Letter pubs.acs.org/macroletters
Mechanisms of Polymer Adsorption onto Solid Substrates David Nieto Simavilla,† Weide Huang,†,‡ Philippe Vandestrick,† Jean-Paul Ryckaert,† Michele Sferrazza,‡ and Simone Napolitano*,† †
Laboratory of Polymer and Soft Matter Dynamics, Faculté des Sciences, Université libre de Bruxelles (ULB), Boulevard du Triomphe, Bâtiment NO, Bruxelles 1050, Belgium ‡ Department of Physics, Faculté des Sciences, Université libre de Bruxelles (ULB), Boulevard du Triomphe, Bruxelles 1050, Belgium S Supporting Information *
ABSTRACT: Controlling polymer/substrate interfaces without modifying chemistry is nowadays possible by finely tuning the formation of adsorbed layers. The complex processes leading to irreversible attachment of chains onto solid substrates are governed by two mechanisms: molecular rearrangement and potential-driven adsorption. Here we introduce an analytical method to differentiate these two mechanisms. By analyzing experiments and simulations, we investigate how changes in thermal energy and interaction potential affect equilibrium and nonequilibrium components of the adsorption kinetics. We find that the adsorption process is thermally activated, with activation energy comparable to that of local noncooperative processes. On the other hand, the final adsorbed amount depends on the interface interaction only (i.e., it is temperature independent in experiments). We identify a universal linear relation between the growth rates at short and long adsorption times, suggesting that the monomer pinning mechanism is independent of surface coverage, while the progressive limitation of free sites significantly limits the adsorption rate.
T
mechanisms of adsorption are dictated by noncooperative rearrangements due to spontaneous fluctuations. Further work10,11 confirmed the validity of eq 1 for other polymer systems. Regardless of its success in describing the nonequilibrium component of the kinetics of adsorption, eq 1 has two main limitations. First, it cannot capture the final stage of the kinetics, where the adsorbed amount is expected to saturate to a constant valuethe adsorbed amount at thermodynamic equilibrium. We remark however that such a regime is not often observed in experiments because of material degradation. Second, eq 1 does not allow us to directly discriminate between the mechanisms of adsorption. Allegedly, the adsorption rate is governed by the fastest process between: (1) The molecular motion or conformational changes at molecular level and (2) effect of long-range (van der Waals) forces of the interaction potential acting on the macromolecules. Changes in the annealing temperature have a strong effect on the molecular motion (thermal activation energy Ea ≈ 50−100 kJ mol−1) without significantly impacting the interaction potential (∼kBT, ≈2−5 kJ mol−1). Hence, we expect that those features of the kinetics affected by molecular motion are enhanced by an increase in temperature, while those limited by the interfacial
he formation of an irreversibly adsorbed layer at the interface between a polymer melt and a solid substrate results in interface properties that are far from those exhibited by the bulk material.1−5 Such deviations from the bulk behavior are of great importance in applications such as flexible electronics,6 organic solar cells,7 and membrane separation8 among others. Previous research shows that the early stages of the chain pinning process responsible for the formation of the adsorbed layer proceed via a zero-order reaction mechanism until surface coverage limits the attachment of new chains to the formation of loops.9 Housmans et al. proposed a model where the adsorption kinetics, experimentally investigated by the measure of the time evolution of the thickness of the adsorbed layer hads, is divided into two regimes: a linear growth at short times followed by a logarithmic one9
where tcross and hcross represent the crossover point between regimes; h0 is some initial adsorbed thickness; and ν and Π are the growth rates, respectively, in the linear and in the logarithmic regimes. The analysis of the adsorption kinetics of polystyrene (PS) on silicon oxide by Housmans et al. showed also that both adsorption rates ν and Π scale with the square root of the molecular weight, implying that, at each given time, the number of adsorbed macromolecules does not depend on chain length. Additionally, it was shown that ν followed a thermally activated law, suggesting that the © XXXX American Chemical Society
Received: June 29, 2017 Accepted: August 21, 2017
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DOI: 10.1021/acsmacrolett.7b00473 ACS Macro Lett. 2017, 6, 975−979
Letter
