Juan Luis Jiménez

Jordi Perdiguero

Regional Finance and Competition Policy: the Canary Islands petrol market

Keywords: L13 -Oligopoly and Other Imperfect Markets &lt, L1 -Market Structure, Firm Strategy, and Market Performance &lt, L -Industrial Organization, L71 -Mining, Extraction, and Refining: Hydrocarbon Fuels &lt, L7 -Industry Studies: Primary Products and Construction &lt, L -Industrial Organization, H22 -Incidence &lt, H2 -Taxation, Subsidies, and Revenue &lt, H -Public Economics, H23 -Externalities, Redistributive Effects, Taxes and Subsidies &lt, H2 -Taxation, Subsidies Regional Finance, Oligopolistic Competition, Gasoline Market, Conduct Parameter Regional Finance, Oligopolistic Competition, Gasoline Market, Conduct Parameter. JEL Classifications: L13, L71, H22, H23, H32

Market competition levels affect all agents of an economy: businesses, consumers and the State. Traditional analysis has evaluated the State's effects on the other agents, but no analysis has been conducted regarding the inverse relationship. Thus, the aim of this study is to estimate the tributary income losses that low levels of competition in the retail petrol market could cause in it, using for this aim the data from Canary Islands Autonomous Community. Firstly, we will use Parker and Röller´s methodology (1997) to measure the level of competition and confirm a deficiency. Then, using estimated rates, we will determine the differences that would appear in tributary income if the market were to behave as a Cournot´s model. Our results show that the lack of competition causes a substantial loss of tributary income for this region, somewhere between 5 and 10 percent of the real income from the tax on unleaded petrol for the year 2004.

Introduction

The existence of market competition directly affects not only the consumers and the operating companies, but also a third economic agent: the State. This fact indirectly affects public income as well since the greater the competition level, the greater the quantity exchanged, according to the different market structures. The result is greater economic activity, and thus, more income from direct taxes, indirect taxes, etc. This phenomenon is especially relevant within the hydrocarbon market.

The multiple uses and high consumption of petrol products emphasise the importance of this sector in any economy, both publicly and privately. Over the last two decades, the petrol tax has increased, signifying a large amount of income for the State (and Autonomous Communities in Spain).

All areas of this sector in Spain have undergone considerable change during the last two decades 3 , having progressed from a public monopoly to complete liberalisation, excluding the pipeline transport network, which is still somewhat regulated. This restructuring can be divided into three stages (Comisión Nacional de la Energía, 2003). The first stage lasted until 1984 and featured a high level of state market intervention and thus, a public petrol monopoly. The liberalisation process began in the second stage, which occurred between 1984 and 1992. The objectives during this time were to abolish the public monopoly, moving from the regulation of administrative prices to a regulation of maximum prices, and to partially privatise Repsol, the public company operating in this sector. Finally, 1992 marked the beginning of the third stage, when the liberalisation process intensified. The most significant progress included the deregulation of maximum 3 For a discussion of this process see [START_REF] Bel | Privatization: Public offerings and political objectives[END_REF]. prices, introducing a free market pricing system; the elimination of a minimum distance between petrol stations; and complete privatisation of Repsol. As a result, the Spanish petrol market is one of the most liberalised markets, and one which experienced a relatively shorter deregulation period.

Despite this transition, Spanish market structure has not changed significantly.

It still has a high concentration of wholesale production (in 2002, Repsol's refinement capacity comprised 61 percent of Spain's total capacity), with a similar situation in the retail sector, despite an increase in points of sale derived from the removal of certain opening requirements4 (in 2002, the 3-firm concentration ratio ( 3 CR ), with regards to the number of retail points of sale, was 72 percent, according to the Enciclopedia del petróleo, petroquímica y gas, 2002).

Market concentration can result in less competition among companies, especially when the end consumer is located in a geographically limited area, as is the case with the Canary Islands. According to [START_REF] Gal | Competition policy for small market economies[END_REF], there are three possible effects on competition and companies in smaller markets: natural monopoly behaviours, dominant firms and oligopolistic conduct. The first does in effect take place in this market, whereas the other two, which are interrelated, shall be analysed in the first objective of this study.

However, this sector's structure is not the only element that has undergone significant change over the last two years. Tax policies related to hydrocarbon consumption have also changed substantially. A series of tax reforms has sparked a gradual increase in petrol taxation on the Spanish mainland (although Spain still has the lowest petrol taxes in Europe) as well as the introduction of a special tax for the Canary Islands Community. As we will see in section 3, this tax is an important source of income for the Canary Islands financing system, making the analysis of the potential impact that competition may have on this tax all the more significant.

Considering this situation, this study will be conducted as follows. We begin with two reviews: one on the main theoretical and empirical studies that show a link between fiscal policies and the petrol market; and one on the most important contributions in the competition analysis of this sector (section 2). We then reveal the main characteristics of the Canary Islands' hydrocarbon market from two different perspectives: tax and petrol market data (section 3). In section 4, we present the empirical model used to confirm competition in the retail petrol market, allowing us to estimate the level of competition in section 5. In section 6, we show what effects this behaviour may have on the region's tributary income and section 7 summarises the conclusions of this report.

Literature and theoretical framework

Studies that link tributary income with the petrol market revolve around two issues: on the one hand, the effects that changes in petrol taxation have on collection, prices and social welfare; and on the other, the ability of petrol taxes to internalise the negative external consequences of its consumption (mainly pollution).

A good example of the first approach is the study by Uri and Boyd (1998). By implementing a model of general equilibrium consisting of 14 production sectors and 14 consumer sectors, they evaluate how a change in petrol and gas oil taxation would affect the United States' economy. One of the limitations of these calculations is that they assumed elasticity-price of the demand is zero. The study concludes that a tax decrease would bring about a higher output level, an increase in goods and services consumption, as well as a boost in welfare. On the other hand, government income would decreases. Although this scenario represents a 66 percent increase of welfare, it is worth mentioning that the study does not assess other possible effects, such as the short-and long-term environmental consequences that this tax reduction may entail.

As regards Spain, [START_REF] Labandeira | La imposición de los carburantes de automoción en España: algunas observaciones teóricas y empíricas[END_REF] find little effect on wealth distribution despite possible tax reforms, mainly due to the firm nature of the demand. [START_REF] Romero | El impuesto sobre las ventas minoristas de determinados hidrocarburos. Una evaluación de sus efectos económicos[END_REF] also analyse the results of a new petrol tax in the Spanish market. The authors find the new tax causes a slight decrease in social welfare.

In turn, [START_REF] Besley | Vertical externalities in tax setting: evidence from gasoline and cigarettes[END_REF], analyse the possible interrelation between state and federal taxes. By using an estimate through least ordinary squares and focusing on the petrol and cigarettes taxes, the authors conclude that when the federal government increases taxes, states respond by raising theirs in turn.

Likewise, the authors find empirical evidence that states with larger petrol and cigarettes output have fewer taxes on these goods, which they feel is indicative of political pressure from business lobbies. At a local level, [START_REF] Hawkins | Source of income effects for demand decisions and taxable consumption[END_REF] analyze what are the effects of changes in the demographics for a taxing jurisdiction. Using household data and focusing on some commodities (including motor fuel), they argue that "(…) An exemption for food at home provides relatively less relief for working households and relatively more for retired and transfer-pay-reliant households while a decrease in the rate on motor fuel is more beneficial for the same working constituents". For this reason, they conclude that commodity tax policies have to establish relative group priorities when evaluating tax changes. Along the same lines, [START_REF] Chouinard | Incidence of federal and state gasoline taxes[END_REF] use a data panel to determine how much final retail and wholesale prices vary with regard to the percentage variation of federal and/or state tax in the United States. This study's weakness is that it assumes the wholesale petrol market operates in perfect competition. One noteworthy conclusion is that the state tax is higher in states with relatively less petrol consumption, as found in the previous study.

The second part of the analysis of the relationship between the petrol market and tributary income concerns the use of petrol taxes to correct polluting effects.

West and Williams III (2004) focus on the regressive nature of the environmental petrol tax. The authors consider progressive/regressive nature of taxing petrol when the share of taxes rises/decreases with income. Using consumption data and the methodology described by Deaton and Muellbauer (1980), these authors find that: first, the less elastic the demand, the higher the tax regression; and second, the use of petrol tax increases to finance a decrease in labour taxes makes the policy less regressive, despite the fact that using fiscal income to finance fixed taxes actually makes it progressive.

