surface energy finn - ramé-hart Surface Science …

1 1. The Measurement of Surface energy of polymer by means of contact angles of liquids on solid surfaces A short overview of frequently used methods by finn Knut Hansen Department of Chemistry University of Oslo 2. Definitions Surface tension and Surface energy L F. dx Surface tension form force: The force, F, involved in stretching a film is: F = L = Surface tension (constant). This means: = F/L force/unit length Units: N/m or mN/m (= dyn/cm in units). Surface energy from work: The work, dW, involved in increasing the Surface by a length dx is: dW = dG = L dx = dA. This means: = dG/dA free energy /unit area Units: J/m2 = N/m Surface tension and Surface energy are interchangeable definitions with the same units Work of adhesion and work of cohesion Work of adhesion The work of adhesion between 2 (incompatible).

2 Substances is: 1. Wa = W12 = 1 + 2 - 12. 12. 12. W12. 2 or: 12 = 1 + 2 - Wa Work of cohesion The work of cohesion of a single substance is: 1 Wc = W11 = 1 + 1 - 0 = 2 1. W11. 1 12 = (Wc1 + Wc2) - Wa 3. Young's equation When the liquid does not spread, a drop has a 1 contact angle on the Surface . The balance between the forces on the Surface gives: Gas(air). Youngs Equation: 2 = 12 + 1 cos . 2 12. NB: Only valid in dry wetting . In cases with wet wetting , the Surface pressure of the liquid vapor on the solid is substantial. In these cases, 2 becomes lowered by the Surface vapor pressure . So that: 2 = + 12 + 1 cos . Expressed by the work of adhesion we can write: Wa = 1 + 2 - 12 = 1 + 1 cos = 1(1+cos ) This is the Young - Dupree equation Critical Surface tension - Zisman plot c Zisman et al. (1950)1 found an empirical connection between cos and 1: If we measure the contact angle of many Polymer: PTFE.

3 Liquids on the same Surface , and plot cos against 1, we get a curve that can be extrapolated to cos =1. cos . The extrapolated value is called the critical Surface tension of the solid 0- Surface . Note: This is not necessarily the same as the Surface tension of the solid, 2. 0 10 20 30 40 50 60 70 80. 1 (mN/m). There are 2 problems: 1. The line is not really straight (it is more hyperbolic). 2. c is not the same as 2 (only if 12= 0 when = 0). In DROP image the Zisman Plot tool performs an ordinary linear Zisman plot. 4. The interaction parameter and the work of adhesion The work of adhesion has been expressed by Good and Girifalco (1960)2 by the geometric mean of the Surface tensions in the same way as the Hamaker constant: W a = 2 ( 1 2 ). 1/ 2. where is the Interaction parameter, < < is a function of the molar volumes of substance 1 and 2: =.

4 4r1r2 A12 where r1, r2 = molecular radii ( r1 + r2 )2 ( A11 + A 22 )1/ 2. and A is the sum of London constants (or corresponding) for all types of intermolecular forces (dispersive, polar, acid-bas, etc.). If we insert for Wa in the Young-Dupree equation, we get: W = 2 ( 1 2 ). a 1/ 2. = 1 (1 + cos ) or 2 = 1. (1 + cos )2. 4 2. has been calculated theoretically, but the results have often been misleading. It is possible to calculate empirical values for by using values of measured by liquid/liquid interactions in systems of similar polarity. In a recent publication, Kwok and Neumann (K&N)3 have argued for using an analytical expression, and equation of state for . Their expression is: = exp ( 1 2 ) . 2.. It is easily seen that if 1 = 2 then = 1. The magnitude of is therefore crucial in giving a universally correct work of adhesion, if such an expression is possible.

5 K&N have determined this experimentally from an extensive amount of measurements of low energy polymer surfaces . They found = (m2/mJ)2 to give the best all-over results, although it varied some. This method has been implemented in DROP image's Surface energy (One Liquid) tool. 5. Fowkes' theory Fowkes' theory is based on 2 fundamental assumptions: Additivity and the geometric mean 1. Surface forces (energies) are additive: = d + p + h + i + ab + .. where d = dispersion force p = polar force h = hydrogen bonding force i = induction force (Debye). ab = acid/base force etc. 2. Geometric mean is used for the work of adhesion for each type of force ( energy ): ( ) ( ) ( ). 1/ 2 1/ 2 1/ 2. W d12 = 2 1d 2d , W p12 = 2 1p 2 p , W h12 = 2 1h 2 h , etc. The general expression for W12 is: W12 = 1 (1 + cos ) = W d12 + W p12 +.

