Article pubs.acs.org/Macromolecules
Kinetics of Irreversible Chain Adsorption Caroline Housmans,† Michele Sferrazza,‡ and Simone Napolitano†,* †
Laboratory of Polymer and Soft Matter Dynamics, Faculté des Sciences, Université Libre de Bruxelles, Boulevard du Triomphe, Bâtiment NO, Bruxelles 1050, Belgium ‡ Département de Physique, Faculté des Sciences, Université Libre de Bruxelles, Boulevard du Triomphe, Bruxelles 1050, Belgium S Supporting Information *
ABSTRACT: Recent experimental evidence showed a strong correlation between the behavior of polymers under confinement and the presence of a layer irreversibly adsorbed onto the supporting substrate, hinting at the possibility to tailor the properties of ultrathin films by controlling the adsorption kinetics. At the state of the art, however, the study of physisorption of polymer melts is mainly limited to theory and simulations. To overcome this gap, we present the results of an extensive investigation of the kinetics of irreversible adsorption of entangled melts of polystyrene onto silicon oxide. We show that the process of chain pinning proceeds via a first order reaction mechanism, which slows down at large surface coverage, and the adsorbed amount scales with the predictions of reflected random walk. We propose an analytical form of the time evolution of the thickness of the adsorbed layer with two well-defined regimes: linear at short times and logarithmic at longer times, separated by a temperature independent crossover thickness and a molecular weight independent crossover time, in line with simulations and theory.
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INTRODUCTION Placed in contact with a nonrepulsive interface, polymer chains tend to form irreversibly adsorbed layers already at monomer/ surface interactions on the order of kBT (physisorption).1,2 Connectivity, in fact, stabilizes against desorption, which, in the case of consecutively attached monomers, requires the cooperative detachment of the whole set of adsorbed segments.3 Recent work has shown a striking correlation between the deviation from bulk behavior and the presence of a layer irreversibly adsorbed onto the host substrate.4,5 In particular, it was experimentally verified that it is possible to tune the glass transition temperature,6−8 the viscosity,9 the crystallization rate,10 the wettability,11 and the hydrophobic/hydrophilic character12 of thin polymer layers by simple thermal annealing procedures that modify the adsorption degree, without affecting the interfacial chemistry. To achieve a deeper understanding of the properties of polymers upon confinement, it is thus necessary to unveil the molecular mechanisms responsible for irreversible chain adsorption. The formation of adsorbed layers is well characterized in the case of dilute solutions.13 On the contrary, although extensive theoretical and modeling efforts, a broad comprehension of the adsorption of polymer melts is still missing. In addition to large experimental difficulties related to the characterization of buried interfaces and extremely thin organic layers, further constraints limiting the comprehension of the formation of stable polymer/ solid interfaces come also from the use of analytic functions to fit the experimental data where the information on the macromolecular architecture is lacking. The kinetics of © 2014 American Chemical Society
thickening of the adsorbed layer is, in fact, commonly described by saturating exponential function of the type max hads(t ) = ht = 0 + hads [1 − exp( −t /τ )]
(1)
based on a first order mechanism where, for t > 0, the growth rate of the thickness of the adsorbed layer hads is proportional to [hads − (hmax ads − ht=0)]/τ, with τ a characteristic time, ht=0 the thickness t = 0, and hmax ads the increment in thickness at t/τ ≫ 1. The interpretation of data via eq 1 is biased by the assumption that mechanism of adsorption and the conformation of interfacial chains are independent of surface coverage, which is disproved by large experimental evidence.14 Here, we propose an analytical form of the kinetics of irreversible adsorption based on an adaptation of the model developed by Ligoure and Leibler for end-functionalized polymers in solution.15 Our previous work, based on a very limited data set, was in line with this model.6 Here, an extensive investigation of the temperature and molecular weight dependence of the melt physisorption of polystyrene on silicon oxide, permitted to identify two kinetics regimes in line with our analytical form, other experimental reports, and simulations.16
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EXPERIMENTAL SECTION
Films of monodisperse atactic polystyrene (PDI < 1.05, Polymer Source) were prepared by spin-coating dilute solutions of the polymer Received: March 9, 2014 Revised: April 8, 2014 Published: May 15, 2014 3390
