Langmuir 2008, 24, 9551-9557
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Inverse Gas Chromatographic Method for Measuring the Dispersive Surface Energy Distribution for Particulates Pirre P. Yla¨-Ma¨iha¨niemi,† Jerry Y. Y. Heng,† Frank Thielmann,‡ and Daryl R. Williams*,† Department of Chemical Engineering, Imperial College London, London SW7 2AZ, U.K., and Surface Measurement Systems Limited, 5 Wharfside, Alperton, London HA0 4PE, U.K. ReceiVed May 30, 2008. ReVised Manuscript ReceiVed June 24, 2008 Inverse gas chromatography (IGC) is a widely used method for determining the dispersive component of the surface energy (γsd) of particulate and fibrous solids. Such measurements are normally conducted at very low solute concentrations (infinite dilution), and they result in a single numerical value of γsd for homogeneous materials which exhibit Henry’s Law adsorption behavior. However, many real solid surfaces are heterogeneous and this may be demonstrated by the nonlinear isotherms obtained at low solute surface coverages resulting in reported γsd values which are not unique. This paper presents a new method for determining of γsd distributions as a function of the solute surface coverage using adsorption isosteres for an homologous series of hydrocarbon adsorbates. γsd distributions reported here were successfully determined using two different solid materials (glass beads and alumina particles) up to typical surface coverages of ∼10% and clearly show significant variations in γsd with solute surface coverage. The effects of sample aging and pretreatment also exhibited clear differences in the γsd distributions obtained. γsd was determined using both the Dorris-Gray and Schultz methods, with the Dorris-Gray method exhibiting a much lower experimental error. It was established that the errors associated with this statistical measurement of surface energy were strongly dependent on the quality of the experimental data sets obtained. R2 for the linearity of fit of the retention data to the Dorris-Gray γsd analysis was found to be a valid criterion for predicting the robustness of γsd distributions obtained. Detailed discussions of other critical experimental and analysis factors relevant to this methodology, as well as the reproducibility of γsd profiles are also presented. This paper establishes that IGC can be used for determining the γsd distributions of particulate solids and is demonstrated that this method is very useful way for studying the surface energy heterogeneity of complex particulate solids.
Introduction The surface free energy of particulate and fibrous materials plays a key role in numerous industrial applications and processes. For example, the surface free energy of solids is crucial in determining adhesion in composites and coatings; thus influencing the properties of the final product.1 Surface chemical interactions for catalyst and adsorbent surfaces determine their catalytic and adsorption properties.2 The surface energy is important in effecting particle agglomeration phenomena, particle interactions with adhesives, wetting phenomena as well as the behavior of particle dispersions in liquids.3 Since the surface interactions of solids govern a wide rage of applications, the characterization of surface energetics can provide important information for the improvement of surface properties such as in surface modification4 as well as for the fundamental understanding of surface science. Thus, it has been the topic of intense interest for the past 50 years.5,6 * To whom correspondence should be addressed. E-mail: d.r.williams@ imperial.ac.uk. † Imperial College London. ‡ Surface Measurement Systems Limited.
(1) Wu, S. Polymer interface and adhesion; Marcel Dekker: New York, 1982. (2) Kowalczyk, P.; Kaneko, K.; Terzyk, A. P.; Tanaka, H.; Kanoh, H.; Gauden, P. A. New approach to determination of surface heterogeneity of adsorbents and catalysts from the temperature programmed desorption (TPD) technique: One step beyond the condensation approximation (CA) method. J. Colloid Interface Sci. 2005, 291, 334-344. (3) Sun, C.; Berg, J. C. The effective surface energy of heterogenous solids measured by inverse gas chromatography at infinite dilution. J. Colloid Interface Sci. 2003, 260, 443-448. (4) Donnet, J. B.; Li, Y. J.; Wang, T. K.; Balard, H.; Burns, G. T. Energy of silica xerogels and fumed silica by inverse gas chromatography and inverse liquid chromatography. Rubber Chem. Technol. 2002, 75, 811-824. (5) Etzler, F. M. Characterization of surface free energies and surface chemistry of solids. In Contact Angle, Wettability and Adhesion; VSP: Ultrecht, 2003. (6) Good, R. J. Contact angles and the surface free energy of solids. In Surface and Colloid Science; Plenum Press: New York, 1979.
