1 Introduction

Porous polymer films have a variety of applications as catalysts [1, 2], separation and adsorbent media [3, 4], chromatographic materials [5], etc. Hence, fabricating them in a simple and controlled manner, with size scalability is of interest. A simple, cost-effective, single-stage method for the fabrication of porous polymer films is breath figure (BF) approach, which was first developed by Francois et al. [6] BF patterns are formed by the condensation of water droplets and their successive evaporation during the solidification of the polymer solution. The preparation steps consist of casting of a polymer solution on a substrate followed by controlled evaporation of solvent in a humid environment. Evaporation of solvent leads to cooling of the substrate/polymer, enabling the condensation of water droplets on the polymer surface and their successive evaporation results in the formation of pores. The schematic diagram of the steps involved in BF formation is shown in Fig. 1.

Fig. 1
figure 1

Schematic representation of the steps involved in BF formation

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Previous studies on the formation of BFs over polystyrene (PS) indicate difficulties in analyzing them, largely because there are conflicting experimental results. A variety of parameters such as type and architecture of the polymer used, solvent, casting conditions and surrounding environment are found to influence the formation of BFs over PS [7]. Influence of the geometry of the PS polymer such as linear homopolymers [8, 9], rod-coil or coil-coil block copolymers [10], starlike homopolymers or copolymers [11] and amphiphilic polyion complexes [8] has been studied. Stenzel et al. [12] observed that only star shaped PS and PS with polar end groups resulted in BF formation while linear PS did not. But Peng et al., Bormashenko et al., Ferrari et al., reported the formation of BFs using linear PS [13,14,15]. Studies of PS [13,14,15,16] based BF formation have looked into the effect of molecular weight, the solvent used, substrate, atmospheric humidity on pore. Peng et al. [13] have used 1 wt.% PS of three molecular weights (29.3, 223.2 and 1970 K) on glass substrates with chloroform, toluene, carbon-di-sulfide (CS2) and tetrahydrofuran (THF) as solvents. Ordered pores were obtained with toluene and chloroform at 60% relative humidity (RH) for molecular weight 223.2 K. The experiment was repeated using toluene varying the RH from 40 to 95% and ordered pores were obtained for RH varying from 46 to 90% with the pore size increasing with the increase in RH, while for RH greater than 90%, a polydispersion of the pore sizes was seen. Of the four solvents used, the evaporation rate of CS2 and THF is higher than toluene and chloroform, in that case, the solvents CS2 and THF completely evaporates before the water droplets form regular packing. While Ferrari et al. [15] used 1 wt.% PS of molecular weight 192 K in chloroform, CS2 and dichloromethane to form breath figures on glass substrates at 75% RH. Only CS2 could form ordered breath figures while chloroform resulted in random pores and dichloromethane with no pores. From the studies so far done, it is difficult to draw a conclusion regarding which solvent and under what conditions, BF formation is possible using PS. Bormashenko et al. [14] used different molecular weights of PS (4.8, 42.5, 227.1, 1000, 2800 K) in a mixture of chloroform (8 wt.%) with dichloromethane (92 wt.%) using 2.5 wt and 5 wt.% solutions under conditions of low humidity (30–40% RH). Bimodal distribution was obtained for molecular weights 4.8 and 42.5 K while at 227.1, 1000 K ordered pores were formed for both 2.5 and 5 wt.%. The 5 wt.% solution of 2800 K did not form a homogenous film while 2.5 wt.% of the same resulted in ordered BFs. Thus, PS is seen to form breath figures under various experimental conditions with no clarity regarding the influence of solvents, RH and molecular weight on the same. The orderliness of BFs over PS has been studied through image analysis involving the Voronoi entropy [17, 18] and fast Fourier transforms (FFT) [19]. Literature reports show that the wettability of the BF patterned surfaces is done and they showed hydrophobic nature [20, 21].

In an attempt to further understand the formation of BF on PS, this work reports the studies on the same for different molecular weights of PS and the influence of casting methods. Further, the influence of underlying symmetry of the substrate is also studied by casting the polymer on the smooth and the grooved surfaces of a commercial DVD, with the ordered grooves providing the necessary asymmetry. The images of the BFs formed under various conditions are analyzed in terms of Voronoi entropy and Fast Fourier Transforms. Contact angle studies of BF surfaces are done to investigate their wetting nature.