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onto wafers of Si covered by a native oxide layer (≈2 nm). Toluene (>99.9%) was used as a solvent. To reduce the systematic errors in the determination of the adsorption rate, we prepared and investigated a large number of samples (>1300), as a function of the annealing time (300 < t (s) < 259200), the temperature of annealing (393 < T (K) < 443), the molecular weight (49.4 < Mw(kg/mol) < 1460, thus above entanglement mass). To effectively reduce the impact of structural relaxation, we preannealed our films (thickness > 8 Rg) for 10 min, after which we fixed the onset of our annealing experiments at the same temperature (tpreANN = 10 min → t = 0). The melts were thus isothermally annealed at the temperature T, for a time t. Soon after annealing, the nonadsorbed chains were removed by soaking for 30 min the films into the same solvent used for spin-coating (Guiselin’s experiment17). At short annealing times, AFM topography images of well-dried samples revealed a pattern typical of spinodal decomposition, and the surface roughness was excessively large to permit assigning a thickness; these samples were not considered in the analysis of the kinetics. Upon further annealing (the minimum annealing time varied with Mw and T), we obtained extremely flat surfaces with a roughness not exceeding 4 Å, in line with previous reports.11,18 Consequently, we modeled our system as continuous films and measured their thickness via ellipsometry considering a simple multilayer model, air/PS/SiO2/Si(substrate). We used a spectroscopic ellipsometer (MM-16, Horiba) with a wavelength range λ = 430−850 nm, and we fitted the measured spectroscopic angles Ψ and Δ using a Cauchy model19 with bulk values. To reduce the number of free parameters, the thickness of the oxide layer was determined before deposition of the organic layer and then fixed to this value during the fitting process of the PS adsorbed layer. For a selection of samples covering the whole investigated range of hads, we determined the thickness also via AFM measurements, considering the height of steps obtained by removing the organic layer with a soft pen, see Figure 1. An excellent comparison between the two approaches validates our ellipsometric model.
number of adsorbed segments increases in time as n(t). Thus, after pinning, each chain contributes with a quantity proportional to the mass of the macromolecule. The last relation implies that (a) the adsorbed amount and thus the thickness of the adsorbed layer increases linearly with time, hads ∼ t, a trend observed in this work, and for melts of PS,6 PMMA20 and PET10 physisorbed on different substrates; b) considering that chains obey a reflected random walk in proximity of a nonrepulsive wall, at any given time hads ∼ N1/2 ∼ Rg, where Rg is the gyration radius. The linear growth process will be dominant until crowding inhibits the first order reaction mechanism. Because of the reduced space available for pinning in this late regime, new chains need to stretch before diffusing through the layer formed by the molecules at the surface. The correlated reduction in the number of allowed configurations yields a severe entropy loss. On this regard, Ligoure and Leibler recognized that chains adsorbed at low surface coverage create a potential opposing the thickening of the interfacial layer;15 under these conditions, the growth rate is logarithmic in the surface coverage, and thus also on t, as a first order reaction ensures this equality. In line with this picture, in the case of adsorption from dilute solutions, Schneider et al. verified that the first chains absorbing onto the substrate adopt flattened conformations (large number of adsorbed monomers/chain), while chains arriving at a later stage pin with a lower number of segments per macromolecule;14 the occurrence of a similar bimodal structure in adsorbed melts was recently confirmed by Koga and coworkers.21 Analysis of the simulations of Linse16 reveals that a transition in the structure of the adsorbed layer takes places at a crossover time separating a linear and a logarithmic regime. With these considerations in mind, we propose a description of the kinetics of irreversible adsorption including a crossover between a linear and a logarithmic growth ⎧ ht = 0 + vt t < tcross hads(t ) = ⎨ ⎩ hcross + Π log t t > tcross ⎪
⎪
(2)
where v and Π express respectively the growth rates in the different regimes, hcross is the value of the thickness at the crossover time tcross, and the value of t in the argument of the logarithm is normalized by t0 = 1 s, to ensure correct dimensionality. Although eq 2 describes a time evolution similar to that of eq 1, only the former contains information on the macromolecular nature. In line with the experimental evidence on the impact of adsorption on deviations from bulk behavior,6,10,21 we introduce a dimensionless parameter t* = t/ tcross, permitting to identify two regimes to which we will refer as linear (t* ≪ 1) and logarithmic (t* ≫ 1), separated by a crossover region crossover (t* ≈ 1). Figure 2 provides an example of the time evolution of hads, in line with the two regimes of eq 2, for melts of PS of different Mw adsorbed at different T on SiO2. At constant temperature, the thickness of the adsorbed layer increases linearly upon annealing up to an Mw−independent crossover time, after which the growth slows down and enters a logarithmic regime. To achieve a deeper view on the mechanisms responsible for thickening of the adsorbed layer, we analyzed the molecular weight and the temperature dependence of v. The adsorption rate in the linear regime increased as Mw0.51±0.03, in line with the expected scaling v ∼ N1/2 ∼ Rg; that is, v/Rg is Mw independent, see Figure 3a. This result implies that the number of chains incorporated into the adsorbed layer does not depend on the
Figure 1. Comparison of the values of the thickness of the adsorbed layer determined via AFM and ellipsometry. The solid line is a linear fit of the experimental data with slope 1.05 ± 0.05.
