CHAPTER 1: Cultural Heritage Artefacts and Conservation: Surfaces and Interfaces

Our appreciation of any work of art belonging to our Cultural Heritage is definitely intertwined with the observation and interpretation of the surface of the object itself. As a matter of fact, whether we are observing a Renaissance fresco, a Maya painting, or the surface of a grotto painted by an unknown artist of our prehistory (see Figure 1.1), our attention is drawn entirely to the surface of the artefact.

An art object is devised so as to observe, read and experience its surface: the surface is the locus where the artist transferred their message and emotions, but it is also the place where different materials, with their own specific chemical composition and mechanical properties, coexist. Surface also plays a leading role in another unfortunately unavoidable process that affects our Cultural Heritage: all works of art deteriorate over time upon exposure to light, temperature stresses and relative humidity cycles, insects, or microorganisms, depending on the particular location and exposure to the environmental factors. The effects of deterioration may proceed deeper into the artefact but the first screen and the first point of attack is undoubtedly what the object exposes to the external surroundings: its surface, or better the interface with the world outside the art object. No matter whether the causes of deterioration are physical, chemical or biological, the surface will be the first frontier to be modified both in structure and composition. Exposure of the work of art to the atmosphere will result sooner or later in the growth of nano- or microlayers of different chemical composition readily adsorbed on the surface, as depicted in Figure 1.2. The mechanism and the kinetics of interactions of these compounds as well as their correct removal can be understood by proper application of the principles of physical chemistry of surfaces.

In fact, a proper conservative intervention should proceed only if the properties of the chemical media used are known and the mechanism with which these systems interact with the artefact's surface is understood.

It has long been recognized and described in several textbooks^1,2  and reference books³  that surface science extends its branches in many realms of science and technology, but its importance in art restoration and conservation has often been undervalued and only in recent times has a schematic scientific framework been attempted.

Art conservators should therefore acquire a sound competence not only in the nature and behaviour of materials but they should also master the science of surface phenomena. In addition, surface phenomena play a leading role in dictating the behaviour of many of the nanosystems conceived for art restoration that will be described in this book. Nanosystems, including nanoparticle dispersions, micelles, micro- and nanoemulsions, and polymer gels, will be described and their applications to art conservation illustrated.

The subject of this chapter is the thermodynamics of surface and interfacial phenomena involved in many aspects of art restoration and conservation, including their interpretation in terms of basic physics and chemistry. Both the general thermodynamic principles and the theoretical approach for the determination of molecular properties are widely discussed in literature,^4,5  and will not be reported here.

The thermodynamic treatment will be presented in the case of a planar surface (as far as microscopic scale domains are concerned, curved surfaces found in statues or bas-reliefs are still considered planar). Extension to the important case of fluid curved surfaces will be described in section 1.4.2.

Interfacial properties are modified by changing the adjoining phases, so that the thermodynamic properties of these bulk phases must be mastered and understood in the first place. A complete description of classical thermodynamics is beyond the scope of this book but the interested reader may refer to several textbooks on this subject reported in the “Further Suggested Reading” section.^4,5  This chapter will present the thermodynamic basis of surface and interface science, underlining those aspects that can be readily employed in art restoration and conservation. This chapter is directed to restorers searching for the scientific basis of their own work, as well as to students in applied chemistry and restoration techniques.

Table 1.1 reports a summary of some of the thermodynamic phenomena and variables that will be dealt with in the remainder of this chapter, indicating how they are correlated with the specific application in art conservation.

Readers unfamiliar with the physical chemistry of interfaces are certainly aware of many everyday life phenomena that are strictly correlated with the surface properties reported in Table 1.1: plants receive water and nutrients from the ground and many common insects such as water spiders may actually walk on the surface of a pond. The above phenomena share common roots in the physical chemistry of interfaces; in particular, they are examples of the larger domain of wetting phenomena, a domain that will be proven to be of relevance when conservation and restoration are involved.

This section deals with the discussion of a physico-chemical approach to surfaces and interfaces. The discussion on surfaces will lead to the definition of a very important physical entity, surface tension, which will be found repeatedly through this entire book. What we provide in this section is therefore a general and fundamental approach that underlies the following sections.

How to define and locate the surface of an object exactly is not a trivial question. The surface of a painted table or canvas may be approximated by a geometric plane, but when a section of the pictorial layer is enlarged we can easily prove that the surface of separation between the two phases is somewhat more extended and heterogeneous (see Figure 1.3).

Interfaces are boundaries between different phases, but the physical and chemical properties of the interface differ from those of the adjacent bulk phases. It is customary to use the symbols S, L and G to denote a solid, a liquid and gaseous phase, respectively. Using this terminology we can summarize different interfaces as SS, SL, SG, LL and LG interfaces as schematically described in Figure 1.4.

Examples of such interfaces are ubiquitous in the real world. Specific cases where art conservation is involved will be dealt with separately in this book, including solid–liquid interfaces (colloidal particles for wall painting consolidation), liquid–liquid interfaces (oil–water: micro- and miniemulsion for the cleaning of paintings), solid–solid interfaces (glue–cement, glue–canvas: adhesives).

The notion of “interface” is indeed the most general one, whereas “surface” is more restrictive, for example it is a boundary between a gas phase and a condensed phasewhen gas–liquid or gas–solid boundaries are considered.

The term “surface” is often also used when referring to boundaries of a particle, no matter what its dimensions are, i.e. from macro to nanoparticles, and independently of what is around the particle. A surface has a different physico-chemical nature with respect to the associated bulk phases, but as we approach smaller dimensions surface effects become much more dominant. This concept is easily visualized in Figure 1.5: assuming that they have the same overall volume, a single large particle exhibits a total surface area smaller than the total surface area of a collection of smaller objects filling the same total volume. In other words, the higher the surface-to-volume ratio the larger the predominance of surface forces with respect to bulk forces.

The smaller the particles the greater the specific area defined as the surface area per unit weight. The same concept applies also to a sequence of crystalline solid phases: the more finely the material is divided, the larger the surface area. It is therefore apparent that the surface rules the behaviour of the entire system as far as nano-objects are concerned, e.g. Ca(OH)₂ (calcium hydroxide) nanoparticles for the treatment of wood acidity or for the consolidation of wall paintings. Definition and modelling of interfaces are fundamental in order to describe the parameters that rule all the phenomena occurring between two phases (e.g. degradation reactions of artefacts).

The three-dimensional region of contact between two generic phases, α and β, is called the interfacial region or interfacial layer. In two-phase systems where one of the phases is crystalline it may be tempting to identify the division surface (DS) with the geometrical plane that intersects the centres of the atoms forming the first surface layer, as depicted in Figure 1.6. This simple case may be extended to any solid surface, as in a typical case of a marble, wood or bronze surface in contact with air.

When planar liquid phases are concerned, the location of the dividing surface is much more controversial: at the liquid–vapour and at some liquid–liquid interfaces the boundary layers extend over the dimension of few molecules, and more rarely several molecular layers can be involved. Although this boundary region may appear static, in real systems the interface is in a very turbulent state: for a liquid–vapour interface, the liquid is in equilibrium with its vapour, meaning that molecules from the vapour phase hit and condense on the surface while molecules from the liquid bulk phase escape from the surface and evaporate.

In many cases of interest for the treatment of works of art, liquid–liquid and solid–liquid interfaces will be involved. The interfacial region between two condensed phases is shown schematically in Figure 1.7. It is generally assumed that, in the absence of electrolytes, this region is a few molecules in thickness (approximately 1–2 nm) and only an extremely small fraction of the molecules in the system are present in the interfacial region owing to geometrical constraints.

If a system (for instance an artefact's surface) is in equilibrium with its surroundings, its macroscopic properties are fixed, and the system can be defined as a given thermodynamic state. Practically, a system is in equilibrium if no further spontaneous changes take place at constant surroundings. Out of equilibrium, a system is under stress, and tends to equilibrate to a fully relaxed state. Many degradation reactions occur at the interfaces of artefacts (metal oxidation, tarnishing, etc.) and such systems evolve to a stable state that may hinder the readability of the surface.

In order to inquire further into surface thermodynamics it is necessary to recall a fundamental state function,¹ i.e. the Gibbs free energy of the system, which is the maximum amount of work a system can do at constant pressure (isobaric changes). The importance of this function for the description of phenomena related to the chemistry of art conservation is immediately apparent once we notice that in conservation studies all the systems considered are usually at constant pressure.

For closed² systems at equilibrium with a fixed temperature (T) and pressure (P), the Gibbs free energy reaches a minimum. All spontaneous, irreversible processes (e.g. the degradation of monuments) occurring at constant T and P proceed in a direction such that the total Gibbs energy of the system still decreases:

Thus the equilibrium state of a heterogeneous closed system is the state with the minimum total Gibbs energy attainable at the given T and P.

In the derivation of the previous equation, we ignored any special change at the dividing interface (boundary), or the effect of the variation of the interfacial area.

Gibbs⁶  treated this thin layer as a quasi-two-dimensional phase having no volume (see Figure 1.7). The Gibbs dividing plane concept is a departure from the physical reality but it is consistent and allows us to apply thermodynamics to surface processes. Extensive thermodynamic quantities can thus be written as a contribution to the Gibbs free energy from the system bulk phases plus a surface term.

