Solid surface tension, contact angle state equation

Keywords Solid surface tension Solid surface energy Contact angle Work of adhesion Zisman method Surface tension component mefliod Fowkes method Owais-Wendt-Rabel-Kaelble mefliod Extended Fowkes mefliod Equation of state... 

The advancing contact angles, measured on smooth silicon surfaces coated with the polymer brushes or the silane, were used to calculate the solid surface tension ysv according to the equation of state approach (EQS) [39] ... 

Contact angle measurement is probably the most common method for solid surface tension measurement in condensed state. Young [71] described the equilibrium at three-phase boundary in terms of the vectorial sum, as shown in Fig. 3, resulting in the following equation of equilibrium forces balance... 

In a praetical sense, it is not necessary to eliminate completely all evidence of roughness and heterogeneity. If the average contact angle and liquid surface tension measurements for a variety of liquids all give the same solid surface tension via the equation of state (11. then effectively the surface is sufficiently smooth and homogeneous. The required level of accuracy will determine the acceptable solid surface quality. 

The coefficients p and Pi are determined experimentally by measuring the contact angles on 15 solid surfaces with a series of testing liquids. Kwok and Neumann [36, 37] also suggested to adjust the coefficients and the solid surface tension simultaneously to get more precise calculation of the solid surface tension. They further demonstrated that despite the different formulations and coefficients, the three equations of states have yielded the same ysv values, based on various set of experimental contact angles [36, 37],... 

In summary, there are three basic approaches to use contact angle data to determine the surface tensions of solid surfaces. These approaches are the Zisman method, the surface tension component methods, and the equation of state. Within these three approaches, there are many variants. It is reasonable to wonder the merit, accuracy, and limitation of some of the methods. The Zisman method is an empirical approach based on the correlation between the cosines of the contact angles on a solid surface versus the surface tensions of the test liquids. With alkanes, linear plots are usually obtained, and the critical solid surface tension (yc) is determined by extrapolating... 

For the solid-liquid system changes of the state of interface on formation of surfactant adsorption layers are of special importance with respect to application aspects. When a liquid is in contact with a solid and surfactant is added, the solid-liquid interface tension will be reduced by the formation of a new solid-liquid interface created by adsorption of surfactant. This influences the wetting as demonstrated by the change of the contact angle between the liquid and the solid surface. The equilibrium at the three-phase contact solid-liquid-air or oil is described by the Young equation ... 

Neumann, A.W. and Good, R.J., Hope, C.J. and Sejpal, M. (1974). An equation od state approach to determine surface tension of low energy solids from contact angles. J. Colloid. Interface Sci. 49, 291-303. 

There has been no shortage of attempts to estimate surface (Helmholtz-) energies from contact angles, by invoking some model. A controversial issue is Neumann s equation of state method ) which is based on the assumed validity of a second relationship between interfacial tensions, so that and y can be individually estimated. Another route starts by assuming [5.7.5] to be valid. For an apolar liquid on a solid S (y = y ), combination with Young s law gives... 

When a drop of a liquid is placed on a solid surface, the system will try to establish a state of minimum total surface free energy. Depending upon the relative values of the three interfacial tensions involved, the contact angle, 0, between the liquid and the solid phase will vary from 0° to 180°. The correlation between y and 6 is given by Young s equation... 

Some researchers [30-33] have challenged the validity of the equation of state. For example, to verify the equation of state experimentally. Spelt et al. [34] reported that the contact angles of two different testing liquids on a solid surface were identical when the liquid surface tensions were equal. On the contrary, van Oss et al. [31] showed that testing liquids of different surface tension values produced the same contact angle on the same solid, so that the results of Spelt et al. [34] could be completely explained by the theory of surface tension component. Johnson et al. [32] and Morrison [33] also criticized the method using Neumann s equation of state for its thermodynamic basis. However, Neumann et al. [35,36] rejected these criticisms and insisted on the thermodynamic validity of their approach. 

Hence the work of adhesion is directly related to the surface tension of the liquid and the contact angle that the liquid makes with the solid. This equation states that the maximum work of adhesion occurs when 0 = 0. Equation (74) also shows that the work of adhesion can never be 0, since all liquids display a surface tension under normal conditions. 

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