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Surface Energetics Evolution during Processing of Epoxy Resins
Journal of Colloid and Interface Science 222, 55–62 (2000) doi:10.1006/jcis.1999.6613, available online at http://www.idealibrary.com on
Surface Energetics Evolution during Processing of Epoxy Resins St´ephane A. Page,∗ Raffaele Mezzenga,∗ Louis Boogh,∗ John C. Berg,† and Jan-Anders E. M˚anson∗ ,1 ∗ Laboratoire de Technologie des Composites et Polym`eres (LTC), Ecole Polytechnique F´ed´erale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; and †Department of Chemical Engineering, University of Washington, Seattle, Washington 98195–1750 Received April 12, 1999; accepted October 29, 1999
process, that is, from the liquid surface tension at the beginning of the process to the solid surface energy at the end of the process, has not yet been investigated and reported. Liquid surface energetics are relatively easily characterized in terms of surface tension, σL . The simplicity of such characterization is due to the energetic and morphological homogeneity of fluid surface as well as to the availability of a mechanical measurement to determine the surface tension. There are a number of experimental methods for determining the surface tension of liquids (6). One of the most convenient ways to determine surface tension is by the Wilhelmy method using a dynamic contact angle analysis (DCA) system. In DCA, the downward force on a solid of known perimeter slowly advanced into and then pulled from a liquid bath, whose surface tension is to be determined, is measured (7). Since the surface tension is a manifestation of intermolecular forces, it may be expected to be related to other properties derived from intermolecular forces, such as internal pressure, compressibility, and cohesive energy density. An interesting empirical relationship between surface tension and the solubility parameter was first found by Hildebrand and Scott (8). Based on Hansen’s work (9), which stipulated that the solubility parameter can be split into three components— the contributions of dispersion and polar forces2 , and hydrogen bonding—Beerbower (11) proposed a more evolved expression of the relationship, which was finally simplified by Wu (12) as
The surface energetics evolution throughout the entire curing process of two epoxy resins is predicted using a previously developed semiempirical relationship between surface tension and the solubility parameter. Evolution of the temperature and time of both the solubility parameter and density is investigated and used for this prediction, as is the concept of molar volume or mass of the interacting element. The theoretical prediction is compared with measured surface tensions. Experimental data are determined at different times during an isothermal curing process by the Wilhelmy wetting force method for surface tension with viscous drag corrections. Once corrections for viscous effects on measured surface tensions are made, very good agreement is found for the surface energetics evolution. Moreover, the total surface energies of solid cured epoxy resins, which cannot be directly measured, can be estimated with this prediction. Finally, this study provides a tool for further understanding the final adhesive properties of polymeric material considering the time evolution of surface energetics during processing. °C 2000 Academic Press Key Words: epoxy resin curing; surface energetics; solubility parameter; molar volume or mass of interactions; density; viscous effects.
1. INTRODUCTION
In applications involving epoxy systems (1, 2), such as surface coatings, adhesives, polymer composite matrices, and encapsulation of electronic devices, it is the intermolecular interactions across the interface that govern the success of the application. To understand, describe, and ultimately predict such interactions requires, among other things, knowledge of the surface energetics of the materials involved. In the case of an epoxy system, the bulk and surface properties change with time and temperature during the curing process. The molecular interactions and, therefore, the surface energetics are known to be temperature dependent (3). In a previous paper (4), it was found that the liquid surface tension of two different epoxy systems decreases with temperature following a linear regression, as has been shown for many other liquids (3) and molten polymers (5). However, the time evolution of the surface energetics throughout the entire
σL = 0.07147δ 2 V 1/3 ,
[1]
where δ is the solubility parameter and V is the molar volume. This relation proved useful principally for simple organic liquids, molten metals, and salts. In its application to polymers, V should not be identified as the molar volume of the polymer molecule as a whole, nor as that of a repeat unit, since the surface tension of a polymer does not depend on the size of the molecule as such, nor on the size of the repeat unit. Rather, V should be identified as the molar volume of an interacting element, Vi ,
2 In relation to the group additivity theory, polar contributions refer here to dipole forces as defined by Hansen (9). Polar forces are, however, more recently and now commonly reported as short-range interactions, which are predominantly (Lewis) acid–base in nature (10).
1 To whom correspondence should be addressed. E-mail: jan-anders.manson @epfl.ch.
55
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C 2000 by Academic Press Copyright ° All rights of reproduction in any form reserved.
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which, however, is not known a priori, but can be expressed as (12) Vi =
Mi , ρ
[2]
where Mi is the molar mass of the interacting element and ρ is the density of the polymer, both of which can be determined experimentally. There are, in principle, two ways of investigating solubility in high-molecular-weight compounds, such as polymers. The first way is to use other measurable physical quantities besides the solubility parameter, such as swelling criterion (13) and intrinsic viscosity (14, 15), to express the solvent properties of a liquid. The other option is to determine indirectly the three solubility parameter components, corresponding to the three types of interaction forces. Group contribution methods have been developed in an attempt to generalize the physical behavior of matter and have then been used to estimate values of numerous polymer properties. The basic idea of this method is that each individual atom, structural group, and configuration brings a specific contribution to the overall properties of a liquid or a solid. The Hoftyzer and Van Krevelen additive group contribution method (16) allows the prediction of the three solubility parameter components, using the equations P δd =
Fdi , δp = V
qP V
Fpi2
rP , δh =
E hi , V
[3]
where δd , δp , and δh are the dispersion forces, polar forces, and hydrogen bonding contributions to the solubility parameter, respectively, V is the repeat unit molar volume, and Fdi , Fpi , and E hi are group contributions to the dispersion, polar, and hydrogen bonding component of the molar attraction constant, respectively. The different group contributions Fdi , Fpi , and E hi for a number of structural groups have been tabulated (16). This paper attempts to investigate the evolution of surface energetics as a function of the conversion of two different commercially available epoxy resins. The time evolution of the liquid epoxy surface tension is first evaluated at different times by Wilhelmy measurements using DCA. The viscosity of the epoxy strongly increases with time during measurements, indicating that viscous effects also increase and are therefore dramatically overestimating the values of surface tension. Based on Hoffman (17) and Kistler (18), corrections for viscous effects on surface tension measurements have previously been proposed (4) and are applied here. However, measurements can be performed only until the resin viscosity becomes too high to allow rapid surface deformation. Predictive extrapolation is thus required to obtain the full time evolution of surface energetics. To predict the full time evolution of surface energetics using Eq. [1], evolution of both the solubility parameter and density as a function of resin conversion is evaluated. Combining the Hoftyzer and Van Krevelen additive group contribution method with near-infrared
FIG. 1. Evolution of the solubility parameter as a function of conversion obtained by combination of the Hoftyzer and Van Krevelen additive group contribution method with near-infrared spectroscopy (NIR) measurements for an amine-cured DGEBA system (19).