In the case of a system with surface area A:

where G_s is the extra Gibbs free energy per unit area. Although the composition varies in the neighbourhood on the surface, according to Gibbs we consider the system as uniform up to this interface.

For reversible processes at a completely planar interface, the differential Gibbs energy per unit area, γ, can thus be considered a surface energy at constant temperature, pressure, and composition:

The surface excess free energy term is correlated with the work done in generating an interfacial area increment (dA), which can be expressed as γdA. In other words, the surface free energy, γ, is the work that should be supplied to bring the molecules from the interior bulk phase to its surface to create a new surface of unit area (1 m²).⁷ 

The variable γ is of utmost importance in interfacial science and is called the interfacial, or surface, tension.

The dimension of γ is energy per unit area, J m⁻² in the SI system. However, these units are used exclusively for the case solid surfaces whereas for liquid interface the equivalent unit N m⁻¹ is adopted (force per unit length). In practical applications surface tension is reported in mN m⁻¹, equivalent to the obsolete dyn cm⁻¹ units.

From the previous discussion it can be stated that in every interfacial region at constant pressure and temperature, there is a tendency for mobile surfaces to decrease spontaneously in area, in order to decrease the Gibbs free energy of the system, since interfaces are the seats of excess Gibbs energy.

If the interface is fluid, i.e. liquid–liquid or liquid–gas boundaries, the action of the interfacial tension determines thus the final shape of the interface. The smallest surface area for a given liquid volume is geometrically a sphere, without any external force acting on it. For example, as far as gravity is concerned large spherical drops tend to flatten, as in raindrops.

The formation of a new surface includes two separate steps: the first is the formation of two new surfaces leaving unaltered the arrangement of atoms and molecules in space. In the second step, atoms and molecules rearrange at the surface until a new equilibrium state with minimum energy is achieved. Molecular rearrangements in liquids are very fast and surface tension can generally be considered an equilibrium value. Theoretically, the surface tensions of real liquids should be strictly measured in liquid–vacuum conditions. However, since liquids will continually evaporate in a high (or complete) vacuum condition, it is physically impossible to measure their real surface tension. In practice, we can only measure the liquid–air interfacial tension instead, under room conditions.

The situation differs for solids, where the greatly reduced molecular mobility slows down the molecular rearrangement at the surface. Therefore, surface energy for solids strongly depends on the local crystalline structure and, owing to the slow kinetics of rearrangement, also on the specific history of surface formation. In the case of crystalline or polycrystalline solid phases the surface energy correlates with the atomic density and number of nearest neighbours on surface plane, therefore γ is a function of orientation of the surface plane and of the specific crystalline structure, i.e., γ is not homogeneous.

Consequently, surface energies of solid surfaces are not as easily determined, and for solid–liquid and solid–gas interfaces the presence of the interfacial tension can only be established indirectly⁸  (see also Section 1.4.1).

A rough estimate of the surface energy of a solid surface can be obtained from the example reported in Figure 1.8.

If we separate a rectangular crystalline material into two pieces, two new surfaces will be created. This process requires the breaking of bonds between two layers of molecules or atoms. Depending on the orientation of the slicing plane, a different atomic structure will be exposed at the newly created surface. In Figure 1.8, two typical examples of surfaces created from the rupture of a face-centred cubic crystal³ are reported: the surfaces were obtained by cutting the same crystal with planes of different orientation. This translates into the fact that each atom is located in an asymmetrical environment where the inward forces are not balanced by the bonds that have been broken to create the surface. The surface energy that we defined in eqn (1.3) can then be equated to the energy involved in bond breaking for unit area:

where ρ_a is the surface atomic density, i.e. the number of atoms per unit area on the new surface, N_b is the number of broken bonds in each case and ε is half of the bond strength.

In the two cases depicted in Figure 1.8, surface energy will result in two significantly different values: the surface energy for the [111] plane is 0.87 times smaller than the surface energy for the [100] plane.

This rough approximation is only applicable to solids with rigid structure where no surface relaxation occurs; in all other cases where surface relaxation cannot be neglected owing to surface atoms moving inwardly or surface restructuring, the corresponding surface energy will be lower than that estimated.

In the previous section, we discussed surface tension in terms of surface energy per unit area for a macroscopic ensemble of molecules; we should now scale down these concepts and connect the thermodynamic scenario to events occurring at the molecular scale.

In all states of matter, molecules interact with each other, in other words forces are exerted between them, and these interactions determine the dynamic and static properties of both bulk and interfacial systems. In reality “intermolecular forces” is a general term that includes a variety of distance-dependent interactions between atoms or molecules. In this book, the treatment of intermolecular forces is directed towards the understanding of the forces ruling the interactions between colloidal particles (such as alkaline nanoparticles dispersed in a medium, for the deacidification of paper) and molecular interactions at the interfaces, such as those occurring during degradation of artistic surfaces or their cleaning, as well as forces leading to the mixing of two different solvents. Therefore the derivation of intermolecular forces between macro-bodies from pair, or multibody, interactions is not treated explicitly and only referred to in the Further Suggested Reading section.⁹ 

Besides the former microscopic approach, the macroscopic counterpart that considers a more integral treatment has also developed.¹⁰ 

Although a detailed description of the intermolecular forces operating in nano and interfacial systems will be presented in Chapters 4, 5 and 6 of this book, here we introduce briefly the categories of fundamental forces:

1. van der Waals interactions, in particular London, or dispersion forces which are ubiquitous;

2. Electrostatic or double layer forces if the nano-object or the surface is charged;

3. Steric interactions exerted at short range for small molecules or occurring at larger scales for macromolecules.

Gravitational forces are also operative and are explicitly considered for particles of high specific density and when describing capillary phenomena. In specific cases, structural forces, originating from the modification in the liquid structure adjacent to surfaces, or magnetic forces, if magnetic nanomaterials are involved, may prevail and dominate the overall balance. For instance, magnetic forces can be used to ease the removal of magnetic gels used for the cleaning of artistic surfaces (e.g. wall paintings), avoiding any handling of the gel and minimizing the mechanical action onto the surface (see Section 11.4).

Interactions can be expressed in terms of forces, energies or potentials depending on the way in which the mechanical energy is conserved or dissipated and converted into heat during the process. If the process is path independent the force is conservative and can be related to the potential: van der Waals and gravitational interactions are examples of conservative forces. Examples in art conservation are numerous, for instance white spirit, a widely used cleaning solvent in art restoration, is mainly a mixture of hydrocarbons that carries out its action through van der Waals forces (see also Section 5.2).

The molecules near or at the surface experience intermolecular interactions that are different from those that involve molecules in the bulk phase: this translates into the fact that molecules that are situated at the interfaces behave differently from those in the bulk.

The physical mechanism underlying the occurrence of surface tension at the interface is necessarily to be correlated with the imbalance of forces acting in the outer surface layer. Underneath a water–air interface (GL), e.g. within a water droplet, the water molecules are surrounded by identical neighbouring molecules. Here, the molecules will interact with each other in a symmetrical way with interactions of comparable extent acting in every direction. On the other hand, in the vapour phase the interaction between molecules will be very weak. Thus, the water molecules on the GL interface will be attracted by the molecules that are sitting below and by their sides, but there will be no molecule in the vapour phase to interact with. As a consequence, the molecules at the interface will be under an asymmetrical force field, a stress that produces a resultant net force perpendicularly directed inside the liquid. The nearer the molecule to the surface, the greater is the magnitude of the force due to this asymmetry.

The simplistic view described in Figure 1.9 shows how the attraction among molecules of the liquid will be larger in the more condensed phase. The liquid composition is uniform from the interior bulk phase to the surface but the balance of the forces acting on the surface molecules will be different from that in the bulk liquid phase.

As a result, the surface molecules are continuously moving inwards more rapidly than interior molecules, which move upwards to take their places. This process decreases the number of molecules in the surface, and this diminishes the liquid surface area; this surface contraction continues until the interior accommodates the maximum possible number of molecules.

The inward attraction normal to the surface causes the surface to be under a state of lateral tension, thus for a planar surface the surface tension can be viewed as the force acting parallel to the surface. In other words, the cohesion among the molecules supplies a force tangential to the surface so that a fluid surface behaves like an elastic membrane that wraps and compresses the liquid below.

This concept is reflected in a common observation that, due to the surface tension, insects such as the marsh treaders and water striders exploit the surface tension to skate on the water without sinking; other examples include the floating of a metal coin (regardless of its density) on the surface of water.

A typical, dramatic effect of surface tension is found in archaeological and waterlogged wood conservation (e.g. historical shipwrecks): after the wreck is recovered, exposure to air starts the evaporation of water within the wood's pores. The resulting surface tension forces of the evaporating water cause the collapse of the cell walls in the wood. As a result, severe shrinkage and cracking may result (see Section 16.4). Instead, solvents whose surface tension is lower than that of water (see below, at the end of this section) can be used for the gradual dehydration of wood, before consolidation interventions.

