Eric Charmes

Cul-de-sacs, superblocks, and environmental areas as supports of residential territorialisation

Introduction 1

In the suburbs, residential territorialisation is most often associated with common interest developments, homeowners associations, gated communities and socio-spatial segregation. These forms of territorialisation have been the subject of many critical analyses by the academic community (McKenzie, 1994; Low, 2003; Glasze, Webster & Frantz, 2006 2 ). In most cases, critics focus on the role of real estate entrepreneurship or on the demands and attitudes of suburbanites. The advent of neoliberal ideologies is also considered a major factor and is often critiqued. These criticisms, however, frequently discount the significance of the road network layout. In this article, we will show that cul-de-sacs, superblocks and "environmental areas" are key factors influencing the current dynamics of residential territorialisation in the suburbs.

Observations on this topic have already been made by some new urbanists [START_REF] Duany | Suburban Nation. The Rise of Sprawl and the Decline of the American Dream[END_REF], and by several scholars (Pope, 1996;[START_REF] Southworth | The suburban realm I: Its emergence, growth and transformation in the American metropolis[END_REF][START_REF] Carmona | Public Places, Urban Spaces. The Dimensions of Urban Design[END_REF][START_REF] Mangin | La ville franchisée. Formes et structures de la ville contemporaine[END_REF]. They have highlighted the physical similarity between gated communities and residential communities planned according to an environmental area model. The similarity, they argue, is due to mainly one physical factor: the impossibility of people passing through. This factor is related to the mainstream definition of the public realm: a place where unplanned encounters may occur [START_REF] Southworth | The suburban realm I: Its emergence, growth and transformation in the American metropolis[END_REF]. In fact, with the inward-focused enclave or "pod" becoming the dominant planning and design model for residential suburbs, unplanned encounters have become less likely to occur than in conventional suburbs structured along a gridded street system (see Figure 4). Some observers [START_REF] Mangin | La ville franchisée. Formes et structures de la ville contemporaine[END_REF][START_REF] Loudier-Malgouyres | L'effet de rupture avec l'environnement voisin. Des ensembles résidentiels enclavés[END_REF] even consider that the residential pods that have been juxtaposed along suburban main roads during the last decades are very similar to gated communities (see Figure 6). To them, the addition of a gate at the only remaining access point represents merely a minor transformation, at least according to the criteria of effective public use.

This article adds some ground to these analyses. Two main points will be highlighted. First, no-through streets, superblocks and environmental areas provide clear boundaries to groups of residents and delineate a physical territory on which they can assert specific rights. As we will see, the assertion of these rights can be linked to the logic behind the spread of gated communities. Indeed, many gates appear in suburban streets to transform a through street into a cul-de-sac, or to turn a housing estate with several accesses into an environmental area (Section 1). The second section of this article will elaborate on the fact that cul-de-sacs and superblocks give groups of residents not only clear boundaries, but also define areas of community use. As we will see, such a physical background is favourable for the emergence of governing bodies specific to these groups and to these spaces. And, for reasons of scale, those governing bodies are most likely to be private (Section 2).

Cul-de-sacs as Barriers and Environmental Areas as Enclaves

The Cul-de-sac as a Barrier

At the beginning of the 20 th century, both in Europe and in North America, the network of streets giving access to suburban houses was commonly structured along an interconnected grid pattern. Most streets were therefore open to through-traffic. Through out the 20 th century however, the cul-de-sac became a major element of the suburban landscape. By the end of the 20 th century, "in its pure form, all the houses in a subdivision are situated on cul-de-sacs, and as few as possible are placed on the busier and noisier collector streets" (Southworth & Ben Joseph, 2004: 28-29).

Cul-de-sacs existed in cities well before the 20 th century. In fact, as early as the 18 th century, this type of road layout was already used to keep traffic away in London (Kostoff, 1992: 192-193). Nevertheless, even at the beginning of the 20 th century, cul-de-sacs remained scarce. They only became widespread with the generalisation of car use. In the United-States, a major step toward that change was made in Radburn. At the end of the 1920s, Clarence Stein and Henry Wright made Radburn one of the first suburban developments in the United-States where houses were systematically placed around cul-de-sacs with the expressed objective to keep the annoyances of motorized traffic away (Stein, 1957: 41;47). With the Radburn project, the cul-de-sac and its counterpart, the loop street3 , became considered the best way to provide vehicular access to houses.

The needs of suburbanites are well met with no-through streets. The cul-de-sac turns the residential ideal generally associated with moving into the suburbs, into reality. Moving into a suburban house is most often guided by the desire to benefit from a calm and verdant environment; a desire that is incompatible with vehicles passing incessantly in front of the yard. Households that move into residential suburbs also do so in search of an environment well-adapted to family life. Such being the case, as shown by Donald [START_REF] Appleyard | Liveable Streets[END_REF], a road closed to through-traffic is ideal for a family with children. The absence of throughtraffic creates a safer space, both with respect to the dangers of automobile traffic and to the dangers associated with the presence of strangers (the cul-de-sac allows residents to better monitor comings and goings and limits the escape options for a delinquent caught in the act).

The success of dead-end streets can also be explained based on the benefits to developers. Cul-de-sacs diminish the cost of land development: "The pattern is popular with developers not only because it sells well, but also because the infrastructure costs are significantly lower than for the traditional interconnected grid pattern, which can require up to fifty percent more road construction. Cul-de-sacs, being disconnected, adapt better to topography. Since they carry no through traffic, they often have reduced standards for street widths, sidewalks and curbs." (Southworth & Ben Joseph, 2004: 30). [START_REF] Stein | Toward New Towns for America[END_REF]; Frame 1 (top right): the "motorway" (author, 2005); Frame 2 (below right): the "footway" (author, 2005) This development of roads closed to through traffic has profoundly modified the use and ownership rights that are attached to road networks. With use restricted to local traffic, the street has become the equivalent of the spatial unit that constitutes the staircase, the entrance hall, the parking lot and the courtyard in a condominium. Grouped around a cul-de-sac, the houses form a flattened building of sort. As such, residential streets have become spaces whose function determines them as private property. Indeed, to our knowledge, no one seriously contests the practice of giving private status to entrance halls and elevators of vertical condominiums4 . No one wishes for staircases to become public property. By this standard, rather than question the development of private residential roadways [START_REF] Grant | Privatized suburbia: the planning implications of private roads, Environment & Planning B[END_REF], it is perhaps more astonishing to look at the large number of residential culde-sacs that do belong to the public domain, in Europe and in North America alike. This prevalence of the public domain can be chiefly explained by two factors. The first is linked to the dominant representation of the street. The street is considered the quintessential public domain. For many, even if it is closed to through traffic, a lane where cars drive remains a street and must therefore be public property. The debate stemming from the increase in number of private roads is proof of the resonance of this representation. The second fact concerns the cost of maintaining roads. 5 Once a housing estate ages, the perspective of costly roadwork begins to loom on the horizon, and residents begin to consider the transfer of their local roads to the public domain. They ask themselves one simple question: if others do not need to maintain their own roads, why should we? The questions are all the more pointed as the residents of private roads are subject to the same taxes as other residents, such that the municipality maintains public roads in part with their money. Obviously, a dead-end street does not hold the same interest to the general public as a street open to through-traffic, but it is difficult for residents to understand that difference when they observe some residential streets being maintained by the municipality, while theirs is not. Some municipalities resist this pressure, others give in to it (however, the tendency to refuse is becoming more frequent6 ).

