SURFACE CHARACTERIZATION USING HANSEN SOLUBILITY (COHESION) PARAMETERS. Charles M. Hansen. Jens Bornøs Vej 16, 2970 Hørsholm, Denmark

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1 Proceedings of the 28th Risø International Symposium on Materials Science: Interface Design of Polymer Matrix Composites Mechanics, Chemistry, Modelling and Manufacturing Editors: B. F. Sørensen, L. P. Mikkelsen, H. Lilholt, S. Goutianos, F. S. Abdul-Mahdi Risø National Laboratory, Roskilde, Denmark SURFACE CHARACTERIZATION USING HANSEN SOLUBILITY (COHESION) PARAMETERS Charles M. Hansen Jens Bornøs Vej 16, 2970 Hørsholm, Denmark ABSTRACT Surfaces can be reliably characterized by the cohesion energy parameters, of the type commonly called Hansen Solubility parameters (HSP). Data for many fillers fibers, pigments and other surfaces are available. The implication for composites is that the physical affinity or cohesion between fibers and polymer matrix will be a maximum when the energy parameters match. The HSP parameters assigned to many liquids and polymers have recently been confirmed by statistical thermodynamic treatments. 1. INTRODUCTION The purpose of this paper is to confirm that surfaces can be reliably characterized by the cohesion energy parameters of the type commonly called Hansen solubility parameters (HSP) (Hansen 1967a; 1967b; 1967c; 1967d; 1999; 2007). Comparing the HSP of a surface with the HSP of a given solvent or polymer allows prediction of their interaction. The HSP of many pigments, fillers, fibres, and other surfaces have been found by their interaction with a series of well-defined test solvents (Hansen, 1967b; 1967d; 1999; 2007). The HSP of the usual test solvents are derived from their energies of vaporization and are supported by thousands of data points. When a liquid is evaporated, all the bonds holding it together are broken. The total cohesive energy of the liquid is the sum of the different types of interactions holding the liquid together. These are the atomic dispersion interactions (D) that clearly are also present in all molecules, the molecular dipolar interactions (P), and molecular hydrogen bonding (H), which should be more properly called an electron interchange interaction. The sum of the cohesion energy deriving from these three types of interaction is equal to the total cohesion energy as measured by the energy of vaporization. Solution, swelling, chemical resistance, permeation rate, or other effect based on solubility can be used to assign HSP to non-volatile, bulk materials, such as polymers. Surfaces have been characterized by two different techniques. Pigments, fillers, and fibres are usually studied by measuring sedimentation rates in many well-defined solvents. The absolute sedimentation rates are normalized by the solvent viscosities and the density difference between the solvents and sample to arrive at relative sedimentation rates for all the solvents. Those solvents with the longest relative sedimentation times are used to assign the cohesion energy parameters to the 191

