Surface-tension

Surface science is an important branch of physical organic chemistry that studies the behavior and characteristics of molecules at or near a surface or interface. The interface can form between solids, liquids, gases, and combinations of these states. Complex apparatus has been developed to identify and quantify surfaces and interfaces. Polymer surfaces are of special interest in industrial and biological applications examples of the latter include dental implants and body part prosthetic devices. Modification of surfaces of these devices allows formation of controlled interfaces to achieve characteristics such as bondability and compatibility. 

Adhesion is an interfacial phenomenon that occurs at the interfaces of adherends and adhesives. This is the fact underlying the macroscopic process of joining parts using adhesives. An understanding of the forces that develop the interfaces is helpful to the selection of the right adhesive, proper surface treatment of adherends, and effective and economical processes to form bonds. This chapter is devoted to the discussion of the thermodynamic principles and work of adhesion that quantitatively characterize surfaces of materials. 

Two solid or liquid phases in contact have atoms/ molecules on both sides of an imaginary plane called the interface. The interfacial particles differ energetically from those in the bulk of each phase due to being on the boundary of the respective phase and interacting with the particles of the other phase. The composition and energy vary continuously from one phase to the other through the interface. This region has a finite thickness, usually less than 0.1 p,m.  

Surface tension is defined as the work required to increase the area of a surface isotherTnally and reversibly by unit amount. Surface tension (y) is expressed as surface energy per unit area and alternatively as force per unit length. Surface tension of liquids can be measured directly and expressed in the units of work or energy per unit area (erg/cm ), which is then simplified (erg/cm = dyne.cm/cm = 

Handbook of Adhesives and Surface Preparation, ed. Sina Ebnesajjad. DOI 10.1016/B978-1-4377-4461-3.10003-3 2011 Elsevier Inc. All rights reserved. 

Surface tension is usually predicted using group additivity methods for neat liquids. It is much more difficult to predict the surface tension of a mixture, especially when surfactants are involved. Very large molecular dynamics or Monte Carlo simulations can also be used. Often, it is easier to measure surface tension in the laboratory than to compute it. 

Surface tension plays a significant role in the deformation of polymers during flow, especially in dispersive mixing of polymer blends. Surface tension, as, between two materials appears as a result of different intermolecular interactions. In a liquid-liquid system, surface tension manifests itself as a force that tends to maintain the surface between the two materials to a minimum. Thus, the equilibrium shape of a droplet inside a matrix, which is at rest, is a sphere. When three phases touch, such as liquid, gas, and solid, we get different contact angles depending on the surface tension between the three phases. 

The wetting angle can be measured using simple techniques such as a projector, as shown schematically in Fig. 2.54. This technique, originally developed by Zisman [73], can be used in the ASTM D2578 standard test. Here, droplets of known surface tension, at are applied to a film. The measured values of cos / are plotted as a function of surface tension, at, as shown in Fig. 2.55, and extrapolated to find the critical surface tension, ac, required for wetting. 

For liquids of low viscosity, a useful measurement technique is the tensiometer, schematically represented in Fig. 2.56. Here, the surface tension is related to the force it takes to pull a platinum ring from a solution. Surface tension for selected polymers are listed in Table 2.12 [71 ], for some solvents in Table 2.13 [58] and between polymer-polymer systems in Table 2.14 [71], 

Surface Tension.—Both the work a required for the formation of unit surface and the heat development q which is associated with the disappearance of unit surface (without doing work) must, at low temperatures, be equal to one another and independent of the temperature. 

Coefficient of Magnetization.—As was shown by Warburg in discussing some observations made by W. Thomson in 1878, the law for the magnetization of paramagnetic bodies under the influence of a field of intensity k is 

Here m is the magnetic moment per unit mass produced by the magnetic force 1, and M is the heat absorbed in the process. The Second Law gives 

In agreement with this, Oosterhuis f showed that even substances which follow Curie s Law down to low temperatures deviate from it when the cooling is sufficiently intense, in a direction such that the susceptibility begins to be independent of temperature he attempted to indicate an explanation of this behaviour based on molecular theory. 

Surface tension is an important determinant of the surface and adhesion properties of polymers. In both solids and liquids, the forces associated with molecules inside the material are balanced because each molecule is surrounded on all sides by like molecules. On the other hand, molecules at the surface are not completely surrounded by the same type of molecules, generating unbalanced forces. There- 

When two condensed phases are in close contact, the free energy at the interface is called the interfacial energy. Interfacial energy and surface energy in polymeric materials control adhesion, wetting, printing, surface treatment, and fogging. 

Surface tension appears to depend on solvent composition but its dependence on the solution concentration is negligible. Different solvents have different surface tensions. However, a solvent with a lower surface tension will not necessarily always be more suitable for electrospinning. Generally, surface tension determines the upper and lower boundaries of the electrospinning window if all the other variables are held constant. The formation of droplets, bead and fibres can be driven by the surface tension of the solution, while a lower surface tension of the spinning solution favours electrospinning at lower electric fields. 

Surface tension, wetting and capillarity are phenomena acting only at interfaces between fluids (i.e., liquid-gas, or hquid-hquid) while wetting occurs between solids and fluids (i.e., solid-gas, or solid-liquid). Actually, the system must be able to warp in order to minimize its surface energy. Hence capillarity concerns those systems exhibiting mobile interfaces. Usually capillarity is concerned with meniscus and liquid drop studies or soap films. 

Therefore surface tension can be regarded as a force per unit length or energy per unit area  

It is important to note that in practice the wire diameter must be taken into account because it forms a slab of liquid composed of two soap films. Hence the work required is  

On the other hand, the decrease in surface energy is compensated by an increase in the volume energy due to pressure against the wall of the bubble. Therefore, the work variation due to the pressure differential is given by  

At equilibrium, both energy variations are equal, dG = dH, therefore we obtain the following relation  

Surface tension is the force between molecules at the surface of a Uquid that tends to hold the molecules on the surface. (In physics, the word tension refers to a kind of force.) The relative amount of surface tension in a liquid is determined directly by the strengths of the forces of attractions between molecules of that liquid. Nonpolar liquids have almost no surface tension water has a very high surface tension because of hydrogen bonding. 

