Kinetic study of a swelling-induced network of folds in a cross-linked PS-PDMS film

Abstract

Solvent-induced mechanical instability in a cross-linked poly(styrene-block-dimethylsiloxane) (PS-PDMS) film attached to a rigid substrate was systematically investigated. Through swelling with appropriate solvent vapor, a unique network of folds could be constructed successfully without the wrinkle-to-fold transition. Instead, small holes resulting from the mesostructural organization of PS-PDMS formed as nuclei to induce formation and growth of invaginated folds resembling creases which then constructed a network of invaginated folds. A complete network of sharp folds could be obtained after the two edges of a valley were combined into a sharp fold. The morphology and kinetics were closely related to the solvent solubility parameter and saturated vapor pressure. We varied the ratio between a relatively good solvent vapor and a poor solvent vapor, and so produced a slower dynamic process to precisely control the surface morphology. Poorly ordered cylinders with varied sizes resulting from strong cross-linking and spatial restrictions imposed by the network of folds could be obtained.

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1. Introduction

A constrained thin film on a rigid substrate can lead to the spontaneous formation of various kinds of ordered structures under adequate compressive stress.^1–8 This phenomenon is commonly acknowledged as mechanical instability, including wrinkling,^9–12 folding,^13–15 and creasing.^16,17 In general, periodic sinusoidal wrinkles can be constructed by compressing a crust bonded to a soft layer. In this case, after further increasing compressive stress, localized folds will be produced via a wrinkle-to-fold transition. In principle, however, crease structures results from the compression of a soft layer attached to a rigid foundation. Despite different formation conditions, constructing a two-layer structure where neither the modulus nor chemistry are matched prior to loading stimuli is the most fundamental procedure to develop intricate surface patterns. In most cases, in order to form the two-layer structure, various cross-linking technologies can often be carried out, including chemical cross-linking,¹⁸ UV-ozone cross-linking,¹⁹ and plasma induced cross-linking.²⁰ In fact, the difference in molecule modulus between the top layer and lower layer, closely related to cross-linking intensity, can greatly influence the final pattern morphologies and kinetics. Furthermore, varying the external stress will prompt the emergence of diverse surface morphologies with different characteristic dimensions. More recently, mechanical instability has played a significant role in many applications, including sensors,²¹ micro-fluidic devices,²² microlens arrays,²³ responsive coatings,²⁴ and microfabrication.^25,26

Unconstrained films can expand three-dimensionally and isotropically without releasing interior compressive stress during solvent swelling. When it comes to a polymer thin film attached to a rigid substrate, however, the deformation in the lateral dimension is so small that the expansion only occurs in the direction normal to the substrate, giving rise to an equi-biaxial compressive stress.²⁷ Subsequently, the in-plane compressing pressure increases gradually with swelling time, which leads to an increase in mechanical instability.^18,28 Eventually, a drastic surface undulation will result in nonhomogeneous surface deformation. Once the swelling degree is beyond a threshold value, compressive stress can be relieved locally to generate a variety of periodic surface patterns. For instance, Hayward et al. have demonstrated that this critical linear deformation of poly(acrylamide-co-sodium acrylate) hydrogel generating creasing instability is about 1.5 and almost independent of gel thickness and modulus.¹⁸ When the film is weakly bound to a rigid substrate, serious swelling can even induce delamination or large-scale folds with a characteristic dimension nearly equal to the film thickness.^29,30 To precisely control pattern morphologies and obtain excellent surface properties, the dynamics of mechanical instability induced by solvent permeation should be understood more clearly.

In recent years, much work has focused on the study of swelling-induced mechanical instability in homopolymer or random copolymer films,^31,32 but few studies on the dynamics of the fold structure of ultra-thin cross-linked block copolymer (BCP) films swelled by solvent vapor, to our best knowledge, have been reported. Under solvent annealing, the rearrangement of BCP molecules, known as self-assembly, can lead to various ordered nanostructures with nanoscale dimensions.^33–35 Therefore, if the BCP film is slightly cross-linked, the cross-linked polymer network is too small to restrict the molecular movement. Thus, surface molecules will be rearranged because of the mismatch between the integer multiple of the characteristic spacing and initial film thickness to finally form holes or islands.^36–38 Nevertheless, too high a cross-linking degree will inevitably prevent BCP self-assembly or even freeze the movement of chain segments. In this case, a swelling-induced stretch of chains will be restricted by elastic recovery of the highly cross-linked network.³⁹ That is, the swelling degree is not forever proportional to swelling time, but reaches a saturated value dependent on the cross-linking degree.⁴⁰ Once the osmotic pressure is larger than the critical value, the BCP film surface will be forced to buckle into ordered surface patterns. Therefore, the surface instability of cross-linked BCP films is worth researching profoundly.

