Instability of Ultrathin Polymer

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Solvent Assisted Rinsing: Stability/Instability of Ultrathin Polymer Residual Layer A. Beena Unni,†,‡ G. Vignaud,*,† 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, 686560 India § 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, UMR 6283 CNRS, Université du Maine, Le Mans, Cedex 9, 72000, France ‡

ABSTRACT: In the field of miniaturized devices one of the basic but unreciprocated problems is the instability induced dewetting in polymer thin films. The significance of choosing solvents for deconstructing polymer thin films along with their stability is investigated by rinsing supported polystyrene thin films on silicon wafer with native oxide in four different solvents, such as toluene, chloroform, tetrahydrofuran, and acetone. The solvents are chosen according to their relative energy difference with the polymer. The remnant thickness and morphology of the residual polymer subject to solvent rinsing are characterized. Fine tuning of rinsing time leads to a progressive decrement of film thickness that allows the investigation of stability of the residual film resulting from different solvent leaching. The stability of these films is found to be dependent on various interactions involved in the system such as van der Waals dispersive forces, steric repulsions, acid−base interactions, etc. Based on these solvent-specific parameters, the residual films undertake spinodal dewetting at different time scale of rinsing. The experimentally observed solvent specific transition thickness where residual films undergo spinodal dewetting is weighed against theoretical calculations covering all these interactions. It is shown that the solvent polarity is an important factor in provoking the instability of rinsed films. In particular, films rinsed with a polar solvent exhibit an earlier dewetting (i.e., higer transition thickness value) than those rinsed with a nonpolar solvent.

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INTRODUCTION Polymer thin films are of great interest due to an increased demand for nanoscale devices. They have a wide range of applications in biomedical,1 nanoelectronics,2,3 tissue engineering,4 coatings,5 etc. From a fundamental point of view, polymer thin films are interesting to study because their properties differ from those of the bulk when their thickness reaches values smaller than the radius of gyration of unperturbed molecules. Because of the large surface-to-volume ratio, the influence of free surfaces and interfacial layers on the physical properties of films cannot be neglected for ultrathin films (thickness h < 100 nm). At the polymer/air interface, there exists a surface mobile layer which enhances the chain dynamics.6−8 On the other hand, the substrate interface is known to reduce the dynamics because of an immobile polymer adsorbed layer.9−11 However, our understanding of how the properties of thin films depend on the polymer structure at the polymer/substrate interface is still rudimentary. Several research groups have evidenced the formation of an irreversibly adsorbed polymer layers on the substrate with thickness of few nanometers, even without specific interactions of the polymer with the substrate.12−22 A © XXXX American Chemical Society

lot of studies show that this irreversible layer plays a significant role in the physical properties of thin films, such as the enhancement of segmental mobility in proximity to this layer,20,21,23,24 the control of the crystalline structure,25,26 the impact on local viscosity,18 the long-range effects of this interface on the dynamics,27−30 the increase of the density at the polymer/substrate interface,15,31 etc. Solvent rinsing is an effective method to obtain the details on this irreversibly adsorbed polymer on the substrate. Guiselin16 was the first to propose a method of rinsing polymer thin films with pure solvent to characterize the volume fraction profile of an irreversibly adsorbed polymer by removing the unbound polymer. Later Fuji et al.14 and Durning et al.13 successfully obtained a stable residual layer of polystyrene (PS) by the same method and showed that the thickness of the residual layer increased with increasing molecular weights. Despite rinsing with a good solvent, they also found that PS remains bound to a Received: November 9, 2015 Revised: January 22, 2016