ACS Macro Letters potential appear as temperature independent. While investigation of case (1) is easily achieved, e.g., by studying the adsorption kinetics of a given polymer at different annealing temperatures, performing experiments to study case (2) is less straightforward. Since for most polymers the interaction potential is not strongly affected by the interfacial chemistry and its exact determination is not trivial,13 the design of experiments where the potential is subject to change is fairly challenging. Moreover, changing the substrate also results in modification of the interface roughness, which in turn might affect the effective interaction potential14 and significantly alter the molecular mechanisms of adsorption.15 Nevertheless, insight on potential-driven adsorption can be gained from simulations, upon full control of interfacial parameters as monomer/ substrate interaction potential depth. In this letter, we address the two problems and show that a proper treatment of the mechanisms of pinning of monomers onto solid substrates at different surface coverages yields an analytical solution which can be used to disentangle the role of molecular motion and interfacial potential in the nonequilibrium and the equilibrium features of the kinetics of adsorption. In our experiments, we considered thick slabs (>6−7Rg) of polymer melts spin-coated onto Si wafers. Adsorption onto the substrate is induced by annealing in isothermal conditions above the glass transition temperature, Tg, and the nonadsorbed chains are removed following Guiselin’s experiment.16 Using ellipsometry, we determined the residual layer thickness, hads(t), which provides Γ(t), the number of chains irreversibly adsorbed, per unit area, after different annealing times. In dynamical nonequilibrium simulations, we employed a protocol mimicking the experimental procedure: first we equilibrated the film against a substrate with a small monomer/wall interaction ratio, e0 = εw/kBT, sufficient to avoid dewetting of the film; here εw indicates the depth of the monomer/wall potential. Then at t = 0, mimicking the operation of placing a sample previously at room temperature on the hot place at T > Tg, the wall interaction ratio was suddenly increased and set to e1 > e0. We thus monitored the evolution of the adsorbed amount and of the conformations of the adsorbed chains over a time sufficient to observe the plateau corresponding to the new equilibrium. In Figure 1, we show examples of the adsorption kinetics in experiments (left top panel) and simulations (right top). Remarkably, the two types of data sets provide the same form of the kinetics of adsorption (see eq 1). This evidence implies that it is not possible to differentiate the dominating mechanism in the adsorption process by simply looking at the time evolution of the adsorbed amount of a single experiment. Based on the hypotheses considered in the introduction, we have tested whether analyzing how thermal energy affects the growth rates permits disentangling the two mechanisms of adsorption. For the experiments, we notice that adsorption speeds up (v and Π increase) upon increase of the temperature (see Figure 1, top-left), which, in turn, eases molecular motion. Results presented in Figure 1 (center-left) evidence an Arrhenius like dependence of the linear adsorption rate (i.e., ν = ν0 exp(−Ea/KBT), similar expressions are found for Π), with activation energies on the order of ∼80 kJ mol−1. These values and the temperature dependence of ν are in line with local, noncooperative relaxation processes, due to rearrangements of a few atoms.17 Additional details on the activation
Figure 1. Top left (experiments): adsorption kinetics in for PS955k at 160 °C (green circles with white crosses) and 140 °C (filled green circles). Top right (simulations): adsorption kinetics results for chains of N = 20 monomers at different wall potentials, 0.5 (filled black circles) and 1 (empty black circles). Center left (exp.): linear growth rate versus the ratio of activation and thermal energies for PS 955k (green circles, Ea = 51.5 ± 8.3 kJ mol−1) and 560k (green diamonds, Ea = 59.3 ± 16.6 kJ mol−1), PtBS 1210k (red squares, Ea = 91.0 ± 4.7 kJ mol−1), P4MS 74k (blue stars, Ea = 127.2 ± 6.6 kJ mol−1), and PMMA 320k (pink triangles, Ea = 138.9 ± 6.0 kJ mol−1). Center right (sim.): linear regime adsorption rate as a function of the wall potential. Bottom left (exp.): final adsorbed thickness as a function of temperature (symbols as in center left panel). Bottom right (sim.): Final adsorbed amount for this study with N = 20 (black circles) and Virgilis et al.12 with N = 32 (squares) and N = 80 (diamonds) as a function of the depth of the monomer/wall potential in units of thermal energy.