As regards the Spanish market, [START_REF] Asensio | Petrol expenditure and redistributive effects of its taxation in Spain[END_REF] establish the progressive nature of taxing petrol, although from a certain income level, this tax becomes regressive again.

In summary, all studies that link the petrol market with tributary income primarily focus on the general regressive nature of the tax on its consumers (although it depends on income level and elasticity of demand), as well as on its efficiency as an internalising mechanism of external environmental effects generated by hydrocarbon consumption. Nevertheless, our study introduces a number of novel ways of approaching the issue. First, in these aspects, the causal relationship of our analysis is the opposite of the one used in traditional literature. We do not look at the effect the tax may have on company and consumer behaviour. Rather we measure the effect of companies´behaviour on public income.

Second, our study analyses the previously-unstudied Canary Islands market, therefore giving us two advantages when measuring its market competition: a less restrictive assumption when defining the relevant geographic market, and the simultaneous existence of both monopoly and oligopoly markets. Thus, we are able to compare our method's correct specification in order to measure the degree of competition.

In order to conduct our study, we must determine whether the companies' behaviour is competitive. A recurring study within Industrial Economy has focused on the existence of competition, or lack thereof, in different markets.

Precisely within the petrol market, [START_REF] Slade | Conjectures, firms characteristics, and market structure: an empirical assessment[END_REF] rejects the hypothesis of fixedprice competition for the Vancouver retail market. The same author (1987 and 1992) also concludes that petrol prices for Vancouver behave according to a tacit collusion dynamic. This balance is altered by periods of price wars brought about by shocks in demand. [START_REF] Borenstein | Selling costs and switching costs: explaining retail gasoline margins[END_REF], [START_REF] Shepard | Price discrimination and retail configuration[END_REF], and [START_REF] Borenstein | Dynamic pricing in retail gasoline markets[END_REF], obtain very similar results for the North American market.

In reference to Spain, the first results along this line of analysis are those described by [START_REF] Perdiguero | Dinámica de precios en el mercado español de gasolina: un equilibrio de colusión tácita[END_REF]. He analyses the possible strategic performance in price fixing by companies via a dynamic model. The result shows empirical evidence of collusive prices in the petrol market. In this article, we will estimate the level of competition in the Canary Islands petrol market through the methodology proposed by [START_REF] Parker | Collusive conduct in duopolies: multimarket contact and cross-ownership in the mobile telephone industry[END_REF]. Section 4 will discuss the findings further.

The Canary Islands petrol market

There are two main differences between the petrol markets of the Canary Islands and of Spanish mainland: the market structure and the tax system.

As opposed to the Spanish mainland, the Canary Islands market was not a public monopoly that was later privatised. In fact, the company CEPSA owned the first Spanish refinery funded by private capital, which was set up on Tenerife Island in 1930. It wasn't until twenty years later that a second refinery was created on national territory. Thus, private companies sprung up that, although they could not refine petrol themselves, they could still serve the market with supplies from the aforementioned refinery.

Taking into account the performance of hydrocarbon prices in the public sector, this behaviour has been (and still is) absolutely inferior to that registered in Spanish mainland's service stations. This is due to the implementation of a tax on "fuels derived from petrol", which is only in effect in the Canary Islands. This is a single-phase tax applied to wholesale transactions, which is restricted by the regulation not to be above 75 percent of those applied on the Spanish mainland and in the Balearic Islands. 5 Table 1 summarises the type of duty applied until now, depending on the product.

INSERT TABLE 1

INSERT GRAPH 1

As in Spanish mainland, the Canary Islands market structure is highly concentrated in industrial processes. An analysis of the existing service stations at the end of 2004 shows that DISA has 35.6 percent of market share, followed by Shell with 17.9 percent, and Texaco, with 14.3 percent of the Archipelago's service stations. It is worth noting that DISA has a monopoly in the islands of La Gomera and El Hierro, a fact that shall be used to contrast the competition model proposed in section 4 and to obtain two functions of petrol demand, depending on whether they are islands with a monopoly (La Gomera and El Hierro) or islands with more than one operator (the rest of the islands).

Considering this information, it seems the Canary Islands petrol market structure offers conditions conducive to low competition behaviour. This study aims to measure competition via the conjectural variation methodology, which, if we achieve a non-competitive result, will estimate the amount that the Canary Islands Treasury did not obtain in 2004. This calculation will be carried out with our model's estimated rates.

We will concentrate on the data used for the empirical application. This information dates between September 2003 and December 2004 (inclusive). All data is organised by month (except population) and island. The varying quantity is

Tacit collusion: an empirical application

One of the initial aims of this study is to econometrically calculate a model that will gather together the behaviour of Canary Islands petrol market companies.

However, the specific market characteristics affect the creation of this model. First, the analysis will be carried out as an average of each Archipelago island, without trying to determine results of a Hottelling localisation problem; second, and derived from the previous point, companies compete in a relevant geographic market (the island market) to increase their market quota; third, the product is considered homogenous. Parker and Röller´s (1997) proposal was used to develop the conjectural variations methodology, for measuring tacit collusion, or its absence, in the Canary Islands hydrocarbon retail market. More recently, Jiménez andPerdiguero (2006a and[START_REF] Jiménez | ¿Competencia o colusión en el mercado de gasolina? Una aproximación a través del parámetro de conducta[END_REF], who developed the model in more detail, applied it in this very same market. Starting with the operating benefits to be maximised by the company, we obtain the following condition of equilibrium

( ) ( ) ( ) . . . 0, ts ts ts ts ts p Q p CM i Q + = (1)
where N = measures the company performance parameter. This parameter is falls between 0 and 1, and its meaning is as follows: 0 = , behaviour of perfect competition;

1 N = , Cournot-style competition; 1 = , perfect collusion performance.

For its empirical application, we conduct the analysis in two cases with different structures: the La Gomera and El Hierro islands, where DISA has a monopoly; and the rest of the islands, where the competition is intra-island and carried out amongst the companies in the market. The existence of this single proponent on both islands allows this data to be used in a model specification comparison. We must note a lack of broader information, which forces us to estimate an average behaviour parameter on the islands with an oligopoly, instead of one per island.

In order to empirically implement the theoretical model described previously, we will use the following linear demand function 6 :

( ) The solution to the problem involves a total estimate of the demand equation and the balance equation. To achieve this, we use a system of simultaneous equations through non-linear three least squares.

Results

The estimate of the specified model has been carried out in two phases. In the first, we calculate the performance of El Hierro and La Gomera, where DISA has a monopoly. In this case, as we can see in Table 2, the conduct parameter for the islands with a monopoly confirms this fact ( 0.99 =

). In this case, the coefficient that accompanies the price is -3.87; with a significance of 6 percent.

INSERT TABLE 2

Once the monopolised market have been analysed, we must do the same with the remaining five islands to determine the type of competition of each. Table 3 depicts the results obtained from the islands with an oligopoly. The rate accompanying the quantity is less than in the case of the monopoly. Its significance is 1 percent.

INSERT TABLE 3

On these islands, the conduct parameter is an average of 0.81. The econometric results obtained do not allow us to reject the possibility that this parameter may be a Cournot-style outcome ( )

0.16 =
, as is the case of a perfect collusion ( ) 1 = , although it is closer to a collusive balance than a Cournot equilibrium. For both estimates, the chi-squared test guarantees the overall model identification.

As far as the variable consisting of the population plus the number of passengers per airplane, we must conclude it is not significant in any case. The fact that the population varies little over the period analysed (this data is annual), coupled with the seasonal nature of tourism, causes the possible effect of this variable on prices to be grouped with the place and time "dummies" which we included in the model specification and estimate. However, the variable of the price of refined petrol in the Rotterdam market, plus the transport cost shows in all cases the sign that we expected, and its significance is 1 percent.

A priori, companies in each market (island) may behave differently. To prove this, we have carried out the preceding estimates from the differentiated model on the two islands with the highest petrol consumption (Gran Canaria and Tenerife) and the other oligopoly islands (Lanzarote, Fuerteventura and La Palma). Tables 4 and5 depict these results. The conduct parameter does not vary much between these two island groups, nor amongst the group of oligopoly islands (compare with Table 3), although a lack of data provides less precise results.