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RESULTS AND DISCUSSION We considered an adsorption reaction where chains in contact with the surface pin onto the solid substrate via kinetics limited by the characteristic time for the attachment of one monomer (or of small group of monomers). Assuming a first order mechanism where absorbed chains bring n monomers onto the substrate (n scaling with the polymerization degree, N), the 3391
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± 11 kJ/mol, see Figure 3d, comparable to that of local noncooperative rearrangements in PS. Lupaşcu et al.,23 for example, determined an activation energy of ≈ 80 kJ/mol for the helix inversion in sindiotactic regions, intrinsically present in atactic samples. A similar value (70 ± 6 kJ/mol) was reported by Chowdhury et al.24 for the relaxation of nonequilibrium conformations not coupled to the structural relaxation. These mechanisms are not merely associated with surface processes or to the liquid state, but they are active also below Tg and in bulk. In particular, Lupaşcu et al. showed that the helix inversion process is not affected by the structural relaxation.23 Consequently, we associate the rearrangement permitting adsorption to spontaneous fluctuations taking place at length scales smaller than those responsible for the glassy dynamics (typically 3−5 monomers). Similarly as for v, hcross scaled, as expected, as N1/2(hads ∼ Mw0.48±0.08, see Figure 3b) indicating that the crossover in the growth rate (t* ≈ 1) takes place when the size of the adsorbed layer reached a well-precise fraction of the macromolecular size. Comparisons of kinetics at constant Mw revealed that hcross is Tindependent, see Figure 2a and Supporting Information. Further support to this claim is given by the observation that tcross (=hcross/v ∼ N0) is Mw-independent, see Figure 2b, and that the crossover time increases in temperature with an activation energy (−80 ± 16 kJ/mol, see Supporting Information) comparable to that of 1/v. These findings clarify the physical meaning of tcross and hcross and justify their use in eq 2. Considering the lack of Mw−dependence on tcross, we speculate that the crossover takes place when the surface coverage has reached a critical value, not depending on the molecular size. The transition from linear to logarithmic regime would occur when the number of monomers attached to the substrate reaches a critical value nC. Consequently at t* ≈ 1, also the number of chains attached to the substrate is proportional to nC, which further explains why tcross does not depend on N, while hads does. Once hads reaches values comparable to hcross the kinetics becomes logarithmic in time. In this regime, insertion of new segments requires an energy penalty due to the reduction in entropy upon stretching.1,15,25 The larger the entropy drop, the higher the barrier opposing to thickening, and, in turn, the slower the kinetics. Measurements of Π = ∂h/∂[log(t)] should thus allow an estimation of this barrier−smaller values of Π correspond to larger barriers. We found that Π has the same temperature and Mw-dependence as v (∼Mw0.44±0.10, see insets of Figure 2 and Figure 3c), implying that, for t* ≫ 1, after diffusing through the previously adsorbed chains, pinning of new chains proceeds via the same molecular mechanism as for t* ≪ 1. In conclusion, we investigated the kinetics of irreversible adsorption of PS on SiO2 over very large T and Mw ranges. We observed two adsorption regimes, linear at short times and logarithmic at longer times, and analyzed the kinetics via an analytical expression, which takes into account the macromolecular nature and the different conformations upon adsorption. The validity of the equation was ensured by the excellent agreement between our results and the trends predicted by previous models. In our work, we followed the theory developed by Ligoure and Leibler15 for the adsorption of block copolymers in solution, and showed that this formalism can used also in the case of adsorption of homopolymer melts. Moreover, we demonstrated that the two adsorption regimes are separated by a critical crossover
Figure 2. Kinetics of irreversible adsorption of melts of PS of constant molecular weight and different temperatures (a) and at constant temperature and different molecular weight (b). In the left inset, data were plotted as a function of the time normalized to the crossover time; in the right inset, the thickness of the adsorbed layer was normalized to the gyration radius.