The fundamental nature of these surface chemical interactions with a solid surface results from long and short-range intermolecular forces which are commonly described as London dispersive and acid-base interactions respectively.5 The dispersive interactions, due to long-range London dispersion forces (van der Waals force), are nonspecific interactions. Acid-base interactions are specific short-range directional chemical interactions which involve charge redistribution and sharing as exemplified by the formation of weak chemical bonds. Hydrogen bonds, which have been shown to be important surface chemically,7 are an important example of acid-base interactions. Inverse gas chromatography (IGC) has successfully been employed for physiochemical studies of solids for over 50 years and can be used to study the surface energetics of solid materials.8,9 In IGC, known solute molecules are carried by an inert carrier gas through a packed column of the unknown solid material. The physicochemical characteristics of the solid-solute system can be determined from the chromatograms of these known solute molecules.8,9 By selecting an appropriate solute molecule, the nature of the interaction to be studied can be chosen. Dispersive interactions can be investigated by using nonpolar solute molecules (e.g., alkanes), while the studies of acid-base interactions require the use of a polar solute molecule, such as ethanol or water. The dispersive component of the surface energy of a solid γsd can be determined using IGC based on well-known approaches (7) Fowkes, F. M.; Mostafa, M. A. Ind. Eng. Chem. 1978, 17, 3–7. (8) Kiselev, A. V.; Yashin, Y. I. Gas-adsorption chromatography; Plenum Press: London, 1969. (9) Conder, J. R.; Young, C. L. Physicochemical measurement by gas chromatography; John Wiley and Sons: Chichester, 1979.
10.1021/la801676n CCC: $40.75 2008 American Chemical Society Published on Web 08/05/2008
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for data analysis, such as Dorris and Gray10 or Schultz.11 In these γsd determinations, a homologous series of alkane vapors are employed at very low solute concentrations (infinite dilution), resulting in one single numerical value for γsd. Many publications report the determination of γsd using infinite dilution measurements.10–16 The premise of much of this work is that the retention behavior for the alkane probes is independent of injection size; that is, the adsorption isotherm is linear in the region of interest. Though this assumption has been demonstrated for many polymeric materials,10,14 it has become increasing rare for investigators to test this assumption, rather preferring the simple expediency of assuming linearity. Over the past 10 years especially, the popularity of IGC has significantly increased;17 however, methods for data analysis have seen very little development, with little change in the standard methods developed over 25 years ago. Many real solid surfaces are often heterogeneous, and therefore a single value for γsd is in these cases an upper limit estimate not necessarily representative of the whole surface.12,15 Due to different functional surface groups, surface topographies, surface irregularities (e.g., edges or vertices) or impurities, real solids exhibit a range of lower and higher energy sites on their surfaces.15,18 When typical IGC measurements are carried out at infinite dilution concentration, the solute molecules adsorbed cover a small portion of the total surface present, often 0.9999.
It is proposed here that coefficient of the fit, R2, for the γsd determinations, as typified in Figure 1 (the alkane reference line), is one important measure of the quality, indeed accuracy, for γsd determined. We chose to accept only those γsd values that met certain R2 criterion for the straight line formed by alkanes. γsd values that were calculated from alkane reference lines with the R2 > 0.9999 being accepted, resulting in γsd profiles shown in Figure 5 which are based on the Dorris-Gray analysis. The profile calculated using C8-C10 contributes one part of the total γsd profile while the profile of C6-C9 and C7-C10 contributes another parts. These Dorris-Gray based profiles were fully selfconsistent with the γsd values, as expected, decreasing until they reach a plateau at the higher surface coverages. Between 0.02 and 0.04 surface coverage the differences between these 3 curves typically represents an error of about 2% in γsd. This result suggests that once the R2 criterion, and thus data quality is high enough, the use of different alkane combinations works well, giving internally self-consistent results. Since the initial Schultz based γsd profiles (Figure 4) without the selection by R2 varied as much as 35% the Schultz calculation could be concluded as a slightly less reliable approach in the prediction of γsd profiles. This limitation may be due to the uncertainty in the values of the cross-sectional area of a solute molecule a that are involved the Schultz calculations, as distinct from the cross-sectional area of a methylene group involved in the Dorris-Gray determination. The a used in the Schultz may change in finite concentration measurements, or for different substrates simply due to the strength on the adsorption process, and hence cause inaccuracy in the resultant γsd calculations. Uncertainty of γsd As reported above, the selection of acceptable γsd values for the distribution profile by the R2 values of the alkane reference lines proved important. Therefore, an error analysis to evaluate the influence of the uncertainty in the slope of an alkane reference line on the distribution profile was undertaken. The standard deviation of the y-axis values of an alkane reference line was calculated from the residuals in the y-axis (linear least-squares method) using the Dorris-Gray derived data. This standard deviation of the y-axis values was further used to calculate the standard deviation of the slope, which allowed the estimation of the relative error of the γsd value. Only the uncertainty in the slope was taken into account. Various alkane reference lines with different R2 values were employed for the error analysis, and the results are summarized