In summary, our data shows that the company behaviour on islands with more than one petrol company seems to be more collusive than the Cournot-style competition outcome. However we cannot flat out declare the existence of a perfect collusion performance. Despite being different markets, time periods and geographic areas, the results are similar to those obtained by [START_REF] Parker | Collusive conduct in duopolies: multimarket contact and cross-ownership in the mobile telephone industry[END_REF] and [START_REF] Duso | Lobbying and regulation in a political economy: evidence from the U.S. cellular industry[END_REF] for the mobile telephone market, as well as to [START_REF] Fageda | Measuring conduct and cost parameters in the Spanish air transport market[END_REF] evaluation for the Spanish air market. The same methodology was used in all these studies. The parallelism of these results may be explained by the fact that all of these cases involve concentrated network industries.

Fiscal effects of the level of competition

Having analysed the degree of competition and determined a degree of collusion greater than in a Cournot equilibrium, we shall assess whether this lack of competition in the oligopoly islands affects the Autonomous Community's income.

To achieve this, the first step is to calculate the average demand elasticity both in the monopoly and oligopoly markets. In our case, the demand price elasticity will be determined by the following formula:

ts m ts m Q p p Q = where ts ts Q p
is obtained from equation ( 2), and its value is the estimated coefficient 1 ; m Q and m p , are the average quantities and prices, respectively.

With this formula, the results obtained are -0.76 for monopolies and -1.7 for the oligopoly islands. Supposing a linear demand, economic theory has proven that, if companies operate as a monopoly, demand elasticity should be equal to (if 0 MC = ) or greater than 1 . In our case, the estimated elasticity is coherent with economic theory. The elasticity is somewhat greater than those obtained by other studies that exclusively analyse petrol demand, as seen in Table 6.

INSERT TABLE 6

The fact that we presuppose a linear demand explains the high elasticity we find in our study. In his meta-analysis, [START_REF] Espey | Gasoline demand revisited: an international meta-analysis of elasticities[END_REF] finds that the use of linear demand functions brings about greater demand elasticity in the long run. With this data, and having determined that the degree of tacit collusion in the market sets the stage for price reductions, we simulate their decrease and consequences on the autonomy's income through the wholesale hydrocarbon tax. Specifically, using estimated coefficients for the demand and equilibrium equations, we will estimate the prices that may be obtained in the market if the conduct parameter were at the value predetermined by a Cournot level of competition.

From equilibrium equation (3), we predetermined ts Q coefficient, i.e. As may be obvious, prices would decrease if competition increased. This reduction would provoke an increase in petrol consumption. This is in line with a tax collection increase on petrol-related products, in this case unleaded petrol (see Table 1). Table 7 demonstrates the loss of income the Canary Islands administration would have suffered in 2004 in the oligopoly islands (which consume more petrol).

INSERT TABLE 7

As we can see in the preceding table, in 2004 the Canary Islands Community lost almost one hundred million euros, amounting to about 39.1 percent of the total fiscal income derived from hydrocarbon taxation. This percentage increases to 58.1 percent if we only consider the unleaded petrol tax, which is the object of our analysis. This result is not final, since the aim of the proposed model is not to estimate the function of petrol demand, but to derive it from the overall approximation of the equations that explain company performance in this market. Thus, the estimated elasticity value is far greater (for oligopoly islands) than that revealed by economic literature regarding the estimation of functions of hydrocarbon demand predicted at the retail level.

However, Table 8 shows how much income each island's Autonomous

Community is losing, estimating different values of demand elasticity instead of using our model's demand characteristic. As we can see, the losses in fiscal income are significant.

INSERT TABLE 8

The loss of income varies between 1.86 and 9.28 percent of the total income from taxes on hydrocarbons if we use an elasticity of between -0.1 and -0.5 respectively. In absolute terms for the year 2004, it varies between 4.7 and 23.5 million euros, hardly a negligible sum for an Autonomous Community.

The percentage of relative losses increases if we consider the quantity collected by the Administration through unleaded petrol stations: within the range of 2.76 and 13.79 percent of the total, with conditioned elasticity.

Conclusions

There are three reasons that the petrol market is crucial to any economy: first, small consumers' intense demand for this type of product: second, it is a raw material for a large number of industries; third, because the tax system deems them an important source of income for any administration. Just as in Spanish mainland, the Canary Islands petrol market is markedly concentrated, both in wholesale and retail distribution. This oligopolistic structure may accentuate the possible existence of collusive behaviours within the industry.

This study has two interrelated objectives within the framework of this sector:

on one hand, to measure the existence of collusion (or lack thereof) in the Canary Islands retail petrol market, and on the other, to evaluate how sector competition affects the Autonomous Community's tributary income.

Our study is unique for various reasons. First, the causal link of our analysis is contrary to that applied in previous studies. We do not look at the effect taxes have on company and consumer behaviour. Rather, we measure the behaviours' effect on tributary income.

Additionally, our study focuses on the Canary Islands, a market which has not been previously studied. We offer two innovative advantages in the measurement of competition levels: greater ease in defining relevant geographic markets and the simultaneous presence of monopoly and oligopoly markets.

For the first objective, and in order to understand retail companies' behaviour in the Canary Islands market, we have followed [START_REF] Parker | Collusive conduct in duopolies: multimarket contact and cross-ownership in the mobile telephone industry[END_REF] method and, more recently, [START_REF] Jiménez | ¿Competencia o colusión en el mercado de gasolina? Una aproximación a través del parámetro de conducta[END_REF], for this same market.

The latter is based on the estimation of companies' performance parameter in the presence of variations in the quantities offered by other companies. This means each company's objective should be to increase its market quota on each island.

Our study does not create a model or a potential vertical integration between refinery and distributor, or the possible Hottelling horizontal competition.

Our data enables us to estimate a monopoly conduct of ( 1 = ), for those islands where such a market structure exists. On the other hand, the result obtained for the rest of the islands confirms the existence of a more collusive In light of the results regarding companies' performance, this study questions whether the behaviour of retail businesses in this market affects the Canary Islands Autonomous Community's income derived from the application of Law 5/1986 which regulates hydrocarbon taxing.

The decrease of the performance parameter to the level of Cournot competition, that is, equal to a parameter of 0.16 in our case, would mean a price reduction and an increase in quantity consumed. This would provoke an increase of tributary income of about one hundred million euros per year (estimate for 2004) in the Canary Islands.

Despite restrictions on the demand elasticity obtained in this model, if we reduce the value of such elasticity exogenously to values of traditional literature, loss of income would still be significant: at around 5 percent of the total taxes derived from hydrocarbons, and more than 8 percent if we only consider the income from unleaded petrol taxes.

F

  Graph 1 represents the total income from the Canary Islands Economic and Fiscal Regime (R.E.F.) for 2004. We can see that 18.2 percent is obtained from petrol fuel taxes, the second most important. This reveals the significance of this tax for the Canary Island treasury. This trend continues, although the figure has become less representative in the last five years. It acts primarily in favour of the General Indirect Canary Tax (I.G.I.C.), which in 2004 constituted 69.1 percent of the R.E.F´s total income.

  unleaded petrol expressed in cubic metres sold by retail distributors on each island, each month. Both the prices and the quantities sold have been provided by the General Direction of Industry and Energy of the Canary Island Government (We are grateful for their assistance). Petrol's spot price is that of refined 95-octane petrol in the Rotterdam market. This information is obtained from O.P.E.C. The figures regarding population and number of air travel passengers have been taken from the Canary Statistics Institute (ISTAC) and Spanish Airport and Air Navigation (AENA) respectively.Transport and storage costs used have been calculated from the Comisión Nacional de la Energía's (CNE) website.

  if we suppose a Cournot´s model, and the estimated values for 1 are -74.18057 for La Palma, Fuerteventura and Lanzarote, and -1025.586 for Gran Canaria and Tenerife, we can reach that predetermined coefficient. The equations used are those obtained for both groups of islands.

  to quantity-based, or Cournot competition, although without coinciding with the parameter for perfect collusion. Therefore, we can conclude that the deregulation process carried out all over Spain, where the Canary Islands present a greater tradition, does not seem to stimulate competition, in prices or quantities.

Table 1 . Type of duty applied depending on the product.

 1 Slade, M.E. (1987): "Interfirm rivalry in a repeated game: an empirical test of tacit collusion", Journal of Industrial Economics, 35, 499-516. Slade, M.E. (1992): "Vancouvers gasoline-price wars: an empirical exercise in uncovering supergame strategies", Review of Economic Studies, 59, 257-76.

	o r
	P
	e
	e r
	R e v
	i e
	w

Distribution of total income from the Canary Islands Economic and Fiscal Regime (R.E.F.)