The surface tension and the surface free energy of substances are dimensionally equivalent, and for pure liquids in equilibrium with their vapour, the two quantities are numerically equal. However these two terms are conceptually different and surface free energy can be regarded as the fundamental property in thermodynamic terms, while surface tension would be taken simply as its equivalent if there were no adsorption on a surface.

On the other hand, when we consider two immiscible phases and an interface between them, we should define the interfacial tension, γ₁₂, as the force that operates inwards from the boundaries of a surface perpendicular to each phase, tending to minimize the area of the interface. The interfacial free energy between liquids is dimensionally equivalent and numerically equal to their interfacial tension.

As a matter of fact, interfacial tension between two immiscible liquid phases is a central physical parameter that underlies the design of advanced systems for the cleaning of artistic objects of any kind (stone, wall and easel paintings, paper, wood etc.). Surfactants, in fact, act on this parameter, and assemble into complex systems such as microemulsions and micellar solutions, whose structure and effectiveness as cleaning tools will be widely discussed through several sections of this book (see Chapters 6–9).

Surface tension is currently measured with many different experimental set-ups that will be mentioned in Chapter 6.

A plethora of pure liquids have been studied and their surface tension is tabulated in many reference textbooks,¹¹  here we collect the results of some measurements run at 25 °C for solvents including water, alcohols, hydrocarbons and metals that are liquid at room temperature, such as mercury (see Table 1.2).

Acetone, ethanol and hexane (which is one of the main constituents of white spirit), are all standard solvents used in art restoration, for instance in cleaning interventions for wall and easel paintings (see Chapter 5).

Surface tension γ can be regarded as due to the net difference between intermolecular forces acting at the interface, therefore all processes occurring near any interface depend on the molecular orientations and intermolecular interactions. This leads to the introduction of forces of adhesion and cohesion that can be exerted between liquids or between a liquid and a solid, an aspect that finds major applications in surface and colloid science and that is particularly important for Cultural Heritage.

In fact, several processes can be explained in terms of adhesion and cohesion forces. For example we will see later that capillarity results from a combination of adhesion and cohesion involving liquid and solid phases, and the removal of solid or liquid deposit from the surface (dirt removal) may be ruled by these two phenomena.

A distinction is generally drawn between adhesive forces, which act to hold distinct molecules together (the working principle of several adhesives and glues, widely found in restoration) and cohesive forces, which act to hold together like molecules of a single phase. However both forces result from the same properties of matter.

In Figure 1.10 the cartoon explains schematically the process of cohesion and adhesion.

In liquids, the cohesion forces keep the molecules close to each other, while translational and rotational motion of molecules takes place within the liquid with considerable freedom.

The energy necessary to separate two identical interfaces from contact to a virtually infinite separation distance is called the energy of cohesion, and the work (per surface area unit) needed for this process, W^c, is given by:

Where ΔG^C is the free energy of cohesion and γ the surface energy. W^C measures the attraction between the molecules of the two portions. The surface tension γ can be considered as half the work of cohesion; it measures the free energy change involved when molecules are brought from the bulk of the sample to the surface. Thus, two identical interfaces with high surface tension will cohere strongly.

Similarly, if two unlike surfaces are brought from contact to infinite separation distance, the energy required for the process is given by the difference between the final and initial states:

Where W_ij^A is the work of adhesion and the various γ_j, γ_i and γ_ij are the corresponding surface and interfacial energies. This approach leads to the statement that two unlike interfaces with high surface tensions will cohere strongly. The adhesion energy is particularly important when solid surfaces are involved. The adhesion of colloidal particles to solid substrates is of fundamental and technological importance (e.g. pneumatic transport of powders, printing, filtration, detergency, air pollution, glues). Let us consider the case of a solid surface of any nature (frescoes, statues or bronze) with a dirt deposit on it as described in Figure 1.11.

The removal of the contaminating spot can be considered in terms of the surface energy involved. The work of adhesion between solid surfaces and dirt will be given by the equation

The action of the detergent is to lower the surface tension of the dirt–water and solid–water interfaces, thus decreasing the work of adhesion W^A and enhancing the removal of the dirt by mechanical agitation. If the dirt is fluid (oil or grease), the addition of the detergent will lower the contact angle at the triple solid–oil–water boundary and its removal can be considered as a contact-angle phenomenon, which will be discussed later in this chapter.

In the case of liquid–solid interfaces it is useful to consider the tendency of the liquid to spread on the solid surface, that is the spreading coefficient, S.

In general, different limiting cases can occur depending on the nature of the solid and liquid phases and on the adhesion energy. When a drop of a non-volatile low density liquid (A) is placed on the surface of a high density solid sub-phase or on the surface of a liquid (B) which is practically immiscible with liquid (A), there are three possibilities:

1. Liquid (A) forms a non-spreading liquid lens with a defined edge, leaving the rest of the surface clean. The shape of the lens is constrained by the force of gravity;

2. Liquid (A) spreads as a monolayer on the surface;

3. If there is not enough space for all of the liquid (A) to spread fully, it spreads as a polylayer or a relatively thick film on the surface.

Figure 1.12 describes the possible scenarios.

If the liquid spreads over surface A, there is a contraction of the solid–vapour interface with an increment in the LV and SL interfaces. Spreading is spontaneous if the total surface energy decreases. Alternatively, we can describe this situation using the spreading coefficient S, i.e. the difference in the free energy (per unit area) between the solid surface A (or immiscible liquid surface) in contact with the vapour phase and the surface A fully covered with a thick layer of liquid B. Then we have:

Where S is the spreading coefficient, and γ^SV, γ^SL, γ^LV are the interfacial tensions of the solid–vapour, solid–liquid and liquid–vapour interfaces, respectively. Similarly, in the case of two liquids, γ_B, γ_A and γ_AB are the surface tension values of liquid B, liquid A and the interfacial tension of the A–B interface, respectively. Spreading will be complete when S^SLV (or S_A/B)>0.

A typical application of the parameter S in conservation science is related to adhesives. The wetting of a substrate surface by an adhesive or sealant, as well as the work necessary to separate the adhesive from the substrate, can be related to the surface energies of the adhesive, substrate, and the subsequent interface. In an ideal situation for spreading or wetting, the surface of the substrate should always have a higher surface energy than that of the liquid adhesive.

Whereas liquid surfaces readily respond to perturbations in their equilibrium structures, converging in a new homogeneous interfacial composition, solid surfaces are generally in kinetic equilibrium in a highly non-homogeneous organization of atoms and molecules. It is therefore expected that the behaviour of solid surfaces will be highly dependent on their specific history. As a matter of fact, as far as works of art are concerned, the solid–liquid and solid–gas interfaces are by far the most important domains on which degradation and conservation operators act.

Conservative intervention requires in most cases the application of liquid systems on the solid surface of the artefact: this trivial action implies a deeper level of knowledge of why and how the liquid will be able to wet and spread on the surface. In this section we will examine how we can define, measure or predict the wetting behaviour of liquid phases on solid surfaces. We will also consider the common case in which the solid presents porosity of various types and sizes, examining the physical principles that rule capillary phenomena such as the capillary rise.

It is necessary to introduce some essential aspects of solid surfaces in order to understand the issues connected to high reactivity and large deviation from the ideal behaviour exhibited by solid surfaces. We will therefore examine some general aspects concerning the composition and structure of ideal solid surfaces.

Crystalline solids consist of periodically repeating arrays of atoms, ions or molecules. Unfortunately real surfaces are not that simple: not only are surface properties different depending on the facet exposed, but more generally the same surface will expose domains with different Miller indexes, as shown schematically in Figure 1.8. In addition, real surfaces are typically very imperfect and exhibit a heterogeneous mixture of surface sites including a variety of structural defects such as steps, vacancies and isolated adatoms, or sites associated with the terraces of the close-packed surfaces (see Figure 1.13).

The thermodynamic impetus vs. minimization of the surface free energy translates, in the case of solid surfaces with a fixed surface area, into a strong tendency to decrease ΔG. This can occur through a variety of mechanisms: (i) slow surface relaxation, the surface atoms or ions shift inwardly; (ii) solid state diffusion with composition segregation or impurity enrichment at the surface and surface adsorption of contaminants onto the surface. In fact, real surfaces are generally covered by a layer of chemisorbed and physisorbed atoms or molecules (see Figure 1.2) including salts, organic compounds, hybrid organic/inorganic layers, patinas, pollen and microorganisms.

Structural and morphological features of solid surfaces comprise thus a large-scale inhomogeneity at the nano- and micro- scales (see Figure 1.14), among the most common examples of which are surface roughness and porosity, two crucial factors when considering the degradation, cleaning and consolidation of artistic surfaces.

Generally, surface roughness is one of the factors that may influence greatly the process of wetting and adhesion at liquid–solid interface. Surface roughness, r, is defined as the ratio between the real surface extension and the geometrical area of the surface under examination.

