Langmuir 2006, 22, 9251-9253
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Anomalous Sorption of Supercritical Fluids on Polymer Thin Films Xiaochu Wang and Isaac C. Sanchez* Department of Chemical Engineering, UniVersity of Texas at Austin, Austin, Texas 78712 ReceiVed April 21, 2006. In Final Form: August 14, 2006 Unusual sorption has been reported in thin polymer films exposed to near-critical CO2. When the supercritical fluid approaches the critical point, the film appears to thicken, but it is not clear whether the film swells or there is an adsorption layer on the film surface. A combination of the gradient theory of inhomogeneous systems and the SanchezLacombe equation of state has been used to investigate this phenomenon. It is shown analytically that surface adsorption on an attractive surface is proportional to the compressibility of the fluid. We have also investigated numerically the sorption of supercritical CO2 on poly(dimethylsiloxane) and polyisobutylene, and supercritical 1,1-difluoroethane on polystyrene. By calculating the Gibbs adsorption and adsorption layer thickness of the supercritical fluids, we found in all cases (different substrates, different supercritical fluids) that maximum adsorption occurs when the supercritical fluid is near its compressibility maximum.
Introduction Supercritical carbon dioxide is widely used as a regeneration solvent in a range of technical and chemical processes, such as chromatography, extraction, reactor cleanup, and preparation of pharmaceutical products.1 Large changes in the density of a supercritical fluid can be achieved with small variations in pressure and/or temperature, resulting in the ability to tune the densitydependent solvent properties, such as dielectric constant, viscosity, and diffusivity. Recent studies2 of CO2 sorption onto polymer thin films supported on an inorganic substrate have shown interesting anomalous behavior near the CO2 critical point. As the bulk CO2 approaches the critical point, the thin polymer film appears to thicken. The mechanism of the film thickening is unclear: it may be that the CO2 is forming a liquid layer on the surface of the polymer film or the CO2 is absorbing into the film and swelling it. A combination of the gradient theory of inhomogeneous systems and the Sanchez-Lacombe equation of state (EOS) has been used to investigate this phenomenon. Understanding the interaction between supercritical fluids and polymer films will give pathways for developing applications, including polymer welding, polymer synthesis, chemical extraction, semiconductor manufacture, and industrial cleaning. The free energy approach to the theoretical description of interfaces between fluid phases has a long and active history starting from van der Waals.3 Bongiorno and Davis4 derived their interfacial theory by combing the gradient theory5 with the van der Waals equation of state and obtained reasonable results for simple fluids. Poser and Sanchez6 extended the interfacial * To whom correspondence should be addressed. E-mail: sanchez@ che.utexas.edu. (1) McHugh, M. A.; Krukonis, V. Supercritical fluid extraction: principles and practice; Butterworth-Heinemann: Woburn, MA, 1994. (2) Sirard, S. M.; Ziegler, K. J.; Sanchez, I. C.; Green, P. F.; Johnston, K. P. Anomalous properties of poly(methyl methacrylate) thin films in supercritical carbon dioxide. Macromolecules 2002, 35 (5), 1928-1935. (3) Rowlinson, J. S., Translation of van der Waals, Jd: Thermodynamic Theory of Capillarity under the Hypothesis of a Continuous Variation of Density. J. Stat. Phys. 1979, 20 (2), 197-244. (4) Bongiorno, V.; Davis, H. T. Modified van der Waals Theory of Fluid Interfaces. Phys. ReV. A 1975, 12 (5), 2213-2224. (5) Cahn, J. W.; Hilliard, J. E. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 1958, 28, 258-67. (6) Poser, C. I.; Sanchez, I. C. Interfacial tension theory of low and high molecular weight liquid mixtures. Macromolecules 1981, 14 (2), 361-70.
calculation to include polymer liquids by incorporating the Sanchez-Lacombe equation of state.7 In this paper we describe our theoretical investigation of critical adsorption on an attractive wall. Numerical methods are also presented for the adsorption of CO2 on polymer thin films of PDMS8 (poly(dimethylsiloxane)) and PIB (polyisobutylene),9 and (1,1-difluoroethane)10 on a PS (polystyrene) thin film. By calculating the Gibbs adsorption and adsorption layer thickness of the supercritical fluids, we found in all cases (different substrates, different supercritical fluids) that maximum adsorption occurs when the supercritical fluid is near its compressibility maximum.