  Source: Dirección General de Tributos. Government of Canary Islands. Own elaboration.

	100%
	21.8	21.2	21.4	18.6	18.9	18.2
	80%
	60%
	40%
	20%
	0%
	1999	2000	2001	2002	2003	2004
		Total taxes IGIC Tax on registration cars Tax on petrol

Table 2 : Conduct parameter for monopoly islands (La Gomera and El Hierro) Parameter z-Student

 2

	Demand
	Constant	429.452	4.59
	P ts	-3.878036	-1.88
	Population ts +Tourist ts	0.0003451	0.12
	Time	2.818836	1.86
	R 2	0.9682	-
	2	1702.94	-
	Equilibrium equation
	Constant	-31.57995	-0.70
	Q ts	0.2557958	1.40
	Gasolinespot t +Transport ts	97.1314	8.20
	R 2	0.4879	-
	2	107.09	-
	Conduct Parameter		Chi2
		0.99
	=0	-----	7.12
	=1	-----	0.00
	Number of observations = 56; Number of iterations = 3

Table 3 . Conduct parameter for oligopolistic islands.

 3

	Parameter	z-Student

Table 4 . Conduct parameter for the islands: Lanzarote, Fuerteventura and La Palma.

 4

	Parameter	z-Student

Page 24 of 26 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	F o r
	P
	e
	e r
	R e v
	i e
	w

Table 5 . Conduct parameter for the islands: Tenerife and Gran Canaria. Table 6. Demand elasticities in the short-run.

 5

	F o r
	P
	e
	e r
	R e v
	i e
	w

Table 7 . Simulation of tax losses in the oligopolistic islands. Year 2004. (Euros)

 7

	Island	Year lost (€)
	Lanzarote	6,846,147.37
	Fuerteventura	4,351,621.93
	Gran Canaria	37,118,447.63
	Tenerife	47,742,037.01
	La Palma	3,069,309.55
	Total	99,127,563.48
	% of total hydrocarbon taxes	39.1
	% of unleaded gasoline taxes	58.1
	Source: Own elaboration.

Table 8 . Simulation of tax losses in the oligopolistic islands, with different demand elasticities. Year 2004. (Euros)

 8

	Island	=	0.1	=	0.2	=	0.3	=	0.4	=	0.5	=	1.0

In this sense, the only obligations were the obligations of service and of notifying the Comisión Nacional de la Energía (CNE) of the free market pricing.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

The relevant regulations are Royal Decree (RD) 155/1995; RD

6/2000 and RD 114/2001. All these decrees set up the basic framework for service stations in the Canary Islands, in particular the minimum distance and opening requirements. Nevertheless, questions related to urban planning and municipal norms influence the barriers to the opening of new petrol stations more than the aforementioned legislation.

The basic regulation is Law 5/1986. However, the Third Additional Provision of Law

8/1992 detailed the rule of not surpassing 75 percent of the Spanish mainland prices, including the transitory charge established in article 4 of this Law.

Acknowledgements.

Thanks are due to Joan-Ramón Borrell, Javier Campos, Antón Costas, Luis Orea, assistants at seminars given at University of Las Palmas de Gran Canaria and University of Oviedo and an anonymous referee for their helpful comments.

Financial support from "VI Premio Hacienda Canaria -Gobierno de Canarias" are gratefully acknowledged.


I Alig
email: ialig@dki.tu-darmstadt.de

M Bargmann

H Oehler

D Lellinger

M Wanner

D Koch

Investigation of delamination mechanisms in polymer coatings by scanning acoustic microscopy

Keywords: Scanning acoustic microscopy, coatings, delamination, disbonding, blisters, diffusion

Scanning acoustic microscopy (SAM) was used to investigate disbonding, delamination and blister formation in polymer coatings for different layer structures and initial defect depths during exposure to a corrosive environment. The time evolution of disbonding and blister initiation and their growth was investigated by analysing the SAM images exposure to an electrolyte solution (Harrison solution). From investigations of a model system of coatings on steel substrates, it was possible to differentiate between water and/or ion transport (i) through the coating and (ii) along the coating-steel interface. For samples without clear coat randomly distributed blisters appeared at the coating-steel interface after exposure to the electrolyte solution, irrespective of the location of initial defects. The random distribution of growing blisters is related to diffusion of water and/or ions through the coating and "nucleation" at weak points of the substrate or within the polymer. For samples with clear coat a propagating migration front along the coating-steel interface of 3-4 µm height -starting from initial defects -was detected. The linear propagation of this front cannot be explained by Fickian diffusion. Therefore, it is discussed in terms of an accelerated diffusion or crack growth kinetics. Since blistering starts only at sites, where the migration front has passed, the presence of a thin water layer at the coating-steel interface, the loss of adhesion and the following corrosive processes are prerequisites for the nucleation of blisters. The blister growth shows a square-root time dependence which was related to a diffusion controlled transport mechanism.

Introduction

The effective protection of steel substrates from corrosion is an important aspect in coating technology. Besides passivation of the substrate surface (inhibitive effect) and sacrificial protection (galvanic effect), barrier protection is one of the basic protective mechanisms of anticorrosive organic coatings [1]. The protective properties of barrier coating systems are known to depend on numerous factors, including the material properties of the polymer binders, pigmentation, layer structure and thickness, type of corrosive environment, type and pre-treatment of the substrate, the presence of initial defects or impacts etc. [1]. Although the general mechanisms preceding coating failure are basically understood, the exact cause and nature of coating breakdown is still in dispute [1]. The processes involved in coating failure are transport of water, ions and oxygen followed by adhesion loss and corrosive chemical reactions. The transport processes include water diffusion through the polymer matrix, along the coating-metal interface or through cracks [2 -4] as well as migration of ions [1 -3, 5]. These mechanisms are assumed to be the ratedetermining steps for the decrease in adhesion strength between coating and substrate [1,6] ("weak wet adhesion"), cathodic disbonding, blistering, delamination [1 -3, 5, 7 -11] and rust creep [START_REF] Weinell | Non-destructive determination of rust creep[END_REF].

Adhesion is of vital importance for anticorrosive coatings, since weak adhesion permits a loss in the coating's protective properties and corrosion of the metallic substrate. These processes finally result in coating failure [1,6]. Adhesion and deadhesion are interfacial phenomena occurring, in the specific case of coatings, at the coating-metal interface. Usually, for organic coatings adhesion is considered to consist of two factors (see [1] and references therein): (i) mechanical adhesion due to penetration of the coating into surface pits (anchoring) and (ii) chemical adhesion, where bonds are formed between metal and coating. Possible bonds are covalent and ionic (primary bonds), dipole and van-der-Waals (secondary bonds) and hydrogen bonds. It is generally believed that in coating-metal systems hydrogen or secondary bonds between the metal oxide layer and the polymer (e.g. polar groups) are dominant [1,3]. Adhesion can, for example, be improved by using coupling agents. Whereas, on the other hand, swelling and thermal cycling, the resulting mechanical stress, coating cracks and process-related water-soluble contaminants on the substrate negatively influence adhesion [START_REF] Leidheiser | [END_REF].

As stated above, the transport rate of water, oxygen and ions is assumed to control disbonding, delamination and blister formation. In general, one can differentiate between transport (i) through the coating and (ii) along the coating-metal interface. Therefore, we used a model system with different layer structures to differentiate between those possibilities (see chapter 2.2). The transport of dissolved oxygen and water is generally considered to be sufficient to sustain corrosive reactions and therefore not to be the rate determining process (see [1][2][3] and references). For example, the cathodic delamination of epoxy coatings was found to be most probably controlled by the interfacial transport of hydrated cations in a thin aqueous layer at the coating-steel interface [2]. Another mechanism discussed in literature is "weak wet adhesion" [1,14], which refers to adhesion loss due to water molecules at the coating-metal interface replacing hydrogen bonds due to their hydrogen bonding ability, thereby reducing the attractive forces between coating and metal oxides [15]. Supposedly, the resulting thin water film between polymer and metal is regarded as a prerequisite for electrolytes entering the interface and initiating corrosive reactions.

The mechanism of weak wet adhesion is a physical-chemical mechanism that is not limited to corrosive environments.