A

DOI: 10.1021/acs.macromol.5b02435 Macromolecules XXXX, XXX, XXX−XXX

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min. Films were then annealed at 160 °C for 24 h in a primary vacuum. Such a procedure leads to the formation of a homogeneous thin film with a 130 nm thickness as measured by ellipsometry. In the following, the film will be assigned as PS/SiOx-Si considering the PS layer resides on native oxide covered Si. Solvent Rinsing Procedure. Solvent rinsing was then performed at different time of rinsing from 5 s to 2 h using four different solvents: toluene, chloroform, THF, and acetone. The dissolution of loosely attached PS chains from the confined film takes place in less than a second and lasts only a few minutes.34,35 There is no flow-enhanced desorption, and more time is required for partial desorption at low shear rates. Hence, we observed the residual polymer at different stages of rinsing starting from 5 s. A Nima dip coater was used for the solvent rinsing of the films. The dip coater along with the software (Nima TR 8.1) provides control of the sample immersion and withdrawal speeds, rest positions, rest periods, and number of cycles, etc. The samples were dipped and withdrawn at a speed of 48.2 mm/ min. They were kept steady at upright position under different solvents for the desired amount of time. Characterization Techniques. A spectroscopic ellipsometer (HORIBA JobinYvon, UVISEL instrument) having a xenon light source with a spectral range between 190 and 2100 nm, a polarizer, an analyzer, and a grating monochromator that sequentially detected the light for each individual wavelength to the photomultiplier was used to measure the thickness of the samples and their index of refraction. The thickness measurements were done at incident angles 65°, 70°, and 75° at ambient conditions. A multilayer model consisting of Si substrate, SiO2 layer, and the polymer (PS) was considered. The refractive index spectrum was obtained by fixing the thickness value of SiO2 at 17 Å. The incident angle was used as a fitting parameter. A transparent Sellmeier dispersion relation was used for modeling the refractive index of the polymer film as follows

weakly attractive substrate by means of using hydrofluoric acid (HF) treated Si wafer. Recently, Gin et al.15 have shown that this irreversibly adsorbed polymer layer on planar Si substrates is made up of an inner higher density region with a more flattened conformation named flattened layer and an outer bulklike density region named loosely adsorbed layer. They were able to expose the flatten layer of thickness 2−3 nm to the air interface after prolonged (120 days) toluene rinsing. Jiang et al.17 replaced toluene with chloroform to more effectively uncover the lone flattened layer. They studied the effect of the polymer/substrate interactions and the time of annealing on the flattened layer structure by using three different homopolymers: PS, poly(2-vinylpyridine), and poly(methyl methacrylate). If the magnitude of the interactions controls the final thickness and the kinetics of the flattened layer formation, this study also revealed that the flattened layer has microscopic “textures” (partially covered surface) with characteristic lengths irrespective of the polymer used. It is not conclusive yet from this study whether the polymer/solid interaction is the main factor to control the size of the dimple structures. Xue et al.32 also studied the effect of varying annealing time and molecular weight on the architecture of an irreversibly adsorbed layer of PMMA on quartz made by leaching with benzene. More recently, Bal et al.12 came up with the possibility of obtaining stable ultrathin polymer films by the solvent rinsing method. They introduced a two-step top-down approach comprising the preparation of homogeneous thick films by spin-coating and thinning them by rinsing in a good solvent (e.g., toluene) that removes the residual stress and/or the density variation of the PS films inhibiting thermodynamically the dewetting on oxidefree silicon. Although a few studies have been made on solvent rinsing, the role of different solvents on the dissolution or desorption of polymer and thereby on the properties of the residual adsorbed layer remains largely unexplored. In this paper, we discuss the significance of solvent selection while deconstructing PS thin films. Thin films of PS on silicon wafer with native oxide (PS/SiOx-Si) were rinsed with four different solvents: toluene, chloroform, tetrahydrofuran (THF), and acetone with the aim to understand their role on the remnant thickness and morphology of the residual polymer rinsed films. Depending on the solvent used, we evidence that residual PS films may undertake spinodal dewetting at different thicknesses. The transition thickness (htrans) below which films undergo dewetting is obtained both theoretically and experimentally. The reasons behind the origin of the differences are discussed in the framework of the Lifshitz−van der Waals potential and the acid−base interactions. The influence of solvent polarity on the residual polymer is also investigated.

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n2(λ) = 1 + B

λ2 λ − λ02 2

(1)

where λ is the wavelength of incident light, B is a dimensionless parameter that determines the shape of the refractive index in the visible range, and λ0 is the resonance wavelength for which the refractive index diverges. The calculated optical constants were determined by simultaneously fitting the data obtained at three different incident angles (65°, 70°, and 75°). The topography of the films were obtained with an AFM (Multimode, Nanoscope IIIa) in tapping mode before and after the solvent rinsing. Image analysis was performed using WsxM and ImageJ softwares. The thickness was also obtained with AFM after scratching the film. In a few cases, the thickness of bound polymer was ensured also by X-ray reflectivity (XRR) studies using an X-ray reflectometer (Empyrean Panalytical). The contact angles were measured by GBX Digidrop contact angle goniometer which is assisted with the Windrop software. The 1.5 μL of different solvents is deposited on PS films at a speed of 3 μm/s, and the photos are captured at 20 ms after deposition. An average value of contact angle is obtained from around 10 measurements at different places on the film with each solvent.

