## 1 Introduction
### Natural Patinas  
When patinas form as the result of long-term exposure to environment, they appear with a heterogeneous aspect [2, 10, 11]. The heterogeneity will depend on the morphology of the surfaces, their roughness, their inclination, and exposure conditions. Relevant differences in the colour of the patinas can be observed according to their composition. As the first layer of oxides is formed, a thin, quite compact, and reddish-brown layer can be observed [1; 11; 12]. Upon further exposition, moreover, the surface layer turns to a dark brown-black colour. In this case, the composition of the patina can still be constituted only by oxides [11; 12], or the darkening of the colour could be also caused by the interaction of the surface with other pollutants [1; 13]. The commonly observed greenish patina appears instead after several years of exposure when the formation of basic copper sulphates or chlorides occurs [11; 12]. The patina of bronzes and brasses if often constituted by copper salts and minerals, with different compositions depending on the exposure environment. In addition, other corrosion products have been detected due to the presence of alloying elements. Several works reported that patina on copper-based surfaces typically has a two-layer structure [2; 11; 14; 15]. The most internal layer is usually more compact and uniform and is constituted by oxides as cuprite (Cu\({}_{2}\)O), and more seldom tenorite (CuO), but its presence is quite rare in natural patinas since its formation requires high temperatures and high pH values [2; 10], or hydroxides (Cu(OH)\({}_{2}\)) [11]. Therefore, a cuprite layer can normally be found on surfaces that suffered atmospheric corrosion in any type of environment. The outermost layer, instead, forms during the intermediate and final stages of corrosion and is formed after variable periods, according to the specific exposure conditions [10; 11; 16; 17; 18]. The parameters that affect the growth rate and chemical composition of these corrosion products are temperature and relative humidity and more importantly, the concentration and composition of pollutants [11; 15]. During the past centuries, the most commonly observed corrosion products in urban environment were the sulphur-containing ones, since SO\({}_{2}\) was one of the main pollutants of industrialised environment. Several crystalline forms of sulphate-based compounds have been detected in different exposure conditions [2; 5; 10; 11; 16; 17; 19], in particular, posnjakite (Cu\({}_{4}\)SO\({}_{4}\)(OH)\({}_{6}\)-H\({}_{2}\)O), antlerite (Cu\({}_{3}\)SO\({}_{4}\)(OH)\({}_{4}\)) and brochantic (Cu\({}_{4}\)SO\({}_{4}\)(OH)\({}_{6}\)), [10; 11; 15; 20; 21; 22]. Due to the past quite widespread diffusion of sulphur-based atmospheric pollutants, copper hydroxylsulphates are among the most common constituents of patinas of outdoor exposed surfaces. In the cultural heritage field, therefore, they have been largely documented on outdoor exposed bronze statuary [2; 3; 7; 21; 23; 24; 25; 26; 27; 28; 29], on brasses [30; 31; 32], and on architectural elements as copper roof [2; 8; 19; 33]. As previously stated, in recent decades many countries adopted clean air policies that reduced dramatically the concentration of SO\({}_{2}\) in the atmosphere [11; 15; 34]. However, since they are quite recent measures, the main corrosion product of patinas formed in outdoor unsheltered conditions is still brochantic. In fact, the formation of sulphate-based compounds is promoted in almost all rural, urban and marine environments. Moreover, it has been demonstrated that brochantic is by far the most stable compound and it is 100 times less soluble than chlorides and carbonates, and 10,000 times less soluble than nitrates [15; 18]. In parallel to the reduction of SO\({}_{2}\), however, it was observed that the time required for the formation of the typically green brochantic patina has become longer [10; 15; 16]. Copper sulphides, namely chalcogen (Cu\({}_{2}\)S) or covellite (CuS), can also form in sulphur-rich environment.