Here, we systematically present a dynamic study of a cross-linked PS-PDMS film confined on a rigid substrate through combining swelling-induced mechanical instability and self-assembly of PS-PDMS. We employ hyperthermal hydrogen induced cross-linking (HHIC) as a cross-linking approach to construct a two-layer structure, then further investigate the unique mechanism of the swelled PS-PDMS film. Our results suggest this network of folds is closely related to the rearrangement of PS-PDMS molecules during annealing. More significantly, solvent-induced hole structures could induce the growth of invaginated folds with a valley, which then evolve into sharp folds. Finally, a network of sharp folds formed with a characteristic amplitude dependent on the swelling time. By investigating further the impact of the solvent solubility parameter and saturated vapor pressure on the network of folds, we have clearly understood the essential conditions for forming network of folds. However, after etching the PS-PDMS film, few long-range cylinders could be gained and many cylinders with random alignment were isotropically distributed in the network of folds. This suggests that it is a challenge that cannot be overcome until moderate cross-linking is imposed to greatly improve the well-ordered rearrangement of self-assembly for cross-linked PS-PDMS films.

2. Experimental section

2.1. Materials

An asymmetric block polymer of PS-PDMS exhibiting cylinders in bulk with an overall molecular weight of 42 kg mol⁻¹ (M_n, PS = 31 kg mol⁻¹, M_n, PDMS = 11 kg mol⁻¹, M_w/M_n = 1.10) and a PDMS volume fraction of 27.8% and polystyrene (PS) (M_n = 25 kg mol⁻¹, M_w/M_n = 1.04) were purchased from Polymer Source, Inc.; polydimethylsiloxane (PDMS) (Sylgard 184) was purchased from Dow Corning. 1,2-Dichloroethane, tetrahydrofuran (THF), toluene, chloroform, acetone, n-hexane, ethanol used as received were obtained from Aldrich.

2.2. Sample preparation

PS-PDMS was homogeneously dissolved in 1,2-dichloroethane solvent for a certain time to generate 0.5 wt% polymer solution. Moreover, PS was homogeneously dissolved in 1,2-dichloroethane solvent to create 0.5 wt% polymer solution, while PDMS without adding cross-linker was homogeneously dissolved in toluene solvent to produce 0.5 wt% polymer solution, because toluene instead of 1,2-dichloroethane is a good solvent for PDMS. Subsequently, the 0.5 wt% solution was spin coated onto a mica wafer at a speed of 3000 rpm for 30 s; the thickness is about 45 nm, the same as previous work.⁴¹ Initially, the films were treated by HHIC for 30 s to create a two-layer structure. The hydrogen plasma was maintained with 30 W of operating power, and then a dose of solvents was placed in a closed vacuum desiccator. Eventually, the cross-linked films were placed on a perforated platform above the solvent to be swelled under saturated vapor pressure at room temperature. After being swelled for a selected time, the films were removed immediately by removing the saturated vapor. A mixture of THF and ethanol solvents was generated by varying the volume ratio of the two components. To gain the self-assembled patterns, after solvent vapor treatment the PS-PDMS films were first treated with a CF₄ (10 sccm) plasma for 10 s followed by an O₂ (10 sccm) plasma for 20 s with reactive ion etching (RIE) powers of 50 and 90 W, respectively. In this etching, the PS component disappeared while the PDMS component was oxidized to form silica on the substrate. The etching process was accomplished in a Minilock-Phantom III (Trion Technology, Inc., US).

2.3. Characterization

The surface morphology of the film was investigated by atomic force microscopy (AFM) operating in tapping mode using an instrument with a SPI4000 Probe Station controller (SIINT Instruments Co., Japan) at room temperature. Height contrast images were collected. Olympus tapping mode cantilevers with spring constants ranging from 51.2 N m⁻¹ to 87.8 N m⁻¹ (as specified by the manufacturer) were used with a scan rate in the range of 0.8–1.2 Hz.