spectroscopy (NIR) measurements, Mezzenga et al. (19) have shown a linear dependence of the solubility parameter as a function of the reaction conversion of an amine-cured DGEBA system. Figure 1 shows this linear evolution obtained by the authors. The results of Eom et al. (20) also show that the density change during the conversion of an amine-cured TGMDA system can be approximated with a linear regression. Figure 2 shows the density measurements obtained by the authors. In this study, linearity of the evolution as a function of conversion of both the solubility parameter and density is used. The solubility parameter and density are thus evaluated only at zero conversion and at complete conversion using the Hoftyzer and Van Krevelen additive group contribution method and a conventional Archimedes principle method, respectively. Comparisons are finally made between the experimental time evolution of surface energetics, obtained by Wilhelmy measurements and corrected for viscous effects, and the predicted total time evolution, obtained using Eq. [1].
FIG. 2. Evolution of density as a function of conversion obtained by buoyancy change measurements in silicon oil for an amine-cured TGMDA system (20).
SURFACE ENERGETICS EVOLUTION IN EPOXY RESIN PROCESSING
SCHEME 1.
57
Schematic chemical structure of the modified DGEBA system compounds: the epoxy resin, reactive modifier, and curing agent.
2. MATERIALS AND METHODS
hardener weight ratio of 100 to 53 and a two-step cure of 160◦ C for 1.3 h and 180◦ C for 2 h for the modified TGMDA system.
2.1 Epoxy Systems Two different commercially available epoxy systems are investigated: a diglycidyl ether of bisphenol A modified with polypropylene glycol diglycidyl ether (LY 5082, Ciba), which is mixed with an isophorone diamine hardener (HY 5083, Ciba), and a tetraglycidyl methylene dianiline modified with 1,4diglycidyl ether of butanediol (LY 1802, Ciba), which is mixed with a laromin-C diamine hardener (HY 2954, Ciba). Schemes 1 and 2 show the schematic chemical structures of each compound—the epoxy resin, its reactive modifier, and its curing agent—for the modified DGEBA system and modified TGMDA system, respectively. The mix ratio and the cure conditions for both epoxy systems are chosen according to the supplier, that is, a resin-to-hardener weight ratio of 100 to 23 and a one-step cure of 80◦ C for 8 h for the modified DGEBA system, and a resin-to-
SCHEME 2.
2.2 Experimental Methods Surface tension measurements were successfully performed using DCA in a previous study (4). The technique is based on the measurement, during immersion and emersion of a solid, of the downward force exerted by the surface tension of a wetting liquid on a solid partially immersed using the Wilhelmy method (21), so that the difference in weight between the solid suspended in the air and that in the probe liquid is F↓ = σL p cos θ − ρL g Ah,
[4]
where F↓ is the force exerted on the solid, p is the wetted perimeter of the solid, ρL is the net density of the liquid, g is the gravitational constant, A is the cross-sectional area of the solid, and h
Schematic chemical structure of the modified TGMDA system compounds: the epoxy resin, reactive modifier, and curing agent.
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is the depth of immersion of the solid. The first term represents surface tension forces acting along the wetted perimeter of the solid, while the second is the buoyancy of the displaced liquid. The DCA measurements are performed using a dynamic tensiometer (7). The surface tension is measured using a platinized platinum rod of 265-µm perimeter against which the contact angle is zero. The solid rod is suspended with a fine wire from a Cahn D-200 electrobalance, with the liquid epoxy resin in a small Teflon cup mounted atop a Burleigh IW-602 electronic translator and placed below the suspended solid. The platinum rod is advanced 2 mm into the liquid at a 16 µm/s rate and withdrawn at the same rate. Force and time data are digitally collected using a personal computer. To avoid any effects of the solid surface roughness or heterogeneity on surface tension measurements (leading to a falsely low surface tension), the force is measured at the zero-buoyancy condition when the liquid has receded over the platinized rod surface. A series of measurements at different times is performed until the resin viscosity does not allow any more measurements and is repeated three times for each system. Repetitions of the experiments showed a good reproducibility of the measurements: variations less than 3% are observed. The microtensiometer used here is equipped with a heater, and a constant temperature is applied during the series of measurements, that is, 31◦ C and 46◦ C for the modified DGEBA system and modified TGMDA system, respectively. The complex viscosity is measured for each epoxy system at a frequency of 1 Hz and a strain of 1000% using a Rheometrics RDA parallel-plate torsional dynamic rheometer. Isothermal measurements are performed at different times using 25-mmdiameter plates. A viscosity–time plot is obtained at 31 and 46◦ C for the modified DGEBA system and modified TGMDA system, respectively. Isothermal thermograms at two different temperatures are performed for each epoxy system using a Perkin Elmer differential scanning calorimeter. The temperatures chosen are 31 and 80◦ C and 46 and 160◦ C for the modified DGEBA system and modified TGMDA system, respectively. Conversion–time curves under isothermal conditions are obtained by normalizing the integral heat flow curves with the total enthalpy of reaction. The viscosity and thermal analysis results are combined to express the viscosity as a function of conversion. Figure 3 shows the result obtained at low curing temperature for both resins. The solubility parameter is calculated for the uncured liquid epoxy and the fully cured solid epoxy using the Hoftyzer and Van Krevelen group contribution method (16, 19), for which δ is given by δ=
q δd2 + δp2 + δh2 .
[5]
FIG. 3. Evolution of viscosity and of cosine θD as a function of epoxy conversion at low curing temperatures. The vertical dashed line represents the limiting conversion for the surface tension measurements.
