Thermodynamic tension

The principal equation of elasticity theory is the equation of motion, which relates the total force per unit volume pui to the gradient of the thermodynamic tensions a, j and the body force per unit volume f, ... 

If the areal change remains small, then the difference in thermodynamic tension can be approximated by using the surface dilational elasticity m. 

It may be shown that tABdVAB equals the straining work done by the force, taken per unit reference volume. In static equihbrium and for ideal thermoelastic materials for which the stress has its static equilibrimn value at any moment this work adequately represents the change in stored energy, which justifies the name thermodynamic tension used for Iab by some authors. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

The topic of capillarity concerns interfaces that are sufficiently mobile to assume an equilibrium shape. The most common examples are meniscuses, thin films, and drops formed by liquids in air or in another liquid. Since it deals with equilibrium configurations, capillarity occupies a place in the general framework of thermodynamics in the context of the macroscopic and statistical behavior of interfaces rather than the details of their molectdar structure. In this chapter we describe the measurement of surface tension and present some fundamental results. In Chapter III we discuss the thermodynamics of liquid surfaces. 

It was made clear in Chapter II that the surface tension is a definite and accurately measurable property of the interface between two liquid phases. Moreover, its value is very rapidly established in pure substances of ordinary viscosity dynamic methods indicate that a normal surface tension is established within a millisecond and probably sooner [1], In this chapter it is thus appropriate to discuss the thermodynamic basis for surface tension and to develop equations for the surface tension of single- and multiple-component systems. We begin with thermodynamics and structure of single-component interfaces and expand our discussion to solutions in Sections III-4 and III-5. 

Figure III-l depicts a hypothetical system consisting of some liquid that fills a box having a sliding cover the material of the cover is such that the interfacial tension between it and the liquid is zero. If the cover is slid back so as to uncover an amount of surface dJl, the work required to do so will he ydSl. This is reversible work at constant pressure and temperature and thus gives the increase in free energy of the system (see Section XVII-12 for a more detailed discussion of the thermodynamics of surfaces).

Tolman [21] concluded from thermodynamic considerations that with sufficiently curved surfaces, the value of the surface tension itsc//should be affected. In reviewing the subject, Melrose [22] gives the equation... 

D. The Effect of Pressure on Surface Tension The following relationship holds on thermodynamic grounds [26, 27] ... 

We now come to a very important topic, namely, the thermodynamic treatment of the variation of surface tension with composition. The treatment is due to Gibbs [35] (see Ref. 49 for an historical sketch) but has been amplified in a more conveniently readable way by Guggenheim and Adam [105]. 

The equilibrium shape of a liquid lens floating on a liquid surface was considered by Langmuir [59], Miller [60], and Donahue and Bartell [61]. More general cases were treated by Princen and Mason [62] and the thermodynamics of a liquid lens has been treated by Rowlinson [63]. The profile of an oil lens floating on water is shown in Fig. IV-4. The three interfacial tensions may be represented by arrows forming a Newman triangle ... 

A. W. Neumann and J. K. Spelt, eds.. Applied Surface Thermodynamics. Interfacial Tension and Contact Angles, Marcel Dekker, New York, 1996. 

The variation of the integral capacity with E is illustrated in Fig. V-12, as determined both by surface tension and by direct capacitance measurements the agreement confrrms the general correctness of the thermodynamic relationships. The differential capacity C shows a general decrease as E is made more negative but may include maxima and minima the case of nonelectrolytes is mentioned in the next subsection. 

Good, van Oss, and Caudhury [208-210] generalized this approach to include three different surface tension components from Lifshitz-van der Waals (dispersion) and electron-donor/electron-acceptor polar interactions. They have tested this model on several materials to find these surface tension components [29, 138, 211, 212]. These approaches have recently been disputed on thermodynamic grounds [213] and based on experimental measurements [214, 215]. 

It is quite clear, first of all, that since emulsions present a large interfacial area, any reduction in interfacial tension must reduce the driving force toward coalescence and should promote stability. We have here, then, a simple thermodynamic basis for the role of emulsifying agents. Harkins [17] mentions, as an example, the case of the system paraffin oil-water. With pure liquids, the inter-facial tension was 41 dyn/cm, and this was reduced to 31 dyn/cm on making the aqueous phase 0.00 IM in oleic acid, under which conditions a reasonably stable emulsion could be formed. On neutralization by 0.001 M sodium hydroxide, the interfacial tension fell to 7.2 dyn/cm, and if also made O.OOIM in sodium chloride, it became less than 0.01 dyn/cm. With olive oil in place of the paraffin oil, the final interfacial tension was 0.002 dyn/cm. These last systems emulsified spontaneously—that is, on combining the oil and water phases, no agitation was needed for emulsification to occur. 