3. Results and discussion

3.1. The network of folds of cross-linked PS-PDMS film during vapor swelling

Ultra-thin two-layer films attached to the mica substrate were successfully constructed by cross-linking PS-PDMS films using the HHIC technique with an adequate power. Both PS and PDMS chains, where the selective cleavage of C–H bonds occurs in the presence of hydrogen plasma, can be cross-linked.^42–46 Typical surface morphologies are characterized by AFM. Fig. 1a shows the AFM height image of pure PS-PDMS film. The surface is very flat without typical surface undulation, but some small holes can be clearly observed. For the spin-coated BCP film, the formation of these holes, which are internal defects resulting from molecular organization during solvent volatilization, is a common phenomenon. The small holes have not disappeared and are reserved completely for the cross-linked film (Fig. 1b). In addition, as a consequence of the short application time of HHIC, coarsening into larger holes does not occur. Without regard to these defects, the surface is also simultaneously very smooth. Therefore, it is explicit that the intensity of HHIC is small enough not to etch the film surface. In a word, the HHIC conditions ensure the completeness and flatness of the PS-PDMS films for further study.

Fig. 1 AFM height images of surface morphologies produced from (a) pure PS-PDMS and (b) cross-linked PS-PDMS before swelling. The surface morphologies of (c) pure PS-PDMS and (d) cross-linked PS-PDMS swelled for 6 h in THF vapor.

AFM observation confirms that bigger holes with 25 ± 2 nm depth emerge for the pure PS-PDMS film during THF swelling for 6 h (Fig. 1c). This is because the mismatch between the minimum in the Gibbs free energy and the initial free energy impels realignment of the PS-PDMS molecules. To satisfy the minimum in the free energy, the film thickness need to be equal to an integral multiple of the diameter of the cylinders or else islands and holes will form directly. In the presence of cross-linking, however, a complete network of sharp folds with irregular polygonal domains can be clearly observed. Besides, no holes and islands analogous to the result of the pure PS-PDMS film after annealing distinctly emerge, which reveals that the cross-linked films may not have reached equilibrium, or the equilibrium mechanism is not the same as that of the pure films during solvent swelling. However, Fig. S1a and b (see the ESI†) show that the PS and PDMS films cross-linked with the same conditions are swelled for 6 h upon exposure to the THF vapor, but no mechanical instability is generated. This result is not same as that of Kramer et al.⁴⁷ In their experiment, the swelled silica/dPS-P2VP film generated wrinkling instability. Meanwhile, the swelled silica/P2VP film produced creasing instability. They speculated that the instability in silica/dPS-P2VP did not arise necessarily from the mesostructural organization of BCP. However, our result indicates that the network of folds is closely related to mesostructural organization for the swelled PS-PDMS film, while it cannot be produced for the PS and PDMS films.

3.2. Nucleation and growth of the network of folds

The cross-linked PS-PDMS films placed in THF solvent vapor were treated with different swelling times at room temperature. Fig. 2 gives the evolution of the surface morphology of the cross-linked PS-PDMS films. For a short swelling time equal to 2 h, irregular holes exist at the initial stage of continuous swelling (Fig. 2a). Though releasing compressive stress slightly deforms these holes, apparently coarsening is produced for most of the hole structures when compared with the circular holes without exposure to THF vapor (Fig. 1b). Through carefully observing the hole structure (Fig. 2e), the raised hole rim inhibits the tendency to grow bigger, which leads to a preferential accumulation of compressive stress, increasing the local mechanical instability.⁴⁸ In this case, the swelling degree does not reach the threshold value, thus generating an in-plane compressive stress which does not exceed that arising from the elastic recovery of the cross-linked polymer network. Upon further swelling for 3 h, in some areas of the film a few invaginated folds with a valley resembling a crease appear, and small holes do not disappear immediately (Fig. 2b). By observing the corresponding enlargement (Fig. 2g), some holes start to deform seriously to form a short tail-like structure. In this case, the linear swelling degree is beyond the critical value. Indeed, it is a challenge to accurately measure the swelling degree for ultrathin films (∼45 nm). The invaginated structures gradually form along the radial direction of the circular holes. Meanwhile, these results manifest indirectly the compressive stress focused in the peripheral direction. It has been demonstrated that the direction releasing stress is normal to the direction generating stress in much work.^48,49 In fact, the depth of the hole (pointed out by the red arrow in Fig. 2f) is ∼23 nm, while that of the middle part of the left invaginated fold is ∼10.5 nm. In Fig. 2i, the two edges of the valley in the invaginated fold produce a slight out-of-plane bulge (∼3 nm). This result demonstrates that the structure is essentially an invaginated fold and not a crack pattern. In general, desiccation, rather than swelling, results in crack patterns whose depth can approximate the film thickness. Particularly, cracks will be sustained even when the swelling is prolonged. Instead, sharp folds will be constructed after a long swelling time in our results (Fig. 3a). In summary, the average depth of an invaginated fold is lower than that of a hole center, and the hole with a fold is apparently smaller than that without a fold. Hence, it is concluded that the invaginated fold grows from the hole rim and extends outward in the radical direction of the hole.