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EXPERIMENTAL SECTION

RESULTS AND DISCUSSION Thin PS films with a thickness of 130 nm were separately immersed in four different solvents: toluene, chloroform, THF, and acetone. As the solubility can be affected by any specific interactions, especially hydrogen bonding, it cannot be accurately predicted only by the Hildebrand solubility parameter. Hence, the four solvents were selected based on their Hansen solubility parameter (HSP).36 The assignment of Hansen parameters is based on the equation describing the total cohesion energy, E, as the sum of the individual energies corresponding to the three types of interactions:

Sample Preparation. Thin Film Preparation. Polymer thin films were prepared by spin-coating atactic PS solutions (Mw = 136 kg/mol and polydispersity index, Mw/Mn = 1.05 from Polymer Source) on Si(100) wafers. The silicon wafers were diced into pieces of dimension 1 × 1 cm2. They were immersed in piranha solution, which hydrophilize the surface by removing the organic contaminations. The details of piranha treatment are described elsewhere.33 After the treatment all the substrates were rinsed thoroughly by Milli-Q water (resistivity ≈18.2 MΩ cm) and then dried by dry N2. The oxide thickness was measured to be 1.7 nm by means of ellipsometry. Solution with a mass concentration 20 g/L in anhydrous toluene (99.8%) was prepared and filtered by a 0.2 μm PTFE, 50/pk syringe filter. For a better polymer dissolution, an aging time of 24 h was used prior to spin-casting the solution at a rotation speed of 2000 rpm for 1

E = ED + EP + EH B

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Macromolecules Table 1. HSP and Relative Energy Difference Values PS and Some of Its Good Solvents38−40 solvent

δd (MPa0.5)

δp (MPa0.5)

δh (MPa0.5)

Ra/R0 (relative energy difference)

polystyrene toluene chloroform THF acetone

21.28 18 17.3 16.8 15.5

5.75 1.4 3 5.7 10.5

4.3 2 5.6 8 7

0.65 0.67 0.76 1

dipolar moment37 (π/D) 0.375 1.04 1.75 2.88

± ± ± ±

0.010 0.02 0.04 0.03

where ED is the dispersive component, EP is linked to polar interaction, and EH to the hydrogen bond interaction. Dividing this relation by the molar volume gives the square of the total (or Hansen) solubility parameter as the sum of the squares of the Hansen D, P, and H components: E /V = E D/V + E P /V + E H /V

(3)

i.e., the cohesive energy density δ between two substances can be expressed based on dispersive force, polar interaction, and hydrogen bond interaction as follows: 2

δ 2 = δ D2 + δ P 2 + δ H 2

(4)

Figure 1. (a) Optical microscope image of the PS/SiOx-Si film after spin coating and preannealing. (b) The 3D presentation of the topographic image of PS/SiOx-Si film obtained using AFM. (c) The height profile along the drawn red line of (b).

According to eq 4, the solubility parameter of a given solvent can be described as a vector with three components: δD, δP, and δH. This means that each solvent can be located in a threedimensional system as a fixed point with coordinates agreeing with eq 4. The axes of the system are the dispersion axis δD, the polar axis δP, and the hydrogen bonding axis δH. The Hansen characterization for PS is considered as a sphere whose center has δD, δP, and δH values of PS. The radius of the sphere R0 is termed as the interaction radius, which is experimentally calculated.36 The boundary of the spherical characterization is based on the requirement that “good” solvents have a distance from the center of the sphere Ra less than R0. The distance between the center of solubility sphere and the position the compound can be expressed as Ra =

diffuses into the polymer film, and (ii) the polymer chains near the solid−liquid interface become solvated.35 Because of the plasticization of the polymer by the solvent, a gel-like swollen layer is formed along with two separate interfaces: one between a glassy polymer and a gel layer and the other between the gel layer and the solvent.41,42 With the consequent formation of a swollen layer, chain disentanglement is favored and the solvated macromolecules are transported from the film into the solution. The nonadsorbed polymer chains dissolve after a specific induction time. The different steps of dissolution and desorption are illustrated in Figure 2. After the dissolution of nonadsorbed chains, the solvent is in direct contact with the irreversibly adsorbed polymer layer. Such an adsorbed polymer chain is attached to the surface by many segments with a very high adsorption energy per chain.43 The removal of such adsorbed chain from the solid interface requires desorption of

