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Articles Adsorption Kinetics of Amphipathic Polystyrene-block-polybutadiene onto Silicon Wafer and Polystyrene Planar Surfaces M. A. Awan,†,‡ V. L. Dimonie,† L. K. Filippov,‡ and M. S. El-Aasser*,†,§ Emulsion Polymers Institute and Departments of Chemistry and Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015 Received October 13, 1995X
Adsorption kinetics of amphipathic diblock AB copolymers of polystyrene-block-polybutadiene from selective solvent onto planar silicon wafer and polystyrene surfaces have been studied by ellipsometry. A theoretical analysis of the adsorption kinetics was applied to investigate the adsorbed layer thickness, the total amount adsorbed at each concentration, and the area occupied by each copolymer chain. Some insight into the architecture of the buoy in the solution is presented. In these studies we found a strong dependence of adsorption rate on the chemical nature of the substrates and on the bulk concentration of the adsorbent. Further, the kinetics of adsorption at different concentrations and temperatures suggest that both single polymer molecules and micelles are responsible for adsorption.
Introduction The adsorption of macromolecules (e.g., homopolymers, block, and graft copolymers) plays a vital role in various applications: stabilization of colloidal particles,1-4 flocculation,5 dispersion processes,6 biological applications,7 and adhesion.8 Therefore, the adsorption phenomena and surface studies of these polymers are of great interest, both experimentally9 and theoretically.10-13 Polymeric stabilizers have been successfully employed to prepare particles of controlled and uniform sizes.2-4,14-16 In order to control stability, a polymeric stabilizer is necessary to * To whom all correspondence should be addressed. † Emulsion Polymers Institute. ‡ Department of Chemistry. § Department of Chemical Engineering. X Abstract published in Advance ACS Abstracts, January 1, 1997. (1) Napper, D. H. Polymeric Stabilization of Colloidal Dispersions; Academic Press: London, 1983. (2) Tseng, C. M.; Lu, Y. Y.; El-Aasser, M. S.; Vanderhoff, J. W. J. Polym. Sci., Polym. Chem. Ed. 1986, 24, 2995. (3) Awan, M. A.; Dimonie, V. L.; El-Aasser, M. S. Living Polymerizations and Related Processes. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1994, 35 (2), 551. (4) Ober, C. K.; Hair, M. L. J. Polym. Sci., Polym. Chem. Ed. 1987, 25, 1395. (5) Bohuslav, B. Coagulation and Flocculation, Theory & Applications; Marcel Dekker: New York, 1993. (6) Tadros, Th. F. Polym. J. 1991, 23, 5. (7) Acrca, E.; Tian, M.; Webber, S. E.; Munk, P. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1994, 35 (1), 71. (8) Lee, L. H. Adhesion and Adsorption of Polymer; Plenum Press: New York, 1980. (9) Guzonas, D. A.; Boils, D.; Tripp, C. P.; Hair, M. L. Macromolecules 1992, 25, 2434. (10) Alexander, S. J. Phys. (Paris) 1977, 38, 983. (11) de Gennes, P.-G. J. Phys. (Paris) 1976, 37, 1445. (12) de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (13) Cohen Stuart, M. A.; Cosgrove, T.; Vincent, B. Adv. Colloid Interface Sci. 1986, 24, 143. (14) Piirma, I. Polymeric Surfactants; Marcel Dekker: New York, 1992. (15) Schwab, F. C.; Murray, J. G. Polym. Sci. Technol., Adv. Polym. Synth. 1985, 35, 381. (16) Paine, A. A. J.; Luymes, W.; McNulty, J. Macromolecules 1990, 23, 3104.
provide a thick protective layer at the surface of the particles to overcome various kinds of attractive forces such as acid-base, ion-dipole, dipole-dipole, and van der Waals interactions. The most appropriate types of polymers are the amphipathic graft and block copolymers in which one block is anchored strongly to the particle surface, while the other extends fully into the solution to provide an effective barrier against coagulation;17-19 an optimum ratio of these blocks is required to enhance the colloidal stability of dispersions. The subject of this paper is adsorption studies of diblock copolymers onto planar surfaces of polystyrene and silicon wafer. This work is an outgrowth of our attempts to understand the role(s) of diblock copolymers in particle nucleation and particle stabilization in anionic dispersion polymerization in hexane medium.20,21 Various experimental techniques have been used for studying the adsorption kinetics,22 such as ellipsometry,23 small-angle neutron scattering (SANS),24 dynamic light scattering (DLS),25 nuclear magnetic resonance spectroscopy (NMR),26 total internal reflectance fluorescence (17) Piirma, I. Makromol. Chem., Macromol. Symp. 1990, 35 (36), 476. (18) Wu, D. T.; Yokoyama, A.; Setterquist, R. L. Polym. J. 1991, 23, 709. (19) Dawkins, J. V.; Taylor, G. Polymer 1979, 20, 599. (20) Awan, M. A.; Dimonie, V. L.; El-Aasser, M. S. J. Polym. Sci., Polym. Chem. Ed. 1996, 34, 2633 and 2651. (21) Awan, M. A.; Dimonie, V. L.; Ou-Yang, D.; El-Aasser, M. S. Langmuir 1997, 13, 140. (22) Chen, C. H.; Wilson, J.; Chen, W.; Davis, R. M.; Riffle, J. S. Polymer 1994, 35, 3587. (23) Tiberg, F.; Landgren, M. Langmuir 1993, 9, 927. (24) Cosgrove, T.; Heath, T. G.; Rayn, K.; Crowley, T. L. Macromolecules 1987, 20, 2879. (25) Penger, T.; Carvalho, B. L.; Huang, J. S.; Fetters, L. J. ColloidPolymer Interactions Particulate, Amphiphilic, and Biological Surfaces; Dubin, P., Tong, P., Eds.; ACS Symposium Series 532; American Chemical Society: Washington, DC, 1993. (26) Blum, F. D.; Sinha, B. R.; Schwab, F. C. Macromolecules 1990, 23, 3592.