Surface roughness can easily be visualized through modern techniques such as atomic force microscopy.¹²  In Figure 1.15 we report two examples taken from the Cultural Heritage of Florence where surface roughness play a distinctive role in governing the state of conservation of these masterpieces: the Gates of the Baptistery and the David by Michelangelo.¹³ 

Real surfaces can also expose holes, or more generally pores, that extend also underneath the surface through the deeper layers. Porosity can in fact be of various types, but in all cases it has the effect of increasing the effective area of the exposed surface.⁴

The surfaces of granular materials and powders can be regarded as a typical porous material; pores can be of different types and sizes and are classified according to the average dimensions as: macroporous (pore size >50 nm), mesoporous (pore size 2–50 nm) and microporous (pore size<2 nm). Marbles, with pores between 1 and 5 nm fall into the last category, whereas chemical gels for the cleaning of artistic surfaces exhibit pores with radii in the 5–10 µm range. Wood cell walls have a nanoscale porosity, with radii of even less than 10 nm.

It is worth recalling that, in the case of granular materials, porosity depends not only on the dimensions of the solid particles but also on their packing in space. The same number of spheres with the same radius may exhibit different porosity according to the way they are packed: for a cubic packing of spheres the theoretical porosity is 47.65%, whereas if the packing is rombohedrical the porosity decreases down to 25.95%.

Solid surfaces share many peculiar properties, among which are history-dependent surface properties, structural defects and high surface roughness, porosity, site-specific high reactivity, presence of chemical impurities and contaminants. For most works of art, the solid surface under consideration may exhibit many of these features and it is therefore of the utmost importance that a clear knowledge of the limits of the system is obtained before any intervention is planned.

Surface wetting phenomena are ubiquitous and become essential in many applications and processes, such as transport in soil, development of biocompatible surfaces, control of biofouling, detergency, membranes, glues, protective coatings and more importantly art restoration and conservation issues. Wetting is a general term that includes a variety of wetting systems. Figure 1.16 shows a wetting system consisting of a liquid drop on a solid surface, immersed in a fluid that could be a gas or another liquid. A typical situation includes the deposition of a water microdroplet on the surface of a fresco painting or a bronze surface. There are many other possible configurations of solid–liquid–fluid systems, such as a liquid inside a porous medium, or a particle floating on a liquid–fluid interface.

Understanding the physical principles that rule wetting phenomena is therefore of crucial importance not only in understanding how and why a surface has been modified and degraded but also in order to envisage proper interventions to restore the original structure and appearance of the surface itself. Oxidation and corrosion, and formation of patinas, are only a few of the phenomena that inevitably descend from preliminary wetting phenomena.

On the other hand, wetting processes are present in everyday life: different types of fabric may adsorb water to different extents, or even repel it (Figure 1.17).

Restoration of fabric and tapestry cannot avoid taking this feature into proper consideration. Similarly, water collects in large drops on oily surfaces whereas aqueous thin films are formed on clean glass surfaces. A simplistic cartoon of various scenarios for a water drop in contact with a solid surface is sketched in Figure 1.18.

This behaviour reflects the fact that a liquid drop on a solid surface may adhere and spread differently depending on the nature of the solid surface and of the liquid.

We have already discussed the case of total spreading in Section 1.3, now we will explore the range of intermediate cases where wetting can be only partial.

In the above systems, the most important measurable parameter is the contact angle, θ, which is directly related to the wetting properties of the three-phase system under consideration. The contact angle is defined as the angle between the tangent to the liquid–fluid interface and the tangent to the solid interface at the contact line between the three phases (see Figure 1.16).

If we deposit a drop of water on a solid surface, the drop will probably start to spread. When spreading stops, each point of the perimeter of the drop will be at equilibrium. The equilibrium contact angle depends on the nature of the liquid and of the solid. Figure 1.18 shows how the contact angle of water on surfaces of different chemical nature changes, mirroring the wetting properties of the solid: water spreads on glass but does not wet wax surfaces.

The contact angle is a concept related to the adhesion and cohesion phenomena discussed in the previous section: liquid molecules are subject to cohesion forces that keep them close together but at the same time adhesion forces operate between the liquid molecules in contact with the surface and the molecules of the solid material. When the adhesion forces are larger than the cohesion forces the liquid wets the surface, whereas the liquid “refuses” the surface if cohesional attractions prevail. In the scenario depicted in Figure 1.18, a hydrophobic solid surface will be poorly wet by water and will exhibit a contact angle larger than 90°. Conversely, a water contact angle lower than 90° corresponds to a hydrophilic surface.

An applicative example is related to the treatment of hydrophilic artistic substrates, such as several stones (e.g. marble), with coatings so as to prevent water from wetting the surface and producing degradation effects (see Chapter 3). As an effect of the treatment, the contact angle will rise from values typically smaller than 30° (untreated stone) to values close to 80° (when the stone is coated). However, synthetic coatings often produce detrimental effects (both aesthetic and functional), leading to the need for their removal from the treated surface. In this case, the contact angle is a good parameter with which to assess the effectiveness of the cleaning intervention, and an inverted trend (roughly, for a treated marble surface, from 80° to 30°) will be expected upon cleaning.

When a drop of liquid is put in contact with a solid surface its perimeter will shift, contracting or expanding, until equilibrium is established for each point along the perimeter of the liquid drop, as represented in Figure 1.19 where γ^SV is the surface tension at the solid–vapour interface, γ^LV is the surface tension at the liquid–vapour interface and γ^SL is the solid–liquid interfacial tension; the three are in equilibrium.

Therefore, from the balance between the interfacial tensions along the parallel to the interface we may write eqn (1.10):

The pioneering correlation between the contact angle and the interfacial tensions is due to Thomas Young. The Young equation was developed for the case of an ideal solid surface, which is defined as smooth, rigid, chemically homogeneous, insoluble, and non-reactive.^14,15  Young's contact angle depends only on the physico-chemical nature of the three phases, and is independent of gravity. The latter may affect the shape of the liquid–fluid interface, but not θ_c. This corresponds to the state of the solid–liquid–fluid system that has the minimal Gibbs energy. Although it has been recognized that the three interfacial tensions may be influenced by each other at the contact line, for all practical purposes related to the measurement of contact angles of macroscopic drops, the effect of line tension on the contact angle is negligible.

It is worthwhile noting that the Gibbs energy vs. contact angle curve for an ideal solid–liquid–fluid system has only a single minimum at θ_c. In other words, the ideal system is characterized by a single value of the contact angle, which is not always the case for real surfaces.

Since the Young equation defines , a range of wetting behaviour [] can be classified and predicted by measuring the contact angle, as described in Figure 1.18.

The Young equation is widely used to determine the contact angle of liquids on a variety of solids, including the surfaces involved in the conservation of Cultural Heritage items, both to monitor the degradation state of the works of art (such as marbles, frescoes, papers, tapestry, glass windows) or to control the surface modification imposed for protection purposes. In Table 1.3 we report the values of contact angle for typical solid–liquid couples. Such solid materials are often used in cleaning and restoration of works of art, for example wax is widely used for adhesives and coatings as well as a traditional cleaning tool. In this latter case a mixture of bleached beeswax, stearic acid, ammonia and deionized water (waxy emulsion or stearate emulsion) is used to treat the surfaces. This peculiar mixture is also known as “Pappina Fiorentina” (owing to its extensive usage by the conservators of the Opificio delle Pietre Dure, OPD, a public art restoration institute in Florence; see Chapter 9).

Polytetrafluoroethylene (PTFE), commonly known as teflon, is well known for its anti-adhesive properties and widely used for anti-stick coatings for cooking tools. In addition, SiO₂-based materials, together with carbonate rocks, are often encountered in Cultural Heritage, as in sandstone artefacts.

The apparent simplicity of eqn 1.10 when used to assess the wettability of solids is deceptive; first of all γ_SV and γ_SL cannot be measured directly, and more importantly the specific features of solid surfaces described above may induce large deviations of the measured contact angle from the ideal θ_c.

The major causes of incorrect evaluation of the contact angle include surface roughness, chemical heterogeneity of the surface, and surface-active substances that can adsorb both at solid–liquid and at liquid–vapour interfaces and change the contact angle locally. All these effects introduce errors in the measurements, and the contour of a sessile drop is very irregular. This results in non-univocal values for the measurement of the contact angle and hysteresis of the contact angle that will be described in a following section.

Contact angle measurement is a low-cost method of analysis of surfaces that in most cases provides valuable information on the surface of the work of art for different purposes, e.g. to design a appropriate system for its cleaning or protection and to control the surface modification after the treatment. The method is non-invasive, as long as non-aggressive probe liquids are used and water-sensitive substrates are not involved, and can be performed easily with both water and non-polar organic solvents as probe liquids.

The techniques for measuring contact angles can be classified broadly into two categories.

1. Actual measurement of the angle by goniometric observation or some optical technique. This is the simplest and most direct method.

2. Methods that do not give θ_c directly but give γ^LVcos θ_c. Such methods usually involve a force measurement, or compensation of a capillary force, and can be carried out precisely and automatically.

Among the first class, direct visualization is the most convenient method, especially for samples of large area, but the results are often imprecise and scarcely reproducible. Automated systems with a computer-controlled dispensing systems are in most cases the best choice. From a technical point of view, the sessile drop method is most frequently used, because this is the most convenient method; however, other contact angle measurement methods for planar surfaces are used as well. Moreover, in art conservation, it is also possible to encounter other scenarios that require measurement of contact angle for more complex systems, for example in the case of tapestry and carpet restoration it may be necessary to asses the wetting properties of fabrics and, more often, fibres. In this case, contact angles are measured by suspending the fibre vertically from a microbalance and using the Wilhemy plate set-up.