Figure 3. Top panels: molecular weight dependence of (a) the linear growth rate at 433 K, (b) the crossover thickness, and (c) the logarithmic growth rate. Bottom panel: (d) temperature dependence of the linear growth rate normalized to the gyration radius for chains of Mw 325 kg/mol (blue diamonds) and 1460 kg/mol (red diamonds). Each point is the average of the results of at least 6 independent data sets.
polymerization degree. Previous reports on dilute solutions and melts suggested, instead, that v is constant.20,22 Such evidence was, however, not firm. Experimental uncertainties, in fact, did not allow to discriminate between the scaling v ∼ N1/2 and the Mw-independent scenario (v ∼ N0). The latter case would not be consistent with kinetics yielding to adsorbed amount scaling as N1/2 within reasonably short adsorption times. The temperature dependence of v followed a thermally activated law, v ∼ exp(−E/kBT), with activation energy E = 66 3392
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(25) Zajac, R.; Chakrabarti, A. Phys. Rev. E 1995, 52, 6536−6549. (26) Rotella, C.; Napolitano, S.; Vandendriessche, S.; Valev, V. K.; Verbiest, T.; Larkowska, M.; Kucharski, S.; Wübbenhorst, M. Langmuir 2011, 27, 13533.
thickness scaling with the macromolecular size, in line with the reflected random walk. Our extensive experimental data set will be of fundamental support for the test of new and old theories on the structure and dynamics of polymers at the interface. Future work will be addressed on understanding the impact of free surfaces and nanoscopic confinement on the mechanisms of irreversible chain adsorption,5 and to explore other reaction mechanisms yielding a non linear initial growth regime (tα, α < 1) as observed for linear polymers decorated with highly polar moieties.26
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
S Supporting Information *
Figures showing AFM characterization and further fit results. This material is available free of charge via the Internet at http://pubs.acs.org Corresponding Author
*(S.N.) E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS S.N. acknowledges financial support from the funds FER of the Université Libre de Bruxelles. REFERENCES
(1) Granick, S. Eur. Phys. J. E 2002, 9, 421−424. (2) Santore, M. M. Curr. Opin. Colloid Interface Sci. 2005, 10, 176− 183. (3) O’Shaughnessy, B.; Vavylonis, D. J. Phys.: Condens. Matter 2005, 17, R63−R99. (4) Napolitano, S.; Capponi, S.; Vanroy, B. Eur. Phys. J. E 2013, 36, 61. (5) Ediger, M. D.; Forrest, J. A. Macromolecules 2013, 47, 471−478. (6) Napolitano, S.; Wübbenhorst, M. Nat. Commun. 2011, 2, 260. (7) Napolitano, S.; Rotella, C.; Wübbenhorst, M. ACS Macro Lett. 2012, 1, 1189−1193. (8) Napolitano, S.; Cangialosi, D. Macromolecules 2013, 46, 8051− 8053. (9) Koga, T.; et al. Phys. Rev. Lett. 2011, 107, 225901. (10) Vanroy, B.; Wübbenhorst, M.; Napolitano, S. ACS Macro Lett. 2013, 2, 168−172. (11) Glynos, E.; Frieberg, B.; Green, P. F. Phys. Rev. Lett. 2011, 107, 118303. (12) Nguyen, H. K.; Labardi, M.; Lucchesi, M.; Rolla, P.; Prevosto, D. Macromolecules 2013, 46, 555−561. (13) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymer at Interfaces; Chapman & Hall: London, 1998. (14) Schneider, H. M.; Frantz, P.; Granick, S. Langmuir 1996, 12, 994−996. (15) Ligoure, C.; Leibler, L. J. Phys. 1990, 51, 1313−1328. (16) Linse, P. Soft Matter 2012, 8, 5140−5150. (17) Guiselin, O. Europhys. Lett. 1991, 17, 225−230. (18) Fujii, Y.; et al. Macromolecules 2009, 42, 7418−7422. (19) Jenkins, F. A.; White, H. E. Fundamentals of Optics, 4th ed., McGraw-Hill, Inc.: New York, 1981. (20) Durning, C. J.; et al. Macromolecules 1999, 32, 6772−6781. (21) Gin, P.; et al. Phys. Rev. Lett. 2012, 109, 265501. (22) Fu, T. Z.; Stimming, U.; Durning, C. J. Macromolecules 1993, 26, 3271−3281. (23) Lupascu, V.; Picken, S. J.; Wübbenhorst, M. Macromolecules 2006, 39, 5152−5158. (24) Chowdhury, M.; et al. Phys. Rev. Lett. 2012, 109, 136102. 3393
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