Article pubs.acs.org/Macromolecules
Probing the Density Variation of Confined Polymer Thin Films via Simple Model-Independent Nanoparticle Adsorption A. Beena Unni,†,‡ G. Vignaud,*,† J. P. Chapel,*,⊥,# J. Giermanska,⊥,# J. K. Bal,§ N. Delorme,∥ T. Beuvier,∥ S. Thomas,‡ Y. Grohens,† and A. Gibaud∥ †
FRE CNRS 3744, IRDL, Univ. Bretagne Sud, F-56100 Lorient, France International and Inter University Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam, Kerala, India 686560 § Centre for Research in Nanoscience and Nanotechnology, University of Calcutta, Technology Campus, Block JD2, Sector III, Saltlake City, Kolkata 700098, India ∥ LUNAM Université, IMMM, Faculté de Sciences, Université du Maine, UMR 6283 CNRS, 72000 Le Mans, Cedex 9, France ⊥ Centre de Recherche Paul Pascal (CRPP), UPR 8641, CNRS, F-33600 Pessac, France # Centre de Recherche Paul Pascal, Université de Bordeaux, F-33600 Pessac, France ‡
S Supporting Information *
ABSTRACT: After more than 2 decades of intense research, the density variation in confined polymer films still remains a puzzling problem subject to controversy as the methods utilized to determine the density are often model dependent. Here, we propose a direct and model independent method to detect the density/refractive index variations in polymer thin films through the adsorption of ceria nanoparticles (NPs) onto their surface. The amount of adsorbed NP scales with the polymer film refractive index; hence, any increase/ decrease in the NP surface coverage directly indicates an increase/decrease in the film refractive index and density. Experimenting our proposed novel approach on two well-studied polymers, we found that the density of polystyrene (PS) thin films deposited on oxide-free Si substrate increases with a reduction of the film thickness. On the contrary, poly(methyl methacrylate) (PMMA) films deposited on wafers with native silicon oxide show a decrease of their density when the film thickness is reduced.
■
average free volume is to measure the density of a film as a function of its thickness. Indeed, the density is correlated to the free volume.10,21 Vignaud et al.10 showed by combining spectroscopic ellipsometry (SE) and X-ray reflectivity (XRR) that the average density of PS thin films on oxide-free Hterminated silicon wafer (H-Si) increases when reducing the film thickness. This result is in line with the recent results of Gin et al.22 revealing by X-ray and neutron reflectivity experiments that the PS chains at the polymer/substrate interface exhibit a more flattened conformation23 and thus possess a higher density than in the bulk. At odds with these results, XRR measurements reported either no systematic change in density with the film thickness24 or even a decreased electron density near the PS−substrate interface.25 Some of these discrepancies can possibly arise from the sample preparation conditions like the quality and evaporation rate of the spin-coating solvent26 (acting on the entanglement density), the nature of the substrate27 (acting on interfacial interactions), and the annealing time28 (acting on the monomer
INTRODUCTION Miniaturization being a sought-after criteria, a large body of work has been devoted over the past 20 years on confinement effects in polymer thin films. Besides the well-known deviation of the glass transition temperature, Tg, with respect to the bulk value,1 polymer thin films in a confined state show many peculiar properties in their viscosity,2,3 coefficient of thermal expansion (CTE),4,5 physical aging,6,7 surface mobility,8,9 and density10,11 compared to their bulk counterpart. Considering the glass transition properties of supported thin films, beside the film thickness, the solid interfaces and free surfaces are found to be two key factors impacting deeply the thin film physical behaviors.12−17 Recent studies by Napolitano et al.18−20 have evidenced that the knowledge of the film thickness together with interfacial interactions is not sufficient to fully describe the properties of macromolecules under confinement. They have then put forward the concept of interfacial f ree volume (the space available for molecular relaxations at the polymer/substrate interface) which can differ from the bulk free volume due to the packing frustration of the adsorbed layer. Indeed, this local free volume can alter the longrange structural dynamics from the substrate and consequently the Tg.18,19 A well-suited indirect method to characterize the © 2017 American Chemical Society