6 ( ) ( ). 1/ 2 1/ 2. And for 12 thus: 12 = 1 + 2 2 1d 2d 2 1p 2 p .. By using a liquid that only interacts with the Surface by dispersion forces, we can write: 1 (1 + cos ). 2. ( ). 1/ 2. W12 = 1 (1 + cos ) = 2 1 2d ( 1 = 1d) and 2d =. 4. Extended Fowkes' theory The combination of additivity and geometric mean has been used by many: ( ) ( ) ( ). 1/ 2 1/ 2 1/ 2. W12 = 2 1d 2d + 2 1p 2p + 2 1h 2 h (Kitazaki and Hate, 1972)4. ( ) ( ). 1/ 2 1/ 2. W12 = 2 1d 2d + 2 1n 2 n (n = all non-dispersive componenets). By doing measurements with m number of liquids on the same Surface , we can calculate m different components of the Surface energy , if the corresponding components of the liquids are known. By using 2 liquids, A and B, we can write 6. ( ) + 2 ( 1Ap 2p ). 1/ 2 1/ 2. W12A = 1A (1 + cos A ) = 2 1A d 2d W12B = 1B (1 + cos B ) = 2 ( 1Bd 2d ) + 2 ( 1Bp 2 p ).

7 1/ 2 1/ 2. The 2 equations can be linearized to give: ( 1Ad ) ( 1A p ). 1/ 2 1/ 2. ( 2 ). d 1/ 2. ( 2p ) 1 + cos A. 1/ 2. + =. 1A 1A 2. ( 1Bd ) ( 1Bp ). 1/ 2 1/ 2. ( 2 ). d 1/ 2. ( 2p ) 1 + cos B. 1/ 2. + =. 1B 1B 2. These equation set is solved for ( 2d)1/2 and ( 2p)1/2. Usually, one polar (water) and one unpolar (methylene iodide) liquid are used. This is the so- called two-liquid method. In the solution, care must be taken to check if a square root is negative. This indicates errors in the measurements. This procedure is used in DROP image's Surface energy (Two Liquids) tool (Geometric Mean)5. The question of geometric or harmonic mean Fowkes' assumption of the geometric mean is based on Berthelot's hypothesis, again based on London's theory of dispersive forces. The London (Lennard-Jones) attraction constants between like and dislike substances are 3 3 3.

8 A12d = h 1 2 1 2 , A11d = h 1 12 , A 22d = h 2 2 2. 2 1 + 2 4 4 . where h = Planck's constant, = frequency of vibration, = polarizability If is eliminated, we obtain 2( 1 2 )1/ 2. A12d = (A11d A 22d )1/ 2 , and if 1 = 2 , then A12d = (A11d A 22d )1/ 2. 1 + 2. After Girifalco and Good, the works of adhesion are expressed by n1n 2 A12 1 1 n12 A11 1 1 n 2 2 A 22 1 1 . W12 = . 2 2 m 4 . , W11 = . 2 2 m 4 . , W22 = . 2 2 m 4 . 6d12 6d11 6d 22 . 7. where n = molecular density, d = equilibrium distance between the phases, m = the repulsion constant (Lennard-Jones). By eliminating n, and using the expressions for Aij above, we obtain: d1d 2. W12d = 2. (W11d W22d )1/ 2 (There are only dispersion energies here). d12. If then d12 = (d11d22)1/2 we obtain: W12d = (W11d W22d )1/ 2 and therefore W12d = 2( 1d 2d )1/ 2.

9 These are therefore the assumption involved in using the geometric mean. It is, however, possible that some of these assumptions are less acceptable. It is possible to derive another mean, based on slightly different assumptions6: If we eliminate instead of from the equations above, we obtain 2A11d A 22d A12d =. A11d ( 1 / 2 ) + A 22d ( 1 / 2 ). 2A11d A 22d If now 1 = 2 then the expression for A12 is: A12d = , a harmonic mean A11d + A 22d By using the same equations for Wij as above, we now obtain d11 d 22 d1d 2. 2W11d W22d n1 n 2 d122. W12d =. W11d (d11 / n1 ) 2 + W22d (d 22 / n 2 ) 2. If now again d12 (d11d 22 )1/ 2 and in addition n1 / d11 n 2 / d 22 , the work of adhesion becomes 2W11d W22d 4 11d 22d W12d = , and therefore W12d =. W11d + W22d 11d + 22d This is the harmonic mean for the work of adhesion.

10 Wu has claimed that the harmonic mean is better suited for low energy surfaces , such as polymers6. On the next page are shown two figures of the work of adhesion plotted as a function of the dispersive and polar Surface energy components. The plot using the harmonic mean is seen to give generally lower values for the work of adhesion than the geometric mean. 8. Harmonic mean Geometric mean 90 90. 80 80. 70. Work of adhesion (mN/m). 70. Work of adhesion (mN/m). 60 60. 50 50. 40 40. 30 30. 20 20. 10 10. 0 35 0 35. 2. 2. 6. 6. 10. 10. 14. 5 5. 14. 18. 18. 22. 22. 26. 26. 30. 30. Measuring Surface energies with 2 liquids by the harmonic mean In the same way as with using the geometric mean, the harmonic mean may be used to calculate the dispersive and polar components of the Surface energy by measuring the angles of two liquids, A and B.