Fig. 2 (a–d) AFM height images and (e–h) corresponding enlargement images of cross-linked PS-PDMS films after being swelled in saturated THF vapor for (a and e) 2 h, (b and f) 3 h, (c and g) 4 h, and (d and h) 5 h. (i) The corresponding cross-sectional profile along the black line in (f).

Fig. 3 AFM height images of cross-linked PS-PDMS films after being swelled in saturated THF vapor for (a) 6 h, (b) 12 h, (c) 18 h, and (d) 24 h. (e) The corresponding cross-sectional profile along the black line in (a).

Remarkably, when the film is swelled for 4 h, Y-shaped folds with invaginated valleys are gradually constructed (Fig. 2c). A lot of long striped folds whose lengths are far more than film thickness grow from the junction points. In this case, Y-shaped folds including three stripes are commonly observed, and only a few single striped folds are present. However, no complete network forms and these folds spread independently without touching. Invaginated folds do not propagate straight from a junction point due to the mutual interference with each other. To study Y-shaped folds in more detail, the coexistence of a Y-shaped fold and a single striped fold can be seen (Fig. 2g). It is clearly observed that the junction point is actually the previously mentioned hole. Indeed, the irregular intersection angle between the two folds, for the Y-shaped structure, is close to 120°. A corresponding gradual decrease from the hole (∼16 nm) to the end of the fold (∼3 nm) is observed. After being swelled for 5 h, the film surface fabricates a complete network of invaginated folds (Fig. 5d). Initially, the Y-shaped folds continue to grow, subsequently the ends of them start to collide, and then a few folds connect together when the two ends of two folds directly bond, while most fold growth is prevented by mutual interference. Finally, a network texture of invaginated folds with varied characteristic distances emerges immediately. There is no obvious hole in the center of the Y-shaped fold with ∼5 nm depth which is smaller than the depth of the previous holes (Fig. 2h). The hole progressively grows smaller to coalesce into a junction point under the condition that the folds progressively grow longer. The network structure extremely limits the lateral growth of folds, thus the average stripe depth is uniform and about 5 nm, the same as that of the center. Significantly, the few observed holes are not the previous holes but newly formed features resulting from asynchronous rearrangement of the PS-PDMS molecules.

A typical transition from invaginated folds to sharp folds and a complete network of sharp folds with different spaces is observed (Fig. 3a) when the film is swelled for 6 h. The distinctly observed coexistence of invaginated folds and sharp folds and an inhomogenous network of folds demonstrates a stable network has been incompletely formed. Significantly, some of the invaginated folds have not transformed to sharp folds, suggesting that the newly generated holes will induce more invaginated folds when the swelling time is prolonged. In addition, the strong effect of squeezing in junction points results in the fact that the junction points of folds are higher than the surroundings, since folds confront a strong resistance in this point to terminate fold growth. By closely inspecting the area near sharp folds, a gentle height gradient is found from the fold to the network center, as shown in the cross-sectional image (Fig. 3e). This illustrates that there is a surface migration, that the PS-PDMS molecules in the network center are accumulated in the area around the fold. A sharp fold similar to a sinusoidal pattern is found owing to the absence of the invaginated folds. The edges of the invaginated fold simultaneously grow vertically and laterally, which generates delamination resulting in the combination of two edges and the disappearance of the valley. As a result, a relatively complete and stable network of sharp folds is successfully constructed after 6 h swelling. In fact, Stone et al. have demonstrated a network of folds can be constructed through nucleation, growth, and intersection for a cross-linked polyurethane film.⁵⁰ They have noted that nucleation can appear in the local area without the induction of other structures and a wrinkle-to-fold transition is necessary to generate well-identified closed domains. However, in our study, we can clearly observe that the small holes resulting from mesostructural organization as nuclei can induce invaginated fold growth, transform to sharp folds, and then finally fabricate a network of sharp folds. However, no wrinkled state is observed to construct the network of folds. Therefore, the mechanisms of nucleation and growth are different, so the evolution of the network of folds in our system is worthwhile to study. In contrast, such slow kinetics induced by vapor swelling contributes to the clear understanding of each developmental process.