The surface tension of water is responsible for the spherical shape of rain drops and the ability of water to form beads on a freshly waxed surface. Wax is a nonpolar substance, so there is almost no force of attraction between water molecules and wax molecules. The water molecules are much more strongly attracted to other water molecules, hence the beads. Again, water s high surface tension is anomalous. 

Surface tension is the uneven force on molecules at the surface of a liquid that tends to pull molecules back towards the liquid s interior. 

Surface tension and its temperature coefficient are indispensable to describe surface-tension-driven flow at the silicon melt surface during crystal growth. The existence of the surface-tension-driven flow, i.e. the Marangoni flow, of molten 

Przyborowski etal. [79] applied the levitation technique for the first time to measure the surface tension of molten silicon and reported a high level of surface tension at the melting temperature and a steep temperature dependence as a = 783.5-0.65(T-1410) mN/m. The rather large absolute value of temperature 

In this model, two kinds of chemical equilibria are considered, as follows Si + Oj02 = Si02a, OtsiO = 1/2, 0tsiO2 = 1-0, 

Surface tension is a direct measurement of intermolecular forces. The tension in surface layers is the result of the attraction of the bulk material for the surface layer and this attraction tends to reduce the number of molecules in the surface region resulting in an increase in intermolecular distance. This increase requires work to be done, and returns work to the system upon a return to a normal configuration. This explains why tension exists and why there is a surface free energy. 

The surface tension of a liquid is mainly controlled by the intermolecular interaction among the molecules. Thus, it can be determined directly from the properties of the molecule. However, the surface tension of the solid surface is affected by its structure and roughness. When the surface is rough enough to keep gases or vacuum on it, the mean polarizability becomes very low. The water droplets on such a rough surface contact the solid 

This section discusses how the fluorine atom influences the physical and physicochemical properties of organic fluorine compounds. One of the most important factors for a better understanding of such properties would be the low electronic polarizability (refractive index) of the molecules. Of course, we cannot disregard other effects such as the strong electron-withdrawing effect and stiff nature of the perfluoroalkyl moiety. 

Fluorocarbon chains are stiffer than hydrocarbon chains 

Amodel experiment is shown here to clarify the stiffness of the fluorocarbon chains [2 ]. Diester 1 with two pyrene units shows an additional broad fluorescence, characteristic of the intramolecular pyrene excimer (425-600 nm)(Chart A). Meanwhile, diester 2 with two pyrene units separated with a QF 7 segment and 3 and 4 with one pyrene unit show only a weak emission in the region of 425-600 nm (Chart B). Since the excimer arises from the intramolecular interaction of two pyrene units, no excimer from 2 indicates that there exists no intramolecular interaction between pyrene emits in 2, demonstrating that the stiffness of the fluorocarbon chains does not allow the intramolecular interaction. 

and Smart, B.E. (1990) /. Am. Chem. Soc. 112, 2821-2823. Charts A and B were reprinted from [2] with permission from the American Chemical Society. 

The surface tension of paint solvents is of importance for the rate of evaporation, for the formation of the coating surface, and as for the wetting of the substrates, extenders, and pigments. 

The surface tension of a solvent is related to the cohesive energy density and internal pressure of the liquid. A relationship can be derived between the solubility 

The vapor density is the mass of solvent vapor per cubic meter of air (kg/m ) that is in equilibrium with the liquid at 101.3 kPa. The vapor density thus corresponds to the solvent content in the atmosphere at saturation and is temperature dependent. The relative vapor density of solvents 4 is referred to the density of air and can be calculated according to  

In the ideal case, the relative vapor density is temperature independent. Relative 

The surface tension indicates to which extent a liquid is prone to form drops. In process simulation, its role is comparatively small it is used for hydrodynamic calculations of packings. Its most important application is the calculation of capillary heads, which are directly proportional to the surface tension [89]. 

The surface tension can be correlated with the extended Watson equation 

The surface tension can be estimated by the Brock-Bird-Miller equation, which is based on the corresponding states principle [90]  

Estimate the surface tension of bromobenzene at T = 323.15 K with the Brock-Bird-Miller equation. The given data are 

Estimate the surface tension of a mixture of nitromethane (1) and benzene (2) with a mole fraction X] = 0.6 at T = 298 K using the mixing rule (3.162). The influence of the vapor in Eq. 3.162 should be neglected due to the low pressure. The given data are 

The surface tension of water supports this water stricter. The nonpolar surfaces of its feet also help to repel the water. 

The shape of a soap huhhie is due to the inward force (surface tension] that acts to minimize the surface area. 

Droplets of mercuiy lying on a glass surface. The small droplets are almost spherical, whereas the larger droplets are flattened due to the effects of gravity. This shows that surface tension has more influence on the shape of the small (lighter) droplets. 

The surface tension of a liquid/vapor or liquid/liquid interface can be calculated readily from MD or MC simulations. The goal of these calculations has typically been to test the validity of the force fields utilized, since experimental data on surface tension are readily available. As discussed earlier, the force fields used in simulations of interfacial systems are often optimized to reproduce bulk 

Several approaches for calculating the surface tension have been developed and are briefly summarized here. The fundamental definition of the surface tension y depends on the statistical mechanical ensemble used. For example, at constant N, V, T  

Other approaches for computing the surface tension start from the statistical mechanical expression for the Helmholtz free energy or for the pressure. The Kirkwood-Buff formula for the surface tension of a liquid/vapor interface of an atomic liquid described by the pair potential approximation is  

In the Irving and Kirkwood method the surface tension is expressed as the integral over the difference between the local components of the pressure tensor 

It is important to point out that being an equilibrium property, the surface tension can be calculated in a molecular dynamics or Monte Carlo simulation. The force calculations are of course already done in the MD code, but the calculation of the potential energy derivatives needs to be added to the MC code if the Kirkwood-Buff or Irving-Kirkwood methods are used. 

The surface tensions a of many molten salts have been compiled by Janz and coworkers [3, 214, 236] as functions of the temperature and the data have been supplemented subsequently in several other publications [138, 237—242]. The values diminish linearly with increasing temperatures and are compared in Table 3.17 at a suitable corresponding temperature, 1.1 Pm according to Reiss et al. [138]. For alkali metal halides, excepting the lithium salts, the surface tension at that temperature was correlated with the cube of the melting point [138]. 

