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Interfaces and Colliods, Part 1: Some General Concepts About Interfaces
Article 1 in a Series of New Articles

     The subject matter covered in these articles is concerned with the regions of our physical world that lie between two distinct and identifiable phases of matter. The bulk characteristics of the various phases will not be considered, except insofar as they affect interfacial interactions. The primary area of interest is that region in which the system undergoes a transition from one phase to another. For purposes of terminology, it is common practice to refer to that transition region as a “surface” or an “interface.” As will become evident, the exact definition of what constitutes a surface or an interface is not always unequivocal. While the two terms are often used to indicate distinct situations, they are in practice interchangeable, exact usage depending as much on personal preference as on any physically definable differences. In general, however, one usually finds that the term "surface" is applied to the region between a condensed phase (liquid or solid) and a gaseous phase or vacuum, while "interface" is more often used in reference to systems involving two condensed phases. Where complete generality is implied, "interface" is probably the better term.       

     The several types of interfaces that are recognized include: solid-vacuum, liquid-vacuum, solid-gas, liquid-gas, solid-liquid, liquid-liquid, and solid-solid. From a practical standpoint, solid- and liquid-vacuum interfaces are of little concern, except, perhaps, to NASA. They are most often encountered in the context of theoretical derivations, since the absence of a second phase simplifies matters greatly, or in studies of high-vacuum processes such as deposition, sputtering, etc. The true two-phase systems (assuming that a vacuum is not considered to be a true "phase") are the ones which are of most importance in practical applications and that are addressed in most detail here. A list of commonly encountered examples of these interfaces is given in Table 1.1.

Table 1.1: Common Interfaces of Vital Natural and Technological Importance

The Nature of Interfaces

     For two phases to exist in contact, there must be a region through which the intensive properties of the system change from those of one phase to those of the other, as for example in the boundary between a solid and a liquid. In order for such a boundary to be stable it must possess an interfacial free energy such that work must be done to extend or enlarge the boundary or interface. If such is not the case, and if no other external forces such as gravity act to separate the phases by density, etc., then no energy will be required to increase the interfacial area and random forces, including the uncertainty principle, Brownian motion or the chaotic butterfly, will distort, fold, and convolute the interface until the phases become mixed. In other words, if the interface does not have a positive free energy, it cannot exist as a stable boundary between two phases.

     In order to define an interface and show in chemical and physical terms that it exists, it is necessary to think in terms of energy, keeping in mind that nature will always act so as to attain a situation of minimum total free energy. In the case of a two-phase system, if the presence of the interface results in a higher (positive) free energy, the interface will spontaneously be reduced to a minimum - the two phases will tend to separate to the greatest extent possible within the constraints imposed by the container, gravitational forces, mechanical motion, etc. If the condition or composition of the system is altered, the energetic situation at the interface may also be altered, possibly producing a lower interfacial energy or some other effect that results in an increase in the time required for complete phase separation. That is, the change may alter the energetic drive to phase separation or it may alter the rate at which the phase separation occurs (i.e., its kinetics), or both. Overall, the interfacial energy will still be positive, but the changes caused by the alteration may prolong the "life" of any "excess" interfacial area. Such an effect may be beneficial, as in the case of a cosmetic emulsion, or detrimental, as in a petroleum-sea water emulsion. The important point is that although thermodynamics is almost always working to reduce interfacial area, we have access to tools that allow us to control, to some extent, the rate at which area changes occur.

     In interface and colloid science the term "stable" is or can be a relative term. One must always have clearly in mind just what is intended by the term in a given situation. Our "chemical" world is one controlled by both thermodynamics and kinetics, so that even if a system is thermodynamically unstable (i.e., diamond), it may require a rather long time for it to reach its most stable configuration (graphite). Such systems may be considered kinetically stable, although they are also sometimes referred to as being "metastable." While thermodynamics is an essentially irresistible drive to a lower energy state, we can sometimes use kinetics as a tool to slow that drive for periods of time sufficient to achieve a particular technological goal. As will be seen in articles to follow, that “tool” is of vital importance in many applied interfacial and colloidal systems.

     There are innumerable practical situations in which the energetic balance of interfacial regions must be controlled in order to make use of the unique characteristics of a system. The primary purpose of this article is to present in a “bare bones” way some fundamental concepts related to interfaces and illustrates how those concepts can (in principle) be employed to manipulate the characteristics of systems to achieve a desired or desirable result.

Surface Free Energy

     Before beginning any discussion of interfaces, it is important to have a clear concept of just what is meant by surface free energy. The unique characters of interfaces arise from the fact that atoms and molecules located in that region usually possess energies and reactivities significantly different from those of the same species in a bulk or solution situation.