(2δ D,PS − 2δD,S)2 + (δP,PS − δP,S)2 + (δ H,PS − δ H,S)2 (5)

where S stands for the solvent. The smaller Ra, the more likely they are to be thermodynamically compatible. It is also important to calculate the relative energy difference (RED) that determines the quality of solubility. The lesser the RED, the better the solubility. RED =

Ra R0

(6)

Thus, from Table 1, the compatibility of selected solvents with PS is in the increasing order from toluene > chloroform > THF > acetone. The initial state of the spin-coated and annealed film (PS/ SiOx-Si) which is going to be rinsed later is shown in Figure 1a. From this optical microscopic image, the film seems to be continuous over a large scale. The AFM image shown in Figure 1b provides the 3D perspective of PS/SiOx-Si film after spin coating and preannealing (i.e., the annealing before solvent rinsing). The step observed in the profile is due to the scratch made on the left end of the film to obtain the thickness with AFM. The thickness is found to be 130 nm. A smooth continuous film is observed with an average roughness value ≈0.3 nm. All the experiments were performed with such films. When a homogeneous polymer thin film is in contact with a good solvent, two distinct processes can occur: (i) the solvent

Figure 2. Schematic representing the desorption mechanism of PS/ SiOx-Si in contact with a good solvent. The substrate, the polymer, and the solvent are shown in black, orange, and blue, respectively. C

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takes place.69,70 As depicted in the inset of Figure 4, the fast Fourier transform (FFT) of the images reveals a ring pattern indicating the existence of a preferred wavelength of the instabilities which is the signature of a spinodal dewetting. The blue dotted line points out the transition where the film undergoes a spinodal dewetting. In the particular case of the THF rinsing, the film is already no more uniform after 5 s of rinsing (thus before the marked dotted line), indicating that the film has started a dewetting process. However, within the experimental error, no correlations of hole sites can be detected from FFT after 5 s of rinsing, which rules out the possibility of a spinodal dewetting. Yet, the presence of a native oxide layer probably makes the film metastable, so that only nucleation (randomly distributed holes) can drive such a thick film (47.5 nm) toward dewetting.49 From Figure 4, another striking effect is that all the films after solvent rinsing undergo spinodal dewetting at different instants of rinsing time, i.e., at different values of hres. In the case of toluene rinsed films, the spinoidal dewetting is observed after 20 min of rinsing (hres = 2.1 nm) while the films rinsed with chloroform exibits spinodal dewetting after 3 min of rinsing (hres = 2.8 nm) and after 30 s for THF rinsed films (hres = 5.5 nm). This raises the question: what property of the solvent influences the onset of spinodal dewetting at different hres? The dewetting can be influenced by a lot of factors like composition of polymer,50 film thickness,51 type of substrate used,52 disjoining pressure involved,53 etc. Among the underlying causes of dewetting, Sharma54 pointed out the fact that the polar interactions cannot be neglected for a thin film sandwiched between a substrate and a semi-infinite fluid. In a similar way, Lee et al.47 differentiate between thermal dewetting and solutal dewetting where in the former case the instability is caused due to the long-range force of Lifshitz−van der Waals interactions, and in the latter one it can be attributed to the short-range force of polar interactions. Recently, Xu et al.48 demonstrated that PS films which are stable under thermal annealing are rendered unstable to dewetting when contacted by acetone. They explained by the introduction of destabilizing polar interactions, notwithstanding the stabilizing apolar Lifshitz−van der Waals interactions. The work by Verma and Sharma55 is an another good example where they found that strong polar solvents play a significant role in the dewetting process. They were able to fabricate submicron droplets and arrays by the dewetting of ultrathin PS using optimal mixture of water, acetone, and methyl ethyl ketone overcoming the weak destabilizing Lifshitz−van der Waals forces and the high surface energy penalty required for deformations on small scales. Thus, from these studies, two key factors that can influence the instability of films which are in contact with a solvent are the solvent polarity and the Lifshitz−van der Waals interactions in the system. In our case, the solvents we used present a significant difference in their dipole moment (tabulated in Table 1). From our experimental observations (Figure 4) we can surmise that the films rinsed with a solvent having higher polarity dewet faster than the ones rinsed with weakly polar solvents. Hence, the THF rinsed film dewets before the one rinsed with chloroform. The film rinsed with toluene which has the weakest polarity value undergoes dewetting at a later stage. Figure 5 shows a series of optical microscopy images of PS films with different residual thicknesses after immersion in acetone. After 5 s of rinsing, we can observe that the smooth film breaks up by the creation of randomly distributed holes. It is not surprising that the dewetting starts very early as the