Figure 1 (left): A map of a cul-de-sac in Radburn

In any case, whether it is public or private, the reserved and exclusive character of a cul-desac does not change. The cul-de-sac has strong links to local exclusiveness and territorialisation. The logic behind the development of cul-de-sacs even bears resemblance to the logic behind the development of gated communities. The installation of gates is motivated less often than one would think by the desire to completely control access to the road. Based on their study done in the United-States, Edward Blakely and Mary Gail Snyder observe that "[t]raffic is the second major reason [after crime] that neighbourhoods turn to gates and fences. Residents dislike the noise and disruption of through traffic, they worry about their children playing in the streets, they fear that easy automobile access gives criminal free entrance and quick escapes" (1997: 166). The same observation was made following a study on gating of residential roads in France (Charmes, 2005: 85-91).

It has been argued, in fact, that gates and other sorts of barriers may be used solely to close a street to through-traffic. Indeed, many fences and gates appear across roads not to completely block access but to simply transform the roads into cul-de-sacs. The French study, mentioned above, showed that it is not uncommon to place devices that restrict access only on one side of the street, with completely free access remaining on the other side [START_REF] Charmes | La vie périurbaine face à la menace des gated communities (Paris, L'Harmattan) Charmes E[END_REF]: see also Frame 3). 7 Admittedly, gated communities are developments that are completely closed, which is an important difference. In developments that remain accessible, security is not the issue as it is for gated communities. However, just like the gates at the entrance of a gated community, those erected to prevent cars from passing through, assert the exclusive rights of the residents to these roads. Residents often associate keeping motorized traffic away with keeping "others" away, and legitimize this separation based on a belief that they have exclusive rights of use. For residents of such streets, the conversion to a cul-de-sac is a way of affirming their right to tranquillity and to oppose any reduction in this tranquillity from automobile traffic. 7 Donald Appleyard established a similar link between fences and diversion of traffic in his studies of streets in Berkeley's city centre (1981: 215-239; 303).

From Superblocks to Environmental Areas

In many suburban residential estates, the main feature is not the cul-de-sac, but the integration of cul-de-sacs within a "superblock". Some projects, in both the United-Kingdom and the United-States, foreshadowed this association between cul-de-sacs and superblocks, but Radburn gave it new significance [START_REF] Moley | Les abords du chez-soi. En quête d'espaces intermédiaires[END_REF]. In Radburn, Clarence Stein and Henry Wright created superblocks consisting of a dozen residential dead-end streets, all surrounding green spaces accessible only on foot. Through-traffic is discharged on arterial roads that define the boundaries of superblocks (see Figure 2 and Frame 4). The prefix "super" can thus be understood in a literal manner: the "super" block is a "big" block where the traditional building's courtyard becomes a large community garden. Just as the block is the building block of the traditional urban landscape, the superblock is the building block of the suburban landscape.

Unlike with the traditional block however, the superblock's "courtyard" is not a secondary space onto which utility rooms and bedrooms open, but a central space onto which the principal rooms, such as the living room, open. Whereas in the traditional urban landscape the principal rooms open onto roads that are open to all, in the superblock these rooms turn their back on the roads that service their habitations. This difference is critical. Moreover, these roads are nothing more than cul-de-sacs from which all traffic is excluded. In such a way, the residence is almost totally removed from street life; the latter is invisible from the windows of the principal rooms. The space visible from these windows is limited to the residential grouping established by the superblock. In the Radburn project, the superblock tends to be a residential territory defined by the communal enjoyment of a green space (Stein, 1957: 41, 49-51). superblocks [START_REF] Stein | Toward New Towns for America[END_REF] But planning ideas during the 20 th century evolved beyond Radburn's design. In Clarence Stein and Henry Wright's plan of Radburn, superblocks are not as spatially isolated as are the large majority of contemporary suburban developments. Indeed, the roads that define the boundaries of the superblocks in Radburn still form an interconnected network. It is only with the advent of planning principles specific to traffic engineering that the superblock became a veritable spatial isolate. The report, Traffic in Towns, submitted in 1963 to the Ministry of Transports of the United-Kingdom by Colin Buchanan, is an important step in this evolution. This report proposed a new theoretical framework for the planning and design of road networks. One of its key concepts is the "environmental area" (see Figure 3): according to Colin Buchanan, environmental areas should be designed to have no extraneous traffic, that is, they should have no traffic filtering through unless there are businesses in the area (Buchanan, 1963: 65). In Buchanan's design, unlike the roads delineating the Radburn superblocks, the roads providing access to dead-end streets do not make an interconnected and continuous network [START_REF] Marshall | Streets & Patterns[END_REF]. They are accessible only from arterial or distributor roads at one intersection. Within such a road network layout, residential areas are better insulated from vehicular traffic. At the same time, traffic flow from main roads is less frequently interrupted by cars coming in or out of residential roads. From a traffic engineering perspective, the environmental area improved on Radburn's design and planning principles which partly explains the wide-spread success of the environmental area in the planning community. The influence of traffic engineers on the planning and design of suburban landscapes during the second half of the 20 th century is indeed well known.

Frame 4: A road delineating a superblock in Radburn (author, 2005) Figure 3: "The principle of Radburn Planning" as interpreted by Colin Buchanan (1963: 69) Frame 5: View of a suburban housing estate south of Paris (Essonne), whose planning and design fit well with the environmental area model (Yann Arthus Bertrand, Altitude)

Figure 4: From the grid to a juxtaposition of monofunctional enclaves [START_REF] Mangin | La ville franchisée. Formes et structures de la ville contemporaine[END_REF] 8

As a planning concept, the environmental area did not only apply solely to the planning of housing estates. As Colin Buchanan indicated: "It cannot be emphasized too strongly that the environmental areas envisaged here may be busy areas in which there is a considerable amount of traffic" (1963: 65). By definition, people should not enter an environmental area unless they have business to do so, although there may be many things to do in such an area and thus reasons to enter. From this perspective, a large retail development with only a few access points from main roads could be considered an environmental area; a university campus or an office park with limited access could also be considered as such. It can thus be argued that the environmental area is a ubiquitous model for the planning of suburbs. As shown in Figure 4, the concept of the environmental area greatly helps make sense of the contemporary suburban landscape and, more specifically, distinguishes it from the landscape structured by a gridded street system.

The Environmental Area as a Residential Territory

The environmental protection made possible by the environmental area has had some consequences. First, when combined with the single-use zoning that became the norm in the planning of suburbs, environmental areas became a collection of mono-functional enclaves. Many criticisms ensued, including the loss of an urban public realm and car dependency [START_REF] Southworth | The suburban realm I: Its emergence, growth and transformation in the American metropolis[END_REF]. Second, environmental areas led to an increase in the scale of privatism, especially in residential areas [START_REF] Mangin | La ville franchisée. Formes et structures de la ville contemporaine[END_REF]. The small bubble insulated from car traffic, created by cul-de-sacs, became enlarged to accommodate the scale of an entire residential development.

Just like with cul-de-sacs, environmental areas and gated communities share some similarities regarding the logic behind residential territorialisation. Indeed, much like the gating of residential streets to transform them into cul-de-sacs, many barriers and gates appear at the entrances of suburban developments with the primary objective to discourage through-traffic.