Received: December 6, 2016 Revised: January 12, 2017 Published: February 2, 2017 1027
DOI: 10.1021/acs.macromol.6b02617 Macromolecules 2017, 50, 1027−1036
Article
Macromolecules
we used instead a 0.1%/w dispersion and an adsorption time of 20 min (due to a lower adsorption due to a lower refractive index; see Table 1). The pH of the CeO2 NP dispersion was 1.5 (HNO3) with 0.04 M
density at the polymer/substrate interface). Another possible source of controversy is related to the way experimental results coming from ellipsometry and XRR are analyzed. For XRR, the density profile is determined according to a guessed model that is refined by fitting the model dependent calculated data to the measured ones.29 This approach has however a serious limitation as the phase of the reflected radiation is lost. Hence, it prevents the uniqueness of the density profile determination from the data.30 For ellipsometric measurements, the thickness and refractive index values are strongly correlated in particular for thinner films (h < 10 nm).31 Because ellipsometry is sensitive to the product of the refractive index and the film thickness (i.e., the optical path length), the absolute value of the index of refraction may be dubious for an unknown thickness. Hence, probing subtle changes in the density of ultrathin films remains a very challenging issue. Here we propose a novel method based on the adsorption of ceria (CeO2) NPs at the surface of polymer thin films to get this most desired information. The study is carried out on two well-studied polymers, namely PS and PMMA. The proposed method allows a direct assessment of the film refractive index variation without relying on any model. Note that according to the Clausius−Mossotti relation the index of refraction of a film must also evolve in the same way as its density.10,32
■
Table 1. Different Bulky Polymer Substrate Used To Monitor CeO2 NP Adsorption polymer
Mwa
PDIb
Tgc (°C)
n545 nmd
n633 nmd
PS PMMA PP PiBMA PiPMA α-PMS SiO2−HMDSe
250 120 174 31 100 374 N/A
2.5 2.1 2.32 1.35 N/A 1.10 N/A
100 105 0 62 81 177 N/A
1.585 1.48 1.49 1.473 1.471 1.599 N/A
1.578 1.478 1.485 1.47 1.467 1.591 1.41f
a
Molecular weight. bPolydispersity index (Mw/Mn). cGlass transition temperature. dRefractive index measured by spectroscopic ellipsometry. eOne monolayer of grafted HMDS molecule is considered here (∼1 nm). fBulk value measured with a Fresnel refractometer. NaNO3 salt to weaken/screen the strong inter-NP electrostatic repulsions so as to increase the overall adsorbed amount. According to the total concentration of NO3− ions in solution, the Debye screening length is estimated to κ−1 ∼ 1.14 nm. AFM Measurements. AFM measurements were performed in air in tapping mode using a silicon cantilever to determine the NP surface coverage (%) of the polymer thin films. Two different samples were measured for each thickness and polymer. At least three AFM images were acquired on different zones of the sample (i.e., 2 × 3 AFM images for one film thickness) in order to have a good reproducibility and statistics avoiding image artifacts. The NP surface coverage was computed from AFM images through image processing using ImageJ software. Thick Films Preparation and Characterization (h ∼ 200 nm). Sample Preparation. Different polymer thicker films with bulky refractive indices were prepared on two different substrates depending on the measurement