderant since the underestimation of carbon calculated mass should be more important in the case TBP/HTP (presence of other species more visible in TGA curves),

• the second hypothesis is an heterogeneous CO2 concentration distribution over the cell, with either a potential accumulation of CO2 in the dead zones or around the resistive sensor (CO2 source) leading to an underestimation of the CO2 sensor measurements.

• the third hypothesis is a loss of soot particles during the sensor mounting in the cell and during the sensor regeneration due to the pressure of formed CO2 that induces expulsion of particles without overcoming combustion. It has been experimentally observed through the transparent glass cell when turning on the heater. Moreover, after the combustion of a low part of the deposited soot remains on the substrate. We believe, it is a reliable hypothesis to explain a big part of the observed uncertainty.

The soot produced by TBP/HTP present more dispersed results than those reported for Mini-CAST soot. This dispersion could be explained by a greater variability of the soot generation process in the test bench described by [START_REF] Lintis | Quantification and prediction of water uptake by soot deposited on ventilation filters during fire events[END_REF]. In addition, the TGA mass loss curves reported for TBP/HTP soot (figure 4) are more complex, in particular for the low temperatures which may explain the generation of different amounts of CO2 during the regeneration process. Since the calculated masses of carbon are globally underestimated compared to the theoretical curve calibration (see figure 9), we propose in figure 10 a prediction curve for soot produced by the Mini-CAST and by the combustion of TBP/HTP. An empirical power-type correlation is thus introduced in order to predict the deposited masses as a function of the variations in CO2 concentrations measured by the gas sensor. Within the dataset, and considering the dispersion for each type of soot, the proposed correlation seems to be relevant for both types of soot and we cannot discern the quantification results of Mini-CAST and TBP/HTP soot particles. Such agreement supports the TGA results and the fact that these two soot mainly produced CO2 during The parameters of this curve were determined using a power function and applying a weighing uncertainty using OriginPRO 8.0.

𝑚 = 𝑐𝑡𝑒 ΔC 𝑏 (7)

Discussion

In our previous paper [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF], we developed a sensing methodology based on "electrical conductance" measurement to characterize soot deposition dynamics on the wall of nuclear basic installation. The method gave good results for "low masses" between 2.8 µg and 19.6 µg corresponding to surface deposit of 230 -1630 mg/m 2 ) but sensor's asymptotic behavior was rapidly observed for TBP/HTP soot which is not compatible with the expected deposited mass during realistic nuclear fire. Therefore, the method presented in this paper, based on CO2 emission measurement of oxidized deposited soot, allowed us to reach higher masses and can be complementary to the "electrical conductance" one. In this paper, the method was successfully calibrated for mass deposits from 15 µg to 350 µg corresponding to surface deposit of 1304 -28525 mg/m 2 . The methods were both based on a calibration towards references of masses, OC-EC analyzer for the "electrical conductance" method developed in previous paper and microbalance for the present method. To make sure that they give results in accordance with each other, masses of both soot, compatibles with both methods (typically between 15 and 20 µg) were deposited on the sensor substrate.

For that purpose, the soot were not deposited manually and the resistive sensor was exposed for a period of one hour using the test bench previously used for the "Electrical Conductance" quantification method of Mini-CAST soot [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF] (by applying a polarization voltage of 10 V). Final conductance was measured and the sensor was regenerated in the sensor cell for measuring CO2 concentrations (before and after regeneration). By applying the protocol explained previously, the difference in CO2 concentration was calculated from the response of the CO2 sensor for the Mini-CAST soot. For this configuration, we obtain a concentration difference 2)), the mass deposited determined by the "CO2 emission" method is then 19.8 ± 7.0 μg. We applied the same protocol, using soot produced by the combustion of TBP/HTP for 1 hour. For this configuration, we obtain a CO2 concentration difference of 17 ± 10 ppm. Using the prediction curve (equation 2), we find a mass deposited by the "CO2 emission" method of 17.1 ± 6.1 µg. Furthermore, the conductance obtained at the end of a one hour exposure were used to determine the deposited masses associated with the "electrical conductance" method. The masses quantified in the case of electrical conductance method were calculated from [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF] by considering the conductance reached after one hour of exposure of 2440 ± 50 µS for soot from Mini-CAST soot and 870 ± 30 µS for TBP/HTP soot. Nevertheless, for the later soot, an underestimation of the deposited mass is expected since, contrary to sensors exposed to Mini-CAST soot and presented in our previous study [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF], a saturation of the electrical conductance has been experimentally reported for the TBP/HTP case. The masses quantified in the same experimental conditions by the two methods and for both types of soot are summarized in table 1. "Electrical conductance" and "CO2 emission" methods gave coherent results in the case of Mini-CAST soot taking into account measurement uncertainties of both methods. In contrast, the values obtained for the TBP/HTP soot are not comparable and a factor of nearly 2.5 is noticed. This result is consistent with the saturation of the electrical conductance signal after exposure of the sensor to high masses of TBP/HTP soot, confirming the relevance of the CO2 emission method for those samples. As expected for CAST soot, the two measurement methods are complementary. Indeed, the first method of "electrical conductance" measurement can be used for masses up to 20 µg of deposited soot while the second method "CO2 emission" can be used in the case of deposited masses greater than 16 µg (corresponding to differences in CO2 concentration greater than the measurable limit of 15 ppm). In addition, this second method can be used both for Mini-CAST and TBP/HTP soot for deposited masses superior to 15 µg i.e. 1304 mg.m -2 on the sensitive surface of the resistive sensor.