In several cases observed in France [START_REF] Charmes | La vie périurbaine face à la menace des gated communities (Paris, L'Harmattan) Charmes E[END_REF] Certainly, an environmental area with one entrance left open cannot be considered like a fully gated community. Security concerns, for example, are not the same. Yet, the environmental area and the gated community maintain a strong relationship. Adding a gate at the junction between an arterial road and the access roads inside an environmental area is not a very material change. In both cases, boundaries around a clear spatial isolate are defined within which outsiders are not supposed to drive [START_REF] Charmes | La vie périurbaine face à la menace des gated communities (Paris, L'Harmattan) Charmes E[END_REF][START_REF] Loudier-Malgouyres | L'effet de rupture avec l'environnement voisin. Des ensembles résidentiels enclavés[END_REF]. The separation of environmental areas from their surroundings is not simply a result of road layout. Indeed, in the configuration proposed by Colin Buchanan, it is no longer just the case of organizing cul-de-sacs around a central green space, but of surrounding a housing development with green spaces. In residential neighbourhoods, these green spaces act as buffers, which separate the homes from arterial roads. This idea is present in many current local planning by-laws with rules stipulating that the land abutting arterial roads is nonbuildable [START_REF] Mangin | La ville franchisée. Formes et structures de la ville contemporaine[END_REF]. This satisfies both an environmental requirement (a buffer zone improves the insulation between residential areas and roads with heavy traffic) and a traffic engineering requirement (activities occurring along roads induce cabotage traffic and reduced traffic speeds).

This idea is reminiscent of earlier ideas of the garden suburbs movement. In his founding work on garden cities, Ebenezer Howard proposed to surround new towns with greenbelts. These cities were supposed to have 30 000 residents or so [START_REF] Howard | Garden Cities of To-morrow[END_REF]. This scale has been reduced however with the garden suburb movement and moved closer to the one which became common for housing developments throughout the 20 th century. The Chatham Village project, conceived by Clarence Stein and Henry Wright immediately following Radburn, is part of this shift (Stein, 1057: 74-85). For this project, initiated at the beginning of the 1930s, the two architects used the organisational principles of Radburn's arterial system but added a greenbelt even though the development had less than 200 houses.

At such a scale, the greenbelt is like a cocoon and the residential area it encloses looks like a bubble isolated from its surroundings. As Clarence Stein wrote later about the Chatham Village project: "a greenbelt, even one as small as that of Chatham, insulates a community from neighbourhood depreciation and external annoyance" (1957: 85). It is, therefore, as much a case of environmental protection as a case of preserving the socio-spatial singularity of a residential complex.

The mini-greenbelt advocated by the garden suburb movement was largely unsuccessful in American and European suburbs. The idea of insulating a community from its surroundings, however, did have a large influence. Simply, instead of becoming enclosed within a green field cocoon, communities became protected through roadway setbacks and/or through walls, as is seen with the increasingly popular gated communities. The leftover space between arterial roads and housing estates is treated with varying levels of attention; most commonly however, the views from suburban roadways are reduced to two long and dull rows of walls and occasionally intersecting access roads.

Supports of Private Management: the Case of Radburn

Residential Territories and Ad Hoc Management

As we have seen, cul-de-sacs and superblocks (especially when transformed into environmental areas) share similarities through the assertion of specific territorial rights by their residents. Nonetheless, this is not sufficient to explain the emergence of ad hoc governments. Though sharing rights over a space provides residents with a common interest, it does not bestow upon them exclusive ownership of the space, any more than it incites them to take responsibility over its management. Residents of a shopping street have a common interest [START_REF] Webster | The nature of the neighbourhood[END_REF], but it is unlikely and would not be considered legitimate that, for this reason, they become owners or managers of their street, primarily because they are not the only users of this space (they must share it with passers-by and merchants). Also, the boundaries defined by the inhabitants of a shopping street are ambiguous and they blur further upon contact with other groups (for example, a group formed by the inhabitants of a block, composed of residents from several streets).

In both cases, cul-de-sacs and environmental areas provide two decisive contributions. The first relates to functional specialisation: there is only one type of user of these spaces, the resident. Those who access the space do so either as residents or as visitors of the residents. Of course, functional specialisation is not inherent to cul-de-sacs or to environmental areas: mono-functional zoning is a planning decision that can be made relatively independently from the design of the road system. Yet, a comparison of how residential suburbs structured along a gridded street system evolve, and how suburbs structured along pods evolve, shows that the former are much more open to functional mixing than the latter [START_REF] Mangin | La ville franchisée. Formes et structures de la ville contemporaine[END_REF].

The second decisive contribution made by cul-de-sacs and environmental areas is that they delineate clear territorial boundaries to the groups of users in question. In this manner, they allow clear identification of who holds the rights of use of the communal space. Thus, the communal space can be established as an exclusive territory and under collective ownership.

These potential territorial assertions of cul-de-sac and superblock residents may explain a similar connection found in the literature on Radburn. Not all aspects of Radburn's innovative design were influential [START_REF] Southworth | The suburban realm I: Its emergence, growth and transformation in the American metropolis[END_REF][START_REF] Martin | The case for residential back-alleys: A North American perspective[END_REF], but as argued in in the first section of this article, historians almost invariably cite Radburn to illustrate the early stages of the separation between automobiles and pedestrians and the organisation of local road networks around cul-de-sacs and superblocks [START_REF] Schaffer | Garden Cities for America: The Radburn Experience[END_REF][START_REF] Southworth | Streets and the Shaping of Towns and Cities[END_REF][START_REF] Girling | Yard, Street, Park, The Design of Suburban Open Space[END_REF]. This is not however, the only major innovation Radburn is credited for. This importance of Radburn as the initial site for the development of the modern homeowners' association in the United-States is all the more puzzling. Considering that, much earlier than Radburn, in both the United-States and in Europe, there were already groups of single-family dwellings, endowed with distinct boundaries and accentuated by, for example, gated entrances and fenced perimeters (Le [START_REF] Goix | Gated communities[END_REF]. These developments experienced significant success with the well-to-do at the end of the 19th century. Why then, did these particular developments not give rise to the modern homeowners' associations?

Our current understanding of the issue does not permit us to arrive at a conclusive answer to this question, and it would require more specific research. Notwithstanding, hypotheses can be proposed. The first, which can be extrapolated from the works of Evan McKenzie (1994)10 , is that in the 19 th century, knowledge was not advanced enough to put forth a concept as elaborate as that proposed by Charles Ascher. Elements of local collective management existed, but any return on experience was lacking. Thus, in developments like Forest Hills near New York or Roland Park, Maryland, a fixed annual fee was implemented, a choice which became problematic due to the inflationary spiral of the Post-World War I period (Schaffer, 1992: 178). The lesson was necessary though and in Radburn fees were regularly revaluated. Moreover, until late in the 20 th century, the juridical context was not favourable for the establishment of local private governments. Indeed, for the United-States, it has been a long process towards the stabilisation of that context [START_REF] Mckenzie | Privatopia, Homeowner Associations and the Rise of Residential Private Government[END_REF]. In France, a country considered to have pioneered in this topic, co-ownership has been regulated since at least 1804. Yet, the first law giving condominiums and homeowners associations a juridical status was enacted only in 1938.