2 Methodology

2.1 Materials

PS of three molecular weights viz 35,000, 1,92,000 and 2,80,000 g/mol were purchased from Sigma Aldrich. Chloroform of purity 99.8% purchased from Nice Chemicals (India) was used as the solvent for the polymers. The smooth and grooved surfaces (cut into 1 × 1 cm2) of the commercially available Sony recordable DVD were used as substrates.

2.2 Experimental details

3 and 5 wt.% of the polymer solutions of the three polymers were prepared by dissolving 0.6 and 0.1 g in 2 ml of chloroform, respectively. A humid atmosphere was created by keeping 3 ml of distilled water in a petri-dish kept inside a closed chamber. 100 μl solution was drop-casted on the smooth and grooved surfaces and was kept in the humid atmosphere saturated with water vapor. The polymer solutions were spin-coated on the smooth and grooved DVD surfaces at 1000 rpm and were kept for pattern formation. The substrates after drying were imaged using the Leica Confocal Laser Scanning Microscope (CLSM) TCS SP8 model. The excitation wavelength of 633 nm was used to image the patterns formed. The diameter of the pores and the Voronoi entropy were calculated using the ImageJ software. Rame-Hart goniometer was used to measure the contact angle of water on various surfaces using static-sessile drop method. Figure 1 shows the experimental set up used for the BF experiment (Fig. 2).

Fig. 2
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Experimental set up used for BF formation

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3 Results and discussions

PS of three different molecular weights dissolved in chloroform (to make 3 and 5 wt.% solutions) up on casting on the smooth and grooved surfaces of the DVD substrate were kept in a humid environment. To avoid the chances of uncertainty using the dynamic method of self-assembly, the static method of self-assembly is used for the pattern formation. After the complete evaporation of the solvent, confocal microscopy is used to observe the morphologies of the patterns obtained.

The patterns observed on smooth and grooved DVD surfaces on drop-casting and spin-coating using PS of three different molecular weights (35, 192, 280 K) using 3 and 5 wt.% solutions are shown in Tables 1, 2 and 3, respectively. Table 6 displays the histograms of the pore size distributions computed using the ImageJ software for the drop-casted samples. These histograms were fitted with a Gaussian curve [17] using Origin software and the mean diameter (MD) and standard deviation were obtained from them which is also tabulated in Table 6. On both smooth and grooved DVD surfaces during drop-casting, the pores observed were mostly circular in shape. For the same molecular weight and weight percentage, the pores on grooved surfaces are smaller than those on smooth surfaces on drop-casting. Also the pores on the grooved surfaces show a uniformity in size for all molecular weight and concentration when compared with the smooth. A similar study using polydimethylsiloxane (PDMS) did not show such a uniformity in pore size [22]. The likely reason for this could be because molecules of PS stack through π–π interactions and any small changes in their environment is known to disturb the same [23]. The underlying grooves on the substrate may disturb the π–π stacking causing water droplets condensation and evaporation easy and resulting in more ordered and uniform pores. A small molecular dynamics simulation of 3 styrene molecules was done to identify the π–π stacking in PS and the same is shown in Fig. 3 along with the chemical structure of PS.

Table 1 CLSM images, FFT, Voronoi tessellations and statistical analysis of polygons on Voronoi tessellations for molecular weight: 35 K on smooth and grooved DVD surfaces
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Table 2 CLSM images, FFT, Voronoi tessellations and statistical analysis of polygons on Voronoi tessellations for molecular weight: 192 K on smooth and grooved DVD surfaces
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Table 3 CLSM images, FFT, Voronoi tessellations and statistical analysis of polygons on Voronoi tessellations for molecular weight 280 K on smooth and grooved DVD surfaces
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Fig. 3
figure 3

a: Chemical structure of PS, b π–π stacking in PS visualized using molecular dynamics

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The pore size of the BFs formed on drop-casted PS is found to increase with the increasing molecular weight and also with the weight percentage used. The effect of molecular weight [13, 14, 20, 24,25,26] and concentration [20, 27] of the polymer in pattern formation were previously studied by many research groups. The polymer molecular weight and the concentration of polymer used are found to have a direct correlation on the pore size irrespective of the substrate used. Higher molecular weight leads to a higher vapor pressure which accelerates the rate of evaporation of the solvent, thus increasing the pore size [24]. Rapid evaporation results in a lower surface temperature, which enhances the water vapor condensation. Since large amounts of water droplets are condensing, coalescence can also occur resulting in larger pores eventually. The increase in pore size with the concentration is attributed to the increasing concentration lengthening the droplet growth period [14, 28, 29].