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(TIRF),27 dual-beam FTIR,28 surface forces apparatus,29 and surface plasmon.30 Ellipsometry was selected for this study because this technique allows measurements of the time-dependent adsorbed polymer concentration during adsorption. From these ellipsometric measurements one can calculate (a) the polymer adsorption rate constant, (b) the diffusion coefficient, and (c) the activation energy for diffusion in the adsorbed layer.31 A recently developed model to study the adsorption kinetics31 was used for analyzing the ellipsometry results and the determination of average values for the adsorbed layer thickness, the amount adsorbed at the surface, the area occupied by each polymer chain, the conformation of the polymer chains, and the mechanism of adsorption. The kinetic, diffusionkinetics, and diffusion-controlled regimes of the adsorption process were identified and discussed. In this paper, evidence is presented on the basis of ellipsometry results at different temperatures and different concentrations of the adsorbate to support the hypothesis that adsorption is due to both single polymer molecules and micelles. The presence of both species in the copolymer solution in hexane has been confirmed by the results presented in the following paper in this issue.21
Langmuir, Vol. 13, No. 2, 1997 131 Table 1. Characteristics of Amphipathic Diblock Copolymers Used for the Adsorption Studies commercial name Steron 730Aa Steron 721Aa
polystyrene type block (%) AB AB
23 7
nb St
Bu
325 2096 84 2153
Mw (× 10-4 g/mol) MW/Mn 14.7 12.5
1.05 1.50
a Polystyrene-block-polybutadiene, from Firestone, Latex and Rubber Division, Akron, OH. b Number of monomer units in each block: (St) polystyrene block; (Bu) polybutadiene block.
Experimental Method and Instrumentation Materials. The silicon wafers (SiO2-Si) with a well-defined oxide layer (250-300 Å) used in this study were donated by the Research Division of IBM. The silicon wafer samples were cut into 2 cm × 2 cm squares and then cleaned by ultrasonification for 15 min in chloroform and acetone. They were then cleaned with 2-propanol. The clean samples were dried with dust-free nitrogen gas, and these were kept under a UV lamp for a period of 10 min to ozonize them. Next, the surface of the silicon wafer was examined by ellipsometry to determine the layer thickness of the silicon dioxide. Polystyrene films were prepared by spin coating the silicon wafer using several linear polystyrene samples with molecular weights in the range 9000-220 000 g/mol and having a narrow molecular weight (donated by Mobil, Experimental Station, Edison, NJ). Polystyrene solutions in toluene (HPLC grade, Aldrich) filtered with a 0.2 µm Millipore filter were used in the spin-coating process. The polystyrene samples with a Mw of 35 000 g/mol and a Mw/Mn of 1.06 (concentration 10 000-20 000 ppm) in toluene were the most suitable, because of their homogeneous surface and film thickness of 150-170 Å, which are desired for these studies. Four to five different spots on each sample were checked to determine the polystyrene film thickness, and the roughnesses of the surfaces were determined via atomic force microscopy. Those samples that showed surface heterogeneity within 5 Å were used for the adsorption studies. Two diblock copolymers of polystyrene-block-polybutadiene, donated by Firestone (Latex and Rubber Division), were used for the adsorption studies from hexane. In a hexane solution, these diblock copolymers form micelles, as evidenced by the results presented in the following paper in this issue.21 The solutions were filtered with 0.2 µm Millipore filters before use. The characteristics of these diblock copolymers are given in Table 1. Ellipsometry. Ellipsometry is an optical technique that measures a change in the plane polarized light due to reflection from a smooth surface. These changes are determined at two angles, ∆ and ψ. Ellipsometry results were used to calculate refractive index and film thickness as a function of time during the adsorption process. A glass cell was used which provided a window for the entrance and exit of a laser beam having an (27) Fleer, G. J.; Lyklema, J. Adsorption Polymers. In Adsorption from Solution at the Solid/Liquid Interface; Parfitt, G. D., Rochester, C. H., Eds.; Academic Press: New York, 1983; p 153. (28) Tripp, C.; Hair, M. L. Langmuir 1992, 8, 241. (29) Marra, J.; Hair, M. L. Colloids Surf. 1988, 34, 215. (30) Francois, J. T.; Siemens, R. L.; Tang, T. W.; Hadziioannou, G.; Swalen, J. D.; Smith, B. A. J. Phys. Chem. 1989, 93, 2106. (31) Filippov, L. K.; Silebi, C. A.; El-Aasser, M. S. Langmuir 1995, 11 (3), 1841.
Figure 1. Optical model used to calculate the adsorbed diblock copolymer layer thickness onto polystyrene films cast on silicon wafer surfaces. incident angle of 70° with minimum diffraction from the cell surface. Solutions of diblock copolymers in hexane, covering the wide concentration range 1-300 ppm, were prepared and then filtered using a 0.2 µm Millipore filter. The HPLC grade hexane used as a solvent was free of any dust. The sample cell was thoroughly cleaned before each experiment. The thicknesses of the polystyrene films and the silicon dioxide layer on the surface of the silicon wafer were measured via ellipsometry before use. The substrate was laid in the cell, and the position of the sample was fixed by adding a small weight of 15 mg. Prefiltered hexane was used. The substrate was kept under hexane for a period of 30 min to examine any changes in the ∆ and Ψ values. No swelling of the polystyrene film in hexane was observed. The film thickness remained the same even after prolonged immersion in solvent, i.e., overnight. Then, the solvent was removed, a solution of the adsorbate of known concentration was added, and the measurements were recorded as a function of time until there was no change in the ∆ and ψ values (i.e., until equilibrium was reached). Analysis of Ellipsometric Data. The kinetics of adsorption of the amphipathic diblock copolymer polystyrene-block-polybutadiene solutions from hexane onto polystyrene and silicon wafer were monitored using the Auto EL ellipsometry. The principle of using plane polarized light to calculate average values for the refractive index and the thickness of the adsorbed layer is shown in Figure 1. The method of analysis of the ellipsometric data is detailed in the Appendix and another publication.31 The ellipsometric data (∆ and ψ) were measured every 15 s. The amount of the adsorbed polymer Γ(t) was calculated using eqs 21-27 in the Appendix, and these values were averaged through 1 min intervals. The difference between the averaged values, Γav(t), for two or three independent runs was no more than 10%. The average adsorbed layer thickness, dad layer, and the average refractive index, nad layer, of the adsorbed layer were found simultaneously by using the following equations.31,32 (32) Filippov, L. K.; Silebi, C. A.; El-Aasser, M. S. J. Appl. Polym. Sci. 1995, 58, 231. (33) Rosenberg, R. M. Principles of Physical Chemistry; Oxford University Press: New York, 1977.