energy for each polymer can be found in the Supporting Information. In agreement with previous experimental evidence,9,10 the final adsorbed thickness h∞ (see Figure 1, bottom-left) shows no dependence on temperature. The different behavior between the growth rate ν and the adsorbed thickness h∞ suggests a different mechanism (i.e., the final adsorbed amount is not governed by molecular motion but by the polymer/ substrate interaction potential). This hypothesis is confirmed by the trends in the simulation results presented in Figure 1 (right panels), where both the adsorption rate and the equilibrium adsorbed amount increase with εw/kBT, hinting at slower adsorption kinetics at higher temperatures. Previous work,12 focusing on equilibrium quantities, showed a saturation of the final adsorbed amount at larger potentials, probably due to the finite compressibility of the material. Jeong et al.’s18 experimental work in vapor-deposited thin layers of poly976
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ACS Macro Letters
loops formed at later stages are longer and thus more unfavorable (larger entropic cost) from an energetic point of view. This continuous reduction of the adsorption rate results in a new regime characterized by logarithmic growth, eventually saturating to the equilibrium adsorbed amount, Γ∞. Considering ideal chain scaling (see SI for a rigorous treatment), the evolution of the adsorbed amount via formation of loops is given by
(ethylene oxide) further supports the dependence of potentialdriven adsorption on the inverse of temperature. In contrast to spin-coated films, in these samples prepared at ultraslow evaporation rates, molecular mobility is strongly suppressed with respect to the bulk. Hence, the adsorption rate is mostly driven by interfacial potential, which results in a reduction in the thickness of the adsorbed layer with increasing temperature. We expect a similar trend in spin-coated films at temperatures approaching the glass transition. Summarizing these observations, while the nonequilibrium components of the kinetics of adsorption (growth rates) are associated with both molecular processes and interfacial potential, the equilibrium adsorbed amount is always bound to the interfacial interactions between polymer and substrate. Although the kinetics of adsorption follows the same form in eq 1, independently of the origin of the adsorption rate, the two cases can be differentiated by considering the impact of temperature. An increase in T speeds up adsorption processes driven by molecular motion (e.g., spin-coated films), while the opposite trend is observed when chain pinning is due to intermolecular potential only (systems with inhibited molecular motion or MD simulations). With this idea in mind, we introduce a theoretical approach to describe the kinetics of adsorption from short times until reaching an equilibrium adsorbed amount. At short annealing times, we consider a zero-order reaction mechanism19 with monomer adsorption rate q due to molecular fluctuations and interfacial potential. Assuming that as soon as a monomer gets in contact with the surface the whole chain is irreversibly adsorbed,20 the number of monomers in the chains adsorbed per unit area and unit time, ∂Γ/∂t, is given by the product of the monomers available at the substrate and the polymerization degree N. The monomer availability is related to monomer density and the ratio between the surface (Zs) and bulk (Zb) partition functions.21 Computing the latter quantity is equivalent to counting the number of contacts a chain makes with a flat surface. Considering the statistics of polymer melts, we get: ∂Γ/∂t = qρ
Zs(N ) N Z b(N )
⎡ ⎛ t − tcross ⎞⎤ ⎟ Γ(t ) = Γ∞ + ln⎢1 − A exp⎜ − ⎝ ⎠⎥⎦ ⎣ τ
where A = [1 − exp(−ΔΓcross)], the characteristic time τ = [exp(−Γ∞)ΦQ]−1, and Q is the equivalent loop adsorption rate. Here Q = cq, where c is a system-dependent constant determining the increase in adsorbed amount in the logarithmic regime. Equation 4 is only valid for a time regime t > tcross and explains the occurrence of a logarithmic growth regime in the adsorption of polymer melts. Since ΔΓcross ≫ 1 and A ∼ 1, we simplify eq 2 for tcross ≪ t ≪ τ to ⎡t ⎤ Γ(t ) ≈ Γ∞ + ln⎢ ⎥ ⎣τ⎦
(5)
