Polymer Crystallization on Nano-Curved Substrates: Distortion vs

Mar 18, 2019 - The effect is analyzed in terms of the interplay of polymer wetting (affecting the interfacial free energy) and lamellar crystallizatio...
1 downloads 0 Views 809KB Size
Subscriber access provided by EDINBURGH UNIVERSITY LIBRARY | @ http://www.lib.ed.ac.uk

C: Surfaces, Interfaces, Porous Materials, and Catalysis

Polymer Crystallization on Nano-Curved Substrates: Distortion vs Dewetting Roberta Ruffino, Nunzio Tuccitto, Grazia Maria Lucia Messina, Erika Kozma, Marinella Catellani, Giovanni Li Destri, and Giovanni Marletta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b12534 • Publication Date (Web): 18 Mar 2019 Downloaded from http://pubs.acs.org on March 18, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Polymer Crystallization on Nano-Curved Substrates: Distortion vs Dewetting Roberta Ruffinoa, Nunzio Tuccittoa, Grazia M.L. Messinaa, Erika Kozmab, Marinella Catellanib, Giovanni Li-Destria*, Giovanni Marlettaa

a.

Laboratory for Molecular Surfaces and Nanotechnology (LAMSUN), Department of Chemical Sciences, University of Catania and CSGI, viale A. Doria 6 Catania 95125 Italy

b.

Istituto per lo Studio delle Macromolecole, Consiglio Nazionale delle Ricerche, via A. Corti 12, Milano 20133, Italy

AUTHOR INFORMATION

Corresponding Author * [email protected]

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT The crystallization of a model semi-crystalline polymer, namely poly-3hexylthiophene, was studied as a function of the curvature at the nanometric scale and substrate surface free energy. Nanostructured substrates with controlled local curvature were prepared by deposition of a 235-nm SiO2 particle monolayer, and their surface free energy was modulated by functionalization with octadecyltrichlorosilane followed by RF plasma oxidation. The crystallization of ultrathin poly-3-hexylthiophene thin films, on the curved portions of the substrate, was found to mostly depend on the substrate surface free energy, while spontaneous wetting occurred in all cases. The effect is analyzed in terms of the interplay of polymer wetting (affecting the interfacial free energy) and lamellar crystallization, implying the modulation of crystallization enthalpy, demonstrating that the balance between surface free energy minimization and crystallization enthalpy maximization governs the phenomenon. The results highlight the role played by the surface nanostructuring in driving soft matter organization.

2 ACS Paragon Plus Environment

Page 2 of 40

Page 3 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Introduction

Polymer thin and ultrathin films have been extensively used as model systems to investigate the behavior of soft matter under nanoscopic confinement at both solid1-3 and liquid interfaces4-7. Given the geometrical constraints imposed by the nanometric thickness and the specific interactions with the substrate, polymer thin and ultrathin films show unique thermal behaviors1, which markedly differ from the bulk behaviors. Additionally, confinement conditions significantly influence the polymer self-assembly behavior, particularly in the case of crystalline polymers8 and block copolymers undergoing microphase separation7, as a number of polymer structures and nanostructures can be obtained by varying the polymer film thickness9, the polymer/substrate affinity10,11, and the substrate nature12-15. The role of these three parameters on the polymer self-assembly, especially for the case of block copolymer microphase separation, is well understood and it has led scientists to investigate more complicated systems, where polymer films are not simply spatially confined, but they are also subject to geometrical distortions at the nanoscale16,17. Few seminal reports have

3 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

shown, by modifying the substrate curvature via particle deposition, the striking role of the substrate nano-curvature on the microphase separation behavior of di-block copolymer thin films18-20. Similar experiments on semi-crystalline polymer films, where the substrate curvature might induce significant distortion of the polymer crystals as well as reduction of the crystallization rate,21 thus affecting the self-assembly behavior, have not yet been performed. Additionally, more precious information would be obtained by studying the combined effect of substrate nano-curvature and surface free energy (SFE), as the substrate/polymer interactions and wettability might favor the substrate coverage by the polymer, thus enhancing or suppressing the distorting effect played by the nanocurvature. However, while wettability characterization as a function of nanostructure has been extensively investigated for substrates with constant SFE22-25, fewer reports have addressed the preparation and wettability characterization of nanostructured substrates with variable SFE.18,26