     If one visualizes an atom or molecule in a bulk phase, it can be seen that, on average, the unit experiences a uniform force field due to its interaction with neighboring units (Figure 1.1a). If the bulk phase is divided isothermally and reversibly in vacuum along a plane that just touches the unit in question (Figure 1.1b), and a distance H separates the two new faces the forces acting on the unit are no longer uniform. Instead, it will continue to "feel" the presence of the adjacent units in the adjoining bulk phase, while having less interaction with those units being removed in the separated section.

     Because the unit at the new interface is in a different energetic environment relative to its nearest neighbors, its total free energy will be different. Since the interactions in the bulk phase produce a net lowering of the free energy of the units, the removal of those interactions results in an increase in the free energy of the units at or near the interface.

     The net increase in the free energy of the system will be proportional to the area, A, of new interface and the density (i.e., number) of interfacial units created. The actual change in system free energy will also depend on the distance of separation, since unit interactions will generally fall off by some inverse power law. When the two new interfaces are separated by what can be termed practical infinity, the free energy of the system becomes constant. The "additional" energy is termed the “surface free energy” or more accurately the "excess” surface free energy. When the term “specific” excess surface free energy is used it refers to energy per unit area, usually in mJ m^-2. It should be remembered that the excess free energy is not equal to the total free energy of the system, but only that part resulting from the presence of the interface.

     Obviously atoms or molecules at an interface will experience a net positive inward (i.e., into the bulk phase) attraction normal to the surface, the resultant of which will be a lateral tension along the surface, giving rise to the concept of “surface tension.” For a flat surface, the surface tension may be defined as a force acting parallel to the surface and perpendicular to a line of unit length anywhere in the surface (Figure 1.2). The definition for a curved surface is somewhat more complex, but the difference becomes significant only for a surface of very small radius of curvature.

     Two different, but actually interchangeable, terms are used when making reference to interfaces. When one phase is a vacuum or gaseous, it is common to refer to “surface energy” or “surface tension”. When both phases are condensed, the terms “interfacial energy” or “interfacial tension” are used. The thermodynamic definition of surface tension for a pure liquid is given as

(1.1)

where A_H is the Helmholtz free energy of the system, W is the amount of reversible work necessary to overcome the attractive forces between the units at the new interface and bring about their separation to “practical” infinity, and A is the area of new interface formed. The proportionality constant s is termed the surface tension and is numerically equal to the specific excess surface free energy for the pure liquid at equilibrium.

     For two pure, mutually immiscible liquids having a flat interface the terms “interfacial tension” and “excess interfacial free energy” are defined based on the same concepts. Unlike atoms or molecules at a liquid-vacuum interface, those at a liquid-liquid interface experience attractions from units in the adjacent phase. Those interfacial interactions lower the net free energy of the system, so that the interfacial tension between two liquids will be less that that of the higher surface tension of the pair.  The specific excess interfacial free energy is dimensionally equivalent to and numerically equal to the interfacial tension.

     When one ventures into the realm of solid surfaces, the situation becomes less clear-cut. In principle, the same concepts of surface formation and surface energetics should apply. However, the special nature of solids - specifically the reduced mobility of the atoms or molecules - means that units at a freshly formed interface cannot re-accommodate themselves to their new situation and true equilibrium will not be obtained (at least over a reasonable time period), unlike in liquids where equilibrium is attained rapidly. The surface tension of a solid, therefore, will not usually be numerically equal to the specific excess surface free energy.

     The SI units of surface tension are mN m^-1, which can be interpreted as a two-dimensional analogue of pressure (mN m^-2). As a concept, then, surface (and interfacial) tension may be viewed as two-dimensional negative pressure acting along the surface as opposed to the usual positive pressures encountered in our normal experience. In liquid-vapor and liquid-liquid systems, the measurement of surface tension is a relatively easy task (with proper precautions, of course). For systems involving solid surfaces, life becomes much more difficult and the determination (or estimation) of surface tension and other thermodynamic quantities becomes very difficult and often very ambiguous.

The Work of Cohesion and Adhesion

     At this point it is convenient to introduce two terms related to Equation 1.1, namely, the “work of cohesion” and the “work of adhesion.” The work of cohesion, Wc, is defined as the reversible work required to separate two surfaces of unit area of a single material with surface tension s (Figure 1.3a). Based on the distinction between solid and liquid surfaces explained above, the definition applies strictly to liquid surfaces, although the concept is useful for solid surfaces as well. Since the process involves the creation of two unit areas of fresh surface, and since the work required for that process is the surface tension, the work of cohesion is

(1.2)

It should be remembered that Wc is a reversible thermodynamic function and represents a minimum amount of work for carrying out the process. Additional work may be expended in associated irreversible processes such as heat generation.