Adsorption on an Attractive Wall Consider the free energy of the semiinfinite fluid in contact with a planar attractive wall at x ) 0. Let us assume that the surface is solid and sharp on an atomic scale and that the interactions between the surface and fluid are sufficiently short range that the contribution to the free energy of a unit area of this surface is Φ(Fs),11 where Fs is the limiting fluid density at the surface-fluid interface, x ) 0.11 We further assume Φ(Fs) is linearly dependent on Fs.
γ ) Φ(Fs) +
dx ∫0∞[∆a + 21κ(dF dx ) ] 2
(1.1)
φ ) -(dΦ/dFs) ) constant where γ is the interfacial tension, ∆a is the excess Helmholtz free energy in the absence of an interfacial density gradient, (1/2)κ(dF/dx)2 is the free energy contribution from the interfacial density gradient, κ scales the contribution of the square gradient term and is a positive constant, and φ is the surface-fluid interaction coefficient (a positive constant). (7) Sanchez, I. C.; Lacombe, R. H. Elementary Molecular Theory of Classical Fluids. Pure Fluids. J. Phys. Chem. 1976, 80 (21), 2352-2362. (8) Pope, D. S.; Sanchez, I. C.; Koros, W. J.; Fleming, G. K. Statistical Thermodynamic Interpretation of Sorption Dilation Behavior of Gases in SiliconeRubber. Macromolecules 1991, 24 (8), 1779-1783. (9) Chang, S. H.; Park, S. C.; Shim, J. J. Phase equilibria of supercritical fluid-polymer systems. J. Supercrit. Fluids 1998, 13 (1-3), 113-119. (10) Garg, A.; Gulari, E.; Manke, C. W. Thermodynamics of Polymer Melts Swollen with Supercritical Gases. Macromolecules 1994, 27 (20), 5643-5653. (11) Cahn, J. W. Critical-Point Wetting. J. Chem. Phys. 1977, 66 (8), 36673672.
10.1021/la061089a CCC: $33.50 © 2006 American Chemical Society Published on Web 09/23/2006
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Wang and Sanchez
Table 1. Binary Interaction Parameter
PDMS PIB PS
CO2 CO2 1,1-difluoroethane
ζ
δ
T (°C)
ref
0.850 0.882 0.940
-0.012 0.026 0.062
35 35 135
8 9 10
By definition, the Gibbs adsorption Γ can be calculated from the equation
Γ)
∫0∞(F - Fc) dx ) ∫FF
κ1/2(F - Fe)
s
(∆a)1/2
e
dF
(1.2)
Figure 1. Surface density profile of CO2 and PDMS (P ) 6 MPa, T ) 35 °C, thickness 7.4 Å).
where Fe is the equilibrium density of the fluid (assumed to be supercritical).
-κ(dF/dx)|x)0 ) [2κ∆a(Fs)]1/2 ) φ
(1.3)
To make progress, ∆a must be evaluated; expanding ∆a in a series around the liquid density yields
1 (F - Fe) + ... ∆a ) 2 F 2β 2
(1.4)
Figure 2. Thickness of adsorption and compressibility vs pressure for PDMS/CO2 (T ) 35 °C).
e
where β is the isothermal compressibility of the fluid. Substitution of eq 1.4 into the boundary condition equation (eq 1.3) and subsequent simple algebra yield
F - Fs ≈ φ(β/κ)1/2Fe
(1.5)
From eqs 1.4 and 1.5, it follows that
Γ)
∫FF
s
e
κ1/2(F - Fe) (2∆a)
1/2
dF ≈ (κβ)1/2Fe(F - Fs) ≈ φFe2β (1.6)
Figure 3. Thickness of adsorption and compressibility vs pressure for PIB/CO2 (T ) 35 °C).
The above analysis suggests that the adsorption is approximately proportional to the compressibility of the fluid and the loci of maximum adsorption and maximum compressibility of the fluid should be very close. This result is independent of the specific properties of the substrate (as long as it is attractive) and the fluid.