In fact, the network of folds is extremely stable once it has been formed, even though the film is subjected to long-time swelling. A series of images of the network of folds is shown in Fig. 3b–d with prolonged swelling time. Obviously, a tendency toward a denser network is present. As the swelling time increases, more invaginated folds develop and transform into sharp folds. Fig. 4 gives the evolution of the average amplitude (A) of the network of sharp folds (measured in the middle of the fold) with the swelling time. The relationship can be divided mainly into two stages. In the first stage, the average amplitude increases with increasing swelling time. For the film swelled for 6 h, A = 22.05 nm, and increases to A = 27.22 nm for the film undergoing 12 h of swelling. The increase of average amplitude reflects that increasing compressive stress can be strongly attributed to surface migration, which then results in an increasing accumulation in the folds and the formation of a more complete network. In the second stage, however, further prolonging swelling time gives rise to a decrease of average amplitude. When the film is swelled for 18 h, the average amplitude decreases to A = 18.99 nm. A sequential decrease to A = 11.38 nm occurs after swelling the film for 24 h. This decrease is the result of the sufficiently complete and stable network of folds resisting the migration from the network center to terminate vertical growth. Constrained migration produces a gradually uniform surface in the whole network and constructs more sharp folds. Even though the deviation of amplitude (∼6 nm) is considerable, it has little influence on the evolution of the vertical growth of sharp folds. In addition, the significant deviation reflects the asynchronism of vertical growth and migration behavior. Note that the gradually slower growth rate of the complete and stable network of folds with swelling time is closely related to the saturated swelling degree. Once the swelling degree reaches this value, unceasingly increasing swelling time will not change the swelling degree. Accordingly, in our results, we can conclude that a long swelling duration has little influence on the development of the network structures, but maintaining this saturated swelling degree is conducive to self-regulation of the network of folds.

Fig. 4 The amplitude of the sharp folds of the cross-linked PS-PDMS film treated by THF saturated vapor as a function of swelling time.

3.3. Effect of solvent vapor on the network of folds

As discussed above, the morphologies of the cross-linked PS-PDMS films are strongly dependent on the swelling degree, closely related to the solvent properties. For cross-linked PS-PDMS films in contact with saturated THF vapor, a relatively stable and complete network of folds has been formed after the film is swelled for 6 h. In general, the folds can form and develop under the effect of a solvent and be reserved when the film is dry without osmotic pressure.^30,31 More specifically, in our results, the formation of folds needs swelling for at least 3 h, but the velocity at which the film becomes dry is so fast (about a few seconds), because of the rapid vaporization of the low boiling point solvent, that the surface structure can be reserved completely. To reveal the influence of the solvent vapor on the morphologies of the PS-PDMS ultra-thin film, a series of low boiling point solvents were used. The corresponding solubility parameters and saturated vapor pressures are listed in Table 1. In bulk, the solubility parameters of the PS and PDMS chains are 9.1 and 7.4 cal^1/2 cm^−3/2, respectively. Spin-coated PS-PDMS films with same thickness were swelled for 6 h upon exposure to different saturated solvent vapors, and the AFM height images are shown in Fig. 5a–c. Only toluene and chloroform vapor (the strongly interactional solvents for the PS) can give rise to fold formation (Fig. 5a and b), although an incomplete network of invaginated folds with valleys is present during treatment with saturated toluene vapour (Fig. 5a and f). The significant difference between the kinetic process in THF vapor and that in toluene vapor is mainly the result of the difference between the two saturated vapor pressures. The saturated vapor pressure of toluene is much less than that of THF, thus less solvent adsorption leads to smaller in-plane compressive stress. By contrast, a complete network of folds has been constructed when the film is swelled in chloroform vapor (Fig. 5b and g). A high enough saturated vapor pressure mainly affects the resulting morphologies, despite the small difference between the two solubility parameters.

Table 1 Solubility parameters and corresponding saturated vapor pressures of solvents at 298 K^a

Solvents	δ (cal^1/2 cm^−3/2)	p* (kPa)
a δ: solubility parameter^51 and p*: saturated vapor pressure.
Tetrahydrofuran	9.5	23.46
Toluene	8.9	3.89
Chloroform	9.3	30.71
Acetone	9.8	30.60
n-Hexane	7.3	20.12
Ethanol	12.9	7.81

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Fig. 5 (a–e) AFM height images and (f–j) corresponding enlargement images of cross-linked PS-PDMS films after being swelled for 6 h in saturated vapor of (a and f) toluene, (b and g) chloroform, and (c and h) acetone; and after being swelled for 24 h in (d and i) acetone vapor, and (e and j) n-hexane.