The problem of contact angle measurement and interpretation is not yet completely solved; therefore it is necessary to understand the difficulties that are involved, in order to choose the best possible path for a specific application. The problems encountered in the measurement of the contact angle are due to the asymmetry of the drop and the relative dimensions of the drop compared with surface heterogeneity.

Solid surfaces are usually rough and chemically heterogeneous; a distinction is therefore necessary between the apparent contact angles, a quantity that can be measured, and the actual or intrinsic contact angle that depends only on the surface energy of the system interfaces. The actual contact angle is the angle between the tangent to the liquid–fluid interface and the actual, local surface of the solid. The apparent contact angle is the angle between the tangent to the liquid–fluid interface and the line that represents the nominal solid surface, as seen macroscopically (see Figure 1.20).

Whereas the Young equation predicts a single value for the static contact angle, it is found experimentally that a finite range of apparently stable contact angles can be measured for real heterogeneous surfaces such as the ones involved in works of art.

Surface roughness may be very high, as in the case of fresco surfaces (for which also porosity acts to disguise the intrinsic contact angle of the material), but also for oil tempera on wood the presence of a siccative oil layer may alter the morphology of the surface. Moreover, most pictorial surfaces present a diversity of chemical composition in a small area, demanding a tailored theoretical treatment. The approach to rough surfaces has been treated by Wenzel,¹⁶  whereas a model for contact angle interpretation of chemically heterogeneous surfaces has been proposed by Cassie and Baxter.¹⁷  In 1936, Wenzel⁹  developed in a rather intuitive way an equation for the apparent contact angle θ_app on a rough surface, averaging the fine details of the roughness. For smooth ideal surfaces we have already demonstrated that:

However, the surface roughness enlarges the surface area of contact between the surface and the liquid and the solid–vapour interface. Wenzel proposed that for rough surfaces the following equation holds:

where r is the roughness ratio, defined as the ratio between the actual and projected solid surface area. With this definition, r=1 for a smooth surface, and >1 for a rough surface. Therefore:

The Wenzel equation is based on the assumption that the liquid completely penetrates into the roughness grooves, as shown in Figure 1.21. This wetting situation on rough surfaces is termed ‘‘homogeneous wetting”.

Interestingly, as shown in Figure 1.21, the increase of surface roughness results in a decrease of the contact angle in the case of θ_true<90°, i.e. θ_rough<θ_true. On the contrary, if θ_true>90°, the apparent contact angle will be larger than the true one, θ_rough>θ_true. This means that extremely rough surfaces can exhibit extremely large contact angles and eventually leads to the superhydrophobic effect (see below) that paves the way to new possibilities for obtaining superhydrophobic protection layers for works of art located in outdoor or unprotected environments. For instance, organic–inorganic composite coating films are being developed to induce artificially an increased roughness of mineral substrates, resulting in water repellency (higher surface contact angle; see Section 14.3).

The Wenzel equation is an approximation that becomes better as the drop becomes larger in comparison with the scale of roughness; if the drop is larger than the roughness scale by two to three orders of magnitude, the Wenzel equation applies satisfactorily (for water, an average droplet has a size of a few millimetres, hence the scale of roughness that satisfies the Wenzel approximation is much smaller than 0.1 mm).

On chemically heterogeneous solid surfaces the surface tension varies from one location to another. Accordingly, the contact angle has a different value at each location also on smooth but inhomogeneous surfaces; this may be due to impurities, polycrystallinity or, in the case of works of art, on the intrinsic nature of the pigments used or on the aged deposits that contribute to the deterioration of the surface. In 1948, Cassie developed an equation for the apparent contact angle on a heterogeneous solid surface¹⁷  and, for the case of a surface with only two different chemical species, the following equation applies:

In this equation, f is the area fraction for each species, and the subscripts 1 and 2 indicate the two different surface functionalities; θ₁ and θ₂ are the true contact angles that correspond to the area fractions f₁ and f₂. More complicated relationships have been proposed,¹⁸  but the Cassie equation still seems to predict experimental results correctly.

This equation can be generalized to state that the cosine of the Cassie contact angle is the weighted average of the cosines of all the contact angles that characterize the surface. As in the case of the Wenzel equation, the Cassie equation is also an approximation that improves when the drop size becomes larger with respect to the scale of chemical heterogeneity.

Under some roughness conditions, air bubbles may be entrapped in the roughness grooves under the liquid, and both roughness and chemical composition will converge in the modification of the measured contact angle. In this case, the solid surface may be considered chemically heterogeneous, and the Cassie equation 1.14 may be applied in the following form:

Where Θ_CB is the CB (Cassie–Baxter) apparent contact angle, f₁ is the fraction of the area of the solid surface that is wet by the liquid, and r_f is the roughness ratio of the wet area. This equation was developed by Cassie and Baxter.¹⁷  When f=1, r_f=r and the CB equation turns into the Wenzel equation 1.13. The transition from homogeneous wetting (Wenzel equation) to heterogeneous wetting (CB equation) has been recently analysed,¹⁹  and it has been found to depend not only on the roughness ratio, but also on the specific geometry. Examples of surfaces where Cassie–Baxter treatment can be readily applied can be found among the superhydrophobic surfaces.

The interaction of surface roughness and capillary phenomena during wetting of a solid surface leads to a number of complex effects. Superhydrophobicity is the enhancement of hydrophobic properties due to roughness and it can be considered as a bio-inspired phenomenon. In fact, the best known example of superhydrophobic phenomenon is the Lotus effect, which involves superhydrophobicity and self-cleaning.¹⁸  The Lotus effect is based on surface roughness caused by different nanostructures, together with the hydrophobic properties of the epicuticular wax, as shown in Figure 1.22.

The surface is covered with microscopic islands or patches of wax and such heterogeneity enhances the hydrophobicity of the leaf enormously. Small water droplets do not wet the surface at all; they remain spherical, and roll off the leaf upon minor disturbance, cleaning the surface of the contaminants in their way (see Figure 1.22). As discussed above, an initially slightly hydrophobic solid surface with a water contact angle θ_true>90° becomes very hydrophobic after roughening, and it may have a θ_app approaching 180°. A roughness-induced superhydrophobic surface, according to the accepted definition, has θ_app>150°.¹⁸  The effect of roughness-induced superhydrophobicity was theoretically predicted and experimentally observed in the 1930s, although the term “superhydrophobicity” was coined later, in the 1990s, when micropatterning technology matured. It then became possible to build superhydrophobic surfaces with desired properties, and these systems started to be exploited as self-cleaning surfaces. Self-cleaning is the ability of many superhydrophobic surfaces to wash out contaminant particles with water drops running upon the surface, as opposed to conventional surfaces that have stronger adhesion to contaminants.

Many fields for application are possible (facades, paints, church windows and historical doors) where such surfaces are advantageous. For instance, it is worth mentioning another important area of application: underwater protection layers. An example of conservation where superhydrophobicity may play a major role could be the treatment of the underwater walls of Venetian buildings (Figure 1.23) treated with highly hydrophobic and nanostructured polymer coatings.¹⁸ 

Finally, we will report a case study of contact angle measurements for Cultural Heritage, concerning the degradation of bronze surfaces located on the doors of the Baptistery of Florence, one of the oldest buildings in the city, built between 1059 and 1128 (Figure 1.24).

Works of art located in outdoor environments are commonly affected by severe degradation induced by factors that are not as easily controlled or monitored as in indoor settings, such as light exposure, humidity, temperature, and rain and air pollution. The last two factors are difficult to monitor exhaustively and have often been overlooked, although their effect on the surface of a work of art can be quite devastating. Among the works mostly affected by the aggression of polluted urban areas stand doors and gates of monuments and historical buildings. In this respect the gates of the Baptistery of Florence represent a paradigmatic case study¹⁸  that has been the object of a three-year-long multidisciplinary investigation that gathered many different characterization techniques to monitor the alteration as a function of time, together with daily analysis of temperature and air compositon.²⁰ 

A variety of surface-specific techniques is accessible nowadays for conservation and restoration purposes, but contact angle measurement is particularly appealing because it is an unsophisticated experimental set-up that provides a variety of significant information on the state of alteration of metallic surfaces,²¹  wood surfaces²²  as well as stone and marble.²³ 

Blocks of multiple bronze replicas were prepared by fusion of the same alloys used in the original artefact¹⁸  by Ghiberti and Pisano, and the sets of replicas were placed on the Gates of Pisano and Ghiberti that face either north towards the entrance of the Baptistery or to the south towards the pedestrian area. The replicas were located at different heights and orientations to gain different protection from water, as demonstrated in Figure 1.24. Continuous atmospheric monitoring was performed over a three-year period: single replicas from each set were collected every six months and characterized with a multitude of physico-chemical measurements, among which was contact angle determination.

Interfacial phenomena find here a major role in determining the state of conservation of these precious artefacts: the spontaneous growth of various layers on the surface occurs, each layer showing different contact-angle and wetting properties. The extent of liquid–vapour interfaces controls oxygen diffusion,²⁴  whereas solid–liquid interfaces have a direct influence on the rate of dissolution of corrosion products. The wetting properties of the surface play a key role in corrosion and in the adsorption of hydrophilic contaminants.