the fraction of polymer that is in contact with the surface overcoming its enthalpic barrier along with its disentanglement from neighboring chains (a diffusive process). Whereas dissolution with a good solvent of a thin PS film takes place in less than a few seconds and lasts only a few minutes,34,35 partial desorption needs more time when there is no flowenhanced desorption. In addition, the inter diffusive chain dynamics gets strongly hindered compared to the bulk when the distance from the substrate is less than 3Rg, where Rg is the radius of gyration of PS.44 It is anticipated that the formation of loops in the adsorbed chains would provide a structure where nonadsorbed polymer chains can effectively entangle and give rise to a high cohesion strength.45 Depending on the thermodynamic compatibility of the solvent with PS, the evolution of the residual layer thickness (hres) with the rinsing time is impacted in a different manner as shown in Figure 3.

Figure 3. Residual thickness (hres) of bound PS after rinsing with different solvents. Here, hres is measured by ellipsometry and complemented with XRR. Note that hres of the acetone rinsed film for 3 and 20 min is not measurable from our techniques due to the large roughness.

At first, it can be seen for all the solvents that the residual film thickness decreases with increased time of rinsing. Then, up to the first 30 s of rinsing, the hres values obtained for each solvent are clearly distinct: 4.5 nm for film rinsed for 5 s with toluene whereas it gradually increases to 18.3, 47.5, and 90.7 nm for films rinsed with chloroform, THF, and acetone, respectively. Thus, the hres value obtained after rinsing with different solvents is found to be related to the nature of solvent. Owing to low RED value, the interaction of toluene with PS is higher compared to the other solvents. Consequently, toluene can easily remove polymer chains by promoting disentanglement. Thus, the lower the RED value, the better the extraction of entangled chains from the adsorbed layer. The morphology of residual films resulting from rinsing with three different solvents is depicted in Figure 4. It clearly appears that the morphology of the residual films evolves with their thickness hres. With an increased time of rinsing, the initially flat film turns into a nonhomogeneous film revealing a bicontinuous surface pattern typically observed in spinodal dewetting.46 All the fluctuations in film thickness are amplified under thermal stimulation even at room temperature (RT) and lead to spontaneous dewetting. Solvent molecules are known to readily diffuse and saturate the PS film, reducing the glass transition temperature of the polymer below the room temperature and thereby rendering it mobile for reorganization.47,48 Thus, once the solvent has leached away the outer loosely attached polymer chains, a solvent-driven dewetting D

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Figure 4. AFM topography (scan size = 5 × 5 μm2) of residual film obtained after rinsing with different solvents: toluene, chloroform, and THF. The dotted line represents the transition to spinodal dewetting.

layer separating the two interfaces. The sign of the second derivative of the free energy indicates whether the film is stable (ΔF″(h) > 0) or dewets spontaneously (ΔF″(h) < 0).49 Thus, the effective free energy of a system can be represented as follows

acetone possess the highest dipolar moment in all solvents. Our observations are in line with the results of Lee et al.,47 who observed that the acetone-laden film would become unstable first followed by the toluene-laden film. With increased time of rinsing the continued coalescence of holes finally leads to the formation of PS droplets generating a regular pattern of polygons as characteristics of thermal annealing.56 The use of a poor solvent like acetone prevents a rapid dissolution of the polymer during the first 30 s of rinsing. Consequently, the film which is still thick initiates a dewetting by hole nucleation. However, numerical simulations57 have highlighted that different morphologies (isolated circular holes, droplets, bicontinuous) and their combinations can all be produced by the spinodal decomposition mechanism depending on the form of the intermolecular potential in an extended neighborhood of the film thickness. Concerning the nanoscopic dewetting observed inside the dewetted holes as shown in Figure 5, a spinodal dewetting is confirmed by the presence of a ring in the FFT as can be seen in the inset of Figure 5. In summary, it is clear from the experimental measurements that when the polarity of the solvents increases, the film is able to dewet earlier, i.e., at a higher residual thickness. Even if experimental results show that solvent polarity is found to be a key factor affecting the instability, it is of paramount importance to quantify the interfacial potential or free energy ΔF(h) and its second derivative ΔF″(h) which determine the stability or instability of polymer films.49 Here ΔF(h) is defined as the excess free energy per unit area necessary to bring two interfaces (the substrate−polymer and the polymer−solvent interfaces) from infinity to a certain distance h. The distance h defines the thickness of the polymer