sentative of the epoxy network, is finally determined using the same weighting. In an amine-cured epoxy system at stoichiometric concentrations, as is the case here, the representative unit volume includes two epoxy groups and one primary amine at zero conversion. After a complete reaction, the epoxy groups change to hydroxyl groups, and the hardener primary amines evolve to tertiary amines. The density measurements of both the uncured liquid epoxy and fully cured solid epoxy are performed by Archimedes principle using a Mettler AT analytical balance. The cured solid epoxy density is determined in deionized, triply distilled water, while the totally uncured liquid epoxy density is evaluated using a glass reference weight. All measurements are made under ambient conditions, except for the temperature dependence measurements of the uncured liquid epoxy for which the resins are rapidly heated and measurements are performed before curing is initiated. 3. RESULTS AND DISCUSSION
The sum of the three different group contributions of the molar attraction constant are first determined for each compound of the system. Weight is then applied according to the concentrations of reactive diluent and hardener in each system. The structural repeat unit molar volume, which is the smallest volume repre-
The evolution of surface tension as a function of conversion is plotted in Fig. 4 for both epoxy systems. The same behavior can be observed: surface tension remains constant up to 5 and 10% conversion—in the case of the modified DGEBA system
SURFACE ENERGETICS EVOLUTION IN EPOXY RESIN PROCESSING
59
and modified TGMDA system, respectively—and then starts to increase slowly with conversion until the viscosity of the resins becomes too high to allow any measurements. A correction for viscous effects on surface tension measurements was proposed for complete equilibrium wetting systems in a previous paper and is expressed as (4) σL, corrected = σL, measured cos θD ,
[6]
where θD is the dynamic contact angle obtained for a given Capillary number, Ca, that is, for a given viscosity, velocity, and surface tension, according to Kistler (18) (
"
µ θD = arccos 1 − 2tanh 5.16
Ca 1 + 1.31Ca0.99
¶0.706 #) , [7]
with Ca =
ηv , σL
[8]
where η is the viscosity of the liquid and v the interline velocity. This dynamic contact angle is a consequence of viscous effects and represents the deviation from the zero contact angle which is expected when measuring surface tensions. The surface tension values corrected using Eq. [6] are plotted in Fig. 4 for both epoxy systems. The results show that the viscous effects on surface tension increase as the reaction conversion advances and become very significant for the last data on each plot. Figure 3 shows the evolution plot of the cosine of θD as a function of conversion and illustrates the extent of the correction due to viscous effects. Sauer and Kampert (22) recently developed a technique to investigate surface tension and viscosity simultaneously. Based on a modified Wilhelmy method, these measurements can be performed up to very high viscosity. As a topic for future work, this technique could be used to measure surface tension up to very high conversions without the requirement of viscous drag corrections. While the surface tension, the solubility parameter, and density can be either measured or calculated, the molar mass of the interacting element cannot be clearly determined. Rather than confirming the measured surface tension values with a theoretical evaluation, this paper aims at following the evolution of surface energetics as a function of epoxy resin conversion. The molar mass of the interacting element is thus evaluated here from Eq. [1] on the basis of the properties of each uncured liquid epoxy system at different temperatures. The density of each uncured liquid epoxy system was therefore measured at different temperatures. Moreover, the surface tension temperature dependence was previously investigated for both systems (4). In both cases, the same temperature dependence is observed: surface tension and density decrease with temperature, following a linear regression. Surface tension and density values at two different temperatures are listed in Table 1. The temperature dependence of the solubility parameter can thus be simply estimated from
FIG. 4. Evolution of surface tension as a function of epoxy conversion at low curing temperatures. Corrections for viscous effects are made on the measured surface tension values and show a high impact of the viscosity on Wilhelmy measurements as the reaction conversion advances.
the temperature dependence of density, since the three different group contributions of the molar attraction constant and the structural repeat unit molar mass remain constant with temperature. The molar mass of the interacting element can now be determined at different temperatures using Eq. [1]. The evolution of the solubility parameter and the molar mass of interactions as a function of temperature can thus also be approximated with a linear regression. Values of the uncured liquid epoxy solubility parameter and molar mass of the interacting element at two different temperatures are listed in Table 1. Physical interpretations of the values obtained for the molar mass of interactions are not self-explanatory. However, the tendency seems to be in agreement with the chemical structure and composition of both systems. A higher density of strong interactions has been found in the modified TGMDA system and has been attributed to the higher concentration of amines (4). The density and solubility parameter of the fully cured solid epoxy are measured and calculated, respectively, and presented in Table 1. At this point in the investigation, it was assumed that the molar mass of the interacting element is constant through the total reaction conversion of an epoxy resin. This assumption can be subject to question. For example, a change in structural groups during curing might affect the “interacting element” and, thus, its molar mass. However, the definition and interpretation
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PAGE ET AL.
TABLE 1 Corrected surface tension, σL a (mJ/m2 )
Density, ρ (g/cm3 )
Solubility parameter, δ (J1/2 /cm3/2 )
Molar mass of interactions, Mi b (g/mol)
Modified DGEBA system Uncured liquid at 31◦ C Uncured liquid at 80◦ C Fully cured solid at RT
35.0 33.6 35.1
1.10 1.07 1.15
20.2 19.8 23.1
1151 1077 —
Modified TGMDA system Uncured liquid at 46◦ C Uncured liquid at 160◦ C Fully cured solid at RT
36.5 28.4 35.5
1.07 1.02 1.13
18.4 17.6 22.0
2190 1241 —
a The values indicated have been previously measured and published (4). The values indicated for the fully cured solid epoxy are the Lifshitz–van der Waals components of the surface energy. b The molar mass of the interacting element is assumed to be temperature dependent and constant only during the reaction conversion.
of this physical entity are not clearly stated and, furthermore, no existing method to accurately determine it is available to our knowledge. In addition, the most important factor influencing the predicted behavior of surface energetics is certainly the solubility parameter. The surface tension is indeed increasing with the square of the solubility parameter in Eq. [1], whereas the molar mass of the interacting element is to the power of one-third. The probable error induced by the assumption is thus considered to be minimal. The predicted evolution curve of surface tension is shown in Fig. 5 for both systems at a low curing temperature, namely, 31 and 46◦ C for the modified DGEBA system and modified TGMDA system, respectively. Surface tension evolution was calculated using Eq. [1] from the density and solubility parameter linear dependences, which are evaluated from the uncured liquid values at the corresponding temperature and the fully cured solid values, as well as the molar mass of interactions at the corresponding temperature. Very good agreement can be observed at the beginning of the reaction conversion between the experimentally measured and corrected values and the prediction of surface energetics for both epoxy systems. At low curing temperatures, however, the reaction is not complete, and a conversion of less than 50% is reached for both epoxy systems (Fig. 5). Since the prediction is suitable at low temperatures, it should be applicable to prediction of surface energetics at high curing temperatures for which full conversion can be reached. The evolution of the solubility parameter, density, and molar mass of interactions of the uncured liquid as a function of temperature is known. The surface tensions can thus be calculated using Eq. [1] as before by simply replacing the solubility parameter, density, and molar mass of interaction values of the uncured liquid with those corresponding to a higher curing temperature. Figure 6 shows the predicted evolution curve of surface energetics for the two epoxy systems at high curing temperature, namely, 80 and 160◦ C for the modified DGEBA system and modified TGMDA system, respectively. The starting value of the prediction curve is the measured surface tension of the uncured liquid epoxies, while the final value can be considered the total surface energy of the
fully cured solid epoxies. Unlike liquid surface tension, there is no direct measurement for solid surface energy, since only the Lifshitz–van der Waals component of the total surface energy can be determined. The Lifshitz–van der Waals forces of intermolecular attraction include London (dispersion), Keesom (dipole–dipole), and Debye (dipole-induced dipole) forces. The
FIG. 5. Prediction of surface tension evolution as a function of epoxy conversion at low curing temperatures using Eq. [1]. Good agreement is observed between the calculated and corrected experimental values of surface tension at the beginning of the reaction conversion.