The surface tensions r at 1.1 Pm of a large number of highly ionic molten salts of different types, 1 1, 1 2, 2 1, correlate well with the cohesive energy densities ced of the salts. Table 3.12, as shown by Marcus in Fig. 3.4 [156]. One line pertains to 45 salts with univalent anions  

Although empirical, correlation (3.38) has some theoretical basis as shown for organic liquids and molten metals [242]. For a definite proportionality between a and ced to hold, a dimensionally correct relationship requires the former to be divided by a length, e.g., Essentially a similar linear dependence of and ced was found as (3.38) (rcon = 0.9443), due to the limited variability of which 

Many models have been proposed in the literature, but most of them pertain only to the alkali metal halides. A simplified corresponding states correlation for the alkali metal halides (except Rbl) was suggested by Harada et al. [141], rewritten as  

A model by Yajima et al. [224] for the molten alkali metal halides that involves charge electroneutrality near the surface was also capable of the prediction of the surface tensions, and these were deemed to be nearer the experimental values than those according to the corresponding states model values in [138] and [141]. 

The high surface tension of water keeps the water strider from sinking. 

For any given substance, viscosity decreases with increasing temperature. Octane, for example, has a viscosity of 7.06 X 10 kg/m-s at 0 °C and 4.33 X 10 kg/m-s at 40 °C. At higher temperatures the greater average kinetic energy of the molecules overcomes the attractive forces between molecules. 

Because spheres have the smallest surface area for their volume, water droplets assume an almost spherical shape. This explains the tendency of water to bead up when it contacts a surface made of nonpolar molecules, like a lotus leaf or a newly waxed car. 

We conclude that the surface tension and its derivatives with respect to quantities characteristic of the bulk phases are independent of the choice of the dividing surface for a plane interface. 

In this section we present relationships for the derivatives of the surface tension with respect to various intensive properties of the system. We restrict our considerations to systems in which the phases a and p are fluid systems and in which the interface is planar. 

There are r degrees of freedom in the system of interest, and the right-hand side of Eq. (10-55) contains the variations of r -l- 1 quantities. Thus, the restrictions of Eq. (10-52) must be taken into account when computing derivatives of y. 

The partial derivative of y with respect to T at constant is given by 

If we assume that phase is a vapor phase and phase a is a liquid phase and T Tc, the critical temperature, then 

The direction of the surface tension is parallel to the surface and perpendicular to the cut. The surface tension can also be thought of as the energy in Joules per square meter (J/m ) that is required to create a unit area of new surface. To create an additional amount of surface A, the required energy E would be 

As a numerical example consider water (y = 7.27 x 10 N/m) at a 10 pm nozzle as might be used in an inkjet printing device, as will be discussed later in this chapter. The pressure drop AP would be 1.45 x 10 N/m, or 0.14 atm. 

Water was a very high surface tension, considerably higher than the organic solvents used in solvent borne systems as shown in Table 7-3. This high surface tension explains why water has difficulty in wetting metal surfaces. 

The ease of wetting of a solid substrate may be determined by means of critical surface tension, this is defined as the highest surface tension liquid which will wet the surface. The critical tensions of some common substrates in dynes/cm are given in Table 7-4. 

TABLE 7-4 CRITICAL SURFACE TENSION OF SOME SUBSTRATES 

From Table 7-4 it can be seen that water will not wet Teflon, tinplate or steel but may wet glass. In order for water to wet the other substrates, the surface tension of the water must be reduced by the inclusion of surface tension modifiers, which are often termed wetting agents. 

Water has an extremely high surface tension, which is evident at an interface between water and air and is another result of the strong intermolecular forces in water. Surface tension can be defined as the force per unit length that can pull perpendicular to a line in the plane of the surface. Because of its high surface tension, water can support a steel pin or needle carefully placed on its surface. The surface tension at such an air-water interface is 0.0728 N m-1 at 20°C (see Appendix I for values at other temperatures). Surface tension is also the amount of energy required to expand a surface by unit area —surface tension has the dimensions of force per unit length and also of energy per unit area (IN m-1 = 1 N m m-2 = 1 J m-2). 

The surface tension of an aqueous solution usually is only slightly influenced by the composition of an adjacent gas phase, but it can be greatly affected by certain solutes. Molecules are relatively far apart in a gas — dry air at 0°C and one standard atmosphere (0.1013 MPa, 1.013 bar, or 760 mmHg) contains 45 mol m-3 compared with 55,500 mol m-3 for liquid water — so the frequency of interactions between molecules in the gas phase and those in the 

For a compound to be qualified as a surfactant, it should also exhibit surface activity. It means that when the compound is added to a liquid at low concentration, it should be able to adsorb on the surface or interface of the system and reduce the surface or interfacial excess free energy. The surface is a boundary between air and liquid and the interface is a boundary between two immiscible phases (liquid-liquid, liquid-solid and solid-solid). Surface activity is achieved when the number of carbon atoms in the hydrophobic tail is higher than 8 [3]. Surfactant activities are at a maximum if the carbon atoms are between 10 and 18 at which level a surfactant has good but limited solubility in water. If the carbon number is less than 8 or more than 18, surfactant properties become minimal. Below 8, a surfactant is very soluble and above 18, it is insoluble. Thus, the solubility and practical surfactant properties are somewhat related [1]. 

In order to understand how surfactant reduces surface and interfacial tension, one must first need to understand the concept of surface and interfacial tension. 

The attractive forces between molecules in the bulk liquid are uniform in all directions (zero net force). However, the molecules at the liquid surface cannot form uniform interaction because the molecules on the gas side are widely spaced and the molecular interactions are mainly between surface molecules and the subsurface liquid molecules (non-zero net force). As a result, the molecules at the liquid surface have greater free potential energies than the molecules in the bulk liquid. This excess free energy per unit area that exists in the surface molecules is defined as surface tension (y). Surface tension is a thermodynamic property and can be measured under constant temperature and pressure and its value represents 

As seen in Table 2.2, surface tension of the substances decreases with increasing temperature because increasing temperature reduces the cohesive energy between molecules. At the critical temperature, surface tension becomes zero. For example, the critical temperature for chloroform is 280°C [11]. 