Simultaneous control of local nano-curvature and SFE can be attained by exploiting soft lithography methods27-30, as the deposition of monodisperse particle monolayers enables

4 ACS Paragon Plus Environment

Page 4 of 40

Page 5 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

the creation of substrates having controlled periodical curvature corresponding to the particle radius. Additionally, simple chemical modifications such as, for the silica particles herein

employed,

piranha

treatment31

and

octadecyltrichlorosilane

(OTS)

functionalization32, allow fine-tuning of the substrate SFE over a significantly wide range. In this framework, we report the preparation of nano-curved substrates with controlled SFE by chemical modification and plasma oxidation of a silica particle (diameter 235 nm) monolayer prepared via soft colloidal lithography (see the Methods section for more detail). The wettability of these substrates shows a marked deviation from the corresponding flat ones, and, in particular, the study of the combined effect of nanocurvature and SFE on the crystallization behavior of a model semi-crystalline polymer, namely poly-3-hexylthiophene (P3HT), showed that polymer crystallization on nanocurved substrates does not occur on strongly hydrophobic substrates. The phenomenon, rather than being merely governed by interface thermodynamics, is apparently driven by the balance between minimization of the surface free energy (related to wetting) and maximization of the crystallization enthalpy (related to the curvature–induced distortion of the polymer lamellae). 5 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Methods

Chemicals. Regioregular poly(3-hexylthiophene) P3HT was purchased from Merck and purified by repeated extractions in a Soxlet apparatus with methanol, diethyl ether, hexane, and chloroform solvents. The molecular weight distribution was obtained using a size exclusion chromatography system from a Waters (HT-GPC 150C) instrument with UV-visible diode array detector, in tetrahydrofuran eluent using a calibration curve obtained with polystyrene standards from Mw 1060 to 210,000. The experimental values were the following: Mw = 24.3×103g·mol-1, Mn = 14.9×103 g·mol-1, and the polydispersity Mw/Mn = 1.63. P3HT was dissolved in chloroform, purchased from Sigma Aldrich, at a concentration of 5 mg/mL.

A 5% w/v aqueous suspension of silica particles, nominal diameter 235 nm, was purchased by Microparticles GmbH, Berlin (Germany), and used as received.

6 ACS Paragon Plus Environment

Page 6 of 40

Page 7 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

All the other chemicals (CHCl3, NH4OH, H2O2, octadecyltrichlorosilane, hexadecane, glycerol, and tricresyl phosphate) were purchased from Sigma Aldrich (Milan, Italy) and used as received.

MilliQ grade water was employed for aqueous solutions and contact angle measurements.

Preparation of flat and nano-curved substrates. Flat hydrophilic substrates were prepared by treating a (100) silicon wafer with a basic ‘‘piranha’’ mixture (3 mL NH4OH, 3 mL H2O2, and 15 mL H2O at 60°C for 10 min). Flat hydrophobic substrates were prepared by dipping the silicon wafer, previously treated according to the above-described procedure, in a 40 mM solution of octadecyltrichlorosilane (OTS) in 20 mL hexadecane and 5 mL CHCl3 at 40°C for 1 h.

Nano-curved substrates were prepared by deposition of a particle monolayer via spin coating of the as-received silica particle dispersion onto the piranha-treated flat substrate according to the following recipe: 1 s at 400 rpm, 40 s at 750 rpm, and 30 s at 2000 rpm. The monolayer was then baked at 90°C for 10 min to completely remove the residual 7 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

water. Hydrophilic and hydrophobic nano-curved substrates were obtained by treating the particle monolayer with piranha mixture, to obtain the hydrophilic nano-curved substrate, followed by OTS functionalization, to obtain the hydrophobic nano-curved one, following the same procedure employed for the flat substrates.