61
SURFACE ENERGETICS EVOLUTION IN EPOXY RESIN PROCESSING
a predicting equation for the surface energetics of epoxy resins is proposed µ σL (T, α) = 0.07147δ 2 (T, α)
FIG. 6. Prediction of surface tension evolution as a function of epoxy conversion at high curing temperatures using Eq. [1]. The Lifshitz–van der Waals component of the surface energy of the fully cured solid epoxy is indicated. The final value of surface energy obtained with the prediction should be representative of the total surface energy of the fully cured epoxy systems.
Lifshitz–van der Waals component of surface energy was previously evaluated by DCA (4) for both epoxy systems. It was calculated from the static advancing contact angle obtained with the neutral diiodomethane and α-bromonaphthalene against fully cured epoxy resins. Its value is indicated in Table 1 and shown in Fig. 6. As can be observed, the value of the Lifshitz–van der Waals component of surface energy is lower than the final value of the prediction curve for both systems. The difference between the two previous values can thus be estimated as the potential for other interactions, i.e., other than nonspecific interactions, of the fully cured solid epoxies, such as Lewis acid–base interactions including hydrogen bonding. It is finally worth noting that the prediction of surface energetics revealed here proposes a unique way to determine the total surface energy of a solid. As a consequence, the respective evolution during the curing process of the different types of interactions involved can be deduced. The time evolution of surface energetics through the entire process, that is, from the liquid surface tension at the beginning of the process to the solid surface energy at the end of the process, had never been investigated before. It has been shown here that it is possible to predict this time evolution using a bulk property, such as the solubility parameter. From an empirical relationship,
Mi (T ) ρ(T, α)
¶1/3 .
[9]
Here T is the temperature and α is the conversion. Investigators have long sought to predict the level of interfacial adhesion in terms of one or a limited number of thermodynamic criteria, which, in turn, might be determined by relatively simple independent measurements. This is perhaps an unrealistic objective in the most general sense, in view of the varied and disparate mechanisms thought to be responsible for adhesion, each calling for different and sometimes contradictory criteria. Nonetheless, it is widely believed that there are a large number of situations for which a simple adsorption mechanism is applicable. In these situations, it seems reasonable to seek a correlation between the mechanically measured adhesion strength and the energy of molecular interaction, per unit area, across the adhesive–adherend interface, that is, the thermodynamic work of adhesion. Nevertheless, the requirements for demonstrating a meaningful relationship between mechanical adhesion properties and surface energy parameters or related thermodynamic work of adhesion remain very stringent. Here, the surface energetics evolution during processing of polymeric materials might be a step forward in understanding such a relationship. 4. CONCLUSIONS
Based on an empirical relationship between surface tension and the solubility parameter, the evolution of surface energetics through the entire curing process of epoxy resins is predicted. Very good agreement is obtained by comparing the experimental evolution of surface tension measured by the Wilhelmy wetting force method and the predicted evolution of surface energetics. Corrections for viscous effects, however, have to be made on measured surface tensions. The surface energies of solid epoxy have been estimated by this prediction, and the final value obtained can be considered as the total solid surface energy of the fully cured material. Finally, prediction of the evolution of surface energetics during the entire processing of polymeric material should provide a better understanding of the final adhesive properties of the material. ACKNOWLEDGMENTS The Surface, Polymers and Colloids Laboratory at the University of Washington, where the DCA experiments were performed, is gratefully acknowledged. Financial support from the Swiss National Fund for Scientific Research is also acknowledged.
REFERENCES 1. Lee, H., and Neville, K., “Handbook of Epoxy Resins,” McGraw–Hill, New York, 1981.
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2. May, C. A., “Epoxy Resins, Chemistry and Technology.” Marcel Dekker, New York, 1988. 3. Scatchard, G., “Equilibrium in Solutions: Surface and Colloid Chemistry.” Harvard Univ. Press, Cambridge, 1976. 4. Page, S. A., Berg, J. C., and M˚anson, J.-A. E., J. Adhesion Sci. Technol. 5. Wu, S., “Polymer Interface and Adhesion.” Marcel Dekker, New York, 1982. 6. Adamson, A. W., and Gast, A. P., “Physical Chemistry of Surfaces.” Wiley– Interscience, New York, 1997. 7. Berg, J. C., in “Composite Systems from Natural and Synthetic Polymers” (L. Salm´en, A. DeRuvo, J. C. Seferis, and E. B. Stark, Eds.), p. 23. Elsevier, Amsterdam, 1986. 8. Hildebrand, J. H., and Scott, R. L., “The Solubility of Nonelectrolytes.” Reinhold, New York, 1950. 9. Hansen, C. M., J. Paint Technol. 39, 104 (1967). 10. van Oss, C. J., Ju, L., Chaudhury, M. K., and Good, R. J., J. Colloid Interface Sci. 128, 313 (1989).
11. Beerbower, A., J. Colloid Interface Sci. 35, 126 (1971). 12. Wu, S., in “Polymer Blends” (D. R. Paul and S. Newman, Eds.), Vol. 1, p. 243. Academic Press, New York, 1978. 13. Muller, G., Schroder, E., and Arndt, K. F., “Polymer Characterization.” Hanser, Munich, 1990. 14. de Gennes, P. G., “Scaling Concepts in Polymer Physics.” Cornell Univ. Press, Ithaca, NY, 1979. 15. Sperling, L. H., “Introduction to Physical Polymer Science.” Wiley, New York, 1992. 16. Van Krevelen, D. W., “Properties of Polymers.” Elsevier, Amsterdam, 1990. 17. Hoffman, R. L., J. Colloid Interface Sci. 50, 228 (1975). 18. Kistler, S. F., in “Wettability” (J. C. Berg, Ed.), Vol. 49, p. 311. Marcel Dekker, New York, 1993. 19. Mezzenga, R., Boogh, L., and M˚anson, J.-A. E., J. Polym. Sci. 20. Eom, Y. S., Boogh, L., Michaud, V., Sunderland, P., and M˚anson, J.-A. E., Polym. Sci. Eng. 21. Wilhelmy, J., Ann. Phys. 119, 177 (1863). 22. Sauer, B. B., and Kampert, W. G., J. Colloid Interface Sci. 199, 28 (1998).