The second hypothesis rests on the fact that in Radburn the superblock is not only considered a device for protecting homes and gardens from traffic annoyances, but also provides a specific group of homes with areas for community use. Green spaces are the most commonly shared spaces in Radburn, but these shared spaces also include sports facilities such as swimming pools or tennis courts. These communal spaces have much more importance in Radburn than in the posh housing developments built up until then. Radburn was, in fact, financed by the City Housing Corporation, which was created in 1924 with the objective to not only promote the ideas behind the garden suburbs movement, but also to create moderatecost housing. An objective behind the projects developed by the City Housing Corporation, like Sunnyside and Radburn, was to permit a social diffusion of ownership of a single-family dwelling in a verdant environment, a type of dwelling which until then had been reserved for the affluent classes [START_REF] Stein | Toward New Towns for America[END_REF]Schaffer, 1992). For the designers of Radburn, this diffusion could be made possible if spaces which were previously private became shared. Where upper class families each had their own large garden and sport facilities at their disposal, at Radburn, families now only have a small garden and share a vast green space and a common swimming pool with others. Of course, in the case of Radburn, this democratisation project was not successfully completed and the arrangements made did not prevent Radburn from receiving pre-eminently upper middle class households. The concept, however, had been launched, and it would bear great success. Reducing the size of parcels of land, by creating a collective space in place of individual yards, proved to be a good means of increasing the density of housing developments. Offering common spaces and facilities also made for a good marketing tool for selling houses on small lots [START_REF] Mckenzie | Privatopia, Homeowner Associations and the Rise of Residential Private Government[END_REF]. The trade off between individual and communal property was one of the key elements in the transformation of the suburban house market into a mass market open to large sections of society. 11 To be sure, the careful design of Radburn's common spaces has been lost in the process: most cases [today], open space appears to be leftover, unbuildable land rather than part of an overall design" [START_REF] Southworth | The suburban realm I: Its emergence, growth and transformation in the American metropolis[END_REF]. Yet, the idea of selling collective spaces and facilities with individual houses gained momentum throughout the 20 th century.

This collectivisation brought about new management issues. It was no longer a case of merely preserving a residential landscape through covenants (by avoiding, for example, densification or deterioration of the landscape) as was the case in luxury subdivisions created up until then.

It also involved regulating the use of communal spaces. Such an issue was difficult to deal with through covenants that established the rights to use the spaces once and for all. The idea of appealing to ad hoc local governments therefore became important. This was all the more so in Radburn since it was supposed to be a garden city of approximately 25,000 to 30,000 inhabitants (only the 1929 crisis put a halt to the project).12 11 This observation puts into question the idea that common interest developments are an instrument used by the affluent to control their environment to the detriment of the less-affluent. It appears, in fact, that homeowners associations were at first created due to a democratisation of personal property and are based on the pooling of community facilities to share in their cost.

Between Municipality and Homeowners Association

Why then resort to private forms of management and not to municipalities? At the time Radburn was designed, the latter solution was difficult to implement in France and Britain, but this was not the case in the United-States, since in that country municipalities could fairly easily be created through incorporation. Indeed, at the time Charles Ascher designed a government for Radburn, numerous small suburban municipalities, composed mainly of single-family dwellings, were being created [START_REF] Teaford | Post-Suburbia. Government and Politics in the Edge Cities[END_REF]. Charles Ascher himself did not pursue a career in the private administration of residential developments; on the contrary, he came to hold an important position as an expert in public administration [START_REF] Saunier | Little wise men: Three friends and the public administration world they made / Le système circulatoire des savoirs de gouvernement aux lendemains de la seconde guerre mondiale[END_REF].

From the perspective of surburbanites moreover, municipal government presented several advantages: it allowed access to public funding and facilities for infrastructure and utilities development; it also provided access to zoning rights which gave suburbanites the opportunity to restrict urban development on large tracts of land without actually buying them [START_REF] Teaford | The American Suburb: The Basics[END_REF].

The question of scale is central to this discussion. There is probably a threshold between the scale of the neighbourhood unit and that of the superblock. In Housing for the Motor Age (1939: 52-55), Clarence Perry presents various factors to consider in the determination of the desirable size for neighbourhood units. An optimal size, he argues, is based on the population required to operate the central facility: the primary school. Based on the standards of the time, Perry establishes the minimum population of such an institution at 500 students and indicates that the minimum could be as high as 2,500 students in centres of large cities. These numbers predicated that a neighbourhood unit should have between 3,000 and 10,000 inhabitants. The scale of the superblock in Radburn is a magnitude of size lower: it is designed for only about 500 people. However, Radburn's superblock scale better reflects the current European and North American homeowners associations. In 2006 in the United-States, according to the Community Associations Institute13 , there were 286,000 association-governed communities covering 23.1 million housing units, for an average size of 80 units per community and an average population of 200 inhabitants. The standard deviation is admittedly large, ranging from 2 units to several tens of thousands, but the average provides nonetheless a good idea of the most common scale.

If Perry's proposed scale for the neighbourhood unit had prevailed in new suburban housing developments around cities in the United-States, the municipality might have shown itself to be the most appropriate form of government. Though difficult to prove, several factors support this hypothesis. For example, Celebration, one of the most famous American private towns is currently in the process of studying its incorporation as a municipality. 14 A feasibility study 15 proposed a perimeter which, in 2006, contained approximately 7,000 residents and was organized according to a model similar to neighbourhood units. This is not an isolated case: several large privately governed communities have been transformed into municipalities [START_REF] Goix | Gated communities as predators of public resources: The outcomes of fading boundaries between private management and public authorities in Southern California[END_REF]. To be sure, in the United-States there are also large so-called "new towns" that are governed by homeowners associations (like Reston and Columbia near Washington 16 ), but those cases are more the exception than the rule. Moreover, in the case of Reston and Columbia, the county administration is influential.

The question of scale must be linked to the relevant perimeters for the management and financing of facilities and urban services. Curtis [START_REF] Sproul | Common interest communities: private government and the public interest revisited[END_REF] emphasizes that in practice, municipalities have responsibilities and prerogatives that are much more comprehensive than those of privately governed communities. In the great majority of cases, homeowners associations only concern themselves with the upkeep of communal areas of limited size. These areas are usually nothing more than a few cul-de-sacs and small green spaces. Tennis courts are not common and more substantial facilities even less so. Suburban developments with swimming pools large enough to host competitive practice are rare. In any case, sport facilities do not account for the scope of urban local facilities and services, which also include water supply, sanitation, garbage collection, emergency services, etc. Such facilities and services are difficult to manage on the scale of most private communities. The required investments are too large and the potential profits can only be guaranteed over the course of a period too long for the operators of the housing market. It therefore becomes necessary for public authorities or, at the least, for a public-private cooperation to be involved. Likewise, some homeowners associations resort to private security companies, but the scope of services they provide is generally narrow: detention and court appearances remain, for example, the prerogative of public powers (and we should be thankful that it is so).

The municipality (or the special district17 ) imposes itself, therefore, above a particular concentration of population. On the other hand, a municipal government becomes less relevant below a certain threshold. Indeed, Curtis [START_REF] Sproul | Common interest communities: private government and the public interest revisited[END_REF] considers that the prerogatives of joint-ownership communities are so limited that their transformation into public governments would, in most instances, make no sense. The cumbersomeness of procedures required by such a change would render management impossible. It would indeed seem absurd to impose the creation of a municipality to manage a tennis court and a few residential cul-de-sacs. Public administration experts also concur that municipalities should not be incorporated below a certain population threshold. This is the reason why, in the United-States, many measures have been put into place since the 1960s to prevent the creation of midget municipalities [START_REF] Teaford | Post-Suburbia. Government and Politics in the Edge Cities[END_REF]. Today, to return to the example of Florida, incorporation is possible only in settlements of at least 5,000 people (at least in counties with a population of more than 75,000). 18In this way, the scale of cul-de-sacs, superblocks, and even environmental areas corresponds to the scale of homeowners associations in the United-States, but not to the scale of municipalities. This relationship between design and government is hardly surprising. As discussed above, the cul-de-sac echoes the organisation of the entrance hall, the stairwell and the parking lot. In the case of collective housing, the management of these spaces is undeniably under the control of homeowners associations. The superblock, for its part, was conceived according to the model of a communal courtyard within a block. The connection is evident in Stein and Wright's Sunnyside development which preceded the development of Radburn (Stein, 1957: 24;Schaffer, 1992;Esperdy, 1999: 29-30). And yet, in urban centres, courtyards within a block are usually privately owned and their access is commonly restricted.