Corresponding range of deposited mass of soot particles reported during real scale fires and measurement ability of both methods are compared in figure 11. Considering the mean deposited mass on the wall of a room exposed to fire in nuclear facility 1000-25 000 mg.m -2 estimated during real fire tests [START_REF] Kort | Quantification spatiale du dépôt de suies dans un local lors d'un incendie[END_REF][START_REF] Decoster | Contribution à l'étude et à la modélisation du dépôt des suies lors d'un incendie[END_REF][START_REF] Mensch | A Soot Deposition Gauge for Fire Measurements[END_REF][START_REF] Riahi | Faculty of The School of Engineering and Applied Science of The George Washington University in partial satisfaction of the requirements for the The George[END_REF], we can thus conclude that for large-scale quantification, "CO2 emission" method is rather to be privileged since maximum CO2 concentration detectable by CO2 sensor corresponds to a deposited mass of 28525 mg.m -2 .

CONCLUSION AND OUTLOOK

The aim of this work was to present a soot quantification method that can be used for real scale fire. This method is based on CO2 emission measurement during the regeneration phase, using the heating element of a resistive sensor contaminated by soot particles. Thermogravimetric analyses coupled with the analysis of gases emitted by mass spectrometry, have revealed two main pieces of information. The combustion of Mini-CAST and TBP/HTP soot occurs at a temperature between 650 and 700 ° C and the main gas emitted during combustion is CO2. Therefore, the use of a CO2 sensor appeared a relevant solution for the measurement of gaseous species concentration emitted by the combustion of soot deposited on the sensitive face of the resistive sensor. This method has a higher detection limit than the first quantification method proposed by [START_REF] Kort | Quantification of soot deposit on a resistive sensor: Proposal of an experimental calibration protocol[END_REF] based on the measurement of the electrical conductance of the soot sensor, but it will be less effective at detecting low masses.

We have shown proof of feasibility of this second method "CO2 emission" for two types of soot. Moreover, we have proposed a prediction curve for deposited masses which vary between 16 and 350 µg (1304 and 28525 mg.m - 2 ) depending on the measured CO2 concentration. We discussed the applicability of this measurement method to realistic industrial fire situation and the mass range covered is wide and suitable for this application. It is possible to increase the inter-electrode space to reduce the sensitivity of the resistive sensor and thus quantify larger masses with the electrical conductance method. But, these changes lead to a recalibration of the resistive sensors for the electrical conductance method. Calibration between the information delivered by the gas sensor (CO2 concentration) and the mass deposited on the sensitive surface of the resistive sensor, considering representativeness of the mass deposited on an equivalent surface near the sensor, is then made possible. We demonstrated that deposited masses can be evaluated by a gas concentration measurement. A next step is to obtain deposited masses representative of the mass deposited on an equivalent surface near the sensor and to confirm the non-invasive behavior of such system regarding deposition mechanisms. Since thermophoresis (connected to the thermal conductivity of the sensor itself) is a major phenomenon of the deposition rate and that flow conditions are particularly complex in the boundary layer of walls of rooms experiencing fire conditions, this remains a challenge. The objective of "quasi real-time" quantification can be achieved using this method as part of a multi-sensor approach, and several perspectives emerge regarding the "real-time" consideration. This regeneration-based method does not allow continuous monitoring of a deposit in a room on fire. Nevertheless, it allows to have, after calibration, a dynamic monitoring (quasi-real time, regarding the duration of regeneration/measurement cycle) of the deposited mass, usable for in situ measurements in representative fire conditions by using a suitable sampling system. A solution to have a real continuous monitoring would be to use two systems with time-shifted working mode: when one is under regeneration in gas sensor chamber, the second one is under fire conditions (soot exposure).