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2 2 2 1/2 Re(δ) ) (2π/λ)dad layer[nad layer - nsol sin θsol] ; Im(δ) ) 0 (1)
where Re(δ) and Im(δ) are the real and imaginary parts of the phase shift, respectively, λ is the wavelength of light (λ ) 632.8 nm), θsol is the angle of incidence of the He-Ne laser beam, and nad layer and nsol are the refractive indices (average values) of the adsorbed layer and the polymer solutions, respectively. First, the values of dad layer and nad layer from eq 1 are calculated by using ellipsometric data (∆ and ψ) for the model shown in Figure 1. ∆ and ψ contain information about the relative phase shift and attenuation of the component waves perpendicular (s-wave) and parallel (p-wave). The weight fraction of polymer in the adsorbed layer, Xad layer, is calculated from the following equations:31
Xad layer )
Rad layer )
6nad layer(nad layer - nsol) 2 2 (Rpol - Rsol)(nad layer + 2)
2 2 nad nsol -1 layer - 1 ; R ) sol 2 2 nad layer + 2 nsol + 2
(2a)
(2b)
The Gibbs surface excess, Γ, on the planar surface is given by31
Γ ) dadsorbateFadsorbateXadsorbate
(3)
where Γ is the adsorbate concentration per unit surface area, dadsorbate is the average thickness of the adsorbed layer, Fadsorbate is the adsorbate density, and Xadsorbate is the weight fraction of the adsorbate. From the adsorption isotherm at the plateau region, one can determine the surface area occupied by each polymer chain, σm:
σm (nm2) ) MWpolym/Γ°mNA
Table 2. Adsorption Characteristics of Steron 730A Diblock Copolymer, Polystyrene-block-polybutadiene, on Polystyrene Measured by Ellipsometry at 25 ( 1 °Ca c0 (ppm)
Lad layer (nm)
Γ°m (mg/m2)
σm (nm2)
Σsurf (nm)
χArch (Σsurf/Lad layer)
1 5 10 30 80 130
5.45 10.1 10.3 10.4 15.2 20.0
2.9 3.3 3.4 3.9 4.9 5.9
83.0 70.4 66.4 58.1 44.7 40.8
10.3 9.47 9.19 8.6 7.54 7.20
1.9 0.94 0.89 0.83 0.5 0.36
a c , concentration of Steron 730A; L 0 ad layer, thickness of adsorbed layer; Γ°m, amount adsorbed; σm, apparent occupation area per molecule; Σsurf, apparent occupation length; χArch, architecture parameter.
Table 3. Adsorption Characteristics of Steron 730A Diblock Copolymer, Polystyrene-block-polybutadiene, on Silicon Wafer Measured by Ellipsometry at 25 ( 1 °Ca c0 (ppm)
Lad layer
Γ°m (mg/m2)
σm (nm2)
Σsurf (nm)
χArch
5 30 130 300
6.7 7.2 8.8 10.2
0.90 1.10 1.35 1.55
258 211 172 150
18.1 16.4 14.8 13.8
2.70 2.28 1.68 1.35
a c , concentration of Steron 730A; L 0 ad layer, thickness of adsorbed layer; Γ°m, amount adsorbed; σm, apparent occupation area per molecule; Σsurf, apparent occupation length; χarch, architecture parameter.
A
(4)
where MWpolym is the molecular weight of the polymer, Γ°m is the maximum amount of polymer adsorbed on the planar surface corresponding to the plateau, and NA is Avogadro’s number. The occupation length Σsurf (diameter) occupied by each chain can be calculated from eq 5; the resulting value can then be used to estimate the adsorbed layer architecture parameter χArch with eq 6:
Σsurf ) (4σm/π)1/2
(5)
χArch ≈ (Σsurf/Lad layer)
(6)
B
where Lad layer ≡ dad layer and dad layer is calculated via ellipsometry from eq 1.
Results and Discussion Adsorbed Layer Thickness. The average adsorbed layer thicknesses of the Stereon 730A diblock copolymer at various concentrations in hexane on both the polystyrene and the silicon wafer planar surfaces were calculated from the experimental ellipsometric data using eq 1. These results are shown in Tables 2 and 3 and parts A and B of Figure 2, respectively. The adsorbed layer thickness was found to increase with an increase in the bulk copolymer concentration; and at high concentrations, the layer thickness approaches a quasi-plateau value (i.e., constant surface excess). The time required for attaining the constant surface excess was found to decrease with increasing concentration. From Figure 2 it can also be observed that the adsorbed layer thickness on the polystyrene surface is about twice as large as that on the silicon wafer. Adsorbed Amount. The amount of polymer adsorbed at various concentrations was calculated using eq 3. The results are given in Tables 2 and 3 and plotted as a function of concentration in parts A and B of Figure 3, respectively. These results show that the amount of adsorbate at the
Figure 2. Effect of Stereon 730A diblock copolymer (polystyrene-block-polybutadiene) concentration in hexane on the adsorbed layer thickness at 25 ( 1 °C: (A) polystyrene surface; (B) silicon wafer surface.
planar surfaces increases with the bulk polymer concentration and reaches almost a constant value at high bulk polymer concentration. The amount adsorbed on the polystyrene surface was 3.8 times larger than that on the silicon wafer. Adsorption Kinetics. The adsorption kinetics of Stereon 730A onto the polystyrene and the silicon wafer surfaces were also investigated by ellipsometry. The
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A
A
B
B
Figure 3. Adsorption isotherms of Stereon 730A diblock copolymer (polystyrene-block-polybutadiene) from hexane solutions at 25 ( 1 °C: (A) polystyrene surface; (B) silicon wafer surface.