Equation 5 is equivalent to eq 1b) since hcross = h∞ − Π log τ. The advantage of eq 4, which is experimentally undiscernible from eq 5, is the description of the adsorption kinetics until its saturation, a condition recently encountered in experiments.11 Our simulations verified that the conditions required for eqs 4 and 5 occur for t > tcross, where the number of new loops increases, while the rate of formation of trains decreases with respect to the linear regime (see shaded area in Figure 2). Eventually the formation of loops decays as well, for t ≫ τ, in agreement with eq 4. Comparison with eq 3 suggests that a solid test of the validity of eq 4 requires verifying that the ratio between the adsorption rates in the linear and in the logarithmic regimes is a constant, depending only on the polymer/substrate pair. By performing experiments at the different temperatures, we were able to vary the value of q, while keeping constant the polymer/substrate pair;24 in simulations we simply modified the depth of the potential, εw. Figure 3 shows the relation between the pinning rates for both the linear (Φq in eq 3) and the logarithmic (ΦQ in eq 4) regimes. All data sets provide a linear relation between these two parameters suggesting that the mechanism for the attachment of chains (i.e., molecular motion or interfacial potential) is the same in both regimes and that the slowdown in dynamics is produced only by the progressive limitation in available attachment sites as opposed to the availability of chains to attach. The validity of eq 4 also implies that our simple treatment is sufficient to capture the mechanisms of chain adsorption. Finally, we remark that the main difference between the two regimes is related to the parameters affecting the growth. At t ≪ tcross the growth rate depends on the pinning rate q only, while in the later stages of adsorption the velocity of incorporation of new chains is limited also by Γ∞, a parameter given by the interaction potential.
(2)
Integration results in a linear growth of the adsorbed amount Γ with time t in agreement with eq 1a. Γ(t < tcross) = qρN1/2t = qΦt
(4)
(3)
The adsorbed amount Γ is experimentally determined by measuring the thickness of the adsorbed layer h since these two quantities are simply related by the density of the adsorbed layer and the polymerization degree. Note that experiments comparing AFM and ellipsometry measurements of adsorbed layers suggest that the density of the adsorbed layer is equivalent to the bulk density, within experimental uncertainties (∼5%).22 At long annealing times surface crowding inhibits the zeroorder adsorption mechanism, and the growth rate drops. This condition was elegantly pictured by O’Shaughnessey and Vavylonis for adsorption of polymer chains in solution.23 The adsorbed layer formed during the linear growth regime is described as a slab with a limited number of free sites available for attachment of new chains. As a result, adsorption is only possible through the formation of loops between free sites. With time the density of free sites decreases, implying that
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MATERIALS AND METHODS
Experiments. All samples in this study were prepared by spincoating polymer thin films onto a silicon wafer substrate. Before spin coating, wafers were rinsed with the appropriate solvents (typically 977
DOI: 10.1021/acsmacrolett.7b00473 ACS Macro Lett. 2017, 6, 975−979
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ACS Macro Letters
Figure 3. Universal relation between pinning rates in the linear and in the logarithmic adsorption regimes, normalized by a temperatureindependent constant C ≈ exp(Γ∞)/ντ. Experimental results for PtBS 1210k (red squares), P4MS 72k (blue stars), PS 955k (green circles), PS 560k (green diamonds), and PMMA 320k (magenta triangles). The equivalent simulation results are included in the bottom-right inset. The evolution of the adsorbed layer thickness for four of the polymers to show the effect of varying the parameter c is presented in the top-left inset. shows a minimum of valueεw at z = 31/6σw. We fixed σw = σ and tuned the adsorbing potential by varying the ratio e = εw/ε. A chain is considered adsorbed when at least one of its monomers is located within the region of the first peak of the global equilibrium monomer density ρ(x; e). At p = 0 and kT/ε = 1, we defined the equilibrium adsorbed amount as
Γ∞(e) =
Figure 2. Top: adsorbed amount as a function of simulation time for εw/kT0 = 1. The dashed and solid lines represent linear and logarithmic growth regimes, respectively. Center and bottom: trains and loop formation rates, respectively, as a function of simulation time. The pattern area corresponds to a sudden increase in the loop formation rate due to surface crowding, which results in a reduced (logarithmic) growth rate.