Flat and nano-curved substrates having intermediate SFE were obtained by treating the hydrophobic substrates with a radio-frequency plasma at 100 W having an Ar/O2 volume ration of 97/3. SFE modulation was obtained by controlling the plasma exposure time.

Preparation of P3HT films. P3HT films were deposited on flat and nano-curved substrates by spin coating the 5 mg/mL chloroform solution at 2000 rpm for 1 s and 4000 rpm for 59 s. The resultant films had a thickness of 38.4±4.5 nm.

To induce P3HT crystallization, the films were thermally annealed in vacuum at 240°C, corresponding to the highest recorded P3HT melting temperature33, for 30 min and then slowly cooled to room temperature (1°C/min).

8 ACS Paragon Plus Environment

Page 8 of 40

Page 9 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Determination of surface free energy, interface free energy and spreading parameter. Contact angle measurements were performed using an OCA 20 apparatus (DataPhysics Instruments GmbH, Filderstadt, Germany). To calculate the surface free energy of flat substrates and P3HT films, the three liquids technique was applied.34 Surface free energy (γ) might be described as a combination of attractive Lifshitz-Van der Waals and Lewis acid-base polar contributions, 34 as shown by equation 1

𝛾 = 𝛾𝐿𝑊 +2 𝛾 + 𝛾 ―

(1)

where γLW is the Lifshitz-Van der Waals component, γ+ is the acid component, and γ- the basic one. Contact angle measurements of three different liquids on a solid surface make possible – providing surface free energy components of the liquids are known – the determination of the surface free energy of the solid and its expression in terms of LifshitzVan der Waals, acid and basic components by simply solving the three equations that describe the spreading of the three liquids on the solid surface34

𝐿𝑊 + ― ― + (1 + 𝑐𝑜𝑠𝜃)𝛾𝐿 = 2( 𝛾𝐿𝑊 𝑆 𝛾𝐿 + 𝛾𝑆 𝛾𝐿 + 𝛾𝑆 𝛾𝐿 )

9 ACS Paragon Plus Environment

(2)

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 40

The subscript L refers to the liquid surface tension component, and γL is the total surface tension of the liquid, the subscript S refers to the solid surface free energy component.

In our case, the three employed liquids were water, glycerol, and tricresyl phosphate (TCP),whose surface tensions and the three related components are reported in the instrument database.

The interface free energy (IFE) was calculated by considering the Fowkes-Van OssChaudhury-Good (FOCG) model34, which exploits the Good-Girifalco-Fowkes combining rule35 with suitable expressions for the Lewis acid-base interactions across the interface34.

Accordingly, the IFE between solid and liquid was calculated in terms of the surface free energies (SFEs) using the following equation:34

𝐿𝑊 2 ― + + ― + ― ― + 𝛾𝐿𝑆 = ( 𝛾𝐿𝑊 𝑆 ― 𝛾𝐿 ) + 2( 𝛾𝑆 𝛾𝑆 + 𝛾𝐿 𝛾𝐿 ― 𝛾𝑆 𝛾𝐿 ― 𝛾𝑆 𝛾𝐿 )

(3)

The needed values of the SFE and related components for solid substrates were calculated from contact angle measurements performed at a temperature of 25 °C using

10 ACS Paragon Plus Environment

Page 11 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

the three liquids technique (see above). However, given the high acid/base asymmetry of hydrophilic substrates (see Table 1), the IFE between water or glycerol and the highly basic substrates gave rise to negative values34. Therefore, for the calculation of the IFE when using water or glycerol as spreading liquid, the approximated equation34 below was employed:

𝐿𝑊 2 ― + + ― 𝛾𝑆𝐿 = ( 𝛾𝐿𝑊 𝑆 ― 𝛾𝐿 ) + 𝛾𝐿 𝛾𝐿 ― 2( 𝛾𝑆 𝛾𝐿 )