technique used to measure the NP adsorption amount (mg m−2). Optical Reflectometry. PS/PMMA and polypropylene (PP) films with thicknesses around 200 nm and bulky polymer refractive indices as measured by ellipsometry were obtained from a 2%/w toluene and hot xylene solutions, respectively, and spin-coated onto SiO2−Si wafers covered with a 100 nm silica layer. An extra hydrophobic silica layer (water contact angle of 115°) was obtained through the grafting of HMDS silane monolayer (hexamethyldisiloxane) onto a SiO2−Si wafer. NP adsorption was then monitored using a stagnation point adsorption reflectometry (SPAR) approach.36,37 Fixed angle reflectometry measured the reflectance at the Brewster angle on the flat substrate. A linearly polarized light beam was reflected by the surface and subsequently split into a parallel and a perpendicular component using a polarizing beam splitter. As NPs adsorbed at the substrate− solution interface, the ratio S between the parallel and perpendicular components of the reflected light varied. The system was analyzed in terms of Fresnel reflectivities for a multilayer system (substrate, coating, adsorbed layer, and solvent), where each layer was described by a complex refractive index and a layer thickness. According to this model, the sensitivity factor (AS), which is the relative change in the output signal S per unit surface, was found to be proportional to refractive index increment (dn/dc) of the CeO2 NP solution. It also depended on the angle of incidence, the wavelength, and the nature of the collecting surface. The change in S was then related to the NPs adsorbed amount Γ through
EXPERIMENTAL SECTION
Thin Films Preparation and Characterization (6 ≪ h ≪ 140 nm). Sample Preparation. PS thin films (Mw = 136 kg mol−1 and polydispersity index (PDI), Mw/Mn = 1.05) and PMMA (Mw = 152.8 kg mol−1 and PDI = 1.08) were spin-coated on Si (100) wafers at a speed of 2000 rpm for 1 min from a polymer/toluene solution. Their thickness was varied by tuning the solution concentration. The silicon wafers were previously diced into pieces of dimension 1 × 1 cm2 and were immersed in a piranha solution (3:1 mixture of sulfuric acid and 30% hydrogen peroxide) to remove any organic contamination. All the substrates were then rinsed thoroughly with Milli-Q water (resistivity ≈18.2 MΩ·cm) and dried with N2. The native oxide thickness was measured to be around 1.7 nm by ellipsometry. Prior to spin-coating of the PS films, the oxide layer was removed through HF treatment (wafers immersed in 5% HF for 5 min). Piranha treatment yields hydroxyl groups at the surface of the silicon wafer whereas HF acid removes the thin native oxide layer. The chemical treatment efficiency was controlled by contact angle measurements. The polar components of surface energies inferred from the Owens and Wendt33 approach are 43 and 7 mJ m−2 for treated piranha and HF surfaces, respectively. The films were then annealed at 160 °C for 24 h under vacuum to release any trace of solvent and any stress buildup during the spin-coating step. The films were homogeneous and extremely smooth with identical roughness values (root-mean-square) of the order of 4 ± 1 Å on a large area (100 μm2) as revealed by AFM imaging. Nanoparticle (NP) Adsorption. Cerium oxide (ceria)34,35 NP dispersions (10%/w, pH 1.5) were kindly supplied by the RhodiaSolvay Chemical Company (Belgium). The size distribution of the NPs was found to be log-normal with median diameter 8.3 nm and a polydispersity 0.26 as measured from dynamic light scattering. The CeO2 NPs were stabilized at low pH by a combination of repulsive long-range electrostatic forces (CeO2 are positively charged) and short-range hydration interactions. The NPs were then adsorbed from solution onto PS and PMMA films as follows. For PS, a 0.03%/w NP dispersion was dropped over each sample and allowed to adsorb for 30 s (a 100 μL droplet was used for a 1 × 1 cm2 Si wafer). The solution was then removed, and the surface was rinsed with pure nitric acid solution at pH ∼ 1.5. Finally, the surface was cleaned with distilled water (pH ∼ 5.6). The intermediate cleaning step with nitric acid was performed to avoid the precipitation of the NPs that occurs when one directly cleans with water (due do an increase of the pH). For PMMA