Figure 4. Relative amounts of Stereon 730A diblock copolymer (polystyrene-block-polybutadiene) adsorbed at 25 ( 1 °C versus log(t) in hexane at various concentrations onto a (A) polystyrene surface and (B) silicon wafer surface.
amount of polymer adsorbed was calculated using eq 3. Several curves representing the time dependence of the relative amount of polymer adsorbed, Γ(t)/Γ0, onto the polystyrene and the silicon wafer are shown in parts A and B of Figure 4, respectively. The use of the relative amount of adsorbed polymer (where Γ0 ) Γmax in the plateau region) is a more convenient way to compare the adsorption kinetics in various cases. The ellipsometric kinetic data may be used to estimate the rate-determining step of the adsorption process and to calculate the parameters characterizing the adsorption process and the adsorbed layer, utilizing a theoretical treatment which was developed earlier.31 A brief summary of the above theory and its application to the current system are given below. According to this theory, the kinetics of the formation of adsorbed polymer layers can be separated into three steps or regimes.31 In regime I, the adsorption rate of polymer molecules which are very close to the bare surface is kinetic-controlled. The transport of the polymer molecules is due to diffusion through the medium to the bare surface. In this regime the adsorption occurs instantaneously, and the relaxation time characteristic for this process is relatively small, on the order of tenths or hundredths of a second. Thus, the ellipsometric technique is incapable of monitoring this phenomenon at high polymer bulk concentrations. However, at low polymer concentrations, adsorption is slow and can easily be probed by ellipsometry. In regime II, the diffusion of the polymer molecules from the bulk to the surface, which is now sparsely covered by adsorbed polymer molecules, is followed by adsorption. The adsorption of an incoming polymer chain has to overcome the energy barrier imposed by the previously adsorbed polymers. The adsorption process is governed simultaneously by the diffusion of the polymer chains through the adsorbed polymer layer on the substrate with
a very low surface coverage followed by kinetic absorption. Therefore, this process is moderately slow and can easily be probed with ellipsometry. Thus, regime II is referred to as diffusion-kinetics-controlled. During this step, the diffusion of the invading chain has to overcome the diffusion barrier imposed by the already adsorbed polymer at the substrate. In regime III, referred to as diffusion-controlled, the polymer molecules must diffuse through the adsorbed layer in order for adsorption to take place. During this process the diffusion of the invading chain has to overcome the energy barrier imposed by the already adsorbed polymer at the substrate. This process has a relaxation time (or time scale) on the order of hours for adsorption and days for desorption. However, the relaxation times of all three adsorption regimes depend on (a) the molecular weight of the polymer, (b) the structure of the adsorbed layer, (c) the surface coverage, and (d) the interaction between the polymer molecules, the solvent molecules, and the substrate. The relaxation function is a suitable means to estimate the different regimes for the adsorption of polymers at planar surfaces. In the framework of a theory developed in our previous papers,30,31 we consider two limiting cases: case A when the diffusion coefficient is infinite (D0 f ∞) and the adsorption process is governed by the adsorption kinetics and case B when the rate of the adsorption kinetics is infinite (Kad f ∞) and the adsorption process is governed by the diffusion. In case A the relative adsorption, Γ(t)/ Γ0, for the kinetic-controlled step at short times is given by30,31
Γ(t)/Γ0 ) t/tkin
(7a)
tkin ) (Γ0/c0)/Kad
(7b)
where Γ(t) is the amount of polymer adsorbed at time (t),
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Γ0 is the equilibrium amount of polymer adsorbed (t f ∞), Kad is the adsorption rate constant, c0 is the polymer concentration in the bulk, and tkin is the relaxation time due to the adsorption kinetics. In case B the relative adsorption, Γ(t)/Γ0, for the diffusive-controlled step at short times is given by30,31
a0 ) [dΓ(c0)/dc]/(Γ0/c0)
(13b)
Γ(t)/Γ0 ) [4t/(πtdif)]1/2
(8a)
The value of a0 decreases with increasing the bulk polymer concentration c0: at low polymer concentrations (for the linear adsorption isotherm) a0 ≈ 1, at high polymer concentrations a0 , 1, and a0 ) 0 (for a rectangular adsorption isotherm). From eqs 9, 13a, and 13b, the relaxation function is given by
tdif ) (Γ0/c0)2/D0
(8b)
F(t) ) n∞ log(t) - s∞
where D0 is the diffusion coefficient of polymer and tdif is the relaxation time due to the diffusion. As shown in the previous papers,30,31 in order to describe the adsorption process over a wide range of times and to estimate the rate-determining step of the adsorption process, it is suitable to use the relaxation function, F(t), in the following form:
F(t) ) -log[Γ0/Γ(t) - 1] ) n log(t/trel) ) n log(t) - s (9) where s ) -log(trel), n and s are the slope and shift, respectively, of the straight line of the relaxation function, F(t), plotted against log(t), and trel is the relaxation time characterizing the rate of the adsorption process. On the basis of eqs 7a-9, the relaxation functions for the kineticcontrolled step (eq 10) and the diffusive-controlled step (eq 11) are given, respectively, as
F(t) ) n0 log(t) - skin
(10)
where n0 ) 1.0 and skin ) log(tkin), and
F(t) ) n°0 log(t) - s°dif
(11)
where n°0 ) 0.5 and s°dif ) 0.5 log(πtdif/4), where n0, n°0 and skin, sdif are the slopes and shifts, respectively, of the straight line of the relaxation function, F(t), plotted against log(t) for the kinetic-controlled and diffusive-controlled adsorption processes, respectively. A value of the slope, n, may be used to estimate mechanisms controlling the adsorption process. From eqs 10 and 11 it follows that the slope of the straight line of the relaxation function, F(t), versus log(t) depends on the rate-determining step. For the kinetic-controlled step, the slope, n0, should be 1.0, and for the diffusive-controlled step, the slope, n°0, should be 0.5. To estimate mechanisms controlling the adsorption process, the ratio tkin/tdif may also be useful. From eqs 7b and 8b one can write that
tkin/tdif ) D0(c0/Γ0)/Kad
(12)