The surface tension of water at 20°C (72.8 dyne cm-1) is higher than the surface tension of chloroform (27.14 dyne cm-1) but lower than the surface tension of mercury (476 dyne citT1). This indicates that the attractive forces between the water molecules are stronger than the attractive forces between the chloroform molecules but weaker than the attractive forces between the mercury molecules. 

4 Intermolecular Forces In Action Surface Tension, Viscosity, and Capillary Action 

The most important manifestation of intermolecular forces is the very existence of hquids and solids. In liquids, we also observe several other manifestations of intermolecular forces including surface tension, viscosity, and capillary action. 

A fly fisherman delicately casts a small fishing fly (a metal hook with a few feathers and strings attached to make it look like an insect) onto the surface of a moving stream. The fly floats on the surface of the water—even though the metal composing the hook is denser than water—and attracts trout. Why The hook floats because of surface tension, the tendency of liquids to minimize their surface area. 

Surface molecule interacts with only four neighbors. 

A A trout fly can float on water because of surface tension. 

Before we move to the discussion on surface tension, we wish to point out that our discussion on the optics of the lenses is brief. Interested readers are referred to the literature [1,2,4] for more information and detailed analyses. 

Surface tension is a property of the surface of a liquid that allows it to resist an external force caused by the cohesion of similar molecules. It is responsible for many behaviors of liquids. Surface tension has a unit of force per unit length. The Systeme International (SI) unit is the newton per meter (N/m) the commonly used centimeter-gram-second (cgs) unit is the dyne per centimeter (dyn/cm). 

In a bulk liquid, the molecules (A) are attracted equally in every direction by neighboring liquid molecules, resulting in a net force of zero. Such attractive forces between like liquid molecules are often called cohesive forces they can be viewed as residual electrostatic forces and called van der Waals forces. The molecules close to the surface (B) or at the surface (C) are not surrounded on all sides by other molecules and therefore are pulled inward (we have neglected the force exerted from the molecules in the air onto the liquid molecules as their force is much smaller). 

The inward pull creates some internal pressure and forces liquid surfaces to contract to minimal area. Surface tension is responsible for the shapes of liquid droplets. Although easily deformed, droplets of water tend to be pulled into spherical shapes by the cohesive forces of the surface layer. 

As a result of surface area minimization, a surface will assume the smoothest shape it can. Since any curvature in the surface shape results in greater area, a higher energy will also result. Consequently the surface will push back against any curvature in much the same way as a ball pushed uphill will roll back to minimize its gravitational potential energy. 

Except for mercury, water has the highest surface tension of all common liquids. The reason for the surface tension is the mutual attraction of water molecules the molecules on the surface are not surrounded by equal molecules in all directions and therefore, there is a net force acting into the 

High surface tension results in capillary phenomena, such as capillarity of water in the capillaries of soil and rocks, wetting ability, foam formation, and the stability of dust, small insects and pollen grains on the water 

A generalized three-parameter equation for surface tension, y, valid from the triple point to the critical temperature, (where y = 0), has been proposed [1922a]  

A force is required to extend a liquid surface. Surface tension, y, is defined as the reversible work, w, required to increase the surface of a liquid by a unit area  

Knowing the conditions under which this work is done, we can relate surface tension to other thermod5mamic properties. 

Similarly, surface tension can also be written in terms of Gibbs free energy change, dG. From the second law of thermod5mamics, we have  

An expression for surface tension can be obtained from this equation as given in Equation 18.90. The first three terms together inside the second bracket are the Gibbs free energy. 

Therefore, surface tension of a flat surface is the excess free energy per unit area. By differentiating Equation 18.89, we get  

Of the many methods available for measuring the surface tension of liquids (Findlay, 1973), the capillary rise and ring techniques are probably the most useful for general applications. 

In the capillary rise method, the surface tension, 7, of a liquid can be determined from the height, h, of the liquid column in a capillary tube of radius r. If the liquid completely wets the tube (zero contact angle). 

The ring technique, and its many variations, is widely used in industrial laboratories. Several kinds of commerical apparatus incorporating a torsion balance are available under the name du Noiiy tensometer. The method is simple and rapid, and is capable of measuring the surface tension of a pure liquid to a precision of 0.3% or better. 

The force necessary to pull a ring (usually of platinum or platinum-iridium wire) from the surface of the liquid is measured. The surface tension is calculated from the pull and the dimensions of the ring after the appropriate correction factors have been applied. 

It is often possible to predict the surface tension of non-aqueous mixtures of solvents by assuming a linear dependence with mole fraction. Aqueous solutions, however, generally show a pronounced non-linear behaviour and prediction is not recommended. 

For a liquid with known critical temperature and surface tension at one temperature, use the nomograph to estimate its surface tension at other temperatures. 

Surface tension for most liquids can be estimated for temperatures other than the ones given in the literature (usually 15 or 20°C) by using the following equation  

An Example. Determine the surface tension of benzene at 100°C. Its surface tension is 29 dynes/cm at 20°C and its critical temperature is 288.5°C. 

On the nomograph, find the point where the critical temperature line 1 for T = 288.5°C intersects the lower 

The measured surface tension for benzene at 100°C is 18.2 dynes/cm. Hence the error for the estimated value does not exceed 4.5% of the measured value. 

G2 = surface tension at temp. T2 Tc = critical temperature of the liquid 

Frisch and Frisch speculated that the minimum in surface tension might be due to a large entropic contribution to the reversible work of wetting. This, in turn, may have been caused by an elastic straining of the immediate surface layers near a critical point of inversion. One of the network components may have been leaving the interface, and the other migrating there at the minimum. 

It is usually difficult to find experimental values for surface tension for any but the more commonly used liquids. A useful compilation of experimental values is that by Jasper (1972), which covers over 2000 pure liquids. Othmer et al. (1968) give a nomograph covering about 100 compounds. 

If reliable values of the liquid and vapour density are available, the surface tension can be estimated from the Sugden parachor which can be estimated by a group contribution method, Sugden (1924). 

The vapour density can be neglected when it is small compared with the liquid density. The parachor can be calculated using the group contributions given in Table 8.7. The method is illustrated in Example 8.13. 

group or bond Contribution Atom, group or bond Contribution 

The surface tension of a mixture is rarely a simple function of composition. However, for hydrocarbons a rough value can be calculated by assuming a linear relationship. 