The surface morphology of the spin-coated and drop-casted patterns is different. Spin-coating of 3 and 5 wt.% of PS solutions on smooth surfaces gives random pores and the images were not amicable for further analysis. Also, pores were not observed on the grooved surface for 3 wt.% solutions of PS of all molecular weight and 5 wt.% solutions of molecular weight 35 K. Random pores were observed with 5wt.% for molecular weights 192 and 280 K, respectively.

The near absence of breath figure patterns on spin-coated surfaces can be attributed to the thickness of the film. The thickness of the film during spin-coating depends on the viscosity of the polymer solution and the speed of rotation [30]. Here the speed of rotation is 1000 rpm, which is kept constant for all the spin-coated surfaces such that the thickness of the film depends on the viscosity of the solution. The viscosity of the polymer solution is related to molecular weight (Mv) by the semi-empirical Mark Houwink relation: \(\eta = {\text{KM}}_{{\text{v}}}^{\alpha }\), where K and α are constants for a given polymer, solvent and temperature [31]. Also the viscosity of the solution is proportional to the concentration of the polymer solution [32]. Also it was previously experimentally observed that the thickness on spin-coating of a polymer solution for a particular spin velocity is directly proportional to both concentration and molecular weight [33]. Thus for 3 and 5 wt.% spin-coated samples, the thickness of the film may be insufficient to allow the formation of ordered BFs.

The length for long-range ordering is often limited in breath figures [34]. The FFT of CLSM (Tables 1, 2 and 3 has the FFT images for BFs formed) images shows a circular pattern which confirms multi-grain morphology and short range ordering. A similar multi-grain morphology has been reported in the BF formed using monocarboxy terminated PS, using FFT analysis [34].

Voronoi entropy (Shannon entropy) or Voronoi tessellation is a mathematical tool used for the quantification of the uniformity of the points arranged on a surface. Thus, this tool can be used to comment on the orderliness of the pores formed by the self-assembly process [35]. A Voronoi polygon is described as being the smallest convex polygon enclosing a point whose sides are perpendicular bisectors of the lines between a point and its neighbors. The number of sides ‘n’ of the Voronoi polygon is known as the coordination number and Pn is the fraction of the polygon having the number of sides ‘n’. Using these values, a conformational entropy known as Voronoi entropy (S) is calculated using Eq. (1):

$$ S = - \mathop \sum \limits_{n} P_{n} \ln P_{n} $$
(1)

The summation is performed from n = 3 to the largest coordination number of any available polygon. The conformational entropy of the breath figure patterns are calculated and is compared with a perfectly hexagon pattern and completely random pattern whose entropy values are 0 and 1.71, respectively [36].

The Voronoi entropy calculated for smooth and grooved surfaces for the three molecular weights are tabulated in Table 4.

Table 4 Voronoi entropy for smooth and grooved surfaces along with the statistical scattering of polygons
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The Voronoi tessellations of smooth and grooved surfaces for 35, 192 and 280 K are given in Tables 1, 2 and 3, respectively, along with the counts of the different polygons in the Voronoi diagram. The Voronoi entropy of BFs on grooved surfaces is less compared to that on smooth surfaces which indicates that the pores are ordered on grooved surfaces. This uniformity in pore distribution is also seen from the confocal images of the BFs. The Voronoi entropies of smooth surfaces are much higher than the grooved surfaces and the most random distribution of pores is observed for PS with 280 K using 5 wt.% solution. This is also evident from the confocal image of the same.

There were studies based on the influence of the substrate surface energy on the pore ordering [15]. For the PS/Chloroform solutions, substrates with higher surface energy formed long range ordering pores while for the PS/CS2 solutions, substrates with the lower surface energy enabled the formation of ordered pores. Thus, from the literature, there are confusions regarding the contribution of the substrate to the ordering of the pores.

In addition to Voronoi entropy, Lewis law, Desch law and Aboav law can be used to study the topological properties of the Voronoi polygons of the BF patterned surfaces [37]. Lewis law relates the average area of n-sided polygon to the number of sides (n) by the relation (2)

$$ A_{n} = \alpha \left( {n - 2} \right) $$
(2)

where α is the proportionality constant, i.e., a linear relationship exist between the average area of n-polygon and n. The analysis of Voronoi polygons of BF patterned surfaces using Lewis Law is shown in Fig. 4.