0
∫∞ ρdads (x ; e)dx
(6)
where ρads(x; e) is the adsorbed monomer density regrouping all monomers of adsorbed chains. To reproduce the experimental conditions discussed in the previous section, we set up a dynamical nonequilibrium adsorption experiment, via different steps: (1) Equilibration of a given film at preset conditions against the substrate with e = e0 = 0.3, a monomer/wall interaction parameter corresponding to a “partial dewetting” condition. (2) Generation of 600 independent microscopic configurations representative of the state equilibrium reached at e0. (3) A kinetic run at wall parameter e1 > e0, starting from the microscopic configurations generated in the previous step. The adsorbed monomer density and its integral are followed over a time sufficiently long to observe the plateau corresponding to the new equilibrium state.
acetone followed by isopropanol and finally toluene). PS, PtBS, and P4MS are readily soluble in toluene (>99% purity). Details on the specific polymer utilized in this study are presented in Table S1 in the SI. Polymer concentration is used to control the deposited layer thickness that is obtained after spin-coating at 4000 rpm. Spin-coated polymer layer thickness L ranges from 100 to 500 nm and is chosen depending on the molecular weight of each specific polymer to ensure that L > 6Rg so that it can be considered a bulk film. The measured adsorbed layers range from 3 to 15 nm. Note that films below ∼3 nm are intrinsically unstable, and they spontaneously dewet, via spinodal decomposition. Coated samples are dried in vacuum for 20 min and preannealed for 10 min slightly above the glass transition temperature. Samples were annealed in a hot plat from 0 to 72 h to allow for adsorption of the polymer into the substrate. After annealing, excess polymer is washed off with the same solvent used to prepare the spincoated solutions (Guiselin’s experiment16). The adsorbed polymer layer thicknesses resulting from the annealing process were measured using ellipsometry (MM-16, Horiba).9,22 Simulations. We used a previously introduced coarse-grained polymer melt and substrate system,25,26 where chains composed of 20 beads interact via a sum of bead−bead Lennard-Jones (LJ) interactions (see Supporting Information for further details). The units for mass, length, and energy are, respectively, given by the bead mass m, the LJ hard core size σ, and the LJ well depth, ε. The polymer/wall potential
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.7b00473. Additional information about the polymer used, derivation of eq 4, and molecular dynamics simulation (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Simone Napolitano: 0000-0001-7662-9858 978
DOI: 10.1021/acsmacrolett.7b00473 ACS Macro Lett. 2017, 6, 975−979
Letter
ACS Macro Letters Notes
(22) Braatz, M.-L.; Melendez, L. I.; Sferrazza, M.; Napolitano, S. Unexpected impact of irreversible adsorption on thermal expansion: Adsorbed layers are not that dead. J. Chem. Phys. 2017, 146, 203304. (23) O’Shaughnessy, B.; Vavylonis, D. Irreversible adsorption from dilute polymer solutions. Eur. Phys. J. E: Soft Matter Biol. Phys. 2003, 11, 213−230. (24) Here we neglected the temperature dependence of density. This approximation is possible considering the weaker temperature dependence of density with respect to that of q. (25) Peter, S.; Napolitano, S.; Meyer, H.; Wübbenhorst, M.; Baschnagel, J. Modeling Dielectric Relaxation in Polymer Glass Simulations: Dynamics in the Bulk and in Supported Polymer Films. Macromolecules 2008, 41, 7729−7743. (26) Peter, S.; Meyer, H.; Baschnagel, J. Thickness-dependent reduction of the glass-transition temperature in thin polymer films with a free surface. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 2951− 2967.
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS D.N.S. and S.N. acknowledge the Fonds de la Recherche Scientifique − FNRS under Grant no. T.0147.16 “TIACIC”
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REFERENCES
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DOI: 10.1021/acsmacrolett.7b00473 ACS Macro Lett. 2017, 6, 975−979