For the polymer adsorption isotherm the ratio of (Γ0/c0) decreases with increasing the bulk polymer concentration c0. Therefore, the relaxation times tkin and tdif and the ratio tdif/tkin also decrease with increasing the bulk polymer concentration c0. The overall adsorption process is governed by the step with the slowest rate. Therefore, at low polymer concentrations, since tkin < tdif, the adsorption process over a wide range of times is governed by the kinetic-controlled adsorption, since the kinetic-controlled step is rate-determining. At high polymer concentrations, since tkin > tdif, the adsorption process over a wide range of times is governed by the diffusion, since the diffusivecontrolled step is rate-determining. For the diffusivecontrolled step the relative adsorption in the analytical form for long times is given by30,31
Γ(t)/Γ0 ) 1 - a0[tdif/(πt)]1/2
(13a)
(13c)
where n∞ ) 0.5 and s∞ ) log[a0(tdif/π)1/2], where n∞ and s∞ are the slope and shift, respectively, of the straight line of the relaxation function, F(t), plotted against log(t) for the diffusive-controlled adsorption processes. At intermediate polymer concentrations the behavior of the adsorption process is complex. For short times (t < tkin) the adsorption process is governed by the adsorption kinetics. In this case the slope, n0, of the straight line of the relaxation function, F(t), versus log(t) should be 1.0. For intermediate times (tkin < t < tdif) the adsorption process is governed by the adsorption kinetics and diffusion simultaneously. In this case the slope, nmid, of the straight line of the relaxation function, F(t), versus log(t) should be variable. At last for long times (t > tdif) the adsorption process is governed by the diffusion. In this case the slope, n∞, of the straight line of the relaxation function, F(t), versus log(t) should be 0.5. This analysis is useful to estimate the rate-determining step for the adsorption process from the experimental data over a wide range of times. The above treatment is convenient for analyzing the experimental adsorption kinetic data in Figure 4 over a wide range of times. Figures 5 and 6 show the relaxation function, Fad(t), plotted against log(t) for different concentrations of Stereon 730A adsorbed at the polystyrene and the silicon wafer surfaces, respectively. At low polymer concentrations (1 ppm on the polystyrene surface and 5 ppm on the silicon wafer surface in Figures 5A and 6A, respectively), the slope of the relaxation function is approximately equal to 1. Thus according to eq 7, the adsorption process is governed by the adsorption kinetics at low polymer concentrations. According to eq 10, these results also show that the adsorption kinetics of the diblock copolymer onto the polystyrene and the silicon wafer are of a typical Langmuir nature, since the relative adsorption is proportional to the polymer concentration. As the polymer concentration is increased (5 ppm for the polystyrene surface and 30 ppm for the silicon wafer), the time dependencies of the relaxation function versus log(t) in Figures 5B and 6B are described by the two straight lines. For this intermediate polymer concentration, the processes of both diffusion and kinetics in the adsorbed layer occur simultaneously, since the slope of the relaxation function versus log time shifts from 1.0 to 0.5. With a further increase in the polymer concentration (30 ppm for the polystyrene surface and 130 ppm for the silicon wafer), the adsorption process becomes completely diffusioncontrolled, as indicated by a slope of approximately 0.5 for the relaxation function versus log(t) in Figures 5C and 6C. Apparent Occupation Area and the Architecture of the Adsorbed Layer. The apparent occupation area of each polymer chain at different concentrations of the amphipathic polymer on the polystyrene and the silicon wafer was calculated using eq 4, and the results are presented in Tables 2 and 3. The results show that the apparent area occupied by each chain on the polystyrene surface is 0.27 times that
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Figure 5. Relaxation function, Fad(t), versus log(t) for the adsorption of different concentrations of Stereon 730A diblock copolymer (polystyrene-block-polybutadiene) from hexane onto a polystyrene substrate: (A) 1 ppm; (B) 5 ppm; (C) 30 ppm.
Figure 6. Relaxation function, Fad(t), versus log(t) for the adsorption of different concentrations of Stereon 730A (polystyrene-block-polybutadiene) from hexane onto a silicon wafer at (A) 5 ppm, (B) 30 ppm, and (C) 130 ppm.
at the silicon wafer surface. This indicates a higher packing density in the adsorbed layer on the polystyrene surface compared to the silicon wafer. The architecture parameters of the adsorbed layer on the polystyrene and silicon wafer surfaces were determined using eq 6. The occupation length was calculated from the area occupied by each polymer chain using eq 5. The ratio of the occupation length to the measured average thickness, presented in Tables 2 and 3, can be used to evaluate the architecture of the adsorbed layer. The much lower values of χArch for the adsorption on the polystyrene surface compared to the silicon wafer surface (2.5 times) suggest once again that the adsorbed layer is much more extended toward the medium (denser packing) for the polystyrene surface compared to the latter. Effect of Anchor Moiety. The adsorption kinetics on the polystyrene surface were studied for two diblock copolymers with different sizes of the anchor moieties (23% polystyrene for Stereon 730A and 7% polystyrene for Stereon 721A; see Table 1). The adsorbed layer thickness and the amounts of both diblock copolymers adsorbed from
hexane solution (130 ppm) on the planar polystyrene surface are shown in Figure 7. Both the adsorption rate and the rate of buildup in adsorbed layer thickness are faster for Stereon 730A compared to Stereon 721A, which has almost the same chain length of the butadiene block but a much shorter PS block (see Table 1). This indicates that each adsorbing segment (anchor) plays a significant role in determining the kinetics of the adsorption. The amount of polymer adsorbed (Γ), the area occupied by each chain (σm), the chain architecture parameters, and the adsorption rate constant (Kad) were determined from the experimental data using eqs 3, 4, 6, and 7. The results are shown in Table 4. The area occupied by Stereon 721A diblock copolymer with a shorter anchoring chain was found to be 1.9 times higher than that of Stereon 730A. Furthermore, the rate constant for adsorption was almost 50 times higher in the latter case. The higher amount of adsorbed copolymer and the larger film thickness of the Stereon 730A on the polystyrene surface compared to the silicon wafer surface suggest a higher polymer chain density at the polystyrene surface.