Fig. 4
figure 4

Area of polygon versus the number of sides a: Smooth; b: Grooved

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Desch law states that there exists a linear relationship between the perimeter of the polygon and the number of their sides. Figure 5 shows the analysis of Voronoi polygons of BF patterned surface using Desch law.

Fig. 5
figure 5

Perimeter of polygon versus the number of sides a: Smooth; b: Grooved

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Aboavs law states that the average number of sides (mn) surrounding a n-sided polygon varies linearly with 1/n. The law is usually written in the form of Eq. (3):

$$ m_{n} = a + \frac{b}{n} $$
(3)

where a and b are constants. Figure 6 shows the analysis of Voronoi polygons of BF patterned surfaces using Aboavs law.

Fig. 6
figure 6

Aboavs Law for a: Smooth; b: Grooved

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Table 5 summarizes the fitting parameter R2 value obtained during the linear fitting for the three laws. The Aboav’s law is well verified with the experimental data with the R2 value in the range 0.96–0.99 for both smooth and grooved surfaces. The Lewis law also shows a good fitting with the R2 value > 0.91 except for PS 35 K 5 wt.% smooth, and on grooved 192 K-3 and 5 wt.% and 280 K-5 wt.%. The linear fitting of Desch law is also good with R2 value 0.921–0.987 except for a few. It was observed in literature that Lewis law and Desch law does not hold good for monodisperse compact packing with packing fraction of 0.45 or greater than 0.45 due to steric exclusion which gives high values of area and perimeter for lower order polygons [38] (Fig. 7) (Table 6).

Table 5 The fitting parameter R2 value obtained during the linear fitting for the three laws
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Fig. 7
figure 7

Schematic representation of a water droplet on solid surface showing the quantities in Youngs equation

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Table 6 Histogram of the pore size distribution on smooth and grooved surfaces using different molecular weights of PS during drop-casting
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3.1 Wettability studies

The wettability of a solid surface by a liquid is quantified the Young’s equation (Eq. 4), which is a relation between the solid–liquid interfacial tension (γSL), solid–vapor interfacial tension (γSG) and liquid vapor-interfacial tension (γLG) comes into action and the contact angle (θc) formed at the triple phase contact line [39].

$$ \cos \theta_{{\text{c}}} = \frac{{\gamma_{{{\text{SG}}}} - \gamma_{{{\text{SL}}}} }}{{\gamma_{{{\text{LG}}}} }} $$
(4)

Wettability studies of the drop-casted and spin-coated surfaces were done taking water as the test liquid using the contact angle measurements. The results, Fig. 8, indicate that the contact angle over spin-coated surfaces is lesser than over drop-casted surfaces which is because of the formation of BFs on the drop-casted surfaces. A flat PS film has a water contact angle of 89° [40]. It is known that highly porous films may entrap air and remain in the Cassie state [41]. The apparent contact angles can be calculated using the Cassie and Baxter’s law [40] (Eq. 5):

$$ \cos \theta_{{{\text{calc}}}} = \left( {1 - f_{{{\text{pores}}}} } \right)* \, \cos \theta_{{{\text{polymer}}}} + \cos \theta_{{{\text{pore}}}} *f_{{{\text{pores}}}} $$
(5)

where θcalc is the calculated contact angle; fpores -area fraction of pores; θpolymer -contact angle of the polymer; θpore- contact angle of the pore in the Cassie state (180°).

Fig. 8
figure 8

Contact angle values for drop-casted and spin-coated smooth and grooved surfaces using 3 and 5 wt.% PS solutions

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The area fraction of pores are calculated from the confocal images and the calculated contact angle values using Cassie and Baxters law are found to be close to the experimental values which are tabulated below (Table 7). These data confirm the Cassie-Baxter state of wetting of the BF patterned surfaces. The increased hydrophobicity of the BF patterned surfaces may be useful for the fabrication of water repellent surfaces.

Table 7 Contact angle values calculated for drop casted surfaces using the Cassie-Baxter law
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4 Conclusions

The formation of porous polymer film on PS using BF method on smooth and grooved surfaces of the DVD substrate is reported. It is observed that the variation of the molecular weight affects the size of the pores formed. The pore diameters increase with the increasing molecular weight and concentration. On grooved surfaces, a near uniformity of pore diameters is observed, probably due to the disruption of the PS stacking. Voronoi entropy confirms that more ordered pores are formed on grooved surfaces compared to the smooth ones. Wetting studies show the patterned BF surfaces to be hydrophobic, with the hydrophobicity increasing with an increase in the asymmetry of the underlying substrates, namely the grooves.