Γ(t ) =
1 S(t ) − S0 As S0
(1)
where S0 is the signal at t = 0. Quartz Crystal Microbalance. In a second series of experiments, PMMA, PS, α-PMS (poly(α-methylstyrene)), PiBMA (poly(isobutyl 1028
DOI: 10.1021/acs.macromol.6b02617 Macromolecules 2017, 50, 1027−1036
Article
Macromolecules
Figure 1. (a) Zero-frequency (eq 4) and (b) dispersive (eq 5) contributions of the Hamaker constant as a function of the dielectric and the refractive index of the polymer surface for a given dilute CeO2 NP dispersion (with nNP = 1.9, εNP = 25, nsol = 1.33, and εsol = 80). methacrylate)), and PiPMA (poly(isopropyl methacrylate)) thick (∼200 nm) films were obtained from a 2%/w toluene solution through spin-coating onto quartz crystal microbalance sensors (QCMD from Q-Sense AB, Västra Frölunda, Sweden) covered with a 50 nm silica layer. The different polymer films have been annealed under vacuum at Tg + 30 °C for 24 h (see Table 1). NP adsorption was monitored by the decrease in the resonance frequency f n for each odd overtone of the QCM piezoelectric quartz crystal.38 In the case of a thin and homogeneously distributed layer rigidly attached to the sensor surface,39 the quantitative relationship between the frequency change and the adsorbed mass per unit area increment Δm in air can be derived with the help of the Sauerbrey equation: Δfn n
=−
2f0 2 ρq μq
A υ≠ 0 =
/{(nNP 2 + nsol 2)1/2 (n p2 + nsol 2)1/2 [(n p2 + nsol 2)1/2 + (nNP 2 + nsol 2)1/2 ]}
(2)
where f 0 is the resonant frequency of the crystal (5 MHz), ρq the quartz density (2.648 g/cm3), μq the quartz shear modulus (2.947 × 1011 g/(cm s2)), and n the frequency overtone number. Ellipsometry and X-ray Reflectivity Measurements. Spectroscopic ellipsometry was used to determine the refractive index of all polymer films. XRR measurements were carried out on a versatile X-ray reflectometer to investigate the thicknesses of the thinner films. For the data analysis of the ellipsometry measurements, we prefer to fix the thickness to the one determined by XRR to avoid any bias in the calculation of the refractive index reported in Figure 6. Technical details of the instruments and the data analysis methods are described elsewhere.10
■
RESULTS AND DISCUSSION The principle behind the usage of ceria NPs for sensing the variations of polymer thin film density is straightforward. Owing to high dielectric constant, ceria NPs40 adsorb strongly onto any hydrophobic polymer surface. This can be explained through the Lifshitz−van der Waals (LW) interactions between the NPs and the polymer surface. The strength of these interactions is usually described by the total Hamaker constant ATotal which is the sum of a zero-frequency, Aυ=0 (i.e., the orientation (Keesom) and the induction (Debye) forces) and a dispersive Aυ≠0 (i.e., the London contribution) Hamaker constant41
ΔFLW (D , ANP,substrate) =
0 ⎞ 0 0 ⎛ 0 3 ⎜ ϵp − ϵsol ⎟⎛ ϵNP − ϵsol ⎞ ⎟ ⎜ kT ⎜ 0 4 ⎝ ϵp + ϵ0sol ⎟⎠⎝ ϵ0NP + ϵ0sol ⎠
−ANP,substrate ⎧ R ⎛ D ⎞⎫ R ⎟⎬ ⎨ + + ln⎜ ⎝ 2R + D ⎠⎭ ⎩ 6 D 2R + D
(6)
where ANP,substrate is the Hamaker constant of the NP/substrate in the solution media. ANP,substrate can be calculated from eq 3. In this expression, the substrate is made of only one material. As in our study the substrate includes three different materials (layers) at most, the additivity law is used to access to the potential energy of the NP/polymer/SiOx/Si system42−44
(3)
where A υ= 0 ≈
(5)