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Γ(c) ) ΓmaxKp(T)c/(1 + Kp(T)c)
A
(14)
where Γ(c) and Γmax are the amount and maximum amount, respectively, of polymer adsorbed on a planar surface, c is the polymer bulk concentration, Kp(T) is the equilibrium adsorption constant at temperature T, and T is the absolute temperature. In order to calculate the ratio Kp(T)/ Kp(T0), eq 14 can be written in the following form, which is more suitable for the numerical calculation:
Kp(T)/Kp(T0) ) 1/[Γ(c0,T0)(1 + Kp(T0)c0)/Γ(c0,T) Kp(T0)c0] (15) where Γ(c0,T) and Γ(c0,T0) are the amount of polymer adsorbed at the bulk concentration c0 for the temperatures T and T0, respectively. The ratios Kp(T)/Kp(T0) were calculated from the experimental ellipsometric values of the adsorption, Γ(c0,T), at the bulk concentration c0 ) 130 ppm for the two temperatures 5 and 11 °C. Figure 8 shows ln(Kp(T)/Kp(T0)) versus the reciprocal absolute temperature, 1/T. The enthalpy of adsorption may be calculated using the Van’t Hoff equation:33
B
Kp(T) ) K° exp(-∆H/RT)
Figure 7. Time dependence of the adsorbed layer thickness of Stereon 721 (with 7% polystyrene) and Stereon 730A (with 30% polystyrene) diblock copolymers (polystyrene-block-polybutadiene) from hexane solutions on a polystyrene surface. Table 4. Adsorption Characteristics of Two Different Adsorbates on Polystyrene Films Measured by Ellipsometry at 25 ( 1 °Ca adsorbent type Steron 730A Steron 721A
c0 Lad layer Γ°m σm Σsurf Kad (ppm) (nm) (mg/m2) (nm2) (nm) χArch [(ppm s)-1] 130 130
20.0 15.2
5.9 2.7
40.8 78.0
7.2 9.5
0.36 3.8 × 10-5 0.63 7.7 × 10-7
a c , concentration of Steron 730A; L 0 ad layer, thickness of adsorbed layer; Γ°m, amount adsorbed; σm, apparent occupation area per molecule; Σsurf, apparent occupation length; χArch, architecture parameter; Kad, adsorption rate constant.
The observed differences in the adsorption rate and adsorbed amount show that adsorption is dependent on the chemical nature of the substrate. Furthermore, this difference in the mode of adsorption clearly indicates that the higher rate of adsorption on the polystyrene surface as compared to the silicon wafer is due to π-π interactions between the aromatic rings of the polystyrene substrate and the anchoring polymer chain. However, these π-π interactions are absent for the silicon wafer surface. Effect of Temperature. In order to understand the thermodynamics of block copolymer adsorption, ellipsometry adsorption studies of both diblock copolymers Stereon 730A and Stereon 721A (which contain 23% polystyrene and 7% polystyrene blocks, respectively) were carried out from their solutions of the bulk concentration c0 ) 130 ppm in hexane on polystyrene surfaces at three different temperatures [5, 11, and 25 °C ((1)]. First, we found the equilibrium constants, Kp(T0), at temperature T0 ) 298 K (25 °C) from the experimental data presented in Figure 3 by using eq 14 for the Langmuir adsorption isotherm:34 (34) Adamson, A. W. Physical Chemistry of Surfaces; WileyInterscience: New York, 1986. (35) Motschmann, H.; Stamm, M.; Toprakciogly, Ch. Macromolecules 1991, 24, 3681.
(16a)
where K° is the pre-exponential factor, ∆H is the enthalpy of adsorption, and R is the gas constant. To calculate the enthalpy of adsorption, eq 16a is rewritten in a more suitable form as
ln[Kp(T)/Kp(T0)] ) ST/T + β
(16b)
ST ) -∆H/R
(16c)
where ST is the slope of the straight line of ln(Kp(T)/Kp(T0)) versus (1/T), and β ) (∆H/RT0) is a constant. Finally, the adsorption enthalpies were calculated by using eqs 16b and 16c and the experimental data are shown in Figure 8. For both block copolymers the adsorption enthalpies have positive values, higher for Stereon 730A, the block copolymer with the larger polystyrene anchoring moiety. Since the amount of adsorbed block copolymers increases with temperature, it follows that the adsorption proceeds with an increase in enthalpy, and this differs from the conventional adsorption of low molecular substances; that is, heat is evolved. However, in many other cases involving the adsorption of polymers on solid substrates a considerable increase in polymer adsorption with temperature was also observed.47,48 From the temperature dependence of the adsorption, one can calculate the thermal effect of the adsorption, which is a complex function of the intrinsic heat of adsorption, i.e., the heat of interaction of the polymer ), and the sum of polymer with the substrate, (-∆Hsolid the heat of desorption of the solvent molecules from the solvent ), the heat of interaction of substrate surface, (-∆Hsolid polymer polymer chains with the solvent, (-∆Hsolvent ), and the heat of interaction of polymer chains in aggregates polymer ); i.e., (clusters or micelles) in bulk, (-∆Hpolymer polymer solv (-∆H)adsorp ) (-∆Hsolid ) - (-∆Hsolid )polymer polymer (-∆Hsolv ) - (-∆Hpolymer ) (17)
The overall negative heat of adsorption (positive values for enthalpies) indicates that the last three terms of the (36) Daoud, M.; Cotton, J. P.; Farnouex, B.; Jannink, G.; Sharma, G.; Benoit, H.; Picot, C.; de Gennes, P.-G. Macromolecules 1975, 8, 804. (37) Cosgrove, T.; Ferige-Woods, J. Colloids Surf. 1987, 25, 91.