However, randomly distributed small holes can be created by using acetone vapor (a weakly interactional solvent for the PS) as the swelling agent (Fig. 5c) for a 6 h swelling treatment. By closely inspecting the enlargement (Fig. 5h), some holes have a slight deformation. By comparison to the morphology of the original cross-linked film (Fig. 1b), the amount of holes greatly increases and their sizes also become apparently bigger. Obviously, some rims of the bigger holes which bulge outward tend to create invaginated folds. This suggests that it is currently at the initial stage of fold formation and the film is subject to an inappropriate swelling degree below the critical value. In fact, prolonging the swelling time can give rise to the emergence of a network of folds (Fig. 5d). In the condition of a 24 h swelling treatment with saturated acetone vapor, the network is more tremendous and sparser (Fig. 5i). In this case, the two edges of the invaginated fold do not coalesce into a sharp fold. This demonstrates that the solubility parameter is more sensitive for network formation even though the saturated vapor pressure is high enough. Remarkably, a great kinetic difference just results from the tiny difference between the two solubility parameters.

The morphology of the cross-linked PS-PDMS film exposed to selective solvent vapors for the PDMS is also measured. Fig. 5e shows the AFM height image of the film swelled in saturated n-hexane vapor (a strongly interactional solvent for the PDMS). Note that no fold forms, but a few small holes without deformation can be produced accompanied with strong surface fluctuation, even if the swelling time is prolonged to 24 h. Even though the used PS-PDMS is a PS-rich block polymer, the network of folds is induced by the mesostructural organization which is independent of whether the BCP is PS-rich or PDMS-rich. Therefore, this directly indicates that swelling PS chains is a more effective approach than swelling PDMS chains to fabricate a network of folds. By carefully observing the enlargement (Fig. 5j), intense sinusoidal wrinkles over the whole surface are generated. Indeed, it is reasonable that no fold forms in the solvent vapor (a very weakly interactional solvent for each chain). For instance, by using ethanol vapor to swell the PS-PDMS film for 24 h, only a few small holes with constant size can be observed (Fig. S2†). In summary, the solvent solubility parameter and saturated vapor pressure play key roles in surface morphologies. Only when the solubility parameter is close to that of PS will the network of folds be constructed. When the solubility parameter deviates more from 9.1 or the saturated vapor pressure is too small, it is harder to construct a complete network. Hence, it is reasonable that the influence of the solubility parameter and saturated vapor pressure on the surface morphologies can be exploited to precisely control the final structures during solvent swelling.

3.4. Morphology of cross-linked PS-PDMS film during mixed solvent vapor swelling

Previous work has demonstrated that ethanol vapor is useless to construct a network of folds, while using THF vapor is an effective approach to form a network. A relatively complete network of folds has been created by using THF saturated vapor as a swelling agent after 6 h of treatment. As discussed above, the saturated vapor pressure strongly affects the growth rate of the network. Therefore, using the mixed solvent vapors generated by mixing THF and ethanol solvents (a two-miscible-solvent system) can slow down the kinetic rate to clearly enrich the understanding of the formation of the network of folds and the unique nucleation. Fig. 6a–d show the morphologies of cross-linked PS-PDMS films swelled by the mixed vapors evaporated from the mixed solvents with a THF : ethanol volume ratio of 8 : 2. A few small circular holes can be observed when the film is swelled for 3 h (Fig. 6a). By contrast, more small holes are generated, but the size of the holes is not bigger (Fig. 6b), after the film is swelled for 4 h. In fact, the formation of invaginated folds can be seen after swelling the film for 5 h (Fig. 6c). Meantime, some folds have contacted with each other but not formed a complete network. After the film undergoes a 6 h swelling treatment, a complete network of folds has been generated (Fig. 6d). It is obvious that the fold peak is a valley which has not coalesced. By comparison, the valley has coalesced into a sharp fold during THF swelling. In the case that the partial pressure of the saturated THF vapor is smaller than the pure saturated THF vapor pressure, swelling films by the mixed solvent vapor decreases the growth rate. A slower dynamic process is beneficial to control morphology evolution.

Fig. 6 AFM height images of cross-linked PS-PDMS films after swelling in mixed vapors evaporated from mixed solvents with a THF : ethanol volume ratio of (a–d) 8 : 2 and (e–h) 6 : 4 for (a and e) 3 h, (b and f) 4 h, (c and g) 5 h, and (d and h) 6 h.

