Comment pubs.acs.org/JPCC
Surface Tension as a Complex Parameter: A Critique of Experimental Evidence from Energy Dissipation Studies on Fibers Partially Immersed at an Air/Water Interface Brian A. Pethica*
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Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 04544, United States to contact and partially immerse the glass fiber close to one side of the water pool. A standing wave is set up between the fiber and the adjacent wall and the power dissipation is measured over a range of frequencies. Analysis of the results assumes the literature value for the surface tension of water (72.75 mN m−1) at an unstated temperature, presumably 20 °C. It is virtually certain from the cleaning procedures described for the steel block and fiber that this is not the actual surface tension in this study. This is evident by comparison with publications on the methods employed for preparation of critically pure water.10−16 The conductivity of the water is given, but the surface tension was not measured for the water as prepared and, critically, not for the water in the steel block cavity itself before and after fiber immersion and vibration. These experimental omissions alone are sufficient to cast doubt on the results and interpretation. The glass fibers were cleaned with sulfuric acid before being attached to the AFM cantilever with an unspecified glue. Surface-active components from glue can move along the glass fiber surface, which is well hydrated by exposure to water vapor in the sealed experimental chamber at an unstated but probably high relative humidity. Incomplete saturation would cause thermal gradients in the interfacial region. Measurement of the surface tension in situ, for example, using a fully wetted glass rod (or a lighter cylinder) centrally placed over the cavity, must take into account the interaction between the menisci at the rod and wall of the cavity.17,18 Meniscus interactions should also be considered in the glass fiber experiments because the fiber is separated by only 0.5 mm from the wall of the steel cavity, such that the measured vertical force on a static fiber partially immersed in rigorously pure water could differ from that for a fiber far from any wall. This can be tested by comparison of the static force on the fiber as a function of separation from the wall. The water surface is said to be “pinned” at the junctions with the fiber and the steel container wall. This term is not defined. The contact angle on the fiber is shown as an unlikely 90° at a flat surface in ref 3 and as swinging between ∼45 and ∼135° at the terminus of the standing wave at the fiber in ref 4. Such a “swing” would constitute a cycle of large positive and negative contributions to the vertical force on the fiber registered by the cantilever, which is not observed, but the geometries and associated displacements at the fiber surface may not be ignored. The figures and theory for the standing wave describe
INTRODUCTION The damping of capillary waves at liquid interfaces is primarily due to energy dissipation from the viscous drag of the adjacent bulk fluid phases. In Scriven’s classic paper, the additional effects of both shear and dilatational surface viscosities were also shown to be relevant.1 In the broader analysis by Goodrich, the interfacial region is taken as tangentially homogeneous and inhomogeneous in the normal direction, with excess properties analogous to the Gibbs treatment of surface excess functions, leading to the identification of four excess viscosities, two of which correspond to the shear and dilatational viscosities from Scriven’s analysis.2 Numerous experimental results have identified energy dissipation associated directly with dynamic surface area changes such as in the hysteresis of the force-area isotherms of lung surfactant at the air/water interface and in the desorption- resorption cycles for surfactants at liquid interfaces under stress. These dissipation terms are not relevant to rigorously pure liquids but will be observed with incompletely purified liquids such as water. For example, time effects are frequently observed in measurements of the surface tension of water, indicating either the presence of adventitious surface active components or a defect in the measurements such as changes in the contact angle at a Wilhelmy plate. Whether dissipative terms are relevant to periodic surface stresses at the pure water/air interface is addressed by valuable new measurements on glass fibers partially immersed in water with the upper end attached to an ATM-style cantilever operated in the tapping mode and measuring the power dissipation as a function of the depth of immersion of the fiber.3−5 The purpose of this note is to focus on these important new experiments and to indicate additional experiments at the air/water interface and at the lines of contact of the liquid surface with the fiber and the container walls and edges, which can potentially show that the observed energy dissipation in the water surface may be assigned to factors other than or additional to a complex surface tension. Extended references to relevant literature are given in refs 3−9.
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ANALYSIS OF THE NEW EXPERIMENTS References 3−5 share several coauthors and may be discussed together so far as the experimental procedures, results, and interpretation are concerned. The experiments are made on the surface of water filling a cylindrical cavity 10 mm in diameter and 5 mm deep in a stainless steel block that can be raised stepwise. A glass fiber a few microns in diameter is glued to an AFM-type cantilever mounted above the block and operated in tapping mode. The vertical force on the cantilever is measured as the water is raised © 2016 American Chemical Society
Received: January 14, 2016 Revised: March 7, 2016 Published: April 1, 2016 8417
DOI: 10.1021/acs.jpcc.6b00437 J. Phys. Chem. C 2016, 120, 8417−8419
Comment
The Journal of Physical Chemistry C the wave terminating on the fiber at a point as if on a flat surface, whereas the surface is strongly curved. There may be dissipative effects if overlap of the menisci at the wall and fiber gives an effective surface tension in the gap between fiber and wall differs from the ordinary tension on the other side of the fiber, with related gradients around the fiber. The “pinning” of the induced standing wave at the block is also ambiguous and possibly a further source of energy dissipation, particularly if the wave is influenced by transfer of energy between the water surface and its extended contact with a wetting film on the steel. The meniscus and contact angle at the fiber are considered as a secondary spring in ref 5, with the contact angle changing at a fixed point as the fiber is vibrated, thereby contributing to the spring constant. The possibility that the contact angle remains constant and the point of contact moves or some combination of the possible changes is not considered. The surface tension is included as a complex parameter, leading to an estimate of a complex contact angle contribution to the spring constant from the proposed contact-angle oscillations. It is reported that when the fiber touches the water surface there is a large but unspecified increase in the observed vertical force. This fact is used to define the zero for immersion, which may be in error by a few microns for the more sensitive cantilevers described in ref 4 due to the displacement of the cantilever when contact with the surface is made. The contact angle on the fiber is not considered as the probable source of the force increase. Neglecting any small buoyancy correction from partial immersion, the increase in force on fiber contact with the water surface far from a wall will be given by ΠDσ cos θ, where D is the fiber diameter, σ is the surface tension, and θ is the contact angle measured through the water phase, which will be