SAM does not provide direct information on the chemical reactions of cathodic disbonding and blistering, as it is only sensitive to differences in the investigated acoustic properties. For a detailed description of wet corrosion mechanisms we refer to reference [1]. While cathodic disbonding starts near defects, cathodic blistering can also be found on coatings without any evident defects. It is assumed that water penetrating the coating accumulates at sites of reduced adhesion or network density at the polymer-metal interface. An anode is initiated and a cathode develops in the vicinity. At the cathode dissolved oxygen is reduced, resulting in hydroxyl ions and other aggressive reaction products that attack the metal. Water-soluble contaminants on the metal as well as the water-soluble reaction products from the cathodic reaction lead to osmotic pressure between the interfacial region and the outside environment. Due to this the disbonded area fills with water and grows. Although corrosion and coating failure resulting from cathodic disbonding and blistering are issues of large practical relevance, the number of systematic studies on disbonding, delamination and damage kinetics of coatings on metal substrates [2, 3, 7 -9, 16] is limited. In these works experiments were carried out using a variety of coating materials and exposure to different types of corrosive media. Also, most research is concerned with epoxy-coating systems. For example, Crossen et al. [7] found for an epoxypolyamide coating that the widening of the delamination zone follows parabolic kinetics, which indicates a diffusion controlled process. Sorenson et al. [8] reported on the influence of substrate topography on cathodic disbonding of anticorrosive coatings. They found a dependence of the cation transport rate on the tortuosity of the substrate and measured a square-root dependence of the delaminated area on time.

As mentioned above, the delamination behaviour of many anticorrosive coatings has been found to be characterised by a square-root dependence between the extent of delamination and exposure time. In that case, the transport of cations is considered to be the rate determining process, therefore, a proportionality between mean diffusion length, x , and diffusion time, t , has been assumed [3]:

t D x app ∝ . ( 1
)
app D is an apparent diffusion coefficient, taking into account that the transport of the ions is facilitated by an electrical field gradient [2,3] between anode and cathode resulting from the cathodic reaction [START_REF] Leng | [END_REF]. This behaviour can be expressed using the Nernst-Planck equation. However, a novel approach uses [2] Fick's second law to estimate the apparent diffusion coefficient of ions along an ultrathin aqueous layer at the coating-metal interface. In the corresponding experiments an 'induction time' has been found, which is suggested to be the result of the transport processes of reactants through the coating.

In contrast, for polyurethane coatings we recently reported [9] finding an exponential growth (exponent between 1.3 and 1.5) of a blistering zone during a salt spray test.

The exponential growth was related to a nucleation and growth mechanism. In Reference [START_REF] Momber | Blast Cleaning Technology[END_REF], exponents for the time-dependent growth of delaminations of up to 2.6, depending on substrate conditions, were reported.

Using Fick's second law to estimate transport parameters for water and/or ions along an interface or the time dependence of delamination extent it has to be presumed that the diffusion coefficient of the species does not change over time [2]. Regarding the complex situation at a coating-metal interface this seems to be rather restrictive.

For about 60 years it has been established by experiments and simulations [18,19] that the diffusion properties of a penetrated polymer system can change with time as diffusion proceeds. Two mechanisms have been suggested [18]: (i) slow structural changes of the polymer and (ii) different, differential swelling of parts of the polymer sheet as penetrant enters. For 'history dependent' diffusion, it is assumed that the polymer chains reconfigure in order to accommodate the penetrating molecules. A rapid change of the equilibrium diffusion coefficient around the penetrant can lead to an actual 'diffusion front' with a sharp boundary. At this front, the highly swollen side is characterised by a high diffusion coefficient, whereas the non-swollen side exhibits a small diffusion coefficient. This behaviour is typical for glassy polymers or networks where the diffusion coefficient drops several orders of magnitude due to a solventinduced glass-to-rubber transition. This effect not only occurs for organic solvents, but is also evident in water absorption induced "hydroplastification" of polymers. Therefore, mass transport of water or solvents in glassy polymers has to be described by a diffusion equation taking into account moving boundaries. This type of diffusion is "anomalous" with respect to the classical Fickian diffusion [20]. The socalled "Case II" [20] or "Type II" transport [21,22] is characterised by linear penetrant uptake with time and a constant velocity of the moving front, thus differing from the square-root time dependence of the penetrant uptake and the continuous concentration profiles in Fickian diffusion. To solve the differential equation for a "history-dependent" diffusion numerical methods have to be used. An alternative mechanism was discussed by Crank [19], relating the effect to strain-dependant diffusion, which also can lead to an "anomalous" penetrant diffusion. In this case, the sharp boundary between outer, swollen part and inner, non-swollen part is assumed to exert internal stresses, influencing the diffusion. Interestingly, there exists a close analogy between the structural changes involved at the swelling front and those occurring at a crazing front during mechanical deformation [23]. As a result of this analogy, similar boundary conditions and differential equations are used to describe swelling and crazing kinetics under mechanical stress [24].

This brief review of possible transport mechanisms and related experimental findings shows the lack of experimental information concerning diffusion along the coatingmetal interface. Time resolved experiments with sufficient spatial resolution are needed, to estimate transport parameters and to improve understanding regarding the kinetics of migration, disbonding/delamination and defect initiation and growth. The various methods having been used to examine deteriorating coating performance comprise classical methods like the 'cross cut adhesion test' or visual methods (e.g. removal of delaminated coating, measuring the rusted area underneath [3,8]). More advanced methods, based on electrical potential, electrical impedance or acoustic properties of the coating are Scanning Kelvin Probe (SKP) [25 -27], Electrochemical Impedance Spectroscopy (EIS) [6,27,28] and Scanning Acoustic Microscopy (SAM) [25,26,[START_REF] Brand | Ultrasonics Symposium[END_REF], respectively. However, a combination of different methods can provide complementary information [START_REF] Leidheiser | [END_REF][START_REF] Briggs | Acoustic Microscopy[END_REF][START_REF] Koehler | [END_REF].

SAM is a non-destructive method, which allows gathering depth-specific and time resolved information with a lateral resolution of some micrometers. Despite its advantages the application of SAM in coating research is still rare [9, 13, 29 -34]: For example, Briggs and Addison et al. [START_REF] Briggs | An Introduction to Scanning Acoustic Microscopy[END_REF][START_REF] Addison | Proceedings IEEE, Ultrasonics Symposium[END_REF] applied SAM for in-situ monitoring of cathodic disbonding and Crossen et al. [7] examined changes at the interface during cathodic disbonding of an epoxy-polyamide coating exposed to a NaCl solution. More recently, we applied SAM to investigate solvent-and water-borne 2K polyurethane systems and UV-cured acrylic systems after simulated weathering.

In this study, SAM was used to investigate disbonding, delamination and blister formation in polymer coatings of different layer structures and different initial defects during exposure to a corrosive environment. The time evolution of migration of water and/or ions, disbonding and blister initiation and growth was studied by analysing the SAM images after exposure to electrolyte solution (Harrison solution). To this effect, new methods for the analysis of SAM images have been developed. Although SAM does not provide a direct measure of penetrant concentration, changes in the materials' acoustic properties allowed to extract information on surface profiles, propagating migration fronts and blistering and the underlying transport mechanisms.

The results showed the usefulness of SAM for non-destructive investigation of timedependent processes in polymer coatings.

Experimental

Scanning Acoustic Microscopy

SAM works by focusing a short high frequency acoustic pulse -emitted by an ultrasonic transducer and focused by an acoustic lens -on a small area on a target object. The incident ultrasonic wave is scattered, absorbed, reflected or transmitted. Usually, the area of interest is located in the focal plane. For each position the reflected and/or the transmitted acoustic signals can be detected. The sample is scanned by moving the transducer until the entire region of interest has been investigated. Based on the actual operating mode a certain value from the received signal is assigned to the location investigated. Characteristic properties of the signal for each position (like amplitude and phase of the reflected signal in a defined time interval) are assembled into an image of the object. The contrast seen in the image is based on sound absorption, scattering and phase effects of the object and its geometry.