Surface Energetics Evolution during Processing of Epoxy Resins St´ephane A. Page,∗ Raffaele Mezzenga,∗ Louis Boogh,∗ John C. Berg,† and Jan-Anders E. M˚anson∗ ,1 ∗ Laboratoire de Technologie des Composites et Polym`eres (LTC), Ecole Polytechnique F´ed´erale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; and †Department of Chemical Engineering, University of Washington, Seattle, Washington 98195–1750 Received April 12, 1999; accepted October 29, 1999
process, that is, from the liquid surface tension at the beginning of the process to the solid surface energy at the end of the process, has not yet been investigated and reported. Liquid surface energetics are relatively easily characterized in terms of surface tension, σL . The simplicity of such characterization is due to the energetic and morphological homogeneity of fluid surface as well as to the availability of a mechanical measurement to determine the surface tension. There are a number of experimental methods for determining the surface tension of liquids (6). One of the most convenient ways to determine surface tension is by the Wilhelmy method using a dynamic contact angle analysis (DCA) system. In DCA, the downward force on a solid of known perimeter slowly advanced into and then pulled from a liquid bath, whose surface tension is to be determined, is measured (7). Since the surface tension is a manifestation of intermolecular forces, it may be expected to be related to other properties derived from intermolecular forces, such as internal pressure, compressibility, and cohesive energy density. An interesting empirical relationship between surface tension and the solubility parameter was first found by Hildebrand and Scott (8). Based on Hansen’s work (9), which stipulated that the solubility parameter can be split into three components— the contributions of dispersion and polar forces2 , and hydrogen bonding—Beerbower (11) proposed a more evolved expression of the relationship, which was finally simplified by Wu (12) as
The surface energetics evolution throughout the entire curing process of two epoxy resins is predicted using a previously developed semiempirical relationship between surface tension and the solubility parameter. Evolution of the temperature and time of both the solubility parameter and density is investigated and used for this prediction, as is the concept of molar volume or mass of the interacting element. The theoretical prediction is compared with measured surface tensions. Experimental data are determined at different times during an isothermal curing process by the Wilhelmy wetting force method for surface tension with viscous drag corrections. Once corrections for viscous effects on measured surface tensions are made, very good agreement is found for the surface energetics evolution. Moreover, the total surface energies of solid cured epoxy resins, which cannot be directly measured, can be estimated with this prediction. Finally, this study provides a tool for further understanding the final adhesive properties of polymeric material considering the time evolution of surface energetics during processing. °C 2000 Academic Press Key Words: epoxy resin curing; surface energetics; solubility parameter; molar volume or mass of interactions; density; viscous effects.
1. INTRODUCTION
In applications involving epoxy systems (1, 2), such as surface coatings, adhesives, polymer composite matrices, and encapsulation of electronic devices, it is the intermolecular interactions across the interface that govern the success of the application. To understand, describe, and ultimately predict such interactions requires, among other things, knowledge of the surface energetics of the materials involved. In the case of an epoxy system, the bulk and surface properties change with time and temperature during the curing process. The molecular interactions and, therefore, the surface energetics are known to be temperature dependent (3). In a previous paper (4), it was found that the liquid surface tension of two different epoxy systems decreases with temperature following a linear regression, as has been shown for many other liquids (3) and molten polymers (5). However, the time evolution of the surface energetics throughout the entire
σL = 0.07147δ 2 V 1/3 ,
[1]
where δ is the solubility parameter and V is the molar volume. This relation proved useful principally for simple organic liquids, molten metals, and salts. In its application to polymers, V should not be identified as the molar volume of the polymer molecule as a whole, nor as that of a repeat unit, since the surface tension of a polymer does not depend on the size of the molecule as such, nor on the size of the repeat unit. Rather, V should be identified as the molar volume of an interacting element, Vi ,
2 In relation to the group additivity theory, polar contributions refer here to dipole forces as defined by Hansen (9). Polar forces are, however, more recently and now commonly reported as short-range interactions, which are predominantly (Lewis) acid–base in nature (10).
1 To whom correspondence should be addressed. E-mail: jan-anders.manson @epfl.ch.
55
0021-9797/00 $35.00
C 2000 by Academic Press Copyright ° All rights of reproduction in any form reserved.
56
PAGE ET AL.
which, however, is not known a priori, but can be expressed as (12) Vi =
Mi , ρ
[2]
where Mi is the molar mass of the interacting element and ρ is the density of the polymer, both of which can be determined experimentally. There are, in principle, two ways of investigating solubility in high-molecular-weight compounds, such as polymers. The first way is to use other measurable physical quantities besides the solubility parameter, such as swelling criterion (13) and intrinsic viscosity (14, 15), to express the solvent properties of a liquid. The other option is to determine indirectly the three solubility parameter components, corresponding to the three types of interaction forces. Group contribution methods have been developed in an attempt to generalize the physical behavior of matter and have then been used to estimate values of numerous polymer properties. The basic idea of this method is that each individual atom, structural group, and configuration brings a specific contribution to the overall properties of a liquid or a solid. The Hoftyzer and Van Krevelen additive group contribution method (16) allows the prediction of the three solubility parameter components, using the equations P δd =
Fdi , δp = V
qP V
Fpi2
rP , δh =
E hi , V
[3]
where δd , δp , and δh are the dispersion forces, polar forces, and hydrogen bonding contributions to the solubility parameter, respectively, V is the repeat unit molar volume, and Fdi , Fpi , and E hi are group contributions to the dispersion, polar, and hydrogen bonding component of the molar attraction constant, respectively. The different group contributions Fdi , Fpi , and E hi for a number of structural groups have been tabulated (16). This paper attempts to investigate the evolution of surface energetics as a function of the conversion of two different commercially available epoxy resins. The time evolution of the liquid epoxy surface tension is first evaluated at different times by Wilhelmy measurements using DCA. The viscosity of the epoxy strongly increases with time during measurements, indicating that viscous effects also increase and are therefore dramatically overestimating the values of surface tension. Based on Hoffman (17) and Kistler (18), corrections for viscous effects on surface tension measurements have previously been proposed (4) and are applied here. However, measurements can be performed only until the resin viscosity becomes too high to allow rapid surface deformation. Predictive extrapolation is thus required to obtain the full time evolution of surface energetics. To predict the full time evolution of surface energetics using Eq. [1], evolution of both the solubility parameter and density as a function of resin conversion is evaluated. Combining the Hoftyzer and Van Krevelen additive group contribution method with near-infrared
FIG. 1. Evolution of the solubility parameter as a function of conversion obtained by combination of the Hoftyzer and Van Krevelen additive group contribution method with near-infrared spectroscopy (NIR) measurements for an amine-cured DGEBA system (19).
spectroscopy (NIR) measurements, Mezzenga et al. (19) have shown a linear dependence of the solubility parameter as a function of the reaction conversion of an amine-cured DGEBA system. Figure 1 shows this linear evolution obtained by the authors. The results of Eom et al. (20) also show that the density change during the conversion of an amine-cured TGMDA system can be approximated with a linear regression. Figure 2 shows the density measurements obtained by the authors. In this study, linearity of the evolution as a function of conversion of both the solubility parameter and density is used. The solubility parameter and density are thus evaluated only at zero conversion and at complete conversion using the Hoftyzer and Van Krevelen additive group contribution method and a conventional Archimedes principle method, respectively. Comparisons are finally made between the experimental time evolution of surface energetics, obtained by Wilhelmy measurements and corrected for viscous effects, and the predicted total time evolution, obtained using Eq. [1].
