Langmuir 2003, 19, 10457-10458
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Comments rough surfaces can be used in conjunction with Young’s equation
Comment on “Surface Characterization of Hydrosilylated Polypropylene: Contact Angle Measurement and Atomic Force Microscopy”
γlv cos θY ) γsv - γsl
Chen1
Recently, Long and employed advancing contact angle data on two types of supposedly rough polypropylenes for surface energetic interpretation, by means of the Wenzel equation. Their main results are (i) “Antonow’s rule gives the highest surface free energy, and Berthelot’s rule results in the lowest free energy... the results obtained by equation of state approach are most reliable” and (ii) both polymers “can be qualitatively modeled as homogeneous but rough surfaces”. In this comment, it is pointed out that the surface energetic analysis in ref 1 via experimental contact angles is simply false. The falsehood of the claim made in ref 1 is well exemplified by fact that the Wenzel angle θW in the Wenzel equation
cos θW ) γsv - γsl γlv δ
(1)
was misconceived as the advancing angle θA, where γlv, γsv and γsl are respectively the liquid-vapor, solid-vapor, and solid-liquid interfacial tensions and δ is a roughness factor defined as the ratio of a rough surface area to the geometrically projected area. In ref 1, Long and Chen deliberately assumed θW ) θA and expressed the Wenzel equation as
cos θA ) γsv - γsl γlv δ
(2)
Although θW in the Wenzel equation (eq 1) is same as the thermodynamic equilibrium angle of the system θES for a rough surface, it is not amenable to experimental determination.2 Several authors3-6 have recently employed vibrational means to determine the so-called “vibrational” angles. Although such angles might seem to relate to θW, they do not equal to θA on rough surfaces. Even if θW were equal to θA, they would not be equal to the Young angle θY and could not be used in conjunction with Young’s equation.2 It is also well-known that there exist many metastable states between the advancing θA and receding θR contact angles. The Wenzel angle simply corresponds to the absolute minimum in the free energy of the system. Thus, no experimental contact angle on * To whom correspondence should be addressed. Tel.: (780) 4922791. Fax: (780) 492-2200. E-mail:
[email protected]. † University of Alberta. ‡ Institute of Polymer Research Dresden. (1) Long, J.; Chen, P. Langmuir 2001, 17 (10), 2965. (2) Li, D.; Neumann, A. In Applied Surface Thermodynamics; Spelt, J., Neumann, A. W., Eds.; Marcel Dekker, Inc.: New York, 1996; pp 109-168. (3) Andrieu, C.; Sykes, C.; Brochard, F. Langmuir 1994, 10, 2077. (4) Decker, E. L.; Garoff, S. Langmuir 1996, 12, 2100. (5) Volpe, C. D.; Maniglio, D.; Morra, M.; Siboni, S. Colloids Surf., A 2002, 206, 47. (6) Fabretto, M.; Sedev, R.; Ralston, J. Advancing, Receding and Vibrated Contact Angles on Rough Hydrophobic Surfaces; VSP: The Netherlands, 2003; Vol. III.
(3)
where θY is the Young angle; that is, θA * θY on rough surfaces. In general, no equality exists between θA and θY on rough surfaces and all such contact angles are meaningless in terms of Young’s equation. This fact is well-known in the literature and has been documented in refs 2 and 7, which were also cited in ref 1. Thus, the surface energetic interpretation in ref 1 utilizing experimental θA in the Wenzel equation is false and misleading. Another error in ref 1 is connected with the concept of solid surface tensions in the Wenzel equation. Long and Chen combined Young’s equation (3) with the Antonow’s and Berthelot’s rules and the equation of state for solid surface tensions, respectively, by assuming that the cosine of the Young contact angle cos θY equals (cos θA)/δ. This results in the following respective equations,
1 + (cos θA)/δ γlv 2
γsv ) γsv )
[
]
1 + (cos θA)/δ 2 γlv 2
(4) (5)
and
(cos θA)/δ ) -1 + 2 xγsv/γlv exp(γlv - γsv)2
(6)
Immediately following such procedures, Long and Chen1 claimed that “the surface free energy for rough surfaces can be calculated using eqs 14-16” [i.e., the preceding eqs 4-6] by means of experimental contact angles on rough surfaces when δ is known from atomic force microscopy (AFM) measurements. It is noted, however, that the interfacial tensions γsv and γsl in the Wenzel equation correspond only to those for a smooth surface rather than a rough surface, as claimed in ref 1. This fact is ubiquitously in textbooks.8,9 It is also noted that the notion of surface free energy and surface tension was freely interchanged in ref 1 without realizing their difference. Surface/interfacial tension is a thermodynamic property of an interface separating two bulk phases, for example, solid and liquid, and is defined as the energy required to separate a unit interfacial area. However, surface free energy is a more general term to describe the energetics of a surface. Typically, surfaces with higher solid surface tensions, for example, glass and metals, are considered to be highenergy surfaces and those with relatively lower surface tensions, for example, polymers, as low-energy surfaces. (7) Kwok, D. Y.; Lam, C. N. C.; Li, A.; Zhu, K.; Wu, R.; Neumann, A. W. Polym. Eng. Sci. 1998, 38, 1675. (8) Adamson, A. W. Physical Chemistry of Surfaces, 6th ed.; John Wiley & Sons: New York, 1997. (9) Zisman, W. A. In Contact angle, Wattability, and Adhesion; Good, R. F., Ed.; ACS Advances in Chemistry Series 43; American Chemical Society: Washinton, DC, 1964.