Conclusion

This article provides additional support to the hypothesis that exclusionary residential territories exist along a continuum, ranging from no-through streets (exemplified here with cul-de-sacs), superblocks, environmental areas, gated communities and privately managed communities. More research is certainly needed, especially on the establishment of governing bodies, since the case of Radburn is very specific and its practical influence may be overestimated. However, we have clearly demonstrated that the road network layout, prevalent in most contemporary suburbs and exurbs, is based on a logic of residential territorialisation that bears some resemblance to the one behind homeowners associations and gated communities. As discussed in Section 1, the creation of two cul-de-sacs facing each other can be compared to the erection of a barrier in the middle of a street open to throughtraffic. Similarly, environmental areas function as residential enclaves [START_REF] Mangin | La ville franchisée. Formes et structures de la ville contemporaine[END_REF][START_REF] Loudier-Malgouyres | L'effet de rupture avec l'environnement voisin. Des ensembles résidentiels enclavés[END_REF]. To be sure, most environmental areas are not gated communities, since anybody may enter them. Yet, when residents create an environmental area, they claim the right over the roads giving access to their homes and deprive those living in the surrounding areas of the right to use these roads as short-cuts. This is obvious when they do so by erecting barriers and creating specific structures to manage the spaces that they consider their own. Some of the similarities described in this article between gates, private management and types of road layouts are not very surprising. This is especially the case for the cul-de-sac: the culde-sac forms a flattened building of sort. This similarity is worth referencing as it reverses the usual perspective on the privatisation of suburban roads. Indeed, one should not be astonished by this privatisation, but rather by the large number of residential cul-de-sacs that do belong to the public domain. In the same way, considering that environmental areas function like residential enclaves, it is somewhat astonishing that gated communities have generated so many criticisms while critics have stayed relatively silent about superblocks and environmental areas (there are some exceptions however: [START_REF] Pope | Ladders[END_REF][START_REF] Mangin | La ville franchisée. Formes et structures de la ville contemporaine[END_REF].

By highlighting the importance of environmental areas, this article also argues that some projects developed according to principles of New Urbanism may not differ from conventional suburban projects as much as previously claimed. New Urbanists, who are particularly vocal against the lack of interconnection between suburban roads (CNU, 2000;Duany, Plater-Zyberk & Speck, Talen, 2005) tend to forget about the environmental area on a larger scale. As Alex Marshall explains (2001), under the label of New Urbanism, the majority of undertakings are more about amending than questioning the morphology of the suburbs. Most New Urbanism activities only modestly modify the currently prevailing way of doing. If the cul-de-sacs and the loops disappear, or if the detached house makes room for row houses, it is often done only inside an environmental area. In fact, replacing cul-de-sacs with interconnected roads along the grid model is more often done on a local scale. The developments that receive a New Urbanism label are generally inserted within the grid of an environmental area defined by arterial roads. Admittedly, certain developments avoid this drawback, in particular due to their large scale, but the change remains modest.

Frame 3 :

 3 The above development (east of Lyon, France) still has one road entrance left open. Security is obviously not an issue, vehicular traffic control is(author, 2003).

Figure 2 :

 2 Figure 2: Map of Raburn's

Frame 6 :

 6 Closure of one of the entrances of a housing estate in Surrey, south-west of London.Another entrance is left open to cars(author, 2006)

Frame 7 :

 7 View of a typical contemporary suburban landscape in the United States(Alex MacLean, www.landslides.com)

  and in Britain (see Frame 6), the closures are applied to all but one access point. A similar case is reported by Evan McKenzie in a development, established in 1946, of 168 lots in the City of Las Vegas: "Efforts to close off Bonanza from the surrounding areas were in evidence as early as 1981, a group of residents calling themselves the Bonanza Village Homeowners Association successfully petitioned the City of Las Vegas to vacate four of the five intersections from which Bonanza Village could be entered."(Mc Kenzie, 2005: 193). The association was, at that time, mainly concerned with limiting car traffic, as only one entrance was left open to vehicular traffic but pedestrians could still walk into the development through concrete traffic barriers at all other intersections. These efforts at closing off Bonanza Village prove that the planning of an environmental area provides a way of satisfying expectations that otherwise may be satisfied by installing gates and fences 9 .

I wish to thank the anonymous referees and Christian Moley for their valuable comments on early drafts of this paper. All mistakes are still mine however.

Some of the contributions of this latter book give a somewhat positive outlook of the so-called "private cities", most notably the one by Chris Webster.

In this article, cul-de-sacs and loop streets will not be discussed separately, since the essential variable characterising the roads referred to here is that they limit through traffic(Southworth & Ben Joseph, 2004: 29).

There are, of course, some instances where the status of these inside spaces is uncertain. In particular, the status of passages through halls and courtyards of apartment buildings linking one street with another are problematic (a well-known example is the "traboules" of Lyon, France).

For the case of France see(Charmes, 2005: chapter 4). Regarding the United-States, see for example: "Privacy Pricey in Storms. Homeowners Must Clean, Fix Nonpublic Streets", Daily News (Los Angeles), January 17, 2005.

As stated by Robert Lang and Arthur Nelson, suburban municipalities are increasingly reluctant regarding the inclusion of residential streets in their public domain. Many of them allow no new development outside of Homeowners associations(2007: 630). For the case of France, see(Charmes, 2005: chapter 4).

"Transport en commun" means "public transportation", "domicile" means "home" and "école" means "school" or "high school".

At the beginning of the 2000s, Bonanza Village has become a true gated community, and has done so with the marked support of local authorities.

Without, of course, making any assumptions on the opinion of the author regarding this question.

Would Radburn have been built as it was planned, that is like a real garden city of several tens of thousands residents, the government designed by Charles Ascher may well have attracted less attention from historians like Evan McKenzie. But, as the 1929 financial crisis put an end to Radburn's development, Radburn's population culminated at 1,500 inhabitants in the 1930s(Schaffer, 1992) and now stands at slightly more than 3,000 inhabitants.

http://www.caionline.org/about/facts.cfm

http://celebrationfeasibility.org/

http://www.celebrationfeasibility.org/120806FeasibilityStudy.pdf

For a recent account of the development of three large "new communities" (Irvine, Columbia and The Woodlands) see[START_REF] Forsyth | Reforming Suburbia. The Planned Communities of Irvine, Columbia, and The Woodlands[END_REF].

On special districts in the United-States, see[START_REF] Burns | The Formation of American Local Governments. Private Values in Public Institutions[END_REF].