It is usually difficult to find experimental values for surface tension for any but the more commonly used liquids. A useful compilation of experimental values is that by 

Jasper (1972), which covers over 2000 pure liquids. Othmer et al. (1968) give a nomograph covering about 100 compounds. 

The vapor density can be neglected when it is small compared with the liquid density. 

Our previous discussions demonstrate the importance of the surface tension to our heuristic argument of the film stability, interpretation of the surface-enhanced or- 

To reduce the free energy contributed by the surface tension term, the molecules at the liquid crystal/vapor interface favor a layer structure. In the smectic phase, the outermost layers favor a better molecular packing than exists in the interior. The enhanced surface order has been reported for various liquid crystal phases, for example the surface SmA order on the bulk isotropic or nematic sample [50] the surface SmI order on a SmA film [47] the surface SmB gx order on a SmA film [45,48] the surface SmI on a SmC film [17,93] the surface B on a SmA film [49] the surface crystal E order on a SmBhex film [100]. Realizing the importance of the surface tension in characterizing the liquid crystal free-standing films, we 

Different values of surface tension have been obtained from the following three distinct groups of liquid crystal compounds  

2 Physical Properties of Non-Chiral Smectic Liquid Crystals 

The special features of liquid crystal freestanding films should offer a unique opportunity to give a critical examination of the principle of independent surface action. 

A is the cross-sectional area of the hole and m is the molecular mass. This is equal to the number of water molecules hitting a surface area A per second. Water at 25° C has a vapor pressure P of 3168 Pa. With a molecular mass m of 0.018 kgmol 1/6.02 x 1023mol 1 3 x 10 26kg, 107 water molecules per second hit a surface area of 10 A2. In equilibrium the same number of molecules escape from the liquid phase. 10 A2 is approximately the area covered by one water molecule. Thus, the average time a water molecule remains on the surface is of the order of 0.1 (j,s. 

Equation (2.2) is an empirical law and a definition at the same time. The empirical law is that the work is proportional to the change in surface area. This is not only true for infinitesimal small changes of A (which is trivial) but also for significant increases of the surface area AW = 7 AA In general, the proportionality constant depends on the composition of the liquid and the vapor, temperature, and pressure, but it is independent of the area. The definition is that we call the proportionality constant surface tension . 

The surface tension can also be defined by the force F that is required to hold the slider in place and to balance the surface tensional force  

Both forms of the law are equivalent, provided that the process is reversible. Then we can write 

The force is directed to the left while x increases to the right. Therefore we have a negative sign. 

The interfacial tensions between two liquid polymers of finite molecular weight are given in Table 13-2 and compared with the surface tensions of the individual polymers. It can be seen from Table 13-2 that the interfacial tensions are generally higher for increased polarity difference between the two polymers. However, the interfacial tensions are usually small. But the contact angles for polymer 1 on solid polymer 2 and vice versa can be very different. For example, the contact angle of poly(butyl methacrylate) on poly(vinyl acetate) is zero, but for poly(vinyl acetate) on poly(butyl methacrylate) it is 42°. 

The contact angles in a homologous series of liquids vary systematically with regard to a given substrate. It was found empirically that the cosine of this contact angle varies linearly with the surface tension of the liquid 

The critical surface tension of all known solid polymers is lower than the surface tension of water at 72 x 10 N/cm (Table 13-3). All polymers are therefore relatively poorly wetted by water. The critical surface tension of polymers containing fluorine is particularly low, and they are poorly wetted by oils and fats as well as by water. Oils, fats, and glycerol esters 

Actually, a soap film has two surfaces, so both the force and the work will be twice as large as indicated in Eq. (2.1). Surface tension has the units of /nf, or N/tn. In practice, they use units of mNm i (where m in front of N means milli, and the m after N means meter ). The surface tension of water at room temperature is 72 mNm V 

In emulsion polymerizations particularly, it may be of some interest to measure the surface tension of the polymerization. The surface tension can give an indication of whether or not micelles are present, which is important in particle nuclea-tion above the critical micelle concentration (CMC) [18, 19]. 

The on-line method used is usually the bubble pressure method. A dip tube is inserted below the liquid surface and bubbles are formed by compressed gas. Bubbles formed within a liquid are compressed by surface tension. The resulting pressure rises with decreasing bubble radius. This increased pressure, in comparison to the outside of the bubble, is used to measure surface tension. During the process of bubble formation and breakage, the pressure can be measured in the bubble. From the pressure oscillation the surface tension can be calculated. 

We will focus our attention on the physical origin and consequences of the phenomenon of surface tension. 

FIGURE 1.1. Drops and bubbles form perfect spheres. (From A Drop of Water A Book of Science and Wonder, by Walter Wick. Published by Scholastic Press, a division of Scholastic Inc. Photographs 1997 by Walter Wick. Reproduced by permission.) 

Bulk phases contact each other at an interface. The region near the interface differs in physicochemical properties from the bulk phase far from the interface. This difference gives rise to interfadal tension. In this section, the interfacial tension is discussed first in terms of mechanics and then thermodynamics. 

Let us take two homogeneous bulk phases a and (Fig. 8.1). The interfacial layer between them experiences a normal tension t parallel to the Y axis and varying with Z. The origin A is set up at an arbitrary point in the a phase. The only mechanical force is the pressure in the bulk phases, and the interfacial layer is subject to tension. Consider a rectangular plane 

the microscopic state of the interfacial layer determines both the value of the surface tension and the location of the surface of tension (Zy). 

Let us now consider the interfacial tension of a plane interface from the thermodynamic point of view. On the basis of the concept of Guggenheim, the Helmholtz free energy A of the entire system (phases a and j3 plus the interfacial layer) is expressed by the following equation  

For interfacial tension in this case, also, the Z axis is normal to the plane interface. The bottom (A) of the whole system is at Z = 0 in phase a and the top (B) is at Z = A in phase jS (Fig. 8.1). The quantity Cj(Z) is the mean molecular concentration per unit volume of component i at Z, and A,(Z) is the mean contribution of component i to. A at Z. Then, we have 

The attractive nature of intermolecular interactions means that a liquid will, in general, behave to maximize the number of interactions. One effect of this is that the number of molecules at the liquid s surface is minimized. Such surface 

Note that vapor pressure continues to increase past the boilingpoint. Familiar things like popcorn or pressure cookers rely on this fact. 