(4)

The P3HT spreading coefficient on solid substrates having various SFEs was calculated using the following equation:

𝑆 = 𝑆𝐹𝐸 ― 𝛾𝑆𝑢𝑏𝑃3𝐻𝑇 ― 𝛾𝑃3𝐻𝑇

(5)

where γP3HT is the P3HT SFE (21.7 mN/m), which was determined by contact angle measurements, while γSubP3HT is the interface free energy between P3HT and the solid substrate. For the calculation of the interface free energy, the following P3HT SFE components, determined by contact angle measurements, were employed:

γLW 21.4 ± 0.6 mN/m

11 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

γ+ 0.1 ± 0.1 mN/m

γ- 1.1 ± 0.2 mN/m

Wetting simulation. Wetting simulations on nano-curved substrates were performed using COMSOL (www.comsol.com) software by solving the time-dependent differential equation contained in the 2D physics module named “Two-Phase Flow".36 Simulations required to impose the immiscibility between the two fluid phases, air and the spreading liquid respectively, as well as the substrate SFE expressed in terms of the spreading liquid contact angle. Therefore, experimentally determined contact angles at different SFE values were employed. Solving the 2D differential equation enabled us to determine the liquid spreading behavior as a function of time. The results reported in Figure S1–S3 represent the solution of the differential equation after 6 µs, that is, the longest simulation attainable time.

Morphological characterization. Atomic force microscopy (AFM) images were obtained with a Nanoscope IIIa apparatus from Digital Instruments (Santa Barbara, CA) used in

12 ACS Paragon Plus Environment

Page 12 of 40

Page 13 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

tapping mode in air. Tap 300G silicon probes from Budget Sensors, having a nominal resonance frequency of 300 kHz, were employed.

Structural characterization. Grazing incidence x-ray diffraction (GIXRD) was performed with a Rigaku Smartlab equipped with a rotating anode of Cu Kα radiation operating at 45 kV and 200 mA. The incident angle was kept at 0.1°.

Results and discussion

Wetting of nano-curved substrates at various SFEs. Figures 1 a-b show the morphology of the as-prepared silica particle monolayer (a) and after the OTS functionalization (b), together with the corresponding water contact angles, confirming the stability of the nanocurved substrate toward chemical functionalization. SFE modulation was then obtained by varying the treatment time of the OTS-functionalized substrates with an Ar/O2 radiofrequency plasma, to modulate the surface oxidation37. Oxidized surfaces, unlike apolar ones, interact attractively with polar liquids via acid-base interactions. If these

13 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

interactions are sufficiently strong, they enable the effective spreading of polar liquids even on nanostructured substrates. Therefore, substrate wettability, determined by water contact angle measurements, was modulated within a range between approximately 140° and 5° (Fig. 1c). However, as the contact angle between a liquid and a nanostructured surface is affected by the wetting behavior, which might lead to either higher or lower apparent contact angles than the corresponding flat cases, the three-liquid model for SFE determination is not applicable to nanostructured surfaces, as the wetting regime is a

priori unknown and it also varies with the wetting liquid. Thus, SFE determination, via the three-liquids technique (see Methods section for details), was carried on flat substrates functionalized and treated simultaneously with the nano-curved ones, in the assumption that OTS coverage and plasma oxidation are not affected by the substrate curvature. The results, proving that SFE can be modulated within a 40 mN/m range, are reported in Table 1.

14 ACS Paragon Plus Environment

Page 14 of 40

Page 15 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Fig. 1. 1×1 μm2 AFM height image of 235 nm SiO2 particle monolayer treated with piranha mixture (a) and functionalized with OTS (b), the height scale of both images is 150 nm. Below each image, the corresponding water contact angle is reported. In (c) the water contact angles of OTS-functionalized 235 nm SiO2 particle monolayers exposed to RF Ar/O2 plasma for progressively longer times are reported: due to the oxidation of the OTS monolayer, contact angles are progressively lower.