Florida Statute 165.061


Y Ben Amor

E Sutter

H Takenouti

B Tribollet

M Boinet

R Faure

J Balencie

G Durieu

Electrochemical study of the tarnish layer of silver deposited on glass

Keywords: Tarnishing process, voltammetry, electrochemical impedance spectroscopy (EIS), normal power-law distribution

Cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) were used to characterize the tarnished thin layer of silver deposited on glass. Instead of natural tarnishing in air environment, an acceleration of tarnishing process was realized by immersion of Ag covered glass in 10 µM K 2 S medium. The X-ray photoelectron spectroscopy (XPS) shows that tarnishing product formed on the silver surface consisted of Ag 2 S and Ag 2 O. As electrochemical characterization, the measurements were carried out in aerated 0.5 M Na 2 SO 4 solution adjusted at pH 10. The impedance spectra collected in sulphate medium at the opencircuit potential show one capacitive loop in parallel with a high resistance, which reflects a blocking electrode behaviour. However, the equivalent electrical circuit, Rs-(CPE//R) is insufficient to reproduce the experimental results correctly. To minimize the dispersion between the experimental and fitted data, the CPE contribution is replaced by two normal power-law distributions of the local resistivity to interpret the tarnishing process in K 2 S medium with respect to the immersion time. These distributions are associated with the Ag 2 S and Ag 2 O layers.

Introduction

Silver is considered as a noble or semi-noble metal because of its rather high ionization potential. This metal is employed since many centuries for coinage, jewellery, and for making useful or ornamental articles. Its application in industry has increased steeply in recent years.

For continuous challenge to improve the durability of products, many research works deal with the ageing mechanism. Such studies are conducted on glass covered with a silver layer submitted to the outdoor aggression where the lifetime is one of the keen issues. The corrosion phenomenon of silver and silver alloy under atmospheric conditions is frequently called tarnishing [1]. The tarnishing process of silver depends on many factors [2][3][4][5][6][7][8][9], such as pH, humidity, temperature, nature and concentrations of pollutants, and exposure time.

Moreover, it is often noted that silver and silver compounds have strong interactions with sulphur. Numerous investigators [9][10][11] have studied the phase transformation from silver to silver sulphide (Ag 2 S). The standard redox potential for the overall reaction between Ag and Ag 2 S is given by: Ag 2 S + 2 e -→ 2 Ag + S 2- E 0 = -0.691 V SHE (1) The standard equilibrium potential E 0 is low, this is the reason that the silver sulphide is readily formed on silver surface.

For more detailed descriptions of the tarnishing process, two mechanisms are often proposed.

Huong and Parson [8] suggest the formation of silver sulphide through the following equation:

2 Ag + + SH -+ OH -→ Ag 2 S ads + H 2 O E 0 = -0.390 V SH (2) According to this mechanism, an adsorbed silver sulphide layer is formed on the silver surface. It results from reaction between SH -and Ag + ions presumably dissolved at the surface of the silver metal.

The second mechanism was proposed by Birss and Wright [7]. It consists of two consecutive single electron transfer reactions, as shown by the following equations:

Ag + SH -→ AgSH ads + e -

Ag + AgSH ads + OH -→ Ag 2 S ads + H 2 O + e -

The first reaction, equation (3), relatively fast, leads to the formation of AgSH ads as a surface intermediate. During the second reaction (equation ( 4)) the intermediate diffuses rapidly on the surface to react with OH -to form silver sulphide. Besides, a further oxidation of silver or silver sulphide may occur, and leads to the formation of silver oxides such us Ag 2 O and AgO [9][10][11].

To characterize these different tarnish products, several authors [12][13][14][15][16] have used electrochemical methods such as cyclic voltammetry (CV), linear sweep voltammetry (LSV), and square wave voltammetry (SWV). Electrochemical impedance spectroscopy (EIS) has also been applied to study the tarnishing of silver layer and to evaluate the effectiveness of some corrosion inhibitors of metallic silver [17][18]. The EIS measurements have often been analysed by means of equivalent electrical circuit model with two constant phase elements (CPE), which takes into account the diffusion process and the heterogeneity of the working electrode surface [19][20].

In this paper, first, the chemical composition of the tarnish layer was studied by XPS analysis.

Then, the electrochemical methods were used to allow the identification and characterization of thin tarnish layers formed on silver immersed during different periods in 10 µM K 2 S solution. This solution was used to accelerate the tarnishing process with regard to sulphide polluted atmosphere. The interaction between oxide (Ag 2 O) and sulphide (Ag 2 S) was discussed. Blank samples have been reduced at -0.7 vs SSE/V during 10 minutes and used as reference. The impedance data collected under different experimental conditions were analyzed by considering two impedances each one being representation of a layer (Ag 2 S and Ag 2 O), and different parameters were obtained. These parameters were related to the dielectric properties of the tarnish layers formed on the silver electrode surface.

Experimental conditions

Solutions

Electrolytes were prepared of analytical grade reagents: anhydrous sodium sulphate (Na 2 SO 4 ), sodium hydroxide (NaOH), and potassium sulphide (K 2 S). They were dissolved in deionised water. Silver specimens to be tarnished were immersed in a 10 µM K 2 S solution (pH adjusted to 10 by addition of a dilute NaOH) for 2 hours to 3 days at room temperature. In our previous paper, devoted to the protection of silver historical artefacts against a tarnishing, 10 mM Na 2 S solution was used [17]. However, for the present study, this solution was found to be too aggressive for characterization. This is the reason that the experiments were carried out in a very dilute sulphide medium. The electrolyte used for the characterization of tarnished silver was 0.5 M Na 2 SO 4 . The pH of which was adjusted also to 10 by addition of a dilute NaOH.

The tarnished specimens were quickly transferred to this characterization medium after rinsing the specimen surface with deionised water.

Electrochemical measurements

Silver was deposited on glass by an electroless industrial process. The thickness of silver layer obtained was about 100 nm. Glass with silver deposit is then cut into 30 × 60 mm coupon for use as the working electrode. The tarnish layers were characterised by electrochemical impedance spectroscopy (EIS) using a Gamry G300 instrument. The impedance was recorded, after 30 min of stabilization at the open circuit potential, by applying a 10 mV rms perturbation and sweeping frequency from 100 kHz to 10 mHz with 10 points per decade. The measurements were carried out in a three electrodes cylindrical cell (Fig. 1). The working electrode area (1.8 cm 2 ) was limited by a silicon O-ring. A Cu wire ensures the electrical contact with the potentiostat. A saturated sulphate electrode (SSE) and a large platinum plate were used for reference and counter electrodes, respectively. To minimize the artefacts sometimes observed at high frequency domain (HF) due to high impedance of the reference electrode, the latter was coupled with a platinum wire through a capacitor of 0.47 µF [21].

Results and discussion

Composition of the tarnishing layer

To determine the composition of the tarnishing layer, XPS analysis, cyclic voltammetry, and EIS measurements were performed on the reference (cathodically reduced silver) and tarnished electrodes.

XPS analysis

The characterization of the tarnish layer was realized by XPS for ca. The cathodic voltammograms exhibit the presence of a current plateau at -20 µA cm -2 corresponding to the reduction of dissolved oxygen. A peak with a low intensity at -0.05 vs SHE/V, which disappears during the anodic scan, can be observed. The origin of this peak is not clear. Some authors [START_REF] Abd El Rehim | [END_REF] have observed the same peak in alkaline media before the reduction of dissolved oxygen. They attributed this electrochemical behaviour to the reduction of oxygenated species of Ag(I). However, other authors [24] have not observed this peak on silver electrodes that were initially reduced at cathodic potential. Furthermore, a cathodic peak preceding the reduction of dissolved oxygen was also observed with stainless steel in aerated solution of Na 2 SO 4 and natural water. This peak was attributed to the reduction of oxygen and some residual oxide layers formed in air before immersion [START_REF] Marconnet | Electrochimie-Biocorrosion[END_REF].

The charge involved at peak C 1 was evaluated by integration. Table 1 summarizes the results.