Molecules at the surface of a liquid have fewer neighbors, so they experience fewer attractive forces. 

Molecules In the bulk of a liquid have more neighbors, so they experience more attractive forces than do molecules at the surface. 

In engineering applications where surface tension can create problems, molecules called surfactants are often added to decrease the surface tension. Surfactants also rely on an understanding ofintermolecular forces in their design. 

Beaded nanofibers were produced from a water/PEO solution. Addition of ethanol to the water/PEO solution reduces the surface tension of the solution, and production of smooth PEO nanofibers can be obtained. High surface tension causes beaded fibers. On the other hand, smooth fibers without bead formation were seen in PVP/ ethanol solutions having a lower surface tension. Another way is to add a surfactant to the spinning solution. Surfactant contribution to the spinning solution decreases surface tension. An insoluble surfactant is also used to decrease the surface tension. In addition to solvents and surfactants, temperature is another factor for surface tension. In the pure liquid form, the surface tension of the liquid decrease with increasing temperature, as the equilibrium between the surface tension and the vapor pressure would decrease. At a certain (critical ] point, the interface between the liquid and the gas will disappear. 

Any contamination, especially by surfactants, will lower surface tension and lower surface free energy. Some surface tension values of common liquids and solvents are shown in the following Tables 1.2 and 1.3. 

Substance Surface Tension (xlO-3 J/m2) Viscosity (cP) (20°C) Vapor Pressure, Torr (20°C) Boiiing Point (°C) 

Source Adapted and collected from http //macro.lsu.edu/howto/solvents.htm 

The adhesion and uniformity of a film are also influenced by the forces that act between the coating formulation that is in solution form and the core surface of the film-coated surface. The measure of wetting behavior is the contact or wetting angle, which forms between a liquid droplet and the surface of the solid body to which it is applied. 

In microfluidics, surface effects play a dominant role. Surface effects are also known as capillary effects. The capillary has been named after the Latin word capillus for hair. This chapter presents some of the flow physics related to surface tension-dominated flows and their application to microdevices. 

The effects of surface and interfacial tensions give rise to many phenomena in the liquid behavior. But all complex physical-chemical interactions involved are not understood even today. The familiar examples of surface tension are  

The thin capillary tube in which liquid rises to a height greater than that of the pool in which it is placed. 

Break up into drops of a stream of water flowing out of a faucet. This physics is the basis of the ink-jet printer or gel encapsulationprocess to encase perfume or crystal or monoclonal antibodies. 

Liquid drop remaining stationary when placed on a solid surface or spreading of water drop when placed on a clean glass surface. 

Several of the physical properties of a liquid depend on the magnitude of its intermolecular forces. In this section we consider three snch properties surface tension, viscosity, and vapor pressure. 

A qnantitative measnre of the elastic force in the surface of a liquid is the surface tension, the amount of energy reqnired to stretch or increase the surface of a liquid by a unit area (for example, by 1 cm ). A liquid with strong intermolecnlar forces has a high surface tension. Water, for instance, with its strong hydrogen bonds, has a very high surface tension. 

Another illnstration of snrface tension is the meniscus, the curved surface of a liquid contained in a narrow tnbe. Fignre 12.8(a) shows the concave surface of water in a graduated cylinder. (You probably know from your laboratory class that you are to read the volume level with the bottom of the meniscus.) This is caused by a thin film of water adhering to the wall of the glass cylinder. The snrface tension of water causes this film to contract, and as it does, it pulls the water up the cylinder. This effect, known as capillary action, is more pronounced in a cylinder with a very small diameter, such as a capillary tube used to draw a small amount of blood. Two types of forces bring about capil- 

While inside a liquid, from all directions the same attractive forces act on the water molecules of the given example, at the interface of the water drop to the ambient air, such forces are not balanced. Thus, there is a force F directed to the inside of the drop, which tries to draw the water molecules away from the surface into the only inside of the drop. Consequently, the drop aims to reduce its surface, which results in the formation of the spherical/drop form. (The sphere is the geometrical form with the smallest ratio of volume and surface area.) 

Apart from liquids, also solids, such as metals, glasses and plastics have surface tension. Due to the stiffness of these materials, it is invisible to the eye, but metrologically determinable. Thus, with the application of the adhesive, two partners with different surface tensions are joined - depending on the material of the adherend and the adhesive. 

According to the laws of thermodynamics, the difference of surface tension between adherend and adhesive is decisive for the wettability of the system. The surface tension values are given in mN/m (milli Newton per meter) in the following order of magnitude  

From these values it is clear that the respective difference for metals compared to adhesives is rather large, while for plastics compared to adhesives it is rather small. In practice, this means  

The intermolecular attractions we have just discussed can help us understand many familiar properties of liquids. In this section we examine two viscosity and surface tension. 

The surface of water behaves almost as if it had an elastic skin, as evidenced by the ability of certain insects to walk on water. This behavior is due to an imbalance of intermolecular forces at the surface of the liquid. As shown in FIGURE 11.18, molecules in the interior are attracted equally in all directions, but those at the surface experience a net inward force. This net force tends to pull surface molecules toward the interior, thereby reducing the surface area and making the molecules at the surface pack closely together. 

On any surfece molecule, there is no upward force to cancel the downward force, which means each surfece molecule feels a net downward pull 

On any interior molecule, each force is balanced by a force pulling in the opposite direction, which means that interior molecules feel no net pull in any direction 

In this chapter we have focused on liquid-vapor equilibria. The same ideas can be applied to other phase equilibria. For example, the sublimation pressure of a gas over a solid can be computed from Equation (14.23) by replacing the enthalpy of vaporization with the enthalpy of sublimation. Now we consider another process of particle exchange, not between condensed phase and vapor, but between the interior and the surface of a liquid. 

