Surface tension of solids

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

Sacher E (1988) The determination of the surface tensions of solid films. In Ratner BD (ed) Surface characterisation of biomaterials, Elsevier, Amsterdam... 

A. Ya. Gokhstein, Surface Tension of Solids and Adsorption, Nauka, Moscow, 1976, p. 382... 

Ardizzone, S., Longhi, P., Mussini, T., Rondinini, S. J. Chem. Thermodyn. 8 (1976) 557. Gokhstein, A.Y. Surface Tension of Solids and Adsorption, Moseow Nauka, 1976. 

It can now be used for the extremely important purpose of calculating calcium sulphate and 4,000 dyne/cm. for barium sulphate. These figures entirely confirm the conclusion to which we have come on general grounds, that the surface tensions of solids must have high values. The applicability of the Ostwald-Hulett formula is limited, since it is based on Van t Hoff s equation for osmotic pressure, which only holds for small concentrations and, therefore, in the present case, for low solubilities. 

No method so far suggested for measuring the surface energy or surface tension of solids is satisfactory. 

Gokhstein, A. Ya. Surface tension of solids and adsorption. [Russian] Moscow Nauka 1976... 

The same cannot be said about the surface tension of solids. The paper by the late Dr. Nicolson 26) is practically the only extensive theoretical treatment of the subject. It is of interest to note that for NaCl, the calculated surface tension is 562 dynes/ cm. 26), and the calculated surface energy 16) is 187 ergs/cm.. Thus, the surface tension, rather than having the same numerical value as the surface energy, is about three times as large. 

There is a corresponding paucity of experimental determinations of the surface tension of solids, probably because no direct experimental method has been developed. A review of the work on the surface tension of solid metals has been given by Shaler 27). These values were obtained, in most cases, near the melting point of the metals and thermodynamic equilibrium was achieved. These experiments are thus quite different from those where the nonequilibrium state persists, with incomplete relief of surface stress. As this review is mainly concerned with high surface area adsorbents in a state of considerable surface stress in vacuo at least), the above results with metals will not concern us further. 

Surface tension of solid) (ys) = Surface tension of solid/liquid (y SL) +... 

Since the surface tension of water is the same in the two systems, the difference in contact angle can only arise due to the surface tension of solids being different. The surface tension of liquids can be measured directly (as described in Chapter 2). However, this is not possible in the case of solid surfaces. Experiments show that, when a liquid drop is placed on a solid surface, the contact angle, 0, indicates that the molecules interact across the interface. This shows that these data can be used to estimate the surface tension of solids. 

Is It Possible to Measure Surface Tension of Solid Metal and Solution Interfaces In contrast to measurement of surface tension for liquids, the direct measurement of surface tension for solids can be considered an impossible task. However, it is possible to apply indirect measurements to obtain electrocapillary curves of solid electrodes and therefore the information from these curves. 

EXAMPLE 10.5 Particle Engulfment by An Advancing Solidification Front. Experiments were conducted at 80°C in which the solidification front of naphthalene was observed to either engulf or reject dispersed particles of several solids. Table 10.6 lists the observed engulfment (E) or rejection (R) behavior for various systems as well as the surface tensions of the various substances. The surface tensions of solid and liquid naphthalene at 80°C are 26.4 and 32.8 mJ m 2, respectively. Is the surface tension criterion cited above consistent with these observations How might any inconsistencies be explained Evaluate the product (7j/2 - 7i1/2)(t2/2 -7l/2) for these systems. 

When a drop of liquid is placed on a solid surface the liquid may form a bead on the surface, or it may spread to form a film. A liquid having a strong affinity for the solid, i.e., if its surface tension is less than the critical surface tension of the surface, yc, will seek to maximize its contact (interfacial area) and spread to form a film. A liquid with much weaker affinity, i.e., if its surface tension is above yc, will form into a bead. The critical surface tensions of solids range from 18 mN/m for Teflon to about 46 mN/m for nylon. 