Further decreasing the saturated vapor pressure of the effective solvent by changing the volume ratio of the two solvents to 6 : 4 can lead to slower kinetics. Fig. 6e–h show a series of AFM height images of cross-linked PS-PDMS films in these mixed solvent vapors. Fewer small holes can be observed after swelling the film for 3 h (Fig. 6e), as compared to Fig. 6a. Prolonging the swelling time to 4 h (Fig. 6f) generates the coexistence of more small holes and some annular ridges. In addition, an annular ridge with fluctuant roughness possibly results from impurities. As shown in Fig. 6g, the greater swelling degree induces the presence of more and bigger holes for the film swelled for 5 h. From the corresponding enlargement, there are a few smaller holes in the holes and elastic instability is generated in the hole rim with wave deformation owing to serious stress accumulation. Indeed, after the film is swelled for 6 h, a network of folds with low amplitude is observed in Fig. 6h. During this mixed vapor swelling, the lower partial vapor pressure postpones the development of hole structures. Therefore, we clearly understand that the small holes undergo a trend toward bigger and more before they initiate deformation. Most importantly, the small hole rim undergoing an accumulation of compressive stress gives rise to a gradually increased fluctuation before inducing an invaginated fold. However, a lower saturated vapor pressure readily induces the appearance of more intricate and irregular structures.

3.5. Self-assembly of cross-linked PS-PDMS films

We further studied the self-assembly behavior of cross-linked PS-PDMS films and so RIE was carried out to etch the film surface to reveal the ordered nanostructures. In fact, the coexistence between a monolayer and bilayer of cylinders aligned parallel to the substrate can be attained after the pure PS-PDMS film is swelled in THF vapor for 6 h (Fig. S3†). The average domain spacing determined from the AFM image is about 30 nm. In addition, the nanopatterns actually are the silica residues since the PS block is removed entirely and the PDMS block is converted into silica during the etching process. As mentioned above, a migration of PS-PDMS molecules leads to accumulation in the folds. Fig. 7 shows a series of typical AFM height morphologies of cross-linked thin film of PS-PDMS swelled in THF vapor for 6 h after etching. As shown in Fig. 7a, the morphology of the network of folds is retained completely though the film is subjected to the etching process. The valley in the fold peak is obviously present after etching. Only cylinders perpendicular to the substrate with varied sizes are produced in the areas around folds. Remarkably, some spherical silicas of about 100 nm are found in the folds, which suggests that the confined space with steep height gradient imposes restrictions on the hexagonal arrangement of cylinders perpendicular to the substrate. Accordingly, the cylinders in the folds arrange compactly so as to fabricate bigger and denser nanostructures. Fig. 7b shows the zoom-in height image of the square box in Fig. 7a. No nanopatterns with long-range order analogous to the result of Fig. S3† can be observed in the interior of the network of folds, while a variety of short cylinders and spheres distribute randomly. We can speculate that the observed spheres are essentially cylinders perpendicular to the substrate, and some short cylinders are probably cylinders parallel or oblique to the substrate. These fairly disordered cylindrical nanostructures reveal that the morphology of the cross-linked film under saturated THF vapor swelling is far away from equilibrium. Therefore, self-assembly is effectively restricted but can still be carried out. In comparison to the result of the pure sample, the domain spacing does not change. However, both the network of folds and cross-linked polymer networks will have a great influence on self-assembled nanostructures.

Fig. 7 Series of AFM height images of cross-linked PS-PDMS films during THF swelling for (a and b) 6 h after RIE etching. (b) Zoom-in height image of the square box in (a).

3.6. Schematic representation of the evolution of formation and development of a network of folds for a cross-linked PS-PDMS film

The introduction of solvent-induced compressive in-plane stress into cross-linked PS-PDMS film will give rise to the construction of a unique network of folds. In our study, during appropriate vapor swelling, the evolution of formation and development of a network of folds is hypothetically described as shown in Fig. 8 (seen from the angle perpendicular to the surface). At first, without swelling, the cross-linked film surface maintains flatness and integrity. When solvent vapor is absorbed into the film, cross-linking can theoretically naturally constrain molecular movement. However, the mismatch between initial film thickness and the integer multiple of the characteristic diameter for the cylinder forming system will impel formation of a terrace structure. Hence, the balance between the two opposite effects will lead to the formation of a series of small holes with different sizes forming preferentially at internal defects (Fig. 8a). To satisfy this changeable balance resulting from increasing swelling degree, the small holes will become more and bigger with swelling time and then increase to a saturated value (Fig. 8b). Significantly, for a complete film, the small holes, as defects, undergo preferential solvent absorption to generate an accumulation of compressive stress. Once the swelling time is long enough, the hole rim starts to fluctuate and deform (Fig. 8c). An invaginated fold will be created from the outer edge of the hole in a direction normal to the peripheral direction to release the local stress. In other words, the small holes actually are nuclei to create invaginated folds and subsequent sharp folds.