2 Hansen surface by similarity of cohesion energy properties of the good test solvents. Plane surfaces can be characterized by well-defined test solvents in terms of whether or not an applied droplet spontaneously spreads and whether or not an applied film spontaneously retracts. There has been great interest in characterizing surfaces because of the importance that this has for wetting, adhesion, lubrication, adsorption, dispersion of pigments and dyes, surface contamination and cleaning, etc. (Barton 1991). There are far too many references to discuss here, but the general conclusion is that the physical affinities of two materials are at a maximum when their energies match. These energies can be measured using the surface or interfacial free energy or different cohesion parameters, such as those of Hildebrand and Hansen. There is improved predictability when the energy of interest is divided into dispersion and polar parameters. The implication for the performance of composites is that the physical affinities or physical bonding between the matrix polymer and fibres will be a maximum when the energy properties match. It has been recognized in the coatings industry, however, that given segments or groups (alcohol, acid, amine) of the matrix polymer may prefer to adsorb on surfaces with energies (much) higher than that assigned to the polymer. These local segments or groups have energies that are more similar to the surface of the pigment, filler, or fibre, than they have for the rest of the matrix polymer. They will therefore seek the higher energy surface, thus matching energies, and this provides a stable anchor because there is no driving force for desorption. Water can have some influence on this type of bonding, however, since it also has high energy. It should also be recognized that chemical bonding between fibres and matrix polymer can be employed for still stronger bonds. Use of a sizing is a means to alter surface properties. Judicious choice of sizing can improve both processing and bonding, but the question of adhesion of the sizing to the fibres can also be raised. 2. HANSEN SOLUBILITY (COHESION) PARAMETERS The cohesion energy parameters most widely used for the above characterizations are those developed by Hansen (1967a; 1967b; 1967c; 1967d; 1999; 2007). These are now called Hansen solubility (cohesion) parameters. They are based on an extension of the Hildebrand solubility parameter (Hildebrand and Scott 1950; 1962). The HSP assigned to many liquids and polymers many years ago by Hansen have recently been confirmed with amazing agreement using a statistical thermodynamics treatment by Panayiotou (2007). See Table 1. Panayiotou started by calculating the hydrogen bonding parameter discussed below, while Hansen found the hydrogen bonding parameter as a residual after having calculated the other parameters in equation (4). Both Panayiotou and Hansen end with essentially the same values for all three HSP for a large number of liquids and polymers. The total cohesion energy of a liquid, E, can be divided into at least 3 separate parts by experiment or calculation (Hansen 1967a; 1967d; 1999; 2007; Panayiotou 2007). In the Hansen approach these parts quantitatively describe the nonpolar, atomic (dispersion) interactions, E D, permanent dipole-permanent dipole molecular interactions, E P, and the hydrogen bonding (electron interchange) molecular interactions, E H. E = E D + E P + E H (1) E can be experimentally measured by determining the energy required to evaporate the liquid, thus breaking all of its cohesion bonds in the process. E = ΔH RT (2) 192

3 Surface characterization using HSP where ΔH is the measured (or predicted) latent heat of vaporization, R is the universal gas constant, and T is the absolute temperature. Dividing Equation 1 by the molar volume, V, gives the respective Hansen cohesion energy (solubility) parameters according to equation (4). E/V = (E D /V) + (E P /V) + (E H /V) (3) δ² = (δ D)² + (δ P)² + (δ H)² (4) The cohesion energy divided by the molar volume is the total cohesion energy density. The square root of this is the Hildebrand total solubility parameter, δ. (Hildebrand and Scott 1950; 1962). The SI units for all of these are MPa ½. These units are times larger than the units (cal/cc) ½. HSP characterizations can be conveniently visualized using a spherical representation. The HSP are at the center of the sphere, and the radius of the sphere, Ro, indicates the maximum difference in affinity tolerable for a good interaction to take place. Good solvents are within the sphere, and bad ones are outside. A simple composite affinity parameter, RED, standing for Relative Energy, Difference, has been defined as the distance according to equation (5), Ra, divided Ro. Ra 2 = 4(δ D1 - δ D2) 2 + (δ P1 - δ P2) 2 + (δ H1 - δ H2) 2 (5) RED = Ra/Ro (6) The subscripts are for the sample, 1, and test chemical, 2, respectively. Good solvents will have RED less than 1.0. Progressively poorer solvents will have increasingly higher RED. The "4" in equation (5) has been found correct experimentally for all practical purposes in over 1000 correlations using HSP, and agrees with predictions of the Prigogine theory as discussed in (Hansen 1999; 2007). It differentiates the atomic from the molecular interactions, the latter sometimes being referred to as specific interactions. Table 1. Comparision of the δ H parameter in MPa ½ between Hansen (1967) and Panayiotou (2007) HANSEN PANAYIOTOU Toluene Tetralin Acetone Methyl Methacrylate Ethanol Butanol Dimethyl sulfoxide Water