The effect of exposure to the external environment and to the cycling of the seasons was investigated by measuring the contact angle of all replica tiles in the selected positions. Measurements were run on 2×2 cm samples using ultrapure water as a liquid probe. Experiments were repeated in different spots of the sample to estimate the homogeneity and repeated after 24 hours to investigate in more detail the patina formed after the first exposure of the samples to water.

The data evidenced similar contact angles for all replica targets in the range 86°–98°, indicating a low degree of hydrophilicity and wettability of the bronze alloys, as expected for metal surfaces exposing copper and zinc.^25,26  When the measurements were repeated for replicas taken from the door location after six months of exposure, a dramatic change of contact angle was observed, as reported in Figure 1.25, indicating the formation of a surface layer with high hydrophilicity.

For all locations the average contact angle dropped down to small values; the decrease was paralleled by an increase in roughness of the surface, determined by means of atomic force microscopy. Comparison with results obtained for the same samples with analytical surface techniques demonstrated that such behaviour is related to the formation of hydrophilic corrosion products such as oxides, sulfates or chlorides of copper and zinc.²⁷  Interestingly, the decrease in θ was larger for samples placed on the lower positions of the South Door, samples that are less available to rain events that would wash away the hydrophilic deposits. On the other hand, samples placed in water-protected zones showed higher contact angles owing to the presence of cuprite²⁸  or hydrophobic particles. Contact angle investigation was also correlated with the behaviour of temperature, rainfall and the concentrations of various pollutant gases and particles (NO_x, PM₁₀) in the atmosphere during the three years of study. The results revealed many interesting aspects related to these environmental parameters, as shown in Figure 1.26.

Hydrophilicity was found to increase up to summer 2006, followed by a stabilization or partial increase in θ, due to the formation of hydrophobic pollutants, after winter 2007. The increase in water contact angle was more important for unprotected replicas, due to the intense rain volume recorded in that period. A cartoon depicting the rationale suggested by the results obtained from contact angle measurements is reported in Figure 1.27.

The drastic decrease in θ observed in the first 18 months of exposure to the environment reveals the massive presence of hydrophilic corrosion products; interestingly such decrease occured during the summer season, and in particular in periods where extremely high concentrations of ozone were recorded in the central urban area of Florence. This supports a recently proposed hypothesis²⁹  that high ozone concentration may act synergistically with other pollutants to induce corrosion effects that exceed the threshold value established for buildings included in the Cultural Heritage designation.

The concept of surface or interfacial tension described in Section 1.2 implies the presence of a planar interface that separates two adjacent bulk phases.

In smaller-scale systems such as nano- or microdroplets, bubbles, gas cavities in fluids, or liquid in pores, this description may fail because the system is highly heterogeneous.³⁰  These examples are often encountered when nanoscience is applied to art conservation, and in the following chapters a comprehensive description of such heterogeneous nanosystems will be provided. Here we sketch the basic concepts underlying the physical behaviour of such interfaces. A more detailed discussion of thermodynamics is made available by consulting the Further Suggested Reading section.

We have already stated that γ is affected by temperature but also by interfacial curvature (see Section 1.1). This peculiar role of curved surfaces is easily recognized in phenomena such as the difference in vapour pressure of a liquid with curved interfaces, or in the rise of liquids in capillary tubes or complex porosities.

The first observations of liquid rise in thin tubes can be traced at least to medieval times: the phenomenon initially escaped explanation and was described by the Latin word capillus, meaning hair. It became clearly understood only during recent centuries that many phenomena share a unifying feature that involves the interface between two materials situated adjacent to each other. The following chapters will describe how the effect of capillary forces affects the process of deterioration of the Cultural Heritage in many complex systems, spanning from walls, frescoes, woodwork to fabric and paper artefacts (see also Section 2.4.1). But no matter how important its effect will be in complex systems, capillarity is a phenomenon that can be described simply as the rise of a liquid in tubes of small diameter, as depicted in Figure 1.28.

The rise of the liquid above the level of zero pressure is due to a net upward force produced by the attraction of the liquid molecules, i.e. water molecules, to a solid surface, e.g. glass or soil. When the adhesion of the liquid to the solid wall is greater than the cohesion of the liquid to itself, the quantity of the liquid that rises in the tube increases until equilibrium with the weight of the liquid column is reached. For the same liquid, the height of the column increases with a decrement in the tube diameter. Moreover, if liquids with different surface tension are used or surface active agents are added to water, the height reached by the liquid in the same tube will vary. These empirical observations lead to the general relationship between H, the height in the tube, R, the tube radius and the surface tension γ:

Here C is a proportionality constant. Furthermore, changing the thickness of the walls has no effect on the surface, thus suggesting that the forces giving rise to the phenomenon can be significant only at extremely small distances (a more precise analysis indicates a large portion of these forces to be at most molecular in range).

Molecules being pulled toward the walls will force other molecules aside in all directions, resulting in a spread along the walls that is only partly compensated by gravity. Liquid is forced upward along the walls, and cohesive forces carry the remaining liquid column with it.

Equation 1.17 predicts the height reached by a liquid with surface tension γ when rising inside a tube of diameter r, provided the contact angle between the liquid and solid walls is zero:

where ρ is the density of the liquid and g=9.8 m s⁻².

In the case of water (γ=72.8 mN m⁻¹, ρ=1000 kg m⁻³), the column of the liquid will reach different heights depending on the radius of the capillary tube, as reported in Table 1.4.

Moreover, the equation also predicts that the lower the surface tension, the lower the height of the column in the capillary, meaning that the presence of contaminants or “surface active” substance (e.g. surfactants) will affect the magnitude of h.

If the radius of the capillary is larger than 0.5 mm (see Figure 1.29, below) it is not correct to assume the meniscus to be hemispherical and the capillary equation needs to be corrected by adding explicitly a factor correlated to the contact angle θ that the liquid forms on the wall of the tube. The equation will become:

with r being the actual radius of curvature of the meniscus. Tables for such corrections are published in the existing literature (see Further Suggested Reading section). From eqn (1.18), it is clear that the rise or fall of a liquid in a tube will be governed by the sign of cos θ.

For instance, in the case of liquid mercury on glass, the contact angle at hydrophilic solid interfaces is very high (180° in the case of hemispherical meniscus), therefore cos(180°)=−1. In this case we say that the liquid is non-wetting. A capillary depression is observed, as described in Figure 1.29 (c): the picture depicts a situation where r<0, that is to say the liquid meniscus will be inverted and the liquid recedes along the tube walls. In this case, the adhesive forces are weaker than the cohesive forces among the molecules of the liquid, and the fluid is drawn away from the walls of the tube, causing the fluid to sink slightly. The hydrostatic equilibrium is reached by a lowering of the liquid level.

Capillary forces play an important role in all systems where liquids are present in a porous environment, although real-world capillaries or pores are not always circular in shape, as in the case of porous or granular materials encountered in artistic substrates (e.g. paintings on wood and paper, or frescoes).

In any system in which the fluid flows through porous material, it would be expected that capillary forces will be one of the most dominant factors, no matter the shape or extension of the pores, and the rise in capillaries of other shapes, such as rectangular or triangular, can be measured.³⁰  For example, for a porous solid such as paper (or compacted granular media), the height and the time of rise of the liquid follow the well known Washburn equation that allows measurement of the contact angle or surface tension of a porous medium that is regarded as an ensemble of tiny capillary tubes:

where L is the height of rise, γ is the liquid surface tension, r is the pore diameter, t is the time of rise, θ is the contact angle and η is the liquid viscosity.

Conversely, for a liquid of known properties the height of rise is affected by the pore radius and by the contact angle. This rather simple measurement has important effects on the characterization of porous media, allowing for the estimation of the average porosity of powders, and of granular and porous materials.

Capillary phenomena in porous media also affect other processes that may cause important degradation of pictorial surfaces, especially in settings where the capillary rise is important, e.g. church and crypts walls, as in capillary condensation described in the next section.

As stated above, many industrial and natural processes rely on capillary phenomena, ranging from blood flow in the veins to oil recovery in a reservoir. The sponge absorbs water or other fluids as a result of capillary forces, a process known as wicking (as in candlewicks). Properties of fabrics and paper are also governed by capillary forces (wetting etc.) as is the rise of moisture from the soil in the case of plants and trees.

It is common to witness the ability of liquids derived from the soil to penetrate into cracks and pores in building walls. Moreover, along with water, a variety of water-soluble elements may rise and diffuse in the porous media, giving rise to efflorescence, growth of microorganisms and eventually the detachment of layers of the surface. In the case of Cultural Heritage, several materials are affected by these phenomena, e.g. marble and stone artefacts, ceramics, frescoes and decorated walls, painted wood or paper. The presence of water inside the porosities of these materials is detected by the appearance of a whitish border, often formed by the crystallization of salts coming from the soil and migrating to the surface of the artefacts, as shown in the example of Figure 1.30.