From the compact atomic arrangement of Ag for an ideally flat electrode, the charge was transformed into the number of monolayers. 4 to 5 mono-layers were estimated which correspond to a thin layer, but significantly greater than sub-molecular adsorbed O or OH at the silver surface.

A small current peak observed for the silver specimen without cathodic reduction at about 0.9 vs SHE/V may corresponds the reduction of residual tarnish layer formed during the storage of the silver-deposited glass in desiccator.

During the anodic scan (Fig. 2a), an anodic peak (A) situated at 0.8 vs SHE/V was observed and attributed to the oxidation of Ag 2 O to AgO according to the following equation [START_REF] Li | European Corrosion congress[END_REF]:

Ag 2 O + 2 OH -→ Ag 2 O 2 + H 2 O + 2e -E 0 = 0.607 V SHE (5)
It is worth to recall that the equilibrium potential of this reaction in pH 10 medium is ca. 0.85 vs SHE/V.

The formation of Ag 2 O preceding this peak was not clearly observed, therefore the peak A may involve also a direct formation of Ag to AgO.

Cyclic voltammograms of the tarnished silver samples

The cyclic voltammetric curves of tarnished electrodes exhibited the same shape whatever the tarnishing period. Fig. 3a presents the voltammograms recorded for 2, 24, and 78 h tarnishing time in 10 µM K 2 S. Fig. 3b shows the same voltammograms but enlarged current scale to illustrate more clearly various cathodic peaks.

The voltammograms (cf. Fig. 3b) did not show clearly a reduction peak C 1 , but around -0.52 vs SHE/V the second peak C 2 is observed. Fig. 3c presents the voltammograms with enlarged potential and current scale. The tarnish layer is thus likely reduced at this current peak. The equilibrium redox potential of this reaction at pH 10 solution was calculated as -0.69 vs SHE/V, slightly more negative than peak potential C 2 . Its intensity increases with the tarnishing time. The charge and the corresponding number of molecular layers below this peak are indicated in Table 2. The amount of Ag 2 S reduced at this peak is therefore significantly smaller than that evaluated by XPS analyses. Only a small part of the tarnish layer is likely to be reduced at this peak potential. Beyond this peak a plateau between -0.65 vs SHE/V and -0.8 vs SHE/V appears. It was assigned to the reduction of dissolved oxygen as in case of the reference silver electrodes. An increase in the cathodic current is then observed beyond -1.5 vs SHE/V. It corresponds to the reduction of water with hydrogen evolution reaction. An additional peak was observed at ca. -1.2 vs SHE/V before the hydrogen evolution reaction. This peak may be allocated to the reduction of remaining Ag 2 S layer by the following reaction:

Ag 2 S + 2 H + + 2 e -→ 2 Ag + H 2 S E eq = -1.2 V SHE at pH 10 (6)
The peak height is about 10 times grater than C 2 peak, thus with these two peaks, the amount of Ag 2 S accumulated on the silver surface during the immersion in 10 µM K 2 S becomes close to those estimated by XPS measurements. It is important to note that the amount of Ag 2 S increases with immersion period.

During the anodic scan, the peak at around 0.8 vs SHE/V was observed. However, a careful observation of this peak showed in fact three anodic peaks, A 1 (0.62 vs SHE/V), A 2 (0.73 vs SHE/V) and A 3 (0.80 vs SHE/V) as could be seen in Fig. 3d. The peak current densities A 1 and A 2 increase with immersion period whereas the peak height of A 3 decreases. Moreover, it can be noted that the potential of this peak was slightly shifted to less anodic values when the tarnishing time increases.

Since A 3 has a potential close to that observed for reference electrode (peak A), it is allocated to the same reaction. Peak A 2 was attributed to the oxidation of the Ag to Ag 2 O according to the following equation [START_REF] Capelo | [END_REF]:

2 Ag + 2 OH -→ Ag 2 O + H 2 O + 2e - E eq = 0.58 V SHE at pH 10 (7)
The origin of Peak A 1 is difficult to identify, but may be associated with the formation of AgSO 4 according to the following reaction:

Ag 2 SO 4 + 2 e -→ 2 Ag + SO 4 2- E eq = 0.62 V SHE at [SO 4 2-] = 0.5 M (8)
It is worth to emphasize that these peaks are not directly related to the tarnish layer, since they are reduced during the cathodic scan, and the electrolyte used for this measurement does not contains sulphide ions. The difference observed for the anodic peak with respect to the immersion period in tarnishing solution is thus likely to be due to the surface roughness.

Electrochemical impedance

Electrochemical impedance spectroscopy investigations of tarnished silver were performed at open circuit potential (OCP) after 30 min of stabilization in 0.5 M Na 2 SO 4 adjusted at pH 10.

Fig. 4 shows the impedance diagrams in both Nyquist and Bode plots for reference (only Ag 2 O layer) and tarnished samples for 2 h and 78 h. All impedance spectra in Nyquist plot (Fig. 4a) were characterized by one capacitive loop with a high resistance in parallel. The diameter of this loop is greater for the tarnished samples. Fig. 4b shows the corresponding Bode plot. It can be noted also that no significant change of the impedance was observed beyond 4 h immersion. At the same time, at low frequencies, the phase is higher for tarnished sample. This behaviour is probably related to the Ag 2 S layer, which covers the metallic electrode and the oxide layer.

To evaluate the electrochemical behaviour obtained by impedance measurements, in a first approach an equivalent circuit was adopted to reproduce the experimental results (Fig. 5a). In this circuit, R s is the solution resistance, R is the resistance of the tarnish and oxides layers in parallel to a CPE related to the blocking nature for these layers. To assess the agreement between the experimental (Z exp ) and the fitted data (Z fit ), the error on imaginary component was calculated according to the following equation:

) ( Z ) ( ) ( 100 exp exp ) ( im im Z im Z fit im Z    (9)
Fig. 6 shows the presence of systematic and marked divergences on the imaginary part of the impedance (Z(im)) mainly above 100 Hz (curve with solid line). Therefore, another impedance model must be used to correctly reproduce the experimental impedance data.

Power-law model for normal resistivity distribution

One of the manners to characterize a CPE behaviour is the representation by a distribution of the resistivity of the films in the normal direction to the electrode surface [27][28]. The film resistivity was written as [27]:

1 γ 0 δ 0 δ δ ξ 1                          (10)
where ρ 0 and ρ δ are the boundary values of resistivity at the interfaces, ξ = x/δ (x is the distance along the film thickness) and γ is a parameter indicating how sharply the resistivity varies.

This approach assumes that the dielectric constant of the film is independent of the position.

Under this assumption, an impedance response showing CPE behaviour can be explained in terms of a power-law distribution of resistivity. This impedance can be expressed as [27]:

 γ 1) (γ 0 0 γ 1 δ pl j 1 ) (                       g Z ( 11
)
In this equation, j and  represent respectively the imaginary number 1  and the angular frequency (2f with f in Hz),  0 is the vacuum permittivity (9. 10 -14 F cm -1 ) and  is the relative permittivity of the film. The function g was evaluated digitally and can be expressed as a function of  only [27]:

375 . 2 88 . 2 1     g= ( 12
)
(-1)/1 can be replaced by  according to:

   1   ( 13
)
This  is identified as the CPE coefficient.