4 Hansen 3. SURFACE CHARACTERIZATION WITH HSP Beerbower (1971) found a correlation for liquid surface tension (free energy), γ, and HSP (Hansen and Beerbower 1971). Here again the atomic dispersion interactions are differentiated by a constant from the dipolar and hydrogen bonding interactions. γ = V 1/3 [δ D (δ P 2 + δ H 2 )] (7) The constant was actually found to be in the empirical correlation. The units for the cohesion parameters are (cal/cm 3 ) ½ and those of the surface tension are dyn/cm, which, however, are numerically equal to those in mn/m. The constant was separately derived as being equal to by a mathematical analysis in which the number of nearest neighbors lost in surface formation was considered, assuming that the molecules tend to occupy the corners of regular octahedra. This simple relation alone suggests that correlations of surface phenomena can be made with the HSP. 3.1 Pigments, Fillers, and Fibres. The cohesion parameter (HSP) approach to characterizing surfaces gained impetus by experiments where the suspension of fine particles in pigment powders was used to characterize 25 organic and inorganic pigment surfaces (Hansen 1967b; 1967d). Small amounts of the pigments are shaken in test tubes with a given volume of liquid (10 ml) of each of the test solvents, and one then observes sedimentation or lack of the same. When the solid has a lower density than the test liquid, it will float. Rates of floating have also been noted, but the term sedimentation is retained for both sedimentation and floating. The amounts of solid sample added to the liquids can vary depending on the sample in question, and some initial experimentation is usually advisable. If the pigment or filler particle size is large, say, over 5 µm, the surface effects are clearly less significant compared with a sample where the particle size is only 0.01 µm. The larger particle size samples may sediment very rapidly, making characterizations for glass fibres, for example, very difficult. Observations can be made visually. Some pigments have portions which suspend for years in spite of large density differences and relatively low solvent viscosity. Satisfactory results from this type of measurement require some experience regarding what to look for. This can vary from sample to sample. A characterization is less certain if there are only 4 or 5 good liquids out of the perhaps 40 to 45 tested, although this depends somewhat on which liquids are involved. Good here means suspension of particulates is prolonged significantly compared with the other test solvents after compensating for differences in density and viscosity. A relative sedimentation time, RST, can be found by modifying the sedimentation time, t s. RST = t s (ρ p - ρ s )/η (8) ρ p and ρ s are densities of particle and test liquid, respectively, and η is the liquid viscosity. A prolonged RST implies greater adsorption of the given solvent onto the surface in question. Characterizations based on these techniques tend to place emphasis on the nature of the surfaces for the smaller particle size fractions. Reference is made to the presentation by Hélène Launay (2007) at this symposium for more detail on this type of characterization and the conclusions that can be drawn relative to composite materials. 3.2 Plane Surfaces. One can determine the cohesion parameters for surfaces by observing whether or not spontaneous spreading is found for a series of widely different liquids. The liquids used in standard solubility parameter determinations are suggested for this type of surface characterization (Hansen 1999; 2007). It is strongly suggested that none of the liquids be 194

5 Surface characterization using HSP a mixture, as this introduces an additional factor into the evaluations. Droplets of each of the liquids are applied to the surface and one simply observes what happens. If a droplet remains as a droplet, there is an advancing contact angle and the cohesion energy/surface energy of the liquid is (significantly) higher than that of the surface. The contact angle need not necessarily be measured in this simplified procedure, however. Contact angles have generally been found to increase for greater differences in cohesion parameters between the surface and liquid. If spontaneous spreading is found, there is presumed to be some similarity in the energy properties of the liquid and the surface. The apparent similarity may be misleading. As discussed in greater detail elsewhere (Hansen 1999: 2007) the fact of spontaneous spreading for a given liquid does not mean that its HSP are identical with those of the surface being tested. If a given liquid does not spontaneously spread, it can be spread mechanically as a film and observed to see whether it retracts. This can be done according to ASTM D or ISO 8296:1987 (E). This test determines whether or not there is a receding contact angle. Fig.1 shows a complete energy description for an epoxy polymer surface (Hansen and Wallström, 1983; Hansen 1999; 2007) based on the testing procedure described previously. The Hansen polar and hydrogen bonding parameters, δ P and δ H, are used to report the data. The circular lines can be considered as portraying portions of HSP spheres, but the third Hansen parameter, δ D, has not been specifically accounted for in the two-dimensional figure. Fig.1. HSP surface characterization of an epoxy surface showing regions of spontaneous spreading of applied droplets (A), lack of dewetting of applied films (B), and dewetting of applied films (C). This characterization may not be valid for all epoxy surfaces. Units are MPa ½. Fig. 1 shows two curves that are concave toward the origin. The lower of these divides the test liquids into two groups based on spontaneous spreading or not. Below the line one finds that liquids applied as droplets will spontaneously spread. Liquids that are found in the region above the upper curve will retract when applied as films. A test method to determine this is found in 195