At interfaces between materials of different acoustic impedances an ultrasonic pulse is partly reflected and partly transmitted. The acoustic impedance Z for a given material is defined as the product of sound velocity c s and density ρ:

ρ s c Z = (2)
The fraction of amplitude reflected at the interface of two materials is proportional to the acoustic reflection coefficient R, which is given for perpendicular incidence by

2 1 1 2 Z Z Z Z R + - = . ( 3
)
Z and 2 Z are the acoustic impedances of the two materials. Strong reflections occur if the impedances are sufficiently different. Therefore interfaces between water, air, steel and polymer can be clearly distinguished whereas interfaces between two polymer layers in most cases do not provide sufficient difference in acoustic impedance. In these experiments the good acoustic contrast between polymer coating and steel substrate results in a strong reflection from the substrate surface. From the time delay of the reflected echoes combined with the known sound velocity of the material, the thickness of the sample (profiling), the spacing of different layers (multi-layer systems of acoustically sufficiently different materials) and the positions of defects can be calculated. Due to the viscoelastic properties of polymers, ultrasonic waves are attenuated considerably and the penetration depth is limited. However, since industrial polymer coatings utilised e.g. in the automotive industry are very thin, ultrasonic microscopy in the range of ca. 20 -250 MHz offers sufficient penetration depth and spatial resolution to examine such coatings for defects. Detectable defects comprise air and water filled blisters, delamination of the coatings, cracks and pigments [9].

For our investigations a SAM Type "Evolution II" by PVA TePla Analytical Systems GmbH was used in reflection mode. In the experiments presented ultrasonic transducers with a nominal frequency of 30 MHz and 150 MHz were used to examine the multi-layer coatings of a total thickness of approx. 15 -75 µm, depending on the sample's layer composition. The maximum spatial resolution at 150 MHz is in the range of 10 µm. During measurements the transducer tip and the samples were immersed in distilled water at room temperature. Further numerical data analysis was performed for selected signals.

Model system

The model layer composition consisted of rolled steel substrates of approximately 30 x 20 mm² coated with different combinations of primer, base coat and clear coat layers. For the coatings we used an commercial black base coat (Heliotherm-Hydro-Basislack Type 16-123-9731) by Bollig & Kemper GmbH & Co. KG of about 15 µm thickness, an industrial clear coat (ProGloss Type FF99-0778) by BASF Coatings AG of about 40 µm and a corrosion inhibiting primer applied by electrophoretic deposition (EPD) of 15 µm. The base coat is water-based with polyurethane and acrylic dispersion particles and a melamine component, the clear coat acrylate based. Since the investigated coatings are commercial systems, further details are not available.

The base and clear coat were applied separately by spray-coating and pre-cured at 80 °C for 10 min before the next layer was applied. The completed samples were then cured in an oven at 140 °C for another 20 minutes. Into each sample a hole of 0.5 mm diameter with varying depth (see below) was drilled into the coating layer(s) to serve as well defined initial defect; the depth of the defects was checked with a profilometer. The defect depth was varied to get information on the transport processes in the different layers and along the interfaces. Furthermore, two different types of defects, a 'hole' and a 'scratch' (applied by a sclerometer) were compared. The sample edges were left free of coating or other sealants to allow penetration of the water and electrolytes from the edges. In addition, all samples provided sufficient surface area to study coating regions without any initial defect.

The samples are named according to their layer structure from bottom to top (primer: P, base coat: BC and clear coat: CC). The depth of the defect D ('hole') is indicated by the number of affected layers from top to bottom (Fig. 1).

Fig.1:

Layer structure of the model coatings. An explanation of the nomenclature can be found in the text.

To provide the corrosive environment the samples were immersed in Harrison solution (5 g/l NaCl and 35 g/l (NH 4 ) 2 SO 4 in distilled water). Measurements were carried out after exposure intervals of approximately 24 -62 hours. Accumulated immersion times of up to 500 hours provided sufficient time resolution to assess the delamination and damage mechanisms of interest. All experiments were carried out at room temperature.

Results and Discussion

Dependence of damage mechanisms on coating layer structure

The SAM images in Fig. 2 Assuming the blisters to be water-filled this value corresponds to a height of 9 -25.5 µm. The height differences measured in a topographical evaluation (see Fig. 4a) are also about 10 -25 µm. These features indicate that the blisters are filled mainly with water, electrolytes and water-soluble corrosion products. Since the blisters disappear almost completely after the sample's removal from the immersion, only marginal amounts of solid corrosion products like rust are contained in the blisters.

As will be shown below, the micro-blisters growth follows a power law dependence on time.

The 'spinodal' type of blister morphology and the growth kinetics has been linked to the idea of "nucleation and growth" for blister formation [9]. Nucleation and growth describes the kinetics of a phase separation (e.g. crystallisation or second order phase transition), where a nucleus for the new phase forms or "nucleates". Such a nucleus can either be formed spontaneously by fluctuations of the relevant order parameter or at a preferential site like boundaries or impurities. The nucleated phase grows until growth is inhibited or the structures merge. A detailed description can be found elsewhere [36 , 37, 38]. The similarity of blister formation -which in the case of very thin coatings is rather a 2D than a 3D process -to nucleation and growth is that a liquid phase (electrolyte/water) appears at the interface between polymer matrix and substrate and that this phase grows at the expense of its surrounding material. The origin of 'blister nucleation' can be both homogeneous due to fluctuations of the electrolyte concentrations or heterogeneous due to defects at the substrate or inhomogeneities in properties such as network density or adhesion strength. However, it has been stated that before the blistering can begin, water or electrolyte solution has to have penetrated the base coat and reached the substrate, so that a local loss of adhesion and disbonding can start [11]. Blister formation is assumed to take place in "weak spots" [25], that are presumably present due to manufacturing, but the exact reason why blisters form where they form is still under debate [1].

Considering that the first signs of blistering could be detected after about two days of immersion and that the blisters were statistically distributed, without any indication of a dependence on the location of the initial defect (white arrows in Fig. 2 and3), a fast and uniform diffusion of the electrolyte solution through the polymer matrix of the base coat to the substrate region has to be assumed. This shows that the barrier properties of the base coat alone are not sufficient to protect the underlying substrate from exposure to water and corrosive solution or prevent damage mechanisms even if the coating were intact. The samples with clear coat (Fig. 3) showed quite different behaviour. No microblisters could be detected in a time interval of about 300 h. On the other hand there was evidence of a sub-surface migration starting at the unprotected edges and the defect. Most probably water penetrates the interface between polymer and substrate (see Fig. 4a below). Other authors [1,2,3] found that water and oxygen penetrate coatings quickly, facilitating the beginning loss of adhesion by the reduction of the O 2 to OH -Ions, thereby creating the potential gradient that supports the diffusion of ions into the coating. As has been pointed out before, SAM is not able to differentiate between water and electrolyte solution. Therefore, in our experiments no conclusion regarding the exact nature of the penetrating liquid is possible. The SAM images in Fig. 3 clearly show a dependence of the observed effect on defect depth. The migration around the defect only occurred if the hole reached the substrate (Fig. 3 b).

Since none of the ultrasonic images of the other samples (the holes did not reach the metal substrate) showed any changes around the hole after up to 400 hours of Harrison immersion while all of them showed an effect along the sealant-free edges, it can be deduced that the effect occurs in the region of the substrate/coating interface, not at intermediate interfaces. This corresponds to similar results found in other research [5,11].

By visual inspection at the sites where migration was detected by SAM no macroscopic delaminations (coating peeling from the substrate) was evident. Fig. 4a shows an exemplary topographic profile of sample BC/CC/D2 after 388 hours of exposure supporting this. The z-profile (Δh) of the sample was measured horizontally along the y-axis passing close to the initial defect. The position of the profile is indicated by the black line in SAM image in Fig. 4b.

Fig. 4a-b: a) Topographic profile (cross section) of sample BC/CC/D2 after immersion in Harrison solution for approximately 388 h. The height difference

Δh is plotted along a line in y-direction. Different damage types can be seen: water/electrolyte migration zones on the right edge and near the defect (middle), and blisters on the left side and in the middle close to the initial defect. Figure 4b shows the line along which the topography was evaluated.