ΔF(h) = ΔFLW (h) + ΔFAB(h) + c /h8

(7)

where ΔFLW(h) represents the long-range interactions by the Lifshitz−van der Waals potential and ΔFAB(h) represents the polar contribution by the acid−base interactions in the system. The last term includes short-range electrostatic repulsion of strength c whose value is (1.8 ± 1) × 10−77 J m6 for a silicon wafer with 1.7 nm of native oxide.49,52 We first consider the Lifshitz−van der Waals component, ΔFLW(h). As the film is totally immersed in the solvent during the time of rinsing, the system can be thought of a four-layered system like Si/SiOx/PS/solvent in which the last layer is the solvent itself. Accordingly, ΔFLW(h) can be expressed as ΔFLW (h) = −

−ASi/PS/solvent 2

12π (h + dSiOx)

+

−A SiOx /PS/solvent 12πh2

−A SiOx /PS/solvent 12π (h + dSiOx)2

(8)

where ASi/PS/solvent and ASiOx/PS/solvent are the effective Hamaker constants of the Si/PS/solvent and SiOx/Ps/solvent three-layer systems, respectively. The effective Hamaker constant (A132) of a three-layer system is calculated using the relation A123 = ( A11 − E

A 22 )( A33 −

A 22 )

(9)

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The Hamaker constants of solvents were calculated from their surface tension using the relation57,60 γi =

Aii 24πl0 2

(11)

where γi is the surface tension of a solvent i, Aii is the Hamaker constant (solvent/solvent), and l0 corresponds to the cutoff distance which can be taken equal to 1.57 Å.60 The calculated values are given in Table 3. Table 3. Correlation between the Surface Tension of Pure Solvents and the Effective Hamaker Constants of the Three Layer Systemsa

toluene chloroform THF acetone

γsolvent (mN/m)

Asolvent/solvent (10−20 J)

ASiO2/PS/solvent (10−20 J)

ASi/PS/solvent (10−20 J)

28.40 27.50 26.40 25.20

5.28 5.11 4.90 4.68

−0.89 −0.96 −1.05 −1.15

0.15 0.167 0.18 0.2

γsolvent is the surface tension of the pure solvents. Asolvent/solvent is the Hamaker constant of the solvent; ASiO2/PS/solvent and ASi/PS/solvent are the effective Hamaker constants of SiO2/PS/solvent and Si/PS/solvent three-layer systems, respectively. The values are calculated from the average Hamaker constant values in Table 2. a

The substitution of the tabulated values in eq 7 gives the expression for Lifshitz−van der Waals component of the free energy and of its second derivative as a function of the film thickness. The results are represented as in Figure 6 for the four solvents. From Figure 6a, for all the solvents, the excess free energy per unit area, ΔFLW(h) possess both positive and negative values which points to the fact that the system is unstable for small film thicknesses whereas metastable for larger film thicknesses.66,67 The system has to overcome a potential barrier to reach the lowest energy state which is slightly different according to the solvent used. The potential barrier is a bit higher for a film rinsed in acetone and decreases in order for the films rinsed with THF, chloroform, and then toluene. It is readily shown that spinodal dewetting can take place only if the second derivative of ΔFLW(h) with respect to film thickness is negative. From Figure 6b, it is quite amazing to observe that the transition thickness at which the film undergoes spinodal dewetting, htrans, is equal to 2.7 ± 1 nm and is the same for all the solvents. Yet from the experimental results, only the toluene-rinsed film shows a spinodal dewetting for a thickness hres = 2.1 nm less than htrans = 2.7 nm while all other films rinsed with polar solvents experimentally dewet at a thickness which is higher than the calculated value htrans. Since the polarity of toluene is almost negligible, one can logically infer that the difference in these behaviors can be attributed to the contribution of polar interactions. It is thus important to quantify the contribution of the polar component ΔFAB(h) to the total free energy of the system. The acid−base (AB) interactions occur between molecules that display conjugate polarities as measured by their electron (proton) donor and acceptor capabilities. PS is a weakly electron-donor monopolar material, but when the polar solvent molecules enter into the PS film, the polar interactions have to be considered. The contribution by short-range polar interactions can be expressed as

Figure 5. Optical images of PS films rinsed with acetone from 5 s to 2 h (scale bar 100 μm). There is a higher amount of polymer remaining in the acetone rinsed films (as it is comparatively a poor solvent) such that the dewetting process is better viewed by optical microscopy compared to AFM (AFM image scale = 5 × 5 μm).