When ( 0 •• 0 ) -1  ω  (  •• 0 ) -1
, the equation ( 10) can be expressed as:

             1 δ 0 g Q (14)
It can be noted that equation ( 14) is used to relate the CPE parameters to the physical properties of the film. Hirschorn et al. [29] have used this model to characterise various systems such as aluminium oxides and oxides on stainless steel. They obtained good values of the thickness of different studied layers. Equation ( 11) was applied, first, to reproduce the impedance data recorded on a reference sample without tarnishing (reference curve in Fig. 4). The resistivity   of Ag 2 O is fixed to 450  cm. This value was proposed by Hirschorn et al. [27] to reproduce the impedance data of oxide formed on Fe17Cr stainless steel disk in 0.05 M Na 2 SO 4 at pH 4. The values of the relative permittivity of Ag 2 O is fixed to 8.8 [30]. The knowledge of these values allows the characterization of the Ag 2 O layer by the coefficient , the resistivity  0 , and the layer thickness . These parameters were evaluated by a non-linear regression method based on a simplex procedure with a house made software by using the expression of equation (11). The results of these variables are summarized in Table 3. The error margin was evaluated from five replica measurements.

Then, the experimental impedance spectra on tarnished samples were represented by the equivalent circuit presented in Fig. 5b. This circuit takes into account the contribution of two layers, Ag 2 S and Ag 2 O, formed upon the metallic silver layer in agreement with XPS analyses. In this circuit, each layer is represented by a normal distribution of RC elements (Fig. 5c) Integrating this distribution leads to the expression of equation (11). The total impedance is expressed as:

) O Ag ( ) S Ag ( ) ( 2 pl 2 pl s exp Z Z =R Z    (15)
Where Z pl is given by equation (11) The permittivity  and the resistivity   of Ag 2 S  are fixed to 3.5 and 400  cm respectively [30]. The same calculation procedure was applied to determine the characteristic parameters of each layer. The corresponding error (Equation 8) was presented in Fig. 6 (curve with dot line). It was clearly seen that the proposed model no longer induces a systematic error.

Results various parameters obtained by regression calculation

The variation of the different parameters of the adopted equivalent circuit (Fig. 5b) with respect to the tarnishing period was presented in Fig. 7. All parameters, except the coefficient (Ag 2 O), vary scarcely with the K 2 S immersion time. This result indicates that 2 h of immersion in 10 µM K 2 S medium seems to be sufficient to achieve the steady state values of the tarnish layer. The coefficient (Ag 2 O) (Fig. 7a) decreased from 24.4 to 13.5 when the tarnishing time increases from 2 h to 78 h. These values are slightly higher than that determined with the reference sample ((Ag 2 O)=10.2  1.2). However, the value of the corresponding CPE exponent , determined from equation (13), remain above 0.9. Fig. 7a shows also that (Ag 2 S) is substantially constant with the tarnishing time and much lower than (Ag 2 O), with an average value about 2.9. The low value of (Ag 2 S), thus low  value (cf. Eq (13)), suggests that the Ag 2 S layer is relatively heterogeneous. The relative resistivity   of Ag 2 S and Ag 2 O layers were presented in Fig. 7b. It can be noted also that the resistivity of Ag 2 O formed on both reference and tarnished samples present the same magnitude. The corresponding resistivity profiles calculated from equation (10) are presented in Fig. 7c. These curves illustrate the power-law nature of the distribution. The estimated thickness of each layer is presented in Fig. 7d. The Ag 2 S layer thickness is about 4.6 nm, more important than that estimated from C 2 peak in voltammograms (Table 2) but close to that estimated from XPS data. In contrast, the thickness of the oxide layer (Ag 2 O) is much lower (Fig. 7d). An average value is estimated to 0.5 nm, close to the monomolecular thickness (0.38 nm for Ag 2 O crystal). In the presence of the tarnish layer, the Ag 2 O layer becomes thinner. Its estimated thickness on the reference sample is three times higher. The calculated value is about 1.4  0.2 nm (Table 3). Besides, the ratio of Q values (equation 14) corresponding to the Ag 2 O layers formed on the surface of reference and tarnished silver is about 3. These values suggest that during the tarnishing process Ag 2 O is partially converted into Ag 2 S. The Ag 2 S may be also formed from the substrate Ag.

Conclusions

This work was focused on the characterization of tarnish layer formed on a thin silver deposit on glass substrate. The tarnishing process was induced by immersion in 10 µM K 2 S medium adjusted at pH 10. The composition and the nature of the tarnish products were identified by XPS analysis, and cyclic voltammetry is in agreement with this surface analyses. It was shown that sulphide layer (Ag 2 S) covers progressively the Ag 2 O layer during immersion test.

The tarnish layer was then examined in more detail by EIS investigations. Impedance spectra recorded on the tarnished samples show the presence of two impedances. Under the assumption of the uniform dielectric constant for the two layers (independent of the position), two normal power-law distributions of the local resistivity of each layer are consistent with the CPE contributions. The good agreement between the experimental data and the equivalent circuit model used allowed validating the model with the values of the different parameters, which have a physical meaning with respect to tarnishing time. 10), (11), and (15).

  5 nm depth. The recorded spectra show the presence of peaks characteristic of C-H bonds related to the contamination of the samples. The element S is present as soon as the sample was immersed in the tarnishing medium. The energy level of S2p at 161 eV is compatible with the presence of an Ag 2 S layer at the top. Auger spectra identified the presence of Ag 2 O at the upper surface layer on the reference sample and before tarnishing. During the tarnishing process, Ag 2 S covers progressively the Ag 2 O layer.3.1.2. Cyclic voltammetric responses without tarnishingTwo cyclic voltammograms of the working electrode without tarnish layer, and immersed in 0.5 M Na 2 SO 4 are presented in Fig.2. The potentials were referred to the standard hydrogen electrode (SHE) by adding 0.651 V to the experimental potential. The voltammogram with solid line curve was recorded after cathodic reduction at -0.05 vs SHE/V during 10 minutes to reduce a tarnish layer eventually formed during the electrode storage. The dotted curve was directly recorded without cathodic conditioning of the working electrode. In both cases, the potential scanning was performed from the initial potential E i close to the open circuit E oc , then scanned in the cathodic direction, from the open circuit potential (ca. 0.4 vs SHE/V) to -1.245 vs SHE/V and then to anodic potential up to 2.245 vs SHE/V. The scan rate was 5 mV s -1 . Fig.2ashows the whole current range, whereas Fig.2bdisplays the cathodic current in the enlarged scale. The two curves show qualitatively the same shape.

Fig. 1 Fig. 2 :Fig. 3 :

 123 Fig. 1: Electrochemical cell

Fig. 4 :

 4 Fig. 4: Impedance diagrams plotted at open circuit potential in 0.5 M Na 2 SO 4 (pH = 10)

Fig. 5 :Fig. 6 :

 56 Fig. 5: Equivalent electric circuits used to simulate the impedance spectra of the silver

Fig. 7 :

 7 Fig.7: Variation of the fitting parameters calculated from equations(10),(11), and(15).

Table 1 :

 1 Quantity of electricity involved below the cathodic peak C 1

	Cathodic reduction	C 1 (µA s cm -2 )	Molecular layers
	Without	694	4.42
	With	850	5.41

Table 2 :

 2 Quantity of electricity involved below the anodic peak

	Immersion period	C 2	Molecular	A 1	Molecular
	(h)	(µA s cm -2 )	layers	(mA s cm -2 )	layers
	2	-53.0	0.346	68.0	442
	24	-137	0.890	51.8	336
	78	-276	1.792	63.3	411

Table 3 :

 3 Values of Ag 2 O parameters calculated from equation(11)

		 0	
		 cm)	(nm)
	10.2  1.2	8.7 10 13  1.7 10 13	1.4  0.2