The topographical evaluation was done using the time-of-flight information of the reflected ultrasonic signal from the sample surface (see Fig. 5). Since the coupling medium is water, the distance from the transducer to the sample surface can easily be calculated for every point (x, y) on the sample surface using

2 / ) , ( ) , ( c y x t y x s ⋅ =
, where c is the ultrasonic velocity of water, and t is the time-of-flight of the reflected signal. To correct for sample tilt and bending of the substrate, the distance information was used to calculate a "mean sample distance function" by fitting a quadratic function in x and y:

+ + + + + = , (4)
where a 00 .. a 22 are coefficients. Only the non-delaminated inner area of the sample was used for this calculation. The height difference was then calculated by subtracting the mean sample distance function from the actual, measured distance: From left to right the cross section in Fig. 4a indicates a blister (left side), a blister close to the position of the initial defect (middle) which is surrounded by a migration zone and another migration region on the right side of the sample. At the right and left edge of the sample there is an indication of a slight elevation of the surface with a height of about 7 -10 µm in the ultrasonic echo profile. This delamination is supported by visual inspection. In the migration zones the increase of the surface is about 3 -4 µm (see dotted lines in Fig. 4a). These zones can be interpreted as areas where an initial loss of adhesion through weak wet adhesion and possibly disbonding of the polymer coating from the substrate due to migration of water and dissolved O 2 into the interface region took place [1]. In contrast the two blisters (left and middle) have a height of 10 -25 µm.

) , ( ) , ( ) , ( y x s y x s y x h mean - = Δ . ( 5
From these results it can be concluded that the clear coat effectively shields underlying layers from exposure to electrolyte solution, so that no diffusion of solution into the coating through the coating bulk starting from the surface takes place. Hence, no micro-blisters can form. The barrier property of the clear coat is therefore extremely important for preventing damage under exposure. After an induction time during which only the migration could be detected nucleation and growth of blisters started in the migration regions for samples where no primer was used on the substrate. Samples featuring a layer of primer (P/BC/CC/D1 and P/BC/CC/D2) did not show any blisters at any time before the complete delamination of the coatings from the substrate, which can be attributed to an enhanced adhesion of the primer. In most experiments by other researchers samples without primer were used [5,7,9,11,39], impeding a direct comparison of results.

The influence of the layer structure, specifically the absence of clear coat or primer, on the damage mechanisms holds true irrespective of the actual form of the defect. This was confirmed by experiments investigating samples featuring different types of defects (thin and broad scribes, hole or no initial defect at all). The geometry of the defect affects only the shape of the migration zone. A hole results in a roughly circular region expanding outward, while for scribes the front runs parallel to the scribe.

Migration kinetics

The migration kinetics were examined using a time series of SAM images taken after different times of exposure to Harrison solution. Fig. 6 a -f shows such a time series for sample BC/CC/D2. The progression of fluid migration into the polymer due to continuous immersion can be seen. As has been deduced from Fig. 4 this migration of water results most likely in weak wet adhesion [1] and possibly an initial disbonding, but does not yet represent a delamination. The migration fronts in x-and y-direction are indicated by white dotted lines and two short arrows denoted by x and y in the upper right corner of Fig. 6b. Some time after the water/electrolyte migration, delamination occurs. This delamination is represented by the black regions in the top right-hand corner and bottom left-hand corner of Figs. 6 c -f. From the ultrasonic images an anisotropy in the propagation velocity of the migration fronts is apparent.

b) 282 h , c) 325 h, d) 403 h, e) 439 h and f) 540 h of immersion in Harrison solution.

The x-and y-positions of the migration fronts in the SAM images taken after different exposure times were measured vertically and horizontally for the upper and righthand edge of the sample and for the migration zone around the hole. The results can be seen in Fig. 7. Within the bounds of error, the data show a distinct grouping according to direction. The extent of the migration regions was found to depend linearly on time with different expansion velocities in x-and y-direction. The data were fitted using a linear fit (here for the x-direction):

) ( , 0 migr migr t t v x - = , (6)
where v migr is the migration velocity and t 0,migr is the induction time that passes before any migration and possible disbonding can be observed. The resulting values for v migr are 1.8 nm/s for the x-direction (horizontal) and 3.5 nm/s for the y-direction (vertical).

The induction times t 0,migr for x-and y-direction are 60 and 63 hours for the migration around the defect, and 80 and 90 hours for the edges. The differences between the induction times at the hole and along the edges are almost similar, which indicates the same induction process for both locations. Induction times have also been found in other experiments, for example a diffusioncontrolled delamination process in a study on cathodic disbonding [8] and in a study of the influence of various parameters on cathodic delamination of a coating featuring a defect due to exposure to sea water, where the induction times were in the range of 84 -180 hours [3]. In the same experiment the advancing delamination front's velocity was measured to be 2.32 nm/s [3], which corresponds very well to the values measured in our experiments. In reference [2] the induction time is suggested to be controlled by the transport of reactants through the coating. However, no final explanation for the origin of induction time can be given here. The different migration velocities for x-and y-direction on our sample lead to the conclusion that the properties of the substrate are relevant for the propagation of the migration front. This conclusion is supported by other works, where a significant effect of the substrate characteristics on disbonding and corrosion propagation has been reported [8,[START_REF] Momber | Blast Cleaning Technology[END_REF]. In our case the different velocities observed are most likely a result of the rolling of the steel substrate that is part of the manufacturing process. The constant migration velocities and the stepwise change of the topographical profiles at the migration front in Fig. 8a suggest that the observed migration cannot be described by a classical Fickian diffusion mechanism. Although it is not possible to differentiate between water and electrolyte diffusion by SAM, the stepwise increase by about 2 µm can be explained by a migration of a penetrant along the coatingmetal interface which most probably leads to swelling of the polymer near the metal surface. SAM investigation cannot exclude mechanisms like adhesion loss by 'weak wet adhesion' and cathodic disbonding. Parallel investigations with complementary methods could be helpful in future research. Combined experiments using SAM and SKP to investigate a series of similar samples are in progress. Pre-experiments indicate that SKP can detect the migration front, that visible in SAM images.

For the linear rather than square-root time dependence of the propagation of the migration front different explanations are conceivable. As mentioned in the introduction, the linear growth can be related to a type II diffusion [21,22,40], where the diffusion is self-accelerated by structural changes due to the diffusing species. This may be caused by a decrease of the glass transition temperature caused by swelling and hydroplastification. Another mechanism of self-acceleration is a stressdepending diffusion coefficient caused by swelling. As discussed above, the 'historydependent' diffusion shows a close analogy to the mechanisms determining the linear growth of a crazing front during mechanical deformation [23,24]. Similar processes are proposed to describe the linear growth of cracks [41]. Also, electrochemical mechanisms could be responsible for an accelerated diffusion. The facilitated transport of ions in an electrical field gradient [2,3] might be such a process. It has been shown by Reddy and Sykes [25,26] that after cathodic reduction of rust at a defect the site "switches", becoming anodic and the cathodic region advances outward with new anodic sites developing in front of it. The authors state that around the defect easier pathways for currents of ions can develop due to the adhesion loss, thereby making high local currents underneath the coating possible [25,26]. The potential gradients that result from the cyclic cathode/anode switches combined with the easier pathways could be responsible for the fast migration that was detected in our sample.

The finding of a constant migration velocity seems to be in contradiction to other experiments, that use destructive measuring methods, which have found that diffusion of ions (following a square-root dependence) is the rate-determining process for disbonding [5,7,8]. However, it has to be mentioned, that in most of those experiments the extent of the "cathodic delamination" was determined by visual inspection [3,8], whereas the ultrasonic microscope detects changes in the acoustic properties caused by the penetrating fluids. Chemical processes resulting in delamination and corrosive products (obvious in the visual inspection) are not necessary to get acoustic contrast in SAM. Therefore, visual inspection and SAM may detect different processes, which obey different time characteristics. Furthermore, the different polymeric binders can lead to different diffusion mechanisms, as the high glass transition temperature and the strong adhesive strength of epoxy coatings probably impedes self-accelerated transport mechanisms, for example.

Blister growth kinetics

As shown above, blister nucleation and growth can take place in samples with clear coat, in areas, where the migration front, and therefore water, has already been present for some time. Fig. 6 b -f shows the formation and growth of blisters in the migration zones for sample BC/CC/D2. From the images it is apparent that the first blisters appear along the edges and close to the initial defect, with new blisters forming close to the migration front. So the process of blister formation is restricted to areas of prior exposure to water, dissolved oxygen and the reaction products resulting from the reduction of the oxygen.

Despite the error resulting from the difference between ultrasonically visible and actual size due to sound scattering and diffraction, the mean radius of selected blisters was measured for different immersion times. The results are shown in Fig. 9.