Solids also have surface tension because molecules on the surface of a solid particle are subject to fewer attractive forces than molecules in the bulk of the solid. Measurements of the surface tension of solids (usually called the surface energy) are difficult because solids are rarely pure and smooth on the molecular scale. 

There is no known method for determining directly the surface tension of solids against gases. However, we can determine the difference adhesion tension in Eq (11-2) by resolving the surface tension parallel to the solid surface. Thus, for equilibrium... 

The surface energy (critical surface tension) of solids is measured by a method developed by Zisman.9 In this method a series of contact angle measurements are made with various liquids with known surface tensions on the solid to be tested. The contact angle 9 is plotted as a function of the yLV of the test liquid. The critical surface tension is defined as the intercept of the horizontal line cos 9=1 (i.e., when the contact angle is 0°) with the extrapolated straight-line plot of cos 9 against yLV of the liquids. The yLV at this intersection point (i.e., where a hypothetical test liquid would just spread over the substrate) is defined as the critical surface tension of the solid. 

Hulett, Dundon and Mack,4 and others have worked with salts, finding values ranging from 130 to 3,000 dynes per cm. for the surface tension of the solid-liquid interface. F. C. Thompson5 has estimated the surface tension of solid iron carbide against iron as 1,350, by this method. The... 

Theoretical calculations such as these appear the only method at present available for determining the surface tension of solids. 

Estimation of surface tensions of solid polymers from the parachor... 

Due to the fact that the extrapolation of surface tensions of melts to room temperature leads to reliable values for the solid polymer, the surface tension of solid polymers may be calculated from the parachor per structural unit by applying Eq. (8.5). The molar volume of the amorphous state has to be used, since semi-crystalline polymers usually have amorphous surfaces when prepared by cooling from the melt. We have found that the original group contributions given by Sugden show the best correspondence with experimental values for polymers. 

Estimate the surface tension of solid poly(methyl methacrylate) and its contact angle with methylene iodide (y = 50.8 mN/m). 

Solids also have a snrface tension (althongh this cannot be determined by simple methods). Fignre C2-4 shows snrface tensions of some liquids and solids nnder their own vaponr pressure. The values differ only slightly from what they would be under vacuum. There are two groups small liquid molecules and non-polar solids with low snrface tensions (less than 0.1 N m ) and ionic and metallic surfaces with high tensions. Surface tensions of solids are not as well defined as those of liquids. Solid surfaces are usually inhomogeneous, and they can be rough. As a result, their surface tension varies with position. 

Shalel-Levanon S, Marmur A. (2003) Validity and accuracy in evaluating surface tension of solids by additive approaches. / Coll Int Sci 262 489-499 268 272. 

The surface tension of solids has been the subject of several reviews. Theoretical advances are reviewed in a paper of Linford [ 16] and more recently by Rusanov (17). Also reviews about experimental techniques for determining the surface tension of solids in general I8] and of electrocapillary measurements 119], and a collection of experimental results 120], have appeared. Rusanov and Prokhorov provide a detailed review about the theoretical background of more classical experimental methods [2I. ... 

Techniques to measure the surface tension of solids are notoriously difficult and known for their inaccuracies. Reliable surface tension data requires not only a reliable measurement technique but careful control over parameters such as sample purity and the gaseous atmosphere in which the experiments are conducted. TTie zero creep technique is considered one of the most accurate and reliable of these techniques since it requires only a simple length measurement(8). Samples can be either wires or thin foils. Hondros(9) has postulated that the use of thin foils increases the sensitivity of the technique and thus allows more accurate measurements. The thinner the foil, the more it approximates a surface. Wire gauges are limited due to the loads required to strain the sample. Table I lists some of the results obtained using the zero creep foil technique. It should be pointed out that the terms surface tension and surface free energy are often used interchangeably, though they are not equivalent(9,10). 

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