In the case of walls, the water may come from groundwater or from accidentally dispersed water as in liquid spills from badly collected rainwater and aqueducts or, with more devastating effects, in floods. The height from the ground at which the diffuse border appears may vary and it depends on the type of porosity involved including the diameter of the pores and type of porosity, i.e. closed, connected or open; connected porosity is by far the most prone to massive degradation phenomena.

It should be mentioned that the extent of the water rise is also dependent on the thickness of the wall base in contact with the ground, and on its ratio with the surface exposed to water evaporation: maximum rise will be observed for internal walls but it will be less important for isolated pillars. The quantity of capillary water may be significant and reach 30% in volume for construction materials such as mortar and cement; water quantities as high as 300 kg can be adsorbed per cubic metre of wall. In the case of frescoes, or external location of other works of art, the aqueous solution trapped in the porosity of the material may also freeze in severe and uncontrollable climatic conditions; in turn the increase in volume inside the pores will induce a mechanical stress in the material, resulting in cracks and disruption of the object, which is often observed for stone artefacts placed outdoors.

In the previous section we introduced the distinctive features of the solid surface and demonstrated how the solid surface, and hence also the solid–air interface, differs from the surface of a liquid. We recall that the shape and surface structure of a solid surface is generally under kinetic equilibrium and strongly depends on the “history” of its formation, whereas the large mobility of molecules in the liquid phase induces rapid rearrangements of the surface, allowing for fast re-equilibration of the interface.

Moreover, solid surfaces present sites with different properties and surface energies together with many intrinsic defects; this translates into a strong reactivity of the solid surface, which is therefore prone to spontaneous adsorption of any substance that may lower the solid surface energy.

This applies also to the solid–air interface where impurities and contaminants are almost unavoidably adsorbed at the surface. A cartoon of this behaviour was presented in Figure 1.2: these properties of the solid–air interface render any surface exposed to the environment subject to the aggression of gases, particulates or bio-contaminants. With regard to Cultural Heritage, it is evident that, in the case of buildings, facades, church gates or statues exposed in an outdoor environment, the quantity and quality of the air contaminants cannot be controlled and will cause massive adsorption processes that lead to deterioration of the exposed surface. In indoor collections (frescoes, paintings on wood or canvas, books, tapestries and carpets), the concentration of contaminants in the air phase in contact with the solid surface may be partially controlled but only in museum settings does such an approach constitute proper protection of the surface.

The contaminants at the interface may interact following two different routes. In the first case, they may adsorb weakly at the interface and, in many favourable cases, they can be removed by appropriate cleaning procedures. Unfortunately, adsorption may also lead to a chemical reaction between the contaminants and the surface that will irreversibly and severely damage the artefact surface and its readability. These two processes follow different physico-chemical paths that will be briefly described and compared. Classical examples of adsorption-induced damage will be further discussed in this book, including oxidation and corrosion phenomena, formation of patinas, tarnishing upon moisture and sulfur adsorption. A careful investigation of the adsorption processes may lead not only to an understanding of the phenomena that induced the degradation of the artefact, but it will eventually suggest ways and strategies to protect, by adsorption of appropriate substances, the surface from further damage. We will focus in this section on adsorption at the solid–air interface, although the same principle applies also to solid–liquid and liquid–air interfaces.

The thermodynamic driving force for adsorption is the quest for a reduction of surface tension that will result in a minimization of the surface energy. Complex adsorption phenomena (see Adamson (1997), Further Suggested Reading section) are the result of different types of physical interactions at the interface that we can broadly group into the following.

1. Physisorption: a process prompted by van der Waals interactions between the molecules at the interface and the surface. This phenomenon is therefore associated with weak adsorption energies and it is the prevailing process at low temperatures. The molecules coming from the vapour phase collide with the surface but they are free to diffuse at the solid–air interface in search of energetically favourable surface sites.

2. Chemisorption: as the compound approaches the surface, it reacts to form a chemical bond with the atoms of the solid surface; this phenomenon involves higher energies and is favoured by an increase in temperature.

In the case of ionic substances, electrostatic interactions between the adsorbate and the surface also contribute to the adsorption process, and the charge of the compound plays a major role, e.g. trivalent ions such as Al³⁺ are attracted by an OH⁻ group more strongly than an Na⁺ ion.

Two popular theoretical models have been developed to describe adsorption: the Langmuir model and the Brunauer–Emmet–Teller (BET) approach. They apply to monolayer and multilayer formation at the interface, respectively.

In the case of chemisorption and of strongly localized physisorption, Irving Langmuir proposed in 1918 to consider the surface as “a checkerboard with finite number of equivalent adsorption sites”.

In the equilibrium between the gas phase and the adsorbed phase at constant temperature, an increase in pressure will increase the number of molecules adsorbed on the surface; on the other hand the number of molecules adsorbed at any pressure p will also depend on the strength of the adsorbate–surface interaction. At any surface pressure, the amount of adsorption is expressed by the parameter Θ, which assumes a fractional value whose maximum limit is 1, as shown in Figure 1.31.

At the equilibrium, the following equation applies:

Where k_ads and k_des are the rate constants for adsorption and desorption, respectively.

If we define a parameter b as b=k_ads/k_des we obtain a function that relates the fractional coverage to the pressure, expressed by eqn (1.21):

which is an equation popularly known as the Langmuir isotherm. The parameter b is the analogue of the equilibrium constant K_ads for the adsorption process, thus reflecting the strength of the adsorbate–surface interaction. The Langmuir model is limited to perfectly equivalent adsorption sites and it is not valid for heterogeneous surfaces exhibiting sites with different atomic ordering and defects, or cases where lateral interactions between adsorbates in the monolayer cannot be neglected. Nevertheless, the Langmuir model is a useful approximation in many instances, although other complex mathematical models³¹  may fit the experimental data better. The Langmuir model was later extended by Brunauer, Emmet and Teller in 1938,³²  to include the formation of multilayer at the solid–air interface for strong adsorbate–adsorbate interactions.

The properties of the adsorbing surface also affect the adsorption process: roughness, wettability and porosity of the solid surface will drive both the kinetics and the mechanism of adsorption.

The quantity of adsorbed substance, or surface coverage, as a function of the equilibrium concentration of the adsorbate at constant temperature describes what is called the adsorption isotherm. The form of the isotherm is specific for each adsorbate–interface couple.

In Figure 1.32 we report typical International Union of Pure and Applied Chemistry (IUPAC) isotherms that are tabulated in many textbooks (see Further Suggested Reading section). We can extract specific information on the interaction parameters between adsorbate and adsorbent, between adsorbate and adsorbate molecules, and on the porosity of the adsorbing solid by examining the shape of the isotherms.

The first part of the isotherm provides information on the adsorbate–adsorbent interaction and on the adsorption energy: the higher the slope of the curve in this region, the larger the interactions between the molecules and the surface. In the second part of the isotherm, information on adsorbate–adsorbate interaction at the solid–air interface can be extracted: the presence of only one plateau region (type I) means that only one monolayer of adsorbed molecule can be formed and hence that adsorbate–adsorbate interactions are not established. Conversely, if more than one linear arrest is observed, as in type IV, the growth of two or more layers of adsorbate molecules at the interface can be inferred, indicating the presence of significant interaction energies between two adjacent layers of adsorbed molecules.

Furthermore, information on the structure of the adsorbent, and more specifically on its porosity, is described in the last part of the curve: in the case of multilayer adsorption, adsorption and desorption isotherms may not be identical and will show what is called a hysteresis phenomenon.

Such behaviour is often found for porous solids, and is due to a phase transition of the adsorbed gas to the liquid state so that desorption from the pores is hindered. Capillary condensation is due to an increased number of interactions between vapour phase molecules inside the confined space of a capillary. A capillary does not necessarily have to be a tubular, closed shape, but can be any confined space with respect to its surroundings, as for the case of granular materials used in frescoes.

Capillary condensation is an important factor in both naturally occurring and synthetic porous structures. The study of this phenomenon, by means of experimental adsorption isotherm measurements, provides access to the determination of specific area values and pore sizes for a variety of materials.³³ 

Liquid molecules rearrange quickly after a new surface is created, reaching a new thermodynamic equilibrium, whereas solid surfaces are only kinetically stable and may take a long time to relax at their final equilibrium state.

The differences between interfacial and bulk molecular interaction energies are due mainly to the magnitude of the interactions, to the two-dimensional geometry of the surface and also to differences in interfacial structure. In principle, it would be possible to calculate the energy of cohesion between molecules within a single phase and the energy of adhesion for this interface, if the potential energy functions and the geometrical deformation at an interface are known.

However, in practice we are far away from such success. First, the potential energy functions are not well enough known; second, the structures of liquids and the interfacial structures between two liquids are not completely understood. Consequently, at present, it is necessary to apply semi-empirical approaches to interfacial free energy problems, defining the surface free energy and surface tension concepts exclusively in thermodynamics terms.

In practice, the need for interfacial investigation and measurements arises whenever immiscible liquids – those incapable of mixing – reside within the same vessel. It is common experience to see the lighter liquid material rise to the top and the heavier liquid material settling at the bottom of the container. Many processes of everyday life are controlled by the interactions occurring at the interface between two immiscible liquids: the stability of emulsions mainly depends on the interaction of surfactants at oil–water interfaces; solvent extraction and phase transfer catalysis rely on the optimization of reactions at the boundary between two liquids.