where h and k are the Planck and Boltzmann constants, respectively, υe is the main electronic absorption frequency in the UV typically around 3 × 1015 s−1, T is the temperature, np, nsol, nNP and ϵ0p, ϵ0sol, ϵ0NP are the refractive index and the relative permittivity at low frequency of the polymer, of the solution, and of the nanoparticles, respectively. A simulation of Aυ=0 and Aυ≠0 for ceria NPs interacting with polymers has been performed by choosing a medium with a refractive index of nsol = 1.33, i.e., water and NPs with a refractive index of nNP = 1.9, i.e., ceria (Figure 1). When the optical refractive index of the polymer nNP is higher than ∼1.4, which is the case of the polymers that are studied here, the simulation clearly shows that the dispersive contribution, Aυ≠0, is much higher than the zero-frequency term, Aυ=0, and dominates the behavior of ATotal. It is also to be noted that the Hamaker constant is a monotonic growing function of the polymer film refractive index np. In other words, the higher the refractive index of the polymer, the stronger the attractive NPs−polymer interactions. To deal in depth with our understanding of the adsorption of NPs, the free energy ΔFLW of the NP/polymer/SiOx/Si system was calculated. ΔFLW represents the long-range interactions generated by the Lifshitz−van der Waals potential. For a NP of radius R located at a distance D from a substrate, ΔFLW is defined as41
Δm
A Total = A υ = 0 + A υ ≠ 0
3hυe (n p2 − nsol 2)(nNP 2 − nsol 2) 8 2
(4) 1029
DOI: 10.1021/acs.macromol.6b02617 Macromolecules 2017, 50, 1027−1036
Article
Macromolecules
lower np made by silanization was also used. The adsorption on the various substrates was monitored during 2 h using the same CeO2 NP concentration (0.1%/w at pH = 1.5). In a typical QCM (/SPAR) adsorption experiment, the early stage adsorption is controlled by the diffusion of the NPs toward the surface and the van der Waals interaction between the NPs and the polymer surface as discussed above. When the adsorption density (coverage) increases, the adsorption becomes then mainly controlled by reaction.46 Incoming NPs have to find their own way to the surface by interacting with already adsorbed NPs through repulsive electrostatic forces. It is then physically sound to consider the diffusion-controlled stage only to build the adsorbed amount of NPs, Γ, vs n curve (shown in Figure 3) where NPs are interacting with the
ΔFLW (D , ANP,p,SiOx,Si ) = ΔFLW (D , ANP,p) − ΔFLW (D + h , ANP,p) + ΔFLW (D + h , ANP,SiOx ) − ΔFLW (D + h + hSiOx , ANP,SiOx ) + ΔFLW (D + h + hSiOx , ANP,Si )
(7)
where h and hSiOx are the thicknesses of the polymer film and of the SiOx layer, respectively (for more information about eq 7, see Figure S1). By substituting nNP = 1.9, nSi = 3.47, nsol = 1.33 (water), nSiOx = 1.48, hSiOx = 1.7 nm, R = 4.15 nm, D = 0.6 nm, and υe = 3 × 1015 s−1 (i.e., λe = 100 nm) and considering only its dispersive contribution, the interaction energy of a NP with the polymer/SiOx/Si system is shown in Figure 2.
Figure 2. Simulation from eq 7 of the interaction energy between the polymer/SiOx/Si system and a ceria NP of radius R located at a distance D as a function of the refractive index of the polymer (symbol). Solid line is a linear fit. The simulation was done with nNP = 1.9, nSi = 3.47, nsol = 1.33 (water), nSiOx = 1.48, hSiOx = 1.7 nm, R = 4.15 nm, D = 0.6 nm, and υe = 3 × 1015 s−1 and by choosing a bulky polymer thickness of h = 200 nm.
Figure 3. Amount of ceria NPs adsorbed (left axis) onto various hydrophobic (polymer) thick films (h ∼ 200 nm) and corresponding NP surface coverage in percentage (right axis) as a function of the refractive index. NP Coverage has been calculated from Γ knowing the molar mass (200 g/mol) and the average TEM diameter of a NP (7 nm). The hydrophobic silica layer (SiO2-HMDS) was also added. All experiments have been performed with a 0.1%/w CeO2 NP dispersion at pH = 1.5. It should be noted that in some cases the values represent the merging of the two characterization techniques QCM and SPAR (represented as QCM + SPAR) strengthening then our results. The black line is a linear fit to the data.