10.1021/la035736z CCC: $25.00 © 2003 American Chemical Society Published on Web 10/25/2003
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Langmuir, Vol. 19, No. 24, 2003
In the case of two surfaces having the same chemical identities where one is rough and the other is smooth, the former is said to have a lower surface energy (i.e., more hydrophobic as manifested by a higher phenomenological angle) as compared to that of the latter, even though they have the same solid surface tension as a thermodynamic property. Note that the solid surface tensions of rough surfaces cannot be determined from experimental contact angles through Young’s equation. The fact that Young’s equation relates the contact angle to solid surface tensions only for smooth surfaces rather than surface energy on rough surfaces proves the point. Thus, the surface energies of the supposedly rough surfaces in ref 1 simply cannot be determined through Young’s equation and experimental contact angles. Be that as it may, we believe that the two polypropylenes in ref 1 are indeed not rough in the context of contact angle interpretation. This is obvious from their AFM results that the mean roughness Ra various only between 4 and 24 nm and “the average δ is 1.053 08 for SPP [hydrosilylated polypropylene] and 1.025 51 for PP [polypropylene]”. Experience has shown that surface roughness of this order should not have an influence on the experimental advancing and receding angles up to Ra ∼ 40 nm. Direct interpretation of the experimental advancing angles and without considering roughness via eq 16 in ref 1 results in a mean γsv of 26.8 ( 2.6 mJ/m2 for PP and 21.2 ( 2.4 mJ/m2 for SPP, as compared to the reported values of 27.3 ( 0.6 mJ/m2 and 21.8 ( 2.2 mJ/m2, respectively. Assuming that the authors’ contact angle/ roughness calculations were meaningful, the similarity of these two sets of values indeed illustrates that roughness is not an important factor of the experimental conditions. Finally, we wish to emphasize the fact that contact angle
Comments
hysteresis can be due to chemical heterogeneity or surface roughness. It is far too simplistic to claim that “The difference of contact angle hysteresis between PP and SPP is then attributed to the change in surface features as shown in Figures 6 and 7 [AFM images]”, that is, surface roughness exclusively. Because real surfaces are always chemically heterogeneous, there are no guarantees that the PP and SPP in ref 1 can be 100% chemically homogeneous, unless X-ray photoelectron spectroscopy or similar techniques had been used to quantify their chemical compositions. We point out that the reported contact angle hysteresis can also be due to such chemical heterogeneity, and the analysis of contact angles in ref 1 based exclusively on a thermodynamic model of rough surfaces is erroneous. Acknowledgment. This work was supported by the Alberta Ingenuity Establishment Fund, Canada Research Chair (CRC) Program, and Natural Sciences and Engineering Research Council of Canada (NSERC). J.Z. acknowledges the financial support from the Alberta Ingenuity Studentship Fund. Junfeng Zhang,† Karina Grundke,‡ and Daniel Y. Kwok*,†
Nanoscale Technology and Engineering Laboratory, Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada, and Institute of Polymer Research Dresden, Hohe Strasse 6, 01069 Dresden, Germany Received September 16, 2003 LA035736Z