Application to Polymer/Fluid Systems To perform these calculations, we need to determine the binary interaction parameters defined in the Sanchez-Lacombe EOS, ζ and δ. The polymer/fluid systems we consider here include adsorption of CO2 on polymer thin films of PDMS8 and PIB,9 and 1,1-difluoroethane10 on a PS thin film. The two parameters for these systems can be obtained by a nonlinear least-squares fit of experimental swelling data; the parameters are listed in Table 1. The experimental swelling data were taken from the literature cited. Experimentally, CO2 has a critical temperature (Tc) of 31.0 °C and a critical pressure (Pc) of 7.3825 MPa, but the critical parameters calculated from the Sanchez-Lacombe EOS are a little different (Tc ) 31.63 °C, Pc ) 8.91 MPa). For 1,1difluoroethane, the experimental Tc is 113.4 °C and Pc is 4.5 MPa, and the calculated Tc is 132.24 °C and Pc is 6.44 MPa. The compressibility and the adsorption of the fluid is dependent on how far the working condition is from the critical point, and the critical parameters calculated from the equation of state are more important than the experimental critical parameters in this study. To calculate the surface properties, there are two more parameters (ω [)κ12/(κ11κ22)1/2] and κ˜ ) in the EOS that should
Figure 4. Thickness of adsorption and compressibility vs pressure for PS/1,1-difluoroethane (T ) 135 °C).
be determined. ω expresses the deviation of κ12 from the geometric mean approximation, and κ˜ is the dimensionless form of κ (κ ) κ˜ *(V*)5/3, where * and V* are defined in the Sanchez-Lacombe EOS). ω is chosen as 1 to make the calculation simple. κ˜ for the small molecules CO2 and 1,1-difluoroethane is set to 0.62, and that for the polymers PDMS, PIB, and PS is set to 0.55.12 Instead of Gibbs adsorption, here we calculate the thickness of the adsorbed layer. The thickness is defined as the distance from x ) 0 (film surface) to where the mer density of the supercritical fluid drops to 10% of Fmax - Fe, as shown in Figure 1 (the surface thickness is the thick line in the figure). Figures 2-4 show the thickness of the adsorbed layer and compressibility of the fluid vary with the pressure for the systems PDMS/CO2, PIB/CO2, and PS/1,1-difluoroethane, respectively. As can be seen for these supercritical fluids the maximum adsorption occurs on the compressibility ridge. (12) Poser, C. I.; Sanchez, I. C. Surface-Tension Theory of Pure Liquids and Polymer Melts. J. Colloid Interface Sci. 1979, 69 (3), 539-548.
Supercritical Fluid Sorption in Polymer Thin Films
Summary In this paper we describe our theoretical investigation of critical adsorption on an attractive wall. Numerical results are also presented for the adsorption of CO2 on polymer thin films of PDMS8 and PIB,9 and supercritical 1,1-difluoroethane10 on a PS thin film. By calculating the Gibbs adsorption and adsorption layer thickness of the supercritical fluids, we found in all cases (different substrates, different supercritical fluids) that maximum adsorption occurs when the supercritical fluid is near its compressibility maximum. A heuristic view of this phenomenon is as follows: A fluid near its critical point is schizophrenic. It does not know whether it wants to have a gaslike or liquidlike density, and it fluctuates back and forth between these extremes. When an attractive surface is present, the fluctuating fluid is able to “condense” on the attractive surface, analogous to heterogeneous nucleation. This stabilizes a liquidlike layer on the surface. This conclusion that it is adsorption rather than absorption that is responsible for “anomalous sorption” contrasts with what was suggested previously.2 It was hypothesized that anomalous sorption might be caused by low-density fluid sorption at the substrate-film interface (nonuniform absorption). It was this
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conjecture that motivated the present study, and the study has shown that this conjecture was incorrect. This conclusion also disagrees with that reached by Koga et al.13,14 from neutron reflectivity measurements. They concluded that, near the compressibility maximum, supercritical fluid absorption is enhanced in thin films relative to thick films. However, their conclusion is based on the scattering model used to interpret the neutron reflectivity measurements. We believe that a reanalysis of their data using an adsorbed layer model would also be compatible with our conclusion that the observed anomalous sorption is related to critical wetting. Acknowledgment. This work is supported by the STC program of the National Science Foundation under Agreement No. CHE-9876674. LA061089A (13) Koga, T.; Seo, Y.-S.; Zhang, Y.; Shin, K.; Kusano, K.; Nishikawa, K.; Rafailovich, M. H.; Sokolov, J. C.; Chu, B.; Peiffer, D.; Occhiogrosso, R.; Satija, S. K. Density-fluctuation-induced swelling of polymer thin films in carbon dioxide. Phys. ReV. Lett. 2002, 89 (12), 125506/1-125506/4. (14) Koga, T.; Seo, Y. S.; Shin, K.; Zhang, Y.; Rafailovich, M. H.; Sokolov, J. C.; Chu, B.; Satija, S. K. The Role of Elasticity in the Anomalous Swelling of Polymer Thin Films in Density Fluctuating Supercritical Fluids. Macromolecules 2003, 36 (14), 5236-5243.