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Figure 8. Ln(relative rate of adsorption rate constant) of Stereon 730A (with 30% polystyrene) and Stereon 721A (with 7% polystyrene) on a polystyrene surface versus the inverse of absolute temperature.
equation are larger than the first. The spontaneous adsorption process, involving an increase in the enthalpy of the system, should be accompanied by an entropy gain that is appreciably greater than the enthalpy to ensure a negative value of the free energy change during adsorption. The entropy gain has two causes: First, the adsorption of polymer molecules on the substrate surface leads to a transfer of a large number of solvent molecules from the surface into the bulk. Second, the packing of the polymer chains onto the substrate surface is less dense than that in the polymer aggregates in the solution (clusters or the micelle cores). The light-scattering studies of both diblock copolymers21 showed that the polystyrene-block-polybutadiene diblock copolymers form micelles in hexane with a unimodal size distribution and an estimated critical micelle concentration (cmc) for Stereon 730A of 9 × 10-11 mol/L. These micelles are in dynamic equilibrium with the single polymer molecules (free polymer chains). Any increase in the bulk polymer concentration per se should not change the net concentration of the free chains in solution.38 However, the results presented in Figure 4 show a net increase in the rate of adsorption with concentration. Similar results were previously reported in the literature, and two models were proposed: model 1 suggested that micelles never adsorb directly,41 and model 2 suggested that the fast adsorption above the cmc is the outcome of the adsorption of micelles.30 The first model proposes that the soluble block of the micelle (corona) is repelled strongly by the wall of the substrate and creates an enormous energy barrier for adsorption and, therefore, that adsorption is only due to single polymer molecules.41,42 This model suggests that only free chains are responsible for adsorption. However, the second model argues for micellar adsorption, and support for this model is based on (a) adsorption rates which depend on concentration and (b) experimental evidence that adsorption below and above (38) Leiber, L.; Orland, H.; Hweeler, J. C. J. Chem. Phys. 1983, 79, 3550. (39) The results obtained via flow field-flow fractionation21 and by Giddings et al.40 showed that, by increasing the diblock copolymer concentration in hexane, the relative amount of the free polymer chains also increased. It could be possible that micelles of diblock copolymers are not compact structures like the micelles of small molecules. Moreover, upon the further addition of solvent, e.g., hexane, the associated structure becomes loose. The polymer chains may start leaving the micelles. (40) Gidding, J. C.; Miller, M. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1993, 35 (1), 764. (41) Johner, A.; Joanny, F. J. Macromolecules 1990, 23, 5299. (42) d’Oliveira, J. M. R.; Xu, R.; Jensam, T.; Winnik, M. A.; Hruska, Z.; Hurtrez, G.; Riess, G.; Martinho, J. M. G.; Croucher, M. D. Langmuir 1993, 9, 1092.
Figure 9. Schematic model for the adsorption of diblock copolymer polystyrene-block-polybutadiene onto polystyrene and silicon wafer from a solution of micellar aggregates and single polymer molecules. The solvent is hexane [δ ) 7.3 (cal/ cm3)1/2], which is a nonsolvent for polystyrene [δ ) 9.1 (cal/ cm3)1/2] and a good solvent for polybutadiene [δ ) 8.1 (cal/cm3)1/2].
the cmc differed by an order of magnitude. However, the second model did not give a rationale for the driving force for this micellar adsorption, and no experimental evidence pertaining to surface studies was provided to support the model. Obviously, the issue of micelle formation in block copolymer solution and its role in the adsorption process are still controversial. Considering the dynamic nature of the micelles, we are inclined to believe that adsorption is merely the outcome of single polymer molecules. When the single polymer molecules are depleted from the solution, the micelles relax and replenish the solution with single polymer molecules to re-establish the dynamic equilibrium. If adsorption is a net result of single polymer molecules, then the rate of adsorption is only dictated by enthalpic considerations and must be independent of concentration above the cmc. We observed that the layer thickness increased with increasing diblock copolymer concentration in bulk. On the basis of the experimental data, it is reasonable to assume that, at low concentrations, the nonadsorbed portion of the polymer chain, buoy, exists in the form of a random coil, unperturbed chain.35 As the polymer concentration increases, the adsorbed polymer density at the surface increases. Above a critical concentration (c*),36 the surfaces of the two neighboring polymer chains, both present in the unperturbed chain conformation, would tend to overlap. Therefore, due to repulsive interactions between the two chains and increased osmotic pressure in the solvated polymer chains, they would prefer to extend into a brushlike conformation instead of overlapping (see Figure 9).37 As a consequence, the adsorbed layer thickness and the amount of polymer adsorbed increase with time, until they achieve a quasi-plateau region. The plateau region can be considered to be an equilibrium region, and any further addition of polymer leads to either chain exchange or the formation of a “multiadsorbed” layer due to some chain entanglements between the “brush” part of the adsorbed layer and the corona of the copolymer micelles in solution. However, our studies were confined to the near plateau region of the adsorption isotherm. Since we have evidence of a weak adsorption of the polybutadiene (Figures 10 and 11), the soluble moiety of the block copolymers, on polystyrene substrates, the
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Awan et al.
chemical nature of the diblock copolymer. Evidence was presented that the adsorption of diblock copolymers on the silicon wafer and the polystyrene films occurs by adsorption of both single polymer molecules and micelles. Acknowledgment. The authors would like to thank Dr. F. C. Schwab (Mobile Research and Development Center, Princeton, NJ) for providing samples of narrow molecular weight polystyrene. Appendix
Figure 10. Adsorption isotherm of polybutadiene from hexane solution at 25 ( 1 °C onto a polystyrene surface.