in Figure 6. As evident from Figure 6, the relative error of γsd increases as the R2 value decreases as would have been expected. In the glass beads experiments reported here, the chromatographic peaks of undecane observed were very broad. Accordingly, the determination of the retention times of such broad peaks can be inaccurate. The inaccuracy in the retention times can further lead to larger uncertainty in the slope of the alkane reference line (smaller R2 value) and hence larger uncertainty in γsd. As was seen in Figure 5, none of γsd values that met the criterion of R2 > 0.9999 included undecane in the γsd determination. These results indicate that high quality experimental data and large R2 values are critically important in the reliable determination of γsd profiles. Strict R2 > 0.9999 values were required here for these low surface areas samples here, but may not be necessary with other sample materials. Further work will clarify the data quality thresholds. Comparison between γsd Profiles. γsd distribution profiles were determined using two different materials: glass beads and alumina. A comparison between γsd profiles obtained using these solid samples is shown in Figure 7. The γsd profile on the glass beads was obtained by grouping those two glass beads profiles that were shown in Figure 5 (Dorris-Gray calculation for C6-C9 and C8-C10). The γsd values of the glass beads profile are based on the criterion of R2 > 0.9999. γsd profiles on alumina sample were also calculated based on the Dorris-Gray approach but, due to higher total surface area in alumina columns, only data produced by smaller solutes C6-C8 were suitable for the γsd profile calculations. Several alumina profiles were determined using the same column, and less strict criterion for R2 was applied with the alumina columns (R2 > 0.9997). For the first three alumina profiles (as received columns 1-3), a simple column preconditioning was performed; He flow at 30 °C for 2 h. The preconditioned profile was measured after the column preconditioning for 6 h at elevated temperature 115 °C with flowing He to remove any water or other contaminates present on the sample surface. As visible in Figure 7, a clear difference between the glass beads profile and the alumina profiles indicates that the method presented in this paper is able to distinguish between these two different materials. The first three alumina profiles (As received 1-3) provide an estimation for the reproducibility of this determination. These three γsd profiles all fall within a 5% experimental error band. Since the R2 criterion for the alumina columns was less than for glass beads columns (R2 > 0.9997
Measuring the DispersiVe Surface Energy Distribution for Particulates
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Figure 6. Effect of the experimental uncertainty of the slope of the alkane reference line (Dorris-Gray analysis) on the uncertainty in the value of resultant γsd
Figure 7. Comparison of γsd profiles (Dorris-Gray analysis) obtained using glass beads and both treated and untreated alumina materials.
versus R2 > 0.9999), and yet the experimental variation as good as 5% was observed, the R2 criterion may not be as critical for materials having higher surface area, such as alumina here (∼1 m2/gm). The preconditioned alumina profile, which was measured after the column preconditioning for 6 h at 115 °C, shows much higher (∼30%) γsd values than the other alumina profiles. This observation suggests that column preconditioning at elevated temperature 115 °C efficiently removed contaminant molecules, such as water, from the alumina surface, and hence more high surface energy sites were revealed by the γsd profile determination. Sun and Berg33 have conducted a detailed study of the influence of moisture on the surface free energy of mineral oxide samples.
Conclusions
alumina solid materials for adsorbate surface coverages between 0.1% and 10%. For low surface area glass beads the R2 coefficient of the alkane fit for the γsd determinations was found to be critical measure of the quality of γsd determined (R2 > 0.9999). For the alumina sample, less strict R2 criterion (R2 > 0.9997) produced reproducible γsd profiles. The γsd profiles determined based on the Dorris-Gray method were found to have smaller errors than the profiles based on the Schultz method. The γsd profiles obtained using the glass beads and the alumina materials proved that the method presented in this paper was able to distinguish between these two different materials. The alumina profiles, depending on the efficiency of the sample preconditioning, due to surface cleaning effect, showed significant differences.
Distribution profiles for the dispersive component of the surface energy of a solid γsd were determined using glass beads and (33) Sun, C.; Berg, J. C. Effect of moisture on the surface free energy and acid-base properties of mineral oxides J. Chromatogr. A 2002, 969, 59-72.
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