In our case, eq 9 can be written as A SiO2 /PS/solvent = ( A SiO2 /SiO2 −

APS/PS )( A solvent/solvent −

APS/PS ) (10a)

and ASi/PS/solvent = ( ASi/Si −

APS/PS )( A solvent/solvent −

APS/PS ) (10b)

To calculate the two effective Hamaker constants of the system, Hamaker constants of each interface (Table 2) were chosen as the average value of values reported in the literature.58−65 Table 2. Hamaker Constants Reported in the Literature58−65 and Their Average Value Used in Our Calculations Hamaker constants values reported in lit. (J)

av Hamaker constant value (J)

ASi/Si ASiO2/SiO2

(19−24) × 10−20 (5.0−6.6) × 10−20

22.3 × 10−20 5.8 × 10−20

APS/PS

(6.15−7.9) × 10−20

7.56 × 10−20 F

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Figure 7. Contact angle values between a bulk PS substrate and various solvents measured by contact angle goniometry. Photographs corresponding to the measurements are given above the bars.

calculated using eq 13. One can then derive SP by subtracting the long-range Lifshitz−van der Waals dispersive forces SLW to S. For calculating the dispersive forces SLW, we consider the film thickness at dmin, which is the equilibrium film thickness of our system at which the free energy ΔFLW(h) possesses the minimum value. This distance dmin is due to equilibrium between the extremely short-range repulsion and the attractive LW interactions. At dmin, the free energy per unit area and the dispersive forces are related as follows:54 ΔFLW (dmin) = SLW

Knowing the dependence of each term of eq 7 with the film thickness h, we have numericaly simulated the total free energy ΔF(h). We fixed the correlation length l to 1.1 nm and the power α to 7.83 in the short-rage interaction c/d∞ min in order to match the experimental results to the theoritical value htrans. Then the values of SLW calculated from eq 15 with dmin = 6 Å obtained from the simulation (which is matching with the results of Seeman et al.,49 dmin = 8 Å for a 1.7 nm thick native oxide layer) are given in the Table 4 along with the SP values

Figure 6. (a) Simulation of the Lifshitz−van der Waals component of ″ (h) as a the free energy ΔFLW and (b) its second derivative ΔFLW function of film thickness h for PS films for the four-layer system Si/ SiOx/PS/solvent under different solvent media. The effective Hamaker constants are the ones given in Table 3, and the thickness of the SiOx layer was taken to be equal to 1.7 nm.

ΔFAB(h) = SP exp((dmin − h)/l)

(12)

Table 4. Correlation between the Surface Tension γPS/solvent, the Total S, the Lifshiftz−van der Waals SLW, and the Polar SP Spreading Coefficients

where SP is the polar component of spreading coefficient and exp((dmin − h)/l) stands for the decay function describing the short-range of the polar interactions with the correlation length l. The decay function for the polar interactions satisfies the relation exp((dmin − h)/l) = 1 at a cutoff dmin and is 0 at large distances. For water, an estimation of the correlation length is about l = 0.6 nm,54 whereas for polymer l can be taken as 2.5 nm.57 The value of SP can be evaluated from contact angle measurements68 S = SLW + SP = γ23(cos θ − 1)

toluene chloroform THF acetone

(13)

γPS/solvent (mN/m)

S (mN/m)

SLW × 10−5 (N/m)

SP × 10−5 (N/m)

1.1 1.29 1.54 1.85

−0.07 −0.11 −0.14 −0.3

−5.92 −6.69 −7.75 −8.90

−1.53 −4.06 −6.69 −21.35

obtained thereby. In the numerical simulation, it is interesting to note that the power α plays a role on dmin, the location of the minimum of energy (thus affecting the calculation of SLW and SP) and the correlation length l impacts direcly the values of htrans. From Table 4, it can be seen that the spreading parameter SP which represents the contribution of the short-range polar interactions to the total free energy of the system increases with increasing polarity of the solvents. Hence, it is now clear that the instability is accelerated by the polarity of solvents, which increases in the order SP,toluene < SP,chloroform < SP,THF < SP,acetone. Thus, by considering the three contributions, i.e., the effective contribution of Lifshiftz−van der Waals ΔFLW, the polar contribution ΔFP, and the steric repulsion energy c/hα, the excess free energy per unit of area ΔF and its second derivative ΔF″ as a function of film thickness h for PS films on

where the spreading coefficient S is the sum of two terms: the long-range Lifshitz−van der Waals dispersive surface energy SLW and the contribution by short-range polar interactions SP. Hence, it is possible to estimate the spreading coefficient S by knowing the values of the contact angle θ and of the surface tension. The surface tension γ between PS and the solvent is calculated by the following relation with γPS = 40.7 mN/m γPS,solvent = γPS + γsolvent − 2(γPSγsolvent)1/2