15 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 40

SFE (mN/m) γLW (mN/m) γ+ (mN/m) γ-(mN/m) 22.0±0.5

21.8±0.4

0.1±0.1

0.2±0.1

24.8±1.7

23.2±0.8

0.6±0.4

1.0±0.5

37.4±1.4

34.2±0.3

0.2±0.1

14.3±0.6

41.6±1.4

36.1±0.3

0.4±0.2

18.5± 0.8

51.3±1.5

38.7±0.1

1.3±0.2

30.1±1.1

58.7 ±2.1

38.9±0.2

2.9±0.5

34.4±0.6

64.0±0.9

39.3±0.2

3.3±0.2

45.7±0.5

Table 1. SFE and the corresponding apolar (γLW), acid (γ+) and basic (γ-) components measured with the three-liquids method on flat OTS functionalized substrates (SFE = 22.0 mN/m), on plasma-treated OTS-functionalized flat substrates (24.8 mN/m ≤ SFE ≤ 58.7 mN/m) and on piranha-treated flat substrate (SFE = 64.0 mN/m).

16 ACS Paragon Plus Environment

Page 17 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Fig. 2. Water contact angles on nano-curved and flat substrates (a) and the difference between measured water contact angles on nano-curved and flat substrates as a function of SFE (b). Glycerol contact angles on nano-curved and flat substrates (c) and the difference between measured glycerol contact angles on nano-curved and flat substrates as a function of SFE (d). Tricresyl phosphate (TCP) contact angles on nano-curved and flat substrates (e) and the difference between measured TCP contact angles on nanocurved and flat substrates as a function of SFE (f). The difference between measured contact angles on nano-curved and flat substrates is, for water and glycerol, positive at low SFEs and negative at high SFEs, suggesting a transition from Cassie-Baxter to Wenzel behavior with increasing SFE.

17 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Once the SFE is determined, the direct comparison of nano-curved and flat substrates wettability can be performed for the three reference liquids (Fig. 2), providing new insights on the wettability evolution of nano-curved substrates with SFE. Interestingly, the apparent contact angle, that is, the contact angle measured on nano-curved substrates, markedly depends on both the SFE and wetting liquid. In particular, the apparent contact angle evolves from higher to lower than the flat case for water and glycerol with increasing SFE while, when tricresyl phosphate (TCP) is spread, the apparent contact angle is basically always higher or equal to the flat case. This effect is highlighted in Figures 2b,d,f, where the difference between the contact angle measured on nano-curved and flat substrates is reported as a function of SFE, showing – for water and glycerol – a transition from positive to negative values while – for the TCP case – the difference is always positive or almost zero. The value of the apparent contact angle is closely linked to the wetting behavior and, in this framework, two limiting regimes are possible. According to the Wenzel model, the liquid fully wets the nanostructured substrates38 resulting in an apparent contact angle θW:

18 ACS Paragon Plus Environment

Page 18 of 40

Page 19 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

𝑐𝑜𝑠𝜃𝑊 = 𝑟 𝑐𝑜𝑠𝜃

(6)

where θ is the contact angle the liquid forms when spread on a flat substrate while r is the ratio of the actual area of contact between the solid and the liquid and the normally projected area (e.g., the area of contact between the liquid and a flat substrate). On the contrary, the Cassie-Baxter model assumes the formation of a composite interface where the liquid is in contact with both the nanostructured substrate and the air bubbles trapped between the nanostructures,39 as a consequence, the apparent contact angle θCB is given by:

𝑐𝑜𝑠𝜃𝐶𝐵 = 𝑓 ― 1 + 𝑓𝑐𝑜𝑠𝜃

(7)

where θ is the contact angle the liquid forms when spread on a flat substrate while f is the fraction of the surface where the liquid and the solid are in contact. Typically, excluding when θ>>90°, θCB> θW

23,

especially if θ