Surface Tension Describes the Equilibrium Between Molecules at the Surface and in the Bulk 

A surface is defined as the boundary between a condensed phase and a gas or vapor. More generally, an interface is defined as the boundary between any two media. Surface tension is the free energy cost of increasing the surface area of the system. For example, when a water droplet is spherical, it has the smallest possible ratio of surface to volume. When the droplet changes shape, its surface gets larger relative to its volume. Water tends to form spherical droplets because deviations away from spherical shapes are opposed by the surface tension. Here is a model. 

The surface tension is defined as the derivative of the free energy with respect to the total area J4 of the surface, y = (dF/dJA)r,v,N- Because the lattice liquid 

262 Chapter 14. Equilibria Between Liquids, Solids, Gases 

The molecules or ions in the surface of a liquid or solid are in a different state of equilibriinn than those lying in a parallel plane beneath the surface since they lack the influence of particles on one side of the surface. This causes surfaces to try to extend. Small droplets of liquid tend to become spherical by virtue of this effect. The liquid property that measures the tendency for a surface to extend is called surface tension T and the dimensions of are [FLr. The corresponding quantity for a solid is called surface energy and also has the dimensions [FZ, ]. 

The surface tension of liquids gives rise to important forces only when thin Aims are involved. For example, this is the force which holds contact lenses in place on the surface of the eye, and which makes it possible to stack gage blocks in the workshop with negligible error. 

the pressure within the cylinder will be greater than in the air by an amount equal to the ratio of surface tension to the radius of the cylinder. 

The pressure within the meniscus will be less than that of the atmosphere since curvature of the meniscus will be negative. Pressure in the oil film is thus seen to be negative and equal to several atmospheres. This large negative pressure will tend to force the surfaces of the blocks together until the peaks of asperities on the two surfaces are in contact. 

Of the three states of matter, the liquid is the least understood at the molecular level. Because of the randomness of the particles in a gas, any region of the sample is virtually identical to any other. As you ll see in Section 12.6, different regions of a crystalline solid are identical because of the orderliness of the particles. Liquids, however, have a combination of these attributes that changes continually a region that is orderly one moment becomes random the next, and vice versa. Despite this complexity at the molecular level, the macroscopic properties of liquids are well understood. In this section, we discuss three liquid properties— surface tension, capillarity, and viscosity. 

To increase the surface area, molecules must move to the surface, thus breaking some attractions in the interior, which requires energy. The surface tension is the energy required to increase the surface area by a unit amount  

CHAPTER 12 Intermolecular Forces Liquids, Solids, and Phase Changes 

Substance Formula Surface Tension (J/m2) at 20 C Major Force(s) 

Diethyl ether CH3CH2OCH2CH3 1.7X10 - Dipole-dipole dispersion 

The (T of ethanol is 22.3 dyn cm-1 and that of pure water is 71.97 dyn cm-1 at 25°C the latter is the highest or ordinary solvents, varying only slightly with temperature. Any ethanol additions to water (o) therefore lower x0. The j of solids is measurably less than that of liquids. 

To measure the vapor pressure of a liquid, a tiny amount is injected into the barometer. 

When equal volumes of water, ethyl ether, and ethyl alcohol are placed in beakers and allowed to evaporate at the same temperature, we observe that the ether evaporates faster than the alcohol, which evaporates faster than the water. This order of evaporation is consistent with the fact that ether has a higher vapor pressure at any particular temperature than ethyl alcohol or water. One reason for this higher vapor pressure is that the attraction is less between ether molecules than between alcohol or water molecules. 

Substances that evaporate readily are said to be volatile. A volatile liquid has a volatile relatively high vapor pressure at room temperature. Ethyl ether is a very volatile liquid water is not too volatile and mercury, which has a vapor pressure of 0.0012 torr at 20°C, is essentially a nonvolatile liquid. Most substances that are normally in a solid state are nonvolatile (solids that sublime are exceptions). 

Have you ever observed water and mercury in the form of small drops These liquids form drops because liquids have surface tension. A droplet of liquid that is not falling or under the influence of gravity (as on the space shuttle) will form a sphere. Spheres minimize the ratio of surface area to volume. The molecules within the liquid are attracted to the surrounding liquid molecules, but at the liquid s surface, the attraction 

A water strider skims the surface of the water as a result of surface tension. At the molecular level, the surface tension results from the net attraction of the water molecules toward the liquid below. In the interior of the water, the forces are balanced in all directions. 

As we will see in Section 12.8, Ice Is less dense than liquid water because water expands when it freezes due to Its unique crystalline structure. 

A FIGURE 12.2 A liquid assumes the shape of its container Because the molecules in liquid water are free to move aroimd each other, they flow and assume the shape of their container. 

A FIGURE 12.3 Solids have a definite shape In a solid such as ice, the molecules are fixed in place. Flowever, they vibrate about fixed points. 

3 Intermolecular Forces in Action Surface Tension and Viscosity 

These simple experiments show that the air pressure inside the bubble is larger than atmospheric pressure, by an amount Ap and that the latter increases when the bubble radius r decreases. 

work is necessary to increase the area of a liquid film. The physical origin of this phenomenon is at the microscopic level work is required to bring molecules 

Mathematically the work necessary to increase the interfacial area by dA can be expressed as 

1 is valid for liquid/air, liquid/solid and liquid/liquid interfaces. 

For the Helmholtz free energy F and the enthalpy H we can obtain the following relations  

In this section we shall consider some elementary thermodynamics relations involving interfaces [4]. Since molecules at an interface are in a different environment from molecules in the bulk, their energies and entropies are different. Molecules at a liquid-air interface, for example, have larger Helmholtz free energy than those in the Bulk. At constant V and T, since every system minimizes its Helmholtz free energy, the interfacial area shrinks to its minimum possible value, thus increasing the pressure in the liquid (Fig. 5.4). 

The thermodynamics of such a system can be formulated as follows. Consider a system with two parts, separated by an interface of area A (Fig. 5.4). For this system we have, 

Thus surface tension 7 is the change of F per unit extension of the interfacial area at constant T, V and V . This energy is small, usually of the order of lO Jm . Since enlarging an interfacial area increases its free energy, work needs to be done. As shown in Fig. 5.5, this means a force/is needed to stretch the surface by an amount dx, i.e., the liquid surface behaves like an elastic sheet. 