For reasons of clarity the error bars were omitted in the graph. The error of the measurements was between 7 -15 %. The data in Fig. 9 were fitted using a power law:

p b t t a x ) ( , 0 - ⋅ = (4)
yielding an exponent of p = 0.5 ± 0.02 for all curves, which indicates a diffusion controlled transport mechanism. t 0,b is the induction time, x the mean blister radius and a is a fitting parameter. It should be noted that the blister growth process being discussed was detected on the identical sample for which the constant velocity for the propagation of the migration front v migr was found. Therefore it can be concluded that the two observed effects result from different mechanisms or a different combination of mechanisms and are not caused by different experimental conditions. As can be seen in Fig. 9 the blistering does not immediately start with the immersion of the sample. This is represented by an induction time in equation 4. Induction times before cathodic blistering have been found before [7]. The data in Fig. 9 also shows that the blisters can be grouped according to their approximate induction time. These are about the same for all blisters in the same group. In order to relate the induction times for the different groups to the migration front, the distance of the blisters to the edge was measured. The values were in a close range for each group. A linear fit of the dependence of the mean induction time of the blister groups on their mean distance to the edge (Fig. 10a) yields a slope value of 400 s/µm, which leads to a reciprocal value of v blisterfront = 2.5 nm/s. This corresponds within the error limits to the velocities calculated for the migration fronts v migr of 1.7 -3.6 nm/s measured for the identical sample. This supports the assumption that water and possibly ions have to be transported to a given position first, before blistering starts there. Hence, the weak wet adhesion and most probably the cathodic processes starting in those regions are a prerequisite for the initiation or "nucleation" of cathodic blistering. The effective diffusion coefficients calculated for the selected blisters are shown in Fig. 10b, they range from 2.83 -13.62 × 10 -12 m²/s with errors of 10 -20 %. The values correspond in order of magnitude to diffusion coefficients of water in epoxypolyamine and rubber modified systems described elsewhere [2,4,11,42].

Conclusion

In this article it has been shown that ultrasonic microscopy is a method capable of detecting fluid penetration and migration leading to weak wet adhesion and coating failure due to cathodic delamination prior to any visual delamination that occurs after exposure to a corrosive environment. Different damage mechanisms -penetration and migration of water resulting in weak wet adhesion, leading to disbonding, delamination and blister formation -could be identified.

The experiments conducted revealed a dependence of the occurring mechanisms on the layer structure and the depth of an initial defect, whereas no dependence on the form of the initial defect could be detected. As expected the presence of a clear coat was found to be important for the protecting properties of a coating layer structure. For samples without clear coat and primer layer, statistically distributed nucleation of micro-blisters on the metal substrate was observed. In samples with clear coat, migration fronts were detected which started from initial defects and the unprotected edges of the sample. For the systems with clear coat, initial defect depth is important, since defects exposing the substrate lead to migration fronts and subsequent disbonding. The measurements also confirm that the migration and disbonding process takes place in the substrate/coating interface region.

For the samples with a clear coat the ultrasonic images show two distinct processes on the same sample: (i) migration and disbonding and (ii) blister nucleation and growth. The migration process was found to be linear with time with the fronts propagating with velocities of 1.7 -3.6 nm/s. The migration velocities for x-and ydirection differed, which can be explained by the morphology of the substrate (being most probably due to the rolling direction of the steel).

The kinetics of the subsequent growth of blisters has been identified to be a diffusioncontrolled process with power law exponents of 0.5. The blister nucleation induction times were matched with the migration front reaching the nucleation sites. This supports the theory that the presence of water and the resulting corrosive cathodic processes are prerequisites for the nucleation of blisters. Effective diffusion coefficients for blister growth were estimated yielding values of 2.83 -13.62 ×10 -12 m²/s.

Although the method has its limitations in that it does not allow the investigation of separate layers or interfaces of polymers with similar acoustic impedance, the results show that SAM is nonetheless suited for the investigation of transport mechanisms and defect propagation in coating systems. For a better understanding of the underlying processes and their kinetics, further experiments with model systems as well as corroboration of the results by other measuring methods are needed. Also, further improvement of the SAM data analysis -as for example the evaluation of the surface topography that was carried out -would be helpful.

  a -c and Fig.3 a -dshow typical examples of damage effects in polymer coatings after similar times of immersion (between about 250 to 280 hours) in Harrison solution. All samples in Fig.2are without clear coat, whereas all samples in Fig.3feature a layer of clear coat (CC) on top. Only the samples in Fig.3cand 3d contain a primer (P). Depending on the layer structure two different basic mechanisms of defect initiation can clearly be distinguished.

Fig. 2 a

 2 Fig. 2 a -c: Ultrasonic images of samples without clear coat. a) BC/D1 after 267 h 54 min, b) BC/BC/D1 after 285 h 42 min and c) BC/BC/D2 after 246 h 12 min immersion in Harrison solution. White scale bars: 10 mm. The arrows mark the initial defects (holes of 0.5 mm diameter).For the samples without clear coat, shown in the SAM images in Fig.2a -c, microblisters appeared uniformly over the sample area, irrespective of the location and depth of the initial defect. An analysis of the reflected ultrasonic signal at the blister sites reveals the presence of a strong substrate echo and a change in the time of flight of the echo in the range of 12 -34 ns compared to regions without blisters.Assuming the blisters to be water-filled this value corresponds to a height of 9 -25.5 µm. The height differences measured in a topographical evaluation (see Fig.4a) are also about 10 -25 µm. These features indicate that the blisters are filled mainly with water, electrolytes and water-soluble corrosion products. Since the blisters disappear almost completely after the sample's removal from the immersion, only marginal amounts of solid corrosion products like rust are contained in the blisters.As will be shown below, the micro-blisters growth follows a power law dependence on time.The 'spinodal' type of blister morphology and the growth kinetics has been linked to the idea of "nucleation and growth" for blister formation[9]. Nucleation and growth describes the kinetics of a phase separation (e.g. crystallisation or second order phase transition), where a nucleus for the new phase forms or "nucleates". Such a nucleus can either be formed spontaneously by fluctuations of the relevant order parameter or at a preferential site like boundaries or impurities. The nucleated phase grows until growth is inhibited or the structures merge. A detailed description can be found elsewhere[36 , 37, 38]. The similarity of blister formation -which in the case of very thin coatings is rather a 2D than a 3D process -to nucleation and growth is that a liquid phase (electrolyte/water) appears at the interface between polymer matrix and substrate and that this phase grows at the expense of its surrounding material. The origin of 'blister nucleation' can be both homogeneous due to fluctuations of the electrolyte concentrations or heterogeneous due to defects at the substrate or inhomogeneities in properties such as network density or adhesion strength. However, it has been stated that before the blistering can begin, water or electrolyte solution has to have penetrated the base coat and reached the substrate, so that a local loss of adhesion and disbonding can start[11]. Blister formation is assumed to take place in "weak spots"[25], that are presumably present due to manufacturing, but the exact reason why blisters form where they form is still under debate[1].

Fig. 3 a

 3 Fig. 3 a -d: Ultrasonic images of samples: a) BC/CC/D1 after 287 h 12min, b) BC/CC/D2 after 282 h 31 min, c) P/BC/CC/D1 after 285 h 42 min and d) P/BC/CC/D2 after 273 h 07 min immersion in Harrison solution. White scale bars: 10 mm. The arrows mark the initial defects.

)Fig. 5 :

 5 Fig. 5:

Fig. 6 a

 6 Fig. 6 a -f:

Fig. 7 :

 7 Fig. 7: Measured expansion of the migration fronts for sample BC/CC/D2. The measurements were taken in x-direction on the right edge of the sample and around the hole (horizontally), and in y-direction on the upper edge and around the hole (vertically).

Fig.

  Fig.8a-b: a) Topographical profile of the migration front at different exposure times and b) the line for which the topographical profiles are displayed. The stepwise change by about 2 µm is related to the propagating

Fig. 9 :

 9 Fig.9: Time dependence of the mean radius of blisters. The lines represent fits yielding exponents of 0.5 ± 0.02. The mean distances of the blisters from the edges for the three blister groups d 1 -d 3 are indicated below each group.

Fig. 10 a

 10 Fig. 10 a-b: a) Dependence of the induction times on the mean distance to the edge and b) effective diffusion coefficients resulting from the non-linear fits in Fig. 7.

Acknowledgment

Financial support from the Federal Ministry of Economics and Technology (BMWi) through the Federation of Industrial Cooperative Research Associations "Otto von Guericke" (AiF) (IGF-No. 15311 N) is gratefully acknowledged.