FIG. 2. Evolution of density as a function of conversion obtained by buoyancy change measurements in silicon oil for an amine-cured TGMDA system (20).
SURFACE ENERGETICS EVOLUTION IN EPOXY RESIN PROCESSING
SCHEME 1.
57
Schematic chemical structure of the modified DGEBA system compounds: the epoxy resin, reactive modifier, and curing agent.
2. MATERIALS AND METHODS
hardener weight ratio of 100 to 53 and a two-step cure of 160◦ C for 1.3 h and 180◦ C for 2 h for the modified TGMDA system.
2.1 Epoxy Systems Two different commercially available epoxy systems are investigated: a diglycidyl ether of bisphenol A modified with polypropylene glycol diglycidyl ether (LY 5082, Ciba), which is mixed with an isophorone diamine hardener (HY 5083, Ciba), and a tetraglycidyl methylene dianiline modified with 1,4diglycidyl ether of butanediol (LY 1802, Ciba), which is mixed with a laromin-C diamine hardener (HY 2954, Ciba). Schemes 1 and 2 show the schematic chemical structures of each compound—the epoxy resin, its reactive modifier, and its curing agent—for the modified DGEBA system and modified TGMDA system, respectively. The mix ratio and the cure conditions for both epoxy systems are chosen according to the supplier, that is, a resin-to-hardener weight ratio of 100 to 23 and a one-step cure of 80◦ C for 8 h for the modified DGEBA system, and a resin-to-
SCHEME 2.
2.2 Experimental Methods Surface tension measurements were successfully performed using DCA in a previous study (4). The technique is based on the measurement, during immersion and emersion of a solid, of the downward force exerted by the surface tension of a wetting liquid on a solid partially immersed using the Wilhelmy method (21), so that the difference in weight between the solid suspended in the air and that in the probe liquid is F↓ = σL p cos θ − ρL g Ah,
[4]
where F↓ is the force exerted on the solid, p is the wetted perimeter of the solid, ρL is the net density of the liquid, g is the gravitational constant, A is the cross-sectional area of the solid, and h
Schematic chemical structure of the modified TGMDA system compounds: the epoxy resin, reactive modifier, and curing agent.
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PAGE ET AL.
is the depth of immersion of the solid. The first term represents surface tension forces acting along the wetted perimeter of the solid, while the second is the buoyancy of the displaced liquid. The DCA measurements are performed using a dynamic tensiometer (7). The surface tension is measured using a platinized platinum rod of 265-µm perimeter against which the contact angle is zero. The solid rod is suspended with a fine wire from a Cahn D-200 electrobalance, with the liquid epoxy resin in a small Teflon cup mounted atop a Burleigh IW-602 electronic translator and placed below the suspended solid. The platinum rod is advanced 2 mm into the liquid at a 16 µm/s rate and withdrawn at the same rate. Force and time data are digitally collected using a personal computer. To avoid any effects of the solid surface roughness or heterogeneity on surface tension measurements (leading to a falsely low surface tension), the force is measured at the zero-buoyancy condition when the liquid has receded over the platinized rod surface. A series of measurements at different times is performed until the resin viscosity does not allow any more measurements and is repeated three times for each system. Repetitions of the experiments showed a good reproducibility of the measurements: variations less than 3% are observed. The microtensiometer used here is equipped with a heater, and a constant temperature is applied during the series of measurements, that is, 31◦ C and 46◦ C for the modified DGEBA system and modified TGMDA system, respectively. The complex viscosity is measured for each epoxy system at a frequency of 1 Hz and a strain of 1000% using a Rheometrics RDA parallel-plate torsional dynamic rheometer. Isothermal measurements are performed at different times using 25-mmdiameter plates. A viscosity–time plot is obtained at 31 and 46◦ C for the modified DGEBA system and modified TGMDA system, respectively. Isothermal thermograms at two different temperatures are performed for each epoxy system using a Perkin Elmer differential scanning calorimeter. The temperatures chosen are 31 and 80◦ C and 46 and 160◦ C for the modified DGEBA system and modified TGMDA system, respectively. Conversion–time curves under isothermal conditions are obtained by normalizing the integral heat flow curves with the total enthalpy of reaction. The viscosity and thermal analysis results are combined to express the viscosity as a function of conversion. Figure 3 shows the result obtained at low curing temperature for both resins. The solubility parameter is calculated for the uncured liquid epoxy and the fully cured solid epoxy using the Hoftyzer and Van Krevelen group contribution method (16, 19), for which δ is given by δ=
q δd2 + δp2 + δh2 .
[5]
FIG. 3. Evolution of viscosity and of cosine θD as a function of epoxy conversion at low curing temperatures. The vertical dashed line represents the limiting conversion for the surface tension measurements.