Fig. 8 Schematic diagram depicting the evolution of constructing a network of folds on the surface of cross-linked PS-PDMS film during adequate solvent vapor swelling: (a) solvent vapor swells the film and molecular rearrangement induces small holes; (b) more and denser small holes form when the swelling time is prolonged; (c) accumulation of compressive stress in the hole rim leads it to deform and fluctuate; (d) small holes induce formation of a complete network of invaginated folds; (f) the transition from invaginated fold to sharp fold induces a complete network of sharp folds. The black represents dents and the yellow represents bulges.

As the swelling time is prolonged, Y-shaped folds with invaginated valleys growing laterally and in three different directions is the most stable morphology to construct a network of invaginated folds (Fig. 8d). At this time, the small holes gradually vanish in a junction point. Simultaneously, the invaginated folds grow to contact with each other and the depth of them becomes shallower and more uniform. Longer swelling time induces the formation of a network of invaginated folds (Fig. 8e), then increasing compressive stress actuates the occurrence of slight in-plane expansion because of sunken valleys in the surface. The release of compressive stress is easier to arise in the invaginated fold than a stress defect. Thus, there is a migration of PS-PDMS molecules from the network center to folds, in which PS-PDMS molecules start to accumulate. By prolonging the swelling time, this accumulation becomes more serious to induce local delamination, and then two fold edges grow mainly normally and slightly parallel to the surface. The invaginated fold has not been transformed into the sharp fold until enough high compressive stress is applied to make the two edges coalesce together. Finally, a network of sharp folds can be constructed after the film undergoes the transition from invaginated folds to sharp folds (Fig. 8f). Once generated successfully, the network of sharp folds tends to become denser and more complete before a stable and ordered network with a constant characteristic period is eventually constructed as the swelling time increases.

4. Conclusions

During solvent vapor swelling, for the cross-linked PS-PDMS film constrained on rigid substrate, a unique network of folds could be constructed successfully to release increasing in-plane compressive stress. We demonstrate that the wrinkled state is not essential to construct the network of folds. In this article, the slow kinetics induced by the solvent vapor swelling contribute to clearly understand the evolution process. We conclude that this network of folds is closely related to the rearrangement of PS-PDMS molecules. The balance between the cross-linking constraint and the impulse derived from mesostructural organization prompts the formation of small holes during the initial swelling stage. In fact, these small holes act as nuclei and induce the formation of invaginated folds to release compressive stress accumulated in the hole rim. Thereafter, invaginated folds continuously grow into a network of invaginated folds, and then a transition from invaginated folds to sharp folds will be produced to construct a complete network of sharp folds accompanied with molecule migration. At the same time, the cross-linking and network of folds have a strong influence on self-assembly behavior. For cross-linked PS-PDMS film, poorly ordered nanostructures can be fabricated while mostly vertically oriented cylinders can be produced. The unique network morphology and kinetics are strongly dependent on the solvent solubility parameter and saturated vapor pressure. Only when the solvent solubility parameter is approximately that of the PS chains can this surface morphology be constructed successfully. By mixing two-component solvent vapors (a relatively good solvent vapor and a poor solvent vapor), the decreased partial vapor pressure reduces the kinetic rate of formation of the network of folds. In our system, precisely controlling the condition of the solvent vapor is beneficial to precisely control the surface morphology. However, it is also a challenge to fabricate well-ordered morphologies of surface patterns in the absence of external factors. We believe that the formation of an ordered network of folds will offer new insight for the theoretical study of the mechanical instability of cross-linked BCP films and broaden the potential applications such as in micro-fluidic devices and microfabrication.

Acknowledgements

The authors acknowledge financial support from the National Natural Science Foundation of China (51173112, 51121001 and 21274095) and the Foundation of China Academy of Engineering Physics (2013B0302058). We thank Woon-Ming Lau (Chengdu Green Energy and Green Manufacturing Technology R&D Center, Chengdu, China) for carrying out the HHIC treatments.

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Footnote

† Electronic supplementary information (ESI) available: AFM height images of cross-linked PS and PDMS films during THF vapor swelling and cross-linked PS-PDMS film during ethanol vapor swelling. Surface morphology of annealed PS-PDMS film after RIE. See DOI: 10.1039/c4ra13674h

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