     Related to Wc is the work of adhesion, Wa₍₁₂₎, defined as the reversible work required to separate unit area of interface between two different materials (1 and 2) to leave two "bare" surfaces of unit area. The work is given by

(1.3)

where the subscripts refer to the two phases being separated, and the s's are the respective surface or interfacial tensions.

     The environment in which a fresh interface is formed may affect the actual excess surface free energy. If the interface is formed in a vacuum, there are no (or at least very few) atoms or molecules present to interact with the "exposed" interfacial units. Those units, therefore, can be considered to represent the highest energy situation relative to similar units in the bulk. If the interface is formed in the presence of an adjacent fluid phase (liquid or gas), the exposed units can, and almost always will, interact to some extent with units of the fluid phase, thereby losing some of the excess energy gained by virtue of their position. The stronger the interaction between interfacial units and the adjacent phase, the greater will be the reduction in excess surface energy.

      In some cases, such as liquid surface tensions, the difference between a vacuum and a vapor environment may be negligible. For many solid surfaces, however, the difference can be quite significant. For liquid-liquid and solid-liquid interfaces where significant interactions take place, the interfacial tension can be quite low. Even solid-solid interfaces can, over time, show the results of mutual attraction across an interface in the form of sintering or spontaneous weld or joint formation.

     Since the formation of new interface results in an increase in the free energy of the system, it should not be surprising that most systems will be thermodynamically driven to minimize interfacial area. A vivid illustration of the effect is that of a blob of liquid forming itself into an almost perfect sphere when left to its own devices - that is, when no mechanical agitation, gravitational effects, etc., are acting on it. The technological consequences of interfacial thermodynamics are far reaching. Our ability or inability to control interfacial thermodynamics makes its study such a technologically and economically important activity.

     Another interesting demonstration of the extent of the work necessary to form new surface area in a liquid is that of carefully placing a clean needle on the surface of pure distilled water. If properly handled, the needle will float, even though it has a density many times that of the water. In order for the needle to sink, it must penetrate the surface of the water, a process that involves increasing the interfacial area of the water with respect to both the vapor phase and the needle surface. The force inducing the needle to sink, of course, is its mass times the acceleration of gravity. Opposing it is the surface tension of the water.     

     The classical concept of surface tension is to think of the liquid surface as having a membrane under tension stretched across it and supporting the needle. The concept of the stretched membrane gave rise to the picture of a "surface of tension" running parallel to the interface along the bulk phase. In fact the operative phenomenon is really an energy term, so that the surface tension is more correctly a surface energy. The two terms are often interchanged and for liquids are, as we have seen, numerically equal. The units employed are different although dimensionally equivalent - milliNewtons per meter (mN m-1) in SI units (dynes per cm in older publications) for surface tension and milliJoules per meter2 (mJ m-2) (or ergs cm-2) for energy.

     Application of the same concept to solid surfaces is not quite as straightforward. While it is certainly true that the forces and resultant stresses experienced by atoms or molecules at the solid interface differ significantly from those in the bulk, those stresses will not usually be isotropic, as is (or is assumed to be) the case for more mobile liquid systems. Molecularly smooth interfaces are very much the exception in solids so that each atom or molecule may experience a different environment and therefore have a different excess energy. If one defines the surface tension of a solid in the same way as that of a liquid, the tension must be expected to depend on the number of surface units experiencing each “condition” with respect to the bulk material. For a crystalline material, it is necessary to consider the direction in the surface as well as its exact crystal structure. It should be immediately obvious that for a solid the idea of a homogeneous surface tension can become quite complicated and a completely satisfactory definition in those terms difficult to achieve. It is therefore more convenient (and more accurate) when talking about solid interfaces to speak directly in terms of energy and to avoid completely the concept of tensions. In that way many of the various conceptual problems associated with the normally heterogeneous nature of solid surfaces can be avoided.  

     In summary, the surface "energy" and "tension" for solids are not necessarily equivalent and the energy term is most often used. The concept of "tension" is best applied to the interface between two fluid phases, while "energy" is most appropriate with respect to systems involving at least one solid phase. In addition, for solid systems, the actual surface will not generally be molecularly smooth. Rather, it will be irregular with different surface units being located in distinct environments relative to their neighbors. As a result, the free energies of the surface units will vary and the total excess surface free energy will be history dependent and not uniform over the entire surface.