sentative of the epoxy network, is finally determined using the same weighting. In an amine-cured epoxy system at stoichiometric concentrations, as is the case here, the representative unit volume includes two epoxy groups and one primary amine at zero conversion. After a complete reaction, the epoxy groups change to hydroxyl groups, and the hardener primary amines evolve to tertiary amines. The density measurements of both the uncured liquid epoxy and fully cured solid epoxy are performed by Archimedes principle using a Mettler AT analytical balance. The cured solid epoxy density is determined in deionized, triply distilled water, while the totally uncured liquid epoxy density is evaluated using a glass reference weight. All measurements are made under ambient conditions, except for the temperature dependence measurements of the uncured liquid epoxy for which the resins are rapidly heated and measurements are performed before curing is initiated. 3. RESULTS AND DISCUSSION
The sum of the three different group contributions of the molar attraction constant are first determined for each compound of the system. Weight is then applied according to the concentrations of reactive diluent and hardener in each system. The structural repeat unit molar volume, which is the smallest volume repre-
The evolution of surface tension as a function of conversion is plotted in Fig. 4 for both epoxy systems. The same behavior can be observed: surface tension remains constant up to 5 and 10% conversion—in the case of the modified DGEBA system
SURFACE ENERGETICS EVOLUTION IN EPOXY RESIN PROCESSING
59
and modified TGMDA system, respectively—and then starts to increase slowly with conversion until the viscosity of the resins becomes too high to allow any measurements. A correction for viscous effects on surface tension measurements was proposed for complete equilibrium wetting systems in a previous paper and is expressed as (4) σL, corrected = σL, measured cos θD ,
[6]
where θD is the dynamic contact angle obtained for a given Capillary number, Ca, that is, for a given viscosity, velocity, and surface tension, according to Kistler (18) (
"
µ θD = arccos 1 − 2tanh 5.16
Ca 1 + 1.31Ca0.99
¶0.706 #) , [7]
with Ca =
ηv , σL
[8]
where η is the viscosity of the liquid and v the interline velocity. This dynamic contact angle is a consequence of viscous effects and represents the deviation from the zero contact angle which is expected when measuring surface tensions. The surface tension values corrected using Eq. [6] are plotted in Fig. 4 for both epoxy systems. The results show that the viscous effects on surface tension increase as the reaction conversion advances and become very significant for the last data on each plot. Figure 3 shows the evolution plot of the cosine of θD as a function of conversion and illustrates the extent of the correction due to viscous effects. Sauer and Kampert (22) recently developed a technique to investigate surface tension and viscosity simultaneously. Based on a modified Wilhelmy method, these measurements can be performed up to very high viscosity. As a topic for future work, this technique could be used to measure surface tension up to very high conversions without the requirement of viscous drag corrections. While the surface tension, the solubility parameter, and density can be either measured or calculated, the molar mass of the interacting element cannot be clearly determined. Rather than confirming the measured surface tension values with a theoretical evaluation, this paper aims at following the evolution of surface energetics as a function of epoxy resin conversion. The molar mass of the interacting element is thus evaluated here from Eq. [1] on the basis of the properties of each uncured liquid epoxy system at different temperatures. The density of each uncured liquid epoxy system was therefore measured at different temperatures. Moreover, the surface tension temperature dependence was previously investigated for both systems (4). In both cases, the same temperature dependence is observed: surface tension and density decrease with temperature, following a linear regression. Surface tension and density values at two different temperatures are listed in Table 1. The temperature dependence of the solubility parameter can thus be simply estimated from
FIG. 4. Evolution of surface tension as a function of epoxy conversion at low curing temperatures. Corrections for viscous effects are made on the measured surface tension values and show a high impact of the viscosity on Wilhelmy measurements as the reaction conversion advances.
the temperature dependence of density, since the three different group contributions of the molar attraction constant and the structural repeat unit molar mass remain constant with temperature. The molar mass of the interacting element can now be determined at different temperatures using Eq. [1]. The evolution of the solubility parameter and the molar mass of interactions as a function of temperature can thus also be approximated with a linear regression. Values of the uncured liquid epoxy solubility parameter and molar mass of the interacting element at two different temperatures are listed in Table 1. Physical interpretations of the values obtained for the molar mass of interactions are not self-explanatory. However, the tendency seems to be in agreement with the chemical structure and composition of both systems. A higher density of strong interactions has been found in the modified TGMDA system and has been attributed to the higher concentration of amines (4). The density and solubility parameter of the fully cured solid epoxy are measured and calculated, respectively, and presented in Table 1. At this point in the investigation, it was assumed that the molar mass of the interacting element is constant through the total reaction conversion of an epoxy resin. This assumption can be subject to question. For example, a change in structural groups during curing might affect the “interacting element” and, thus, its molar mass. However, the definition and interpretation
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PAGE ET AL.
TABLE 1 Corrected surface tension, σL a (mJ/m2 )
Density, ρ (g/cm3 )
Solubility parameter, δ (J1/2 /cm3/2 )
Molar mass of interactions, Mi b (g/mol)
Modified DGEBA system Uncured liquid at 31◦ C Uncured liquid at 80◦ C Fully cured solid at RT
35.0 33.6 35.1
1.10 1.07 1.15
20.2 19.8 23.1
1151 1077 —
Modified TGMDA system Uncured liquid at 46◦ C Uncured liquid at 160◦ C Fully cured solid at RT
36.5 28.4 35.5
1.07 1.02 1.13
18.4 17.6 22.0
2190 1241 —
a The values indicated have been previously measured and published (4). The values indicated for the fully cured solid epoxy are the Lifshitz–van der Waals components of the surface energy. b The molar mass of the interacting element is assumed to be temperature dependent and constant only during the reaction conversion.
of this physical entity are not clearly stated and, furthermore, no existing method to accurately determine it is available to our knowledge. In addition, the most important factor influencing the predicted behavior of surface energetics is certainly the solubility parameter. The surface tension is indeed increasing with the square of the solubility parameter in Eq. [1], whereas the molar mass of the interacting element is to the power of one-third. The probable error induced by the assumption is thus considered to be minimal. The predicted evolution curve of surface tension is shown in Fig. 5 for both systems at a low curing temperature, namely, 31 and 46◦ C for the modified DGEBA system and modified TGMDA system, respectively. Surface tension evolution was calculated using Eq. [1] from the density and solubility parameter linear dependences, which are evaluated from the uncured liquid values at the corresponding temperature and the fully cured solid values, as well as the molar mass of interactions at the corresponding temperature. Very good agreement can be observed at the beginning of the reaction conversion between the experimentally measured and corrected values and the prediction of surface energetics for both epoxy systems. At low curing temperatures, however, the reaction is not complete, and a conversion of less than 50% is reached for both epoxy systems (Fig. 5). Since the prediction is suitable at low temperatures, it should be applicable to prediction of surface energetics at high curing temperatures for which full conversion can be reached. The evolution of the solubility parameter, density, and molar mass of interactions of the uncured liquid as a function of temperature is known. The surface tensions can thus be calculated using Eq. [1] as before by simply replacing the solubility parameter, density, and molar mass of interaction values of the uncured liquid with those corresponding to a higher curing temperature. Figure 6 shows the predicted evolution curve of surface energetics for the two epoxy systems at high curing temperature, namely, 80 and 160◦ C for the modified DGEBA system and modified TGMDA system, respectively. The starting value of the prediction curve is the measured surface tension of the uncured liquid epoxies, while the final value can be considered the total surface energy of the
fully cured solid epoxies. Unlike liquid surface tension, there is no direct measurement for solid surface energy, since only the Lifshitz–van der Waals component of the total surface energy can be determined. The Lifshitz–van der Waals forces of intermolecular attraction include London (dispersion), Keesom (dipole–dipole), and Debye (dipole-induced dipole) forces. The
FIG. 5. Prediction of surface tension evolution as a function of epoxy conversion at low curing temperatures using Eq. [1]. Good agreement is observed between the calculated and corrected experimental values of surface tension at the beginning of the reaction conversion.