The simulation shown in Figure 2 highlights that ΔFLW is always negative. This reveals the attraction between the NP and the polymer/SiOx/Si system. In addition, ΔFLW is a linear function of np involving the larger np, the stronger LW attractions. As a consequence, any change in the polymer refractive index can be probed and monitored by measuring the adsorption of ceria NPs at the polymer surface. In the framework of this model, one can indeed expect that ceria NPs will adsorb more strongly on polymer films having a larger index of refraction. Conversely, the higher the adsorption of NPs, the bigger the index of refraction of the polymer film. The validity of this model can thus be assessed provided that polymer films having different refractive indices exhibit strong variations in the amount of adsorbed NPs on. To endorse this model, we have thus measured the amount of absorbed NPs on polymer films having different indices of refraction. In a first set of experiments, the adsorption of ceria NPs was monitored by optical reflectometry and quartz crystal microbalance (QCM) onto various polymer films having a similar thickness of about 200 nm for which the index of refraction np was increasing.38,45 In addition, a hydrophobic silica layer SiO2−HMDS (water contact angle ≈115°) with the
polymer surface through van der Waals forces only (see Figure S6 for more details). In any case, in our different experiments we have minimized the reaction stage by using a salted NP dispersion with a Debye screening length of ∼1 nm (coverage has to be quite high to start feeling NP/NP interaction). As shown in Figure 3, the adsorbed amount of NPs was found to change by almost a factor of 2 for films having an index of refraction np going from 1.407 to 1.60 clearly illustrating the sensitivity of this novel approach. The fact that PP and PMMA, for example, two polymers with different water contact angles (PP ≈ 102° and PMMA ≈ 71°) and surface energies (PP ≈30 mJ/m2 and PMMA ≈41 mJ/m2), show nearly similar adsorbed amounts clearly indicates that the LW interactions rather than the surface energy are driving the adsorption. As the refractive index of ceria NPs is large (≈1.8−2.0), their adsorption onto a PS surface for example is very strong and follows a high affinity adsorption isotherm (see Figure S2). After highlighting that the amount of CeO2 NPs adsorbed on the surface of a polymer film increases linearly with the index of refraction of the film, it is now particularly interesting to address whether this amount varies with the thickness of the 1030
DOI: 10.1021/acs.macromol.6b02617 Macromolecules 2017, 50, 1027−1036
Article
Macromolecules
Figure 4. Schematic illustration of the ceria NPs adsorption process. The key parameters are the adsorption time, the refractive index of the polymer thin film, and the NP dispersion, which allows tuning the NP surface coverage on samples of any shape and size.
film for a given polymer. This is a key issue as it raises a paramount question: do the index of refraction and more generally the density of a polymer f ilm deposited on solid substrate depend on its thickness? In order to answer this question and to experimentally bring some evidence, we have in a second set of experiments adsorbed the NPs onto thin PS and PMMA polymer films with variable thicknesses following a straightforward experimental protocol as sketched in Figure 4 (see Experimental Section for details). The overall study could have been performed with the sole QCM technique very sensitive to the adsorbed amount. We have decided to use AFM for the thin films because (i) the material layering inside the commercial sensors is not very wellknown and can possibly influence the adsorption itself when dealing with very thin films, (ii) the passivation of the sensors with HF is likely very delicate to perform although it is routinely performed on silicon wafers, and (iii) to get a good statistics, many samples have been made and measured with cheap silicon wafers. It could have cost a fortune to perform such series of experiments with expensive QCM sensors. An estimation of the amount of ceria NPs adsorbed onto PSH-Si films at different film thicknesses (h) was obtained from AFM topographic images as shown in Figure 5a−c. From these images, one can clearly observe that the 6.7 nm PS film is densely covered by the ceria NPs whereas the coverage on the 143.6 nm thicker PS film is comparatively very low; the 18.8 nm film lies in between. It should be noted that remarkable patterns with a 2D NP self-assembly are observed in Figures 5b and 5c. They may originate from the phase separation occurring when the low NP−NP interactions in the presence of salted solution is replaced by stronger NP−NP interactions in the presence of air upon drying as proposed by Ge and Brus.47 As this 2D structuration takes place just before the complete evaporation of salted solution, it is reasonable to assume that the average NP coverage is not modified by this process. The AFM images clearly indicate that the surface coverage of the ceria NPs decreases with the increase of the PS film thickness (see Figure 5d). According to our initial measurements (Figure 3), this trend can be ascribed to a change in the index of refraction of the film. Namely, thicker films must
Figure 5. AFM topographic images (scan area = 1 × 1 μm2) of ceria NPs adsorbed on PS-H-Si films having different thicknesses, i.e., (a) 6.7, (b) 18.8, and (c) 143.6 nm. (d) NP coverage (in %) as a function of PS film thickness h computed from AFM images where a, b, and c data points correspond to the coverage of the AFM images given above. Dashed line is a guide for the eyes. All other individual AFM images corresponding to each data points of (d) are given in Figure S3.