It is curious that he never conuuented on the failure to fit the analytic theory even though that treatment—with the quadratic fonn of the coexistence curve—was presented in great detail in it Statistical Thermodynamics (Fowler and Guggenlieim, 1939). The paper does not discuss any of the other critical exponents, except to fit the vanishing of the surface tension a at the critical point to an equation... 

Modem scaling theory is a quite powerful theoretical tool (appHcable to Hquid crystals, magnets, etc) that has been well estabUshed for several decades and has proven to be particularly useful for multiphase microemulsion systems (46). It describes not just iuterfacial tensions, but virtually any thermodynamic or physical property of a microemulsion system that is reasonably close to a critical poiat. For example, the compositions of a microemulsion and its conjugate phase are described by equations of the foUowiug form ... 

An inversion of these arguments indicates that release agents should exhibit several of the following features (/) act as a barrier to mechanical interlocking (2) prevent interdiffusion (J) exhibit poor adsorption and lack of reaction with at least one material at the interface (4) have low surface tension, resulting in poor wettabihty, ie, negative spreading coefficient, of the release substrate by the adhesive (5) low thermodynamic work of adhesion ... 

Many of these features are interrelated. Finely divided soHds such as talc [14807-96-6] are excellent barriers to mechanical interlocking and interdiffusion. They also reduce the area of contact over which short-range intermolecular forces can interact. Because compatibiUty of different polymers is the exception rather than the rule, preformed sheets of a different polymer usually prevent interdiffusion and are an effective way of controlling adhesion, provided no new strong interfacial interactions are thereby introduced. Surface tension and thermodynamic work of adhesion are interrelated, as shown in equations 1, 2, and 3, and are a direct consequence of the intermolecular forces that also control adsorption and chemical reactivity. 

Physical Properties. Sulfur dioxide [7446-09-5] SO2, is a colorless gas with a characteristic pungent, choking odor. Its physical and thermodynamic properties ate Hsted in Table 8. Heat capacity, vapor pressure, heat of vaporization, density, surface tension, viscosity, thermal conductivity, heat of formation, and free energy of formation as functions of temperature ate available (213), as is a detailed discussion of the sulfur dioxide—water system (215). 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

PDMS based siloxane polymers wet and spread easily on most surfaces as their surface tensions are less than the critical surface tensions of most substrates. This thermodynamically driven property ensures that surface irregularities and pores are filled with adhesive, giving an interfacial phase that is continuous and without voids. The gas permeability of the silicone will allow any gases trapped at the interface to be displaced. Thus, maximum van der Waals and London dispersion intermolecular interactions are obtained at the silicone-substrate interface. It must be noted that suitable liquids reaching the adhesive-substrate interface would immediately interfere with these intermolecular interactions and displace the adhesive from the surface. For example, a study that involved curing a one-part alkoxy terminated silicone adhesive against a wafer of alumina, has shown that water will theoretically displace the cured silicone from the surface of the wafer if physisorption was the sole interaction between the surfaces [38]. Moreover, all these low energy bonds would be thermally sensitive and reversible. 

The capillary filling of CNTs is basically and usually described using macroscopic thermodynamic approximations. For example, Dujardin et al. [10] concluded that the surface-tension threshold value for filling a CNT was 100-200... 

A typical example of an ideal polarizable interface is the mercury-solution interface [1,2]. From an experimental point of view it is characterized by its electrocapillary curve describing the variation of the interfacial tension 7 with the potential drop across the interface, 0. Using the thermodynamic relation due to Lippmann, we get the charge of the wall a (-a is the charge on the solution side) from the derivative of the electrocapillary curve ... 

First we look at the simpler case of the shrinking of a single cluster of radius R at two-phase coexistence. Assume that the phase inside this cluster and the surrounding phase are at thermodynamic equilibrium, apart from the surface tension associated with the cluster surface. This surface tension exerts a force or pressure inside the cluster, which makes the cluster energetically unfavorable so that it shrinks, under diffusive release of the conserved quantity (matter or energy) associated with the order parameter. 

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