     While it is convenient to consider that the surface of tension exists in a narrow monomolecular region between two phases, experimental evidence indicates that contributions can arise from second, third, and possibly even deeper molecular layers. For that reason it is convenient at times to refer to a surface or interfacial “region” with the understanding that more than one molecular layer must be considered. That can be even truer for solid surfaces in which unit dislocations from equilibrium may be evidenced tens or hundreds of unit lengths into the “bulk” phase. Such an approach can sometimes cause "philosophical" problems in the discussion of an interface using certain models and mathematical approaches. In reality, however, since we still do not fully understand all aspects of molecular interactions in interfacial regions, it is best not to concern ourselves too much with such apparent contradictions. Nature is full of apparent contradictions resulting from our own ignorance of the true situation. For the time being we must use what tools we have that seem to work and hope for further enlightenment in the future.

Standard Reference States

     The simplified description of surface energy given above is far from sufficient to fully explain all of the surface and interfacial phenomena such as wetting, adhesion, and colloidal stability that are of theoretical and practical importance. In fact, depending on the specific situation, it is often necessary, or at least convenient, to approach the question of surface interactions from completely opposite points of view. For example, when one is considering a question of colloidal stability, in which the desired effect is to prevent two surfaces from interacting in an attractive way (or at least reduce such interactions to a significant extent), it is convenient to think in terms of imposing a barrier, either energetic or physical, between the two interacting species which prevents or inhibits the dispersed state from passing to the energetically more favorable state of phase separation. For the case of adhesion, on the other hand, it is convenient to think in terms of increasing the net attractive interactions between the interfaces to be joined, so that it may be conceptually easier to consider the situation in terms of decreasing the interfacial energy between the surfaces.

     In chemistry and physics it is customary to discuss energies with reference to some specified state. That is, instead of stating an absolute energy (which may be difficult or impossible to determine) for a system, the change in energy relative to a standard state is measured. For example, the preceding discussion of surface energy was given in terms of an initial state of zero separation distance between two surfaces, going to a state of some "infinite" separation distance, H. It may be more useful, however, to think in terms of an initial state of infinite separation and measure energy changes as a function of the approach of two surfaces. Because each situation has specific requirements there can be no set rules governing the choice of standard reference for all interfacial interactions. In each specific area of interest, it is important to define the starting point and be consistent throughput further operations.

The Molecular Nature of the Interfacial Region

     It has been stated that the free energy of an interface arises due to asymmetric forces acting on atoms or molecules at or in the boundary region between phases. While the quantitative nature of those forces will be addressed in Articles 4 and 5, it will be useful to develop the qualitative picture of the situation a bit more at this point. To begin with, let us assume that there are only three phases with which we need be concerned - solid, liquid, and vapor. We will for the moment neglect the vacuum "phase" and ignore the existence of the various classes of solids, including crystalline, quasi-crystalline, liquid crystalline, glass, and amorphous. In a practical context, the differences between the classes of solid surfaces cannot be ignored because that nature may greatly affect it surface properties. For now, however, we will attempt to keep life simple.

     When two phases are in contact there is a transition region of molecular dimensions in which the composition of the system changes from that of one phase to that of the other. In the case of a nonvolatile molecularly smooth solid surface in contact with an inert gas, the transition region will be essentially one molecule in thickness. That is, there will be a sharp boundary at which the composition will change abruptly from molecules of the solid to molecules of the gas. For a more common irregular surface, the transition region will reflect the physical irregularities of the surface.

     For a pure liquid in contact with its vapor, the transition will be much less abrupt, going from a molecular density corresponding to the bulk material, through a zone where the unit concentration gradually decreases until the density reaches that of the pure vapor. In such a case, the transition region may be found to be several unit diameters thick. At a mixed liquid-vapor interface, each component will have its own concentration profile depending on such factors as volatility and miscibility. For example, the vapor region directly adjacent to the liquid phase may have a higher concentration of liquid phase units that decreases (relative to other vapor phase components) with distance from the interface. A similar situation holds for the interface between two liquid phases with some finite mutual solubility. In fluid systems, critical phenomena require that the interfacial region become thicker as the temperature of the system is increased, until the point where the critical temperature is reached and the two phases cease to exist as such. That is, the interfacial transition region becomes less distinct as the physical differences between the two phases lessen until a single phase is obtained. Solid-liquid systems will also exhibit the concentration profiles similar to those noted above, although the details will depend on the solubility of the solid in the liquid (and vice versa).

     Quantitative details of the concepts introduced above will be given in later articles. As a beginning, however, it is important that one begins to get a “feel” for the nature of the beast one is to confront as a first step into the twilight zone.

By: Drew Myers, Chemistry Coordinator (read the author's Profile)
drewmyers@arnet.com.ar