(15)

(14)

where γsolvent is taken from Table 3. The measurement of the contact angle between PS and various solvents is carried out by means of contact angle goniometry (Figure 7). It gives the spreading coefficient values G

DOI: 10.1021/acs.macromol.5b02435 Macromolecules XXXX, XXX, XXX−XXX

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the acid base interactions has to be taken in account for the polar solvents. If our numerical simulation undeniably shows the influence of the polar interactions on the transition htrans, we must stress that it is not an absolute calculation but can be considered as a comparative calculation. An example of complexity is the polar AB interactions which decay exponentially for simple liquids, but to date their decay behavior for the polymer−solvent mixtures is not really known.

native oxide-covered Si substrate under different solvent exposures could be simulated. They are plotted in Figure 8.

■

CONCLUSION Polystyrene thin films supported on SiOx-Si substrates were rinsed with four different solvents: toluene, chloroform, THF, and acetone. These solvents can be defined by their Hansen solubility parameter HSP. We observed that the closer their HSP to the one of PS and the faster the dissolution and desorption of the polymer chains. This is in good agreement with the relative energy difference (RED) theory. In addition, we observed for this four-layer Si/SiOx/PS/solvent system that the films exhibited two different morphologies depending on their thicknesses h. For h > htrans, the films were flat whereas they exhibited spinodal dewetting for h < htrans. When toluene was used as solvent, the experimental transition thickness htrans was equal to about 2.8 nm. This value can be explained theoretically by determining the apolar Lifshiftz−van der Waals free energy ΔFLW. However, as soon as the other solvents were used for rinsing, htrans was clearly shifting to higher value. In particular, we highlighted a correlation between htrans and the polarity of the solvent. To go deeper into the analyses, the polar acid−base free energy ΔFAB was determined, and we demonstrated that the addition of this polar term ΔFAB to the LW free energy can perfectly explain the unstable and metastable domains for the four different solvents. Thus, from these results, it is interesting to note that we can tune the thickness, morphology, amount of polymer bound to the substrate, etc., by employing a solvent specific rinsing.

Figure 8. Simulation of (a) the effective free energy ΔF and (b) its second derivative ΔF″ as a function of PS film thickness h for a fourlayer Si/SiOx/PS/solvent system. In these simulations, four solvents are considered: toluene, chloroform, THF, and acetone. The effective free energy takes into account the effective contribution of the Lifshiftz−van der Waals ΔFLW and of the polar ΔFP components as well as the steric repulsion energy c/hα.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Tel 33-2 97 87 45 55 (G.V.).

The consideration of polar contributions along with the effect of steric repulsion paves the way to a drastic change in the resulting free energy curves as shown in Figure 8. In comparison to toluene rinsed samples (Figure 8a), the acetone laden samples depicts an increase in its negative value of free energy for a smaller thickness, which clearly points out the amplification of instability with increasing polar interactions in the system. From the second derivative of the effective free energy (Figure 8b), htrans is found to be increased with the polarity of the solvent. Consequently, the films undergo spinodal dewetting at different thicknesses with respect to the type of solvent used. The htrans value of toluene is found to be around 2.8 nm, where we could experimentally observe the spinodal dewetting pattern when its thickness fall below 3 nm, i.e., at 2.1 nm. In case of chloroform and THF, htrans is observed at 5.5 and 6.7 nm, respectively, whose experimental dewetted results estimate htrans to be in the 2.8−5.7 nm range and 5.5− 47.5 nm range, respectively (Figure 4). The AFM images inside the hole of the films dewetted by acetone rinsing also exhibits a dewetted pattern at a thickness of 8 nm, which is less than its htrans of 8.5 nm. Thus, in the case of solvents owing to the low polarity (case of toluene), the transition thickness htrans below which the film spinodally dewets can be directly obtained by the Lifshitz−van der Waals theory, whereas the contribution of

Notes

The authors declare no competing financial interest.

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