Analysis of Ellipsometry Data The optical system used, as shown in Figure 1, consists of the following layers: bulk silicon (Si) with a complex refractive index, n* ) n4 - ik4, a layer of silica (SiO2) with a refractive index n3 with a thickness d3, the polymer film with a refractive index n2 and a thickness d2, the adsorbed layer with a refractive index n1 ) nad layer and a thickness d1 ) dad layer, and a surrounding solution with the refractive index n0. The reflection coefficients at the boundary of (p) the (k) and (k + 1) layers for the normal (Rk,(k+1) ) and (s) perpendicular (Rk,(k+1)) polarized light for the multilayer film are given by (x) R(k-1),k )
Figure 11. Effect of polybutadiene concentration in hexane on the adsorbed layer thickness at 25 ( 1 °C onto a polystyrene surface.
micellar adsorption cannot be completely ruled out. The adsorption of micelles can be rationalized as follows. The micelles first diffuse and approach the substrate surface, where the core of the micelle and surface overcome the screening effect of the corona. This strong interaction of the core and surface leads to the breakup of the micelle, followed by rearrangement of the polymer chain on the substrate. This rearrangement of the micelle causes an entropic gain. Therefore, we suggest that the adsorption of polystyrene-block-polybutadiene diblock copolymer in hexane above the cmc is a net result of single polymer and micellar adsorption. Other workers43 proposed a direct micelle adsorption. They predicted this in the case of polystyrene latexes mixed with a polystyrene-blockpolyethyleneoxide in a selective solvent for poly(ethylene oxide), e.g. water. This diblock copolymer form micelles in water, and the authors reported their finding that micelles will dominate the adsorption process. Conclusions It has been shown that ellipsometry can be used successfully to study the kinetics of the adsorption of diblock copolymers of polystyrene-block-polybutadiene from hexane solutions in the dilute regimes on different substrates. The adsorption rate, adsorbed layer thickness, and adsorbed amount were found to depend on the concentration and composition of the diblock copolymer. Furthermore, these studies showed the importance of the chemical nature of the substrate; i.e., the polystyrene surface was a better sink for the anchoring moieties as compared to the silicon wafer. The adsorption process can be described on the basis of the concentration and the (43) Xu, R.; D’Unger, G.; Winnik, M. A.; Martinho, J. M. G.; d’Olivira, J. M. R. Langmuir 1994, 10, 2977.
(x) (x) + Rk,(k+1) exp(-2iδk)] [r(k-1),k
; i ) (-1)1/2 (x) (x) [1 + r(k-1),k Rk,(k+1) exp(-2iδk)] (18)
where (x) denotes the normal (p) and perpendicular (s) (p) (s) and rk,(k+1) are direction of the polarized light and rk,(k+1) the Fresnel reflection coefficients for the normal (p) and perpendicular (s) directions for the polarized light:
δk )
(2πλ)n d
k k
cos θk; k ) 1, 2, 3
(19)
where δk is the phase shift in radians of the polarized light. The Fresnel reflection coefficients are given by44 (p) ) rk,(k+1)
(s) rk(k+1) )
(n*(k+1) cos θk - n*k cos θ(k+1)) ; k ) 1, 2, 3 (n*(k+1) cos θk + n*k cos θ(k+1)) (20)
(n*k cos θk - n*(k+1) cos θ(k+1)) ; n* ) nk - ikk (n*k cos θk + n*(k+1) cos θ(k+1)) k (21)
where k and k + 1 are the subscripts of the media n*k and n*k+1, respectively, n*k is a complex refractive index, nk and kk are the real and imaginary components of the refractive index, θk and θk+1 are the incident and reflection angles, respectively, nk is the refractive index of layer k, and θk is the incidence angle at layer k. The refractive indices and the indices angle at layers k and (k + 1) are related to each other according to Snell’s law:45
n*(k+1) sin θ(k+1) ) n*k sin θk; k ) 1, 2, 3
(22)
According to the optical scheme in Figure 1, for the boundary of Si-SiO2 the index k ) 4, for the boundary of the polystyrene film (SiO2-PS) k ) 3, for the boundary of the adsorbed layer (PS-AD) k ) 2, and for the boundary of AD-S (polymer solution) k ) 1, respectively. The angles Ψ and ∆, measured by ellipsometry, are related to the reflection coefficients of the normal (R(p)) and perpen(44) Bashasa, N. M.; Buckman, A. B.; Hall, A. C. Recent Development in Ellipsometry; North-Holland: Amsterdam, 1969. (45) So, S. S.; Vedam, K. J. Opt. Soc. Am. 1972, 62, 16.
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dicular (R(s)) polarized light components according to the following equations:44-46
F ≡ R(p)/R(s) ) tan(ψ) exp(i∆)
(23a)
(s) (p) - r01 C ) Fr01
From eqs 24-27 we find
d1 ≡ dad layer )
( )[
η ) exp(-2iδ1)
(23b)
Then eqs 17-23 can be rewritten into a suitable form for the numerical calculations as
Aη2 + Bη + C ) 0, η ) [-B ( (B2 - 4AC)1/2]/2A (24) (p) (s) (p) (s) R12(Fr01 - r01 ) A ) R12
(25)
]
i ln(η) λ 2 4π (n - n2 sin2 θ )1/2 1 0 0
Im[i ln(η)] ) 0, n1 ≡ nad layer
Let
(27)
(28a) (28b)
The average thickness of the adsorbed layer dad layer and the average refractive index of the adsorbed layer nad layer may be found simultaneously from eqs 27a and 27b. Calculation of the amount of polymer adsorbed onto a planar surface from ellipsometric experimental data was done according to the scheme developed earlier.31 The adsorbed density in the adsorbed layer decreases with increasing distance from the interface. Therefore the adsorbed layer is not homogeneous and the refractive index nad layer and thickness dad layer of the adsorbed layer represent optical average values.31 The physical meaning of the average values of the refractive index and thickness of the adsorbed layer for various adsorbates and polymer mixtures with various segment distributions has been discussed by McCrackin and Colson.47 LA9508708
B)
(s) (p) (p) r01 r01 (FR12
-
(s) R12 )
+
(s) FR12
-
(p) R12
(26)
(46) Azzam, R. M. A.; Bashasa, N. M. Ellipsometry and Polarized Light; North-Holland: Amsterdam, 1987.
(47) McCrackin, F. L.; Colson, J. P. Ellipsometry in Measurements of Surfaces and Thin Films. NBS Technical Note 256; National Bureau of Standards: Washington DC, 1964. (48) Patat, F.; Schliebener, C. Macromol. Chem. 1961, 44-46, 643. (49) Lipatov, Yu. S.; Sergeeva, L. M. Adsorption of Polymers; John Wiley & Sons: New York, 1974; pp 40-47.