6 Hansen the ASTM and ISO standards given previously, for example, except that one uses a large number of pure liquids instead of the liquid mixtures suggested in the standards. Receding contact angles will generally increase for liquids with still higher HSP. Intermediate between the two curves in Fig. 1 is a region where liquids applied as droplets will remain as droplets, while liquids applied as films will remain as films. The energy properties of these liquids are not as close to those of the surface as are the energy properties of the liquids that spontaneously spread. Spontaneous spreading is more related to adhesion since such liquids want to cover the surface spontaneously. The wetting tension test uses an external force to spread the liquids, after which they may continue to remain as a film. The mobility of the surface layer(s) will play a role in the wetting tension test. Hydrophilic segments can (perhaps) rotate toward a water droplet at some rate, for example, and increase the hydrophilic nature of the surface accordingly.. ACKNOWLEDGEMENT This paper was supported by the Framework Programme "Interface Design of Composite Materials" (STVF fund no ). REFERENCES Barton, A. F. M. (1991). Handbook of solubility parameters and other cohesion parameters, 2 nd Ed. (CRC Press, Boca Raton, FL) Beerbower, A. (1971). Surface free energy: a new relationship to bulk energies, J. Colloid Interface Sci., 35, Hansen, C. M. (1967a). The three dimensional solubility parameter - key to paint component affinities I. - solvents, plasticizers, polymers, and resins, J. Paint Techn., 39, No. 505, Hansen, C. M. (1967b). The three dimensional solubility parameter - key to paint component affinities II. - dyes, emulsifiers, mutual solubility and compatibility, and pigments, J. Paint Techn. 39, No 511, Hansen, C. M., and Skaarup, K. (1967c). The three dimensional solubility parameter - key to paint component affinities III. - independent calculation of the parameter components, J. Paint Techn. 39, No. 511, Hansen, C. M. (1967d). Doctoral Dissertation: The three dimensional solubility parameter and solvent diffusion coefficient, their importance in surface coating formulation, Danish Technical Press, Copenhagen. Hansen, C. M., and Wallström, E. (1983). On the use of cohesion parameters to characterize surfaces, J. Adhesion, 15, Hansen, C. M. (1999). Hansen solubility parameters: a user s handbook, (CRC Press, Boca Raton, FL). Hansen, C. M. (2007). Hansen solubility parameters: a user s handbook, 2nd Ed., (CRC Press, Boca Raton, FL). Hansen, C. M. and Beerbower, A. (1971). Solubility parameters, in Kirk-Othmer Encyclopedia of Chemical Technology, Suppl. Vol., 2nd Ed., Ed. A. Standen, (Interscience, New York) Hildebrand, J. and Scott, R. L. (1950). The solubility of nonelectrolytes, 3 rd Ed., (Reinhold, New York). Hildebrand, J. and Scott, R. L. (1962). Regular solutions, (Prentice-Hall Inc., Englewood Cliffs, NJ). Launay, H. (2007). Hansen solubility parameters for a carbon fiber/epoxy composite, Paper 196

7 Surface characterization using HSP presented at the Risø International Symposium, Sept. 3-5, Panayiotou, C. (2007). Statistical thermodynamics calculations of the hydrogen bonding, dipolar, and dispersion solubility parameters. In: Hansen Solubility Parameters; A User s Handbook, 2 nd Ed., Ed. C. M. Hansen (CRC Press, Boca Raton, FL)