The work done, (fdx), equals the increase in the surface energy, ydA = (jldx), in which I is the width of the surface (Fig. 5.5). We see then that the force per unit length (///) = 7. For this reason, 7 is called the surface tension . 

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Gibbs equation of surface concentration This equation relates the surface tension (y) of a solution and the amount (T) of the solute adsorbed at unit area of the surface. For a single non-ionic solute in dilute solution the equation approximates to... 

Qualitatively the equation shows that solutes which lower the surface tension have a positive surface concentration, e.g. soaps in water or amyl alcohol in water. Conversely solutes which increase the surface tension have a negative surface concentration. 

These surface active agents have weaker intermoiecular attractive forces than the solvent, and therefore tend to concentrate in the surface at the expense of the water molecules. The accumulation of adsorbed surface active agent is related to the change in surface tension according to the Gibbs adsorption equation... 

The surface tension is calculated starting from the parachor and the densities of the phases in equilibrium by the Sugden method (1924) J... 

For optimum combustion, the fuel should vaporize rapidly and mix intimately with the air. Even though the design of the injection system and combustion chamber play a very important role, properties such as volatility, surface tension, and fuel viscosity also affect the quality of atomization and penetration of the fuel. These considerations justify setting specifications for the density (between 0.775 and 0.840 kg/1), the distillation curve (greater than 10% distilled at 204°C, end point less than 288°C) and the kinematic viscosity (less than 8 mm /s at -20°C). 

Sugden, S. (1924), The variation of surface tension. VI. The variation of surface tension with temperature and some related functions . J. Chem. Soc., Vol. 125, p. 32. 

The capillary effect is apparent whenever two non-miscible fluids are in contact, and is a result of the interaction of attractive forces between molecules in the two liquids (surface tension effects), and between the fluids and the solid surface (wettability effects). 

Surface tension arises at a fluid to fluid interface as a result of the unequal attraction between molecules of the same fluid and the adjacent fluid. For example, the molecules of water in a water droplet surrounded by air have a larger attraction to each other than to the adjacent air molecules. The imbalance of forces creates an inward pull which causes the droplet to become spherical, as the droplet minimises its surface area. A surface tension exists at the interface of the water and air, and a pressure differential exists between the water phase and the air. The pressure on the water side is greater due to the net inward forces... 

On a microscopic scale (the inset represents about 1 - 2mm ), even in parts of the reservoir which have been swept by water, some oil remains as residual oil. The surface tension at the oil-water interface is so high that as the water attempts to displace the oil out of the pore space through the small capillaries, the continuous phase of oil breaks up, leaving small droplets of oil (snapped off, or capillary trapped oil) in the pore space. Typical residual oil saturation (S ) is in the range 10-40 % of the pore space, and is higher in tighter sands, where the capillaries are smaller. 

General hydrodynamic theory for liquid penetrant testing (PT) has been worked out in [1], Basic principles of the theory were described in details in [2,3], This theory enables, for example, to calculate the minimum crack s width that can be detected by prescribed product family (penetrant, excess penetrant remover and developer), when dry powder is used as the developer. One needs for that such characteristics as surface tension of penetrant a and some characteristics of developer s layer, thickness h, effective radius of pores and porosity TI. One more characteristic is the residual depth of defect s filling with penetrant before the application of a developer. The methods for experimental determination of these characteristics were worked out in [4]. 

Here a - surface tension pa - atmospheric pressure 9 - contact angle of crack s wall wetting by penetrant n - coefficient, characterizing residual filling of defect s hollow by a penetrant before developer s application IT and h - porosity and thickness of developer s layer respectively W - minimum width of crack s indication, which can be registered visually or with the use of special optical system. The peculiarity of the case Re < H is that the whole penetrant volume is extracted by a developer. As a result the whole penetrant s volume, which was trapped during the stage of penetrant application, imbibes developer s layer and forms an indication of a defect. 

Now consider some examples of the influence of sedimentation process upon PT sensitivity. Let us consider the application of fine-dispersed magnesia oxide powder as the developer. Using the methods described in [4] we experimentally determined the next characteristics of the developer s layer IT s 0,5, Re s 0,25 pm. We used dye sensitive penetrant Pion , which has been worked out in the Institute of Applied Physics of National Academy of Sciences of Belarus. Its surface tension ct = 2,5 10 N m V It can be shown that minimum width of an indication of magnesia powder zone, imbibed by Pion , which can be registered, is about W s 50 pm. Assume that n = 1. 

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. 

This is exact—see Problem 11-8. Notice that Eq. 11-14 is exactly what one would write, assuming the meniscus to be hanging from the wall of the capillary and its weight to be supported by the vertical component of the surface tension, 7 cos 6, multiplied by the circumference of the capillary cross section, 2ar. Thus, once again, the mathematical identity of the concepts of surface tension and surface free energy is observed. 

While Eq. 11-14 is exact, its use to determine surface tension from capillary rise experiments is not convenient. More commonly, one measures the height, h, to the bottom of the meniscus. 

The use of these equations is perhaps best illustrated by means of a numerical example. In a measurement of the surface tension of benzene, the following data are obtained ... 

The maximum bubble pressure method is good to a few tenths percent accuracy, does not depend on contact angle (except insofar as to whether the inner or outer radius of the tube is to be used), and requires only an approximate knowledge of the density of the liquid (if twin tubes are used), and the measurements can be made rapidly. The method is also amenable to remote operation and can be used to measure surface tensions of not easily accessible liquids such as molten metals [29]. 

Several convenient ways to measure surface tension involve the detachment of a solid from the liquid surface. These include the measurement of the weight in a drop falling from a capillary and the force to detach a ring, wire, or thin plate from the surface of a liquid. In this section we briefly describe these methods and their use. 

This is a fairly accurate and convenient method for measuring the surface tension of a liquid-vapor or liquid-liquid interface. The procedure, in its simpli-est form, is to form drops of the liquid at the end of a tube, allowing them to fall into a container until enough have been collected to accurately determine the weight per drop. Recently developed computer-controlled devices track individual drop volumes to = 0.1 p [32]. 

Here again, the older concept of surface tension appears since Eq. 11-22 is best understood in terms of the argument that the maximum force available to support the weight of the drop is given by the surface tension force per centimeter times the circumference of the tip. 

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