Liquid–liquid interfaces are most commonly found in the diverse separation processes that are essential to many sectors, including oil recovery and, more importantly for our purposes, in nanotechnology for the cleaning of works of art with multi-phase systems that will be described in the following chapters (see Chapters 6–9), e.g. emulsions and microemulsions.

Broadly speaking the interface may be complex: an emulsion layer with narrow and precise boundaries (a rag layer) may form between the two liquids, and more frequently a broader gradient of mixed liquid phases can be observed.³⁴  On the other hand, when a drop of an insoluble oil is placed on a clean water surface, it may behave in different ways: either it does not spread and it remains as a lens as shown in Figure 1.33(b) or it spreads as a monolayer, leaving excess oil as lenses in equilibrium.³⁵  A third situation may also occur: the liquid spreads as a thin uniform duplex film, a film which is thick enough for two interfaces to establish with characteristic surface tensions, as in Figure 1.33(a).

We may exemplify this statement introducing, in the case of oil on water, what Harkins³⁶  defined as the initial spreading coefficient, S_O/W:

Where γ_WA is the interfacial tension of the water–air interface and γ_OA and γ_OW the interfacial tension of the oil–air and oil–water interface, respectively. The various interfacial tensions are measured before mutual saturation of the liquids in question has occurred.

The condition for initial spreading is therefore that S_O/W≥0, which means that the oil adheres to the water more strongly than it coheres to itself. Impurities in the oil phase (e.g. oleic acid in hexadecane) can significantly reduce γ_OW to make S_O/W positive.

Impurities in the aqueous phase normally reduce S_O/W because γ_WA is lowered more than γ_OW by the dissolved substance, especially for low γ_OW. Hence, short-chain hydrocarbons such as octane will spread on a clean water surface but not on a contaminated surface. For example, when hexanol is spread on water, the initial spreading coefficient at 20 °C will be:

However, if we consider the mutual saturation of hexanol and water (as sketched in Figure 1.34) the water–air surface tension, γ_WA, is reduced owing to the presence of adsorption of hexanol molecules at the interface, and S_H/W decreases to:

The final state of the interface is now just unfavourable for spreading. This causes the initial spreading to be stopped, and can even result in the film retracting slightly to form very flat lenses, the rest of the water surface being covered by a monolayer of hexanol.

Liquid–liquid interfaces, and in particular water–hydrocarbon interfaces, are very common systems where cleaning of artefacts surfaces is concerned; for example, the removal of waxes from wall-paintings by means of oil-in-water microemulsions (see Section 9.5) relies on the behaviour of water–hydrocarbon interfaces stabilized by surfactants, which has to be properly evaluated.^36,37 

A comprehensive list of spreading coefficient estimation based on interfacial tension values can be found in the pertinent literature^38,39  and in physical chemistry handbooks.⁴⁰ 

The interfacial tension at the oil–water interface (γ_ow) used to determine S_OW as discussed above, can be measured experimentally by some of the methods mentioned in Chapter 4. Moreover, γ_ow is a crucial parameter that underlies the formulation of oil-in-water (o/w) systems. Change of the interfacial forces at the oil–water boundary can be achieved by adding small quantities of substances that, migrating and adsorbing at the interface, may induce a lowering in the contribution to surface tension. In this way, one can indeed disperse oil in water, or vice versa (see Chapters 6 and 8).

For instance, solvents with low γ_ow can be used to favour the formation of o/w systems formed by water and solvents with high γ_ow. Such systems can be very useful for the cleaning of undesired coatings from a variety of works of art. Some representative oil–water surface tension values are reported in Table 1.5.

Some of the solvents reported in Table 1.5 (hexane, ethyl ether, ethyl acetate) are used in restoration practice (see Chapter 5), while pentanol has been used for the formulation of o/w systems such as micellar solutions and microemulsions for the removal of natural and synthetic coatings from wall-paintings (see Sections 7.5 and 9.5).

We report here a comprehensive list of fundamental books on physical chemistry and colloid science, to support the content of this chapter and provide the reader with further insight:

• W. Adamson, Physical Chemistry of Surfaces, 5th edn, Wiley, New York, 1990.

• A. W. Adamson and A. P. Gast, Physical Chemistry of Surfaces, 6th edn, Wiley Interscience, New York, 1997.

• P. Atkins and J. de Paula, Atkins’ Physical Chemistry, 9th edn, Oxford University Press, 2009.

• R. S. Berry, S. A. Rice, J. Ross, Physical Chemistry, 2nd edn, Oxford University Press, 2000.

• K. S. Birdi, Surface and Colloid Chemistry, Principles and Applications, CRC Press, London, 2010.

• H. Y. Erbil, Surface Chemistry of Solid and Liquid Interfaces, Blackwell Publishing Ltd, Oxford, 2006.

• P. Hiemenez, Principles of Colloid and Surface Chemistry, 3rd edn, Marcel Dekker, New York, 1997.

• R. J. Hunter, Foundations of Colloid Science, 2nd edn, Oxford University Press, Oxford, 2001.

• G. Kumar and K. N. Prabhu, Review of non-reactive and reactive wetting of liquids on surfaces, Advances in Colloid and Interface Science, 2007, 133, 61–89.

• J. Lyklema, Fundamentals of Interface and Colloid Science, vols I–V, Academic Press, London, 2001.

• D. A. McQuarrie and J. D. Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997.

• J. van Oss, Interfacial Forces in Aqueous Media, Marcel Dekker, Ins., New York, 1994.

This chapter introduces the concept of an interface, outlining the background that supports the following parts of this book. Theoretical parts are integrated with practical examples, to cover a wide range of aspects and implications.

The main points include:

• The definition of surfaces, interfaces and surface tension.

• The concepts of adhesion and cohesion, and their theoretical implications in cleaning of works of art.

• The concepts of surface wettability and contact angle, and a case study concerning the conservation of the doors of the Florence Baptistery.

• Capillarity and its implication in conservation issues.

• A theoretical approach to chemisorption and physisorption of gases onto solid surfaces.

• The definition of the initial spreading coefficient and the interfacial tension of several solvents with water.

1. The surface energy of solids may differ greatly according to the environmental history of the sample itself. Would the surface energy of a clean and polished crystal surface be larger or smaller than the real surface of the same material? What would be the effect of defects roughness of the surface?

2. Would the adsorption of atmospheric gases and related contaminants be higher or lower on high energy surfaces? Consider three exposed clean surfaces of different materials: copper (γ=2000 mN m⁻²), gold (γ=1500 mN m⁻²) and iron (γ=2400 mN m⁻²). Assuming defect-free surfaces, which of the three surfaces will undergo most likely surface contamination through gas adsorption and further damaging reactions?

3. Measurements of adsorption isotherms of a gas on a solid surface present a significant hysteresis phenomenon (see Figure 1.32). Would we expect the appearance of capillary phenomena for that particular material?

4. The apparent contact angle of water on a surface is θ=52°, while the intrinsic contact angle determined for the ideal surface of the same component is 61°. Applying the Wenzel approach, what would the estimated roughness of the test surface be?

5. If the measured capillary rise of water (surface tension γ=72.5 mN m⁻¹) is 52 mm, what is the average diameter of a hydrophilic capillary tube? What would be the rise if the diameter were 0.5 mm? Assuming θ=0°, at what height is water expected to rise on a church wall if the average pore diameter of the material is 0.03 cm?

1. Real crystal surfaces may expose domains with different organization of atoms in space; this translates in significantly different surface energies for each exposed face. For example: surface energy is defined in Section 1.1.1 as with ɛ related to the bond strength, N_b the number of broken bonds and ρ_a the surface density of the atoms in that specific face. In the case of a face-centered-cubic crystal:

   

   Surface defects result generally in sites with large surface energy.

2. High surface energy sites are prone to adsorption of any contaminant that would minimize the total surface energy. Therefore, gold surfaces are less vulnerable to surface adsorption and degradation, as expected from everyday experience.

3. The shape of the desorption isotherm is shifted compared with the curve corresponding to the adsorption cycle. This reflects the porous nature of the solid under investigation; in fact, provided the pore dimensions are small enough, the vapour phase condenses inside the pores and desorption is hindered. Therefore, for such a solid important capillary rise phenomena are expected.

4. The Wenzel equation for rough surfaces relates the roughness factor, r, which is given by the ratio between real and geometrical surface area, to the apparent and intrinsic contact angle by the following equation: .

   Therefore, . The surface is moderately rough.

5. The height of capillary rise, h, is given by the following equation [eqn 1.18]:

   

   where γ is the surface tension of the liquid θ is the contact angle between the liquid and the capillary tube, is the density (=1000 kg m⁻³) and R is the radius of the liquid meniscus. Assuming null contact angle (=1), the radius of the capillary tube equals R and proper substitution yields:

   and R≈0.28 mm. If the diameter is 0.5 mm, the radius is 0.25 mm=0.25×10⁻³ m and  =59 mm. The expected water rise along a church wall if the average pore diameter of the material is 0.03 mm (R=0.015×10⁻³ m) is 0.989 m.