Figure 1 :

 1 Figure 1 : TEM image of a CAST aggregate (from Brugière et al., 2014)

Figure 2 :

 2 Figure 2 : TEM image of a TBP/HTP aggregate a) without adsorbed phase b) with adsorbed phase (from Ouf et al., 2015)

Figure 3 :

 3 Figure 3 : Evolution of mass loss (TGA) (left) and mass Spectrum (right) under air as a function of temperature for soot produced by the Mini-CASTThe thermal behavior of TBP/HTP soot particles is shown in the thermogram obtained in figure4, the analyses being carried out under the same conditions as the Mini-CAST soot. The thermal behavior of the TBP/HTP soot particles appears more complex than the one reported for soot produced by the Mini-CAST. This type of soot has a higher reactivity in a temperature range between 120 and 800 ° C. The existence of 4 temperature zones of mass losses is noted in TGA of figure 4. The first mass loss occurs between 30 and 90 °C, with a maximum rate of mass loss at around 57 °C.

Figure 4 :

 4 Figure 4 : Evolution of mass loss (TGA) (left) and mass Spectrum (right) under air as a function of temperature for soot produced by the combustion of TBP/HTP at 21% oxygen

Figure 5 :

 5 Figure 5 : Experimental protocol of CO2 quantification1 °) the contamination of sensor by Mini-CAST or TBP/HTP soot particles is based on a manual deposit protocol applied to the sensitive surface of the resistive sensor. The manual protocol consists in weighing a soot free sensor. Then, the non-sensitive surface of the sensor is protected by a parafilm to avoid any deposition of soot on the nonsensitive surface of the soot sensor. A mass of soot is set in a petri dish and the resistive surface of the sensor is manually contaminated. The parafilm is then removed and the non-sensitive surface of the sensor was additionally cleaned using a Chemtronics© micropoint cotton tip swab with a constant volume of 0.1 mL of ethanol (ethanol absolute anhydrous 99.9% from Carlo ERBA) to be totally sure that it is free of any soot deposit. Manually contaminated sensor was then weighed (Sartorius MC210P) to determine the mass of the system prior to regeneration in the measuring cell.

Figure 6 :

 6 Figure 6: Response of the CO2 sensor during regeneration of the soot-free resistive sensor

Figure 7 :

 7 Figure 7: Response of the CO2 sensor to the combustion of a) 48 µg of weighed mass (11.25 µg of calculated mass) and b) 120 µg of weighed mass (81.63 µg of calculated mass) of Mini-CAST soot during the regeneration of the contaminated sensor

Figure 8 :

 8 Figure 8: Response of the loaded CO2 sensor to: a) 15 µg of weighed mass (3.74 µg of calculated mass) and b) 160 µg (169.58 µg of calculated mass) produced by combustion of TBP/HTP

Figure 9 :

 9 Figure 9: Evolution of the calculated mass of carbon as a function of the differences of weighed masses of CAST and TBP/HTP soot

  highlighting the relevance of this quantification method for particles mostly made of carbon, oxygen and hydrogen.

Figure 10 :

 10 Figure 10 : Prediction curve for soot produced by the Mini-CAST and TBP/HTP combustion

  10 ppm. Using the prediction curve for the mass deposited as a function of this difference in concentration (equation (

Figure 11 :

 11 Figure 11 : Ranges of measurable masses for the different measurement methods

Table 1 : Mass deposited on the resistive sensor exposed for 1 hour to soot from Mini-CAST and TBP/HTP, quantified with the two measurement methods.

 1

	Quantified mass after a sensor exposition of 1 h at 10 V	Electrical conductance	CO2 emission
	Mini-CAST soot	14.4 ± 1.6 µg	19.8 ± 7.0 µg
	TBP/HTP soot	6.7 ± 1.2 µg	17.1 ± 6.1 µg