exhibit a smaller index of refraction. This result validates our previous work10 where we have evidenced an increase of np with the decrease of h as shown in Figure 6 (experimental details are explained in ref 8). From these two independent measurements one can legitimately state that the NP surface coverage is strongly correlated with the refractive index of the polymer film. In other words, an increase in the NP surface coverage directly indicates the rise of the refractive index and consequently an increase of the film density and vice versa. The change of refractive index with film thickness has also been observed by other studies.48,49 Li et al. have calculated the same 1031
DOI: 10.1021/acs.macromol.6b02617 Macromolecules 2017, 50, 1027−1036
Article
Macromolecules
95.1 nm) spin-coated onto SiOx-Si substrates (native oxide layer thickness ≈1.7 nm). Note that for PS the time of adsorption was 30 s (well before the reaction stage) and 20 min for PMMA because the interaction was much lower (small n and then lower coverage). Only at higher thickness where n reaches bulk value we might see the influence of reaction for PMMA. That is likely why we do not find a real adsorption plateau for PMMA. In this case we have a mixture of VdW (NP/surface) + electrostatic (NPs/NPs) potential. Contrary to the PS/H−Si system, an increase in the NP surface coverage with the film thickness was observed by AFM for the PMMA/SiOx-Si system. Figure 7 indicates that a decrease of the refractive index of PMMA films should occur for decreasing film thickness. Ellipsometric measurements entirely confirm this hypothesis as depicted in Figure 6. A refractive index of 1.50 is measured at a thickness of 95.1 nm, in good agreement with the PMMA bulk value of 1.49.52 A study of PMMA thin films by neutron reflectivity also reports similar decreasing density when the films become thinner.51 Once again, the variation of the NP surface coverage is well correlated to the variation of the refractive index with the film thickness. One can then conclude that this new method appears to be extremely sensitive to probe small variations in the index of refraction of polymer thin films. All our studies were carried out on polymer films with thicknesses in the range of 4−150 nm. It has been reported that the underlying (silicon) substrate could significantly influence various properties of thin films.15,53−55 Hence, it is legitimate to ask if the substrate can directly influence the NP adsorption due to the LW interactions. In a recent study on the effect of longrange interactions on glass transition temperature of thin PS films, Zhang et al.54 portrayed the influence of the Si oxide layer thickness on the long-range effective interfacial potential. They have shown that the relationship between the PS thickness and the long-range interactions is strongly dependent on the thickness of the oxide layer. Substrate effects are noticeably observed when the thickness of the film falls below 10 nm. In order to portray the interaction energy from the substrate on NPs adsorption, we made simulations of ΔFLW (eq 7) for different refractive indices as a function of the film thickness as shown in Figure 8. From these simulations, it appears that below h = 6−8 nm the effect of the substrate on ΔFLW can be noticeably observed: the thinner the film, the stronger the LW attractions on oxidefree Si (H-Si) and on oxide-covered Si (SiOx-Si, SiOx thickness ≈1.7 nm). The effect is slightly pronounced for thin films without native oxide. Thus, for very thin films (