61
SURFACE ENERGETICS EVOLUTION IN EPOXY RESIN PROCESSING
a predicting equation for the surface energetics of epoxy resins is proposed µ σL (T, α) = 0.07147δ 2 (T, α)
FIG. 6. Prediction of surface tension evolution as a function of epoxy conversion at high curing temperatures using Eq. [1]. The Lifshitz–van der Waals component of the surface energy of the fully cured solid epoxy is indicated. The final value of surface energy obtained with the prediction should be representative of the total surface energy of the fully cured epoxy systems.
Lifshitz–van der Waals component of surface energy was previously evaluated by DCA (4) for both epoxy systems. It was calculated from the static advancing contact angle obtained with the neutral diiodomethane and α-bromonaphthalene against fully cured epoxy resins. Its value is indicated in Table 1 and shown in Fig. 6. As can be observed, the value of the Lifshitz–van der Waals component of surface energy is lower than the final value of the prediction curve for both systems. The difference between the two previous values can thus be estimated as the potential for other interactions, i.e., other than nonspecific interactions, of the fully cured solid epoxies, such as Lewis acid–base interactions including hydrogen bonding. It is finally worth noting that the prediction of surface energetics revealed here proposes a unique way to determine the total surface energy of a solid. As a consequence, the respective evolution during the curing process of the different types of interactions involved can be deduced. The time evolution of surface energetics through the entire process, that is, from the liquid surface tension at the beginning of the process to the solid surface energy at the end of the process, had never been investigated before. It has been shown here that it is possible to predict this time evolution using a bulk property, such as the solubility parameter. From an empirical relationship,
Mi (T ) ρ(T, α)
¶1/3 .
[9]
Here T is the temperature and α is the conversion. Investigators have long sought to predict the level of interfacial adhesion in terms of one or a limited number of thermodynamic criteria, which, in turn, might be determined by relatively simple independent measurements. This is perhaps an unrealistic objective in the most general sense, in view of the varied and disparate mechanisms thought to be responsible for adhesion, each calling for different and sometimes contradictory criteria. Nonetheless, it is widely believed that there are a large number of situations for which a simple adsorption mechanism is applicable. In these situations, it seems reasonable to seek a correlation between the mechanically measured adhesion strength and the energy of molecular interaction, per unit area, across the adhesive–adherend interface, that is, the thermodynamic work of adhesion. Nevertheless, the requirements for demonstrating a meaningful relationship between mechanical adhesion properties and surface energy parameters or related thermodynamic work of adhesion remain very stringent. Here, the surface energetics evolution during processing of polymeric materials might be a step forward in understanding such a relationship. 4. CONCLUSIONS
Based on an empirical relationship between surface tension and the solubility parameter, the evolution of surface energetics through the entire curing process of epoxy resins is predicted. Very good agreement is obtained by comparing the experimental evolution of surface tension measured by the Wilhelmy wetting force method and the predicted evolution of surface energetics. Corrections for viscous effects, however, have to be made on measured surface tensions. The surface energies of solid epoxy have been estimated by this prediction, and the final value obtained can be considered as the total solid surface energy of the fully cured material. Finally, prediction of the evolution of surface energetics during the entire processing of polymeric material should provide a better understanding of the final adhesive properties of the material. ACKNOWLEDGMENTS The Surface, Polymers and Colloids Laboratory at the University of Washington, where the DCA experiments were performed, is gratefully acknowledged. Financial support from the Swiss National Fund for Scientific Research is also acknowledged.
REFERENCES 1. Lee, H., and Neville, K., “Handbook of Epoxy Resins,” McGraw–Hill, New York, 1981.
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2. May, C. A., “Epoxy Resins, Chemistry and Technology.” Marcel Dekker, New York, 1988. 3. Scatchard, G., “Equilibrium in Solutions: Surface and Colloid Chemistry.” Harvard Univ. Press, Cambridge, 1976. 4. Page, S. A., Berg, J. C., and M˚anson, J.-A. E., J. Adhesion Sci. Technol. 5. Wu, S., “Polymer Interface and Adhesion.” Marcel Dekker, New York, 1982. 6. Adamson, A. W., and Gast, A. P., “Physical Chemistry of Surfaces.” Wiley– Interscience, New York, 1997. 7. Berg, J. C., in “Composite Systems from Natural and Synthetic Polymers” (L. Salm´en, A. DeRuvo, J. C. Seferis, and E. B. Stark, Eds.), p. 23. Elsevier, Amsterdam, 1986. 8. Hildebrand, J. H., and Scott, R. L., “The Solubility of Nonelectrolytes.” Reinhold, New York, 1950. 9. Hansen, C. M., J. Paint Technol. 39, 104 (1967). 10. van Oss, C. J., Ju, L., Chaudhury, M. K., and Good, R. J., J. Colloid Interface Sci. 128, 313 (1989).
11. Beerbower, A., J. Colloid Interface Sci. 35, 126 (1971). 12. Wu, S., in “Polymer Blends” (D. R. Paul and S. Newman, Eds.), Vol. 1, p. 243. Academic Press, New York, 1978. 13. Muller, G., Schroder, E., and Arndt, K. F., “Polymer Characterization.” Hanser, Munich, 1990. 14. de Gennes, P. G., “Scaling Concepts in Polymer Physics.” Cornell Univ. Press, Ithaca, NY, 1979. 15. Sperling, L. H., “Introduction to Physical Polymer Science.” Wiley, New York, 1992. 16. Van Krevelen, D. W., “Properties of Polymers.” Elsevier, Amsterdam, 1990. 17. Hoffman, R. L., J. Colloid Interface Sci. 50, 228 (1975). 18. Kistler, S. F., in “Wettability” (J. C. Berg, Ed.), Vol. 49, p. 311. Marcel Dekker, New York, 1993. 19. Mezzenga, R., Boogh, L., and M˚anson, J.-A. E., J. Polym. Sci. 20. Eom, Y. S., Boogh, L., Michaud, V., Sunderland, P., and M˚anson, J.-A. E., Polym. Sci. Eng. 21. Wilhelmy, J., Ann. Phys. 119, 177 (1863). 22. Sauer, B. B., and Kampert, W. G., J. Colloid Interface Sci. 199, 28 (1998).