LETTER pubs.acs.org/NanoLett
Stiffness, Strength, and Ductility of Nanoscale Thin Films and Membranes: A Combined WrinklingCracking Methodology Jun Young Chung,† Jung-Hyun Lee,† Kathryn L. Beers, and Christopher M. Stafford* Polymers Division, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
bS Supporting Information ABSTRACT: We establish and validate a measurement method based on wrinklingcracking phenomena that allows unambiguous measurements of three fundamental mechanical properties in nanoscale thin film geometries, including elastic modulus, strength, and fracture strain. In addition to polymer and metal thin films, the method is applied to the active nanolayers of a composite reverse osmosis membrane before and after chlorination, illustrating the ability to detect a ductile-to-brittle transition in these materials indicative of “embrittlement”, a behavior that impairs long-term durability and is detrimental to membrane performance. KEYWORDS: Mechanical properties, nanometrology, nanoscale materials, surface wrinkling, thin-film cracking, membranes
T
he quest to engineer thin layers that are mechanically strong and fracture-resistant requires a comprehensive understanding of their mechanical properties, such as stiffness, strength, and ductility.1 Direct knowledge of these key mechanical properties is needed to provide insight into performance, durability, and underlying degradation mechanisms that may occur over a material’s service life.24 For example, degradation of the thin, fragile polymer layers in certain membrane technologies can lead to the formation of cracks and/or pin-holes, which adversely affects performance.4,5 There is, however, a dearth of information concerning the full mechanical spectrum of these types of thin layers due to the challenge of measuring materials at the nanometer scale. Here we present a combined wrinkling6cracking7 technique as a tool for assessing the mechanical characteristics of nanoscale thin films or membranes. This technique enables the direct determination of a comprehensive set of key mechanical properties previously unobtainable in thin-layer geometries including elastic modulus, strength, and fracture strain. As we show here, our approach is applicable to various polymers and metals and can be used to predict the mechanical robustness of nanoscale thin films or membranes supported by substrates, such as artificial skin, flexible electronics, sensors, fuel cells, and photovoltaics, as well as water/gas separation membranes. An overview of the approach is shown in Figure 1. We transfer a thin rigid film onto a soft, elastomeric substrate and apply an increasing uniaxial tensile strain (ε). At relatively low strains, a critical point is reached where a periodic wrinkling pattern appears parallel to the applied strain with a well-defined wavelength (λ).8 As described previously and extensively investigated, this wavelength can be related to the elastic modulus or stiffness of the film.9 At higher strains, the film begins to crack orthogonal to the strain direction, showing multiple cracks with roughly equal spacing (d) that decreases r 2011 American Chemical Society
with increasing strain. By monitoring the average crack spacing as a function of strain, we can deduce both the fracture strength and onset fracture strain of the film. The ability to measure these three material properties provides key figures of merit for assessing the mechanical characteristics of thin films and membranes. Previous studies have established that at low strains, the wrinkling wavelength can provide a quantitative estimate of the Young’s modulus (Ef) of a thin film by6,9 E̅ f ¼ 3E̅ s
λ 2πhf
3 ð1Þ
where E = E/(1 ν2) is the plane-strain modulus, hf is the film thickness, and ν is the Poisson’s ratio (the subscripts f and s denote the film and substrate, respectively). It has been proven that eq 1 can measure the elastic modulus of glassy films as thin as 5 nm.9 If we apply eq 1 to the wrinkling of the thin active nanolayer (cross-linked aromatic polyamide film having hf ≈ 200 nm) of a composite reverse osmosis (RO) membrane, we obtain Ef = (1.40 ( 0.53) GPa in the dry state and (0.36 ( 0.14) GPa in the hydrated state. This is the first reported measure of the modulus of the active layer of RO or nanofiltration (NF) membranes. While the modulus is a critical material property, it in itself is insufficient to capture the full mechanical behavior of the thin film or membrane. Therefore, we take advantage of the fragility of the film to measure additional properties, such as fracture strength and onset fracture strain. At higher strains (ε > ε*, where ε* is the strain at the onset of cracking), the film begins to Received: May 24, 2011 Revised: June 28, 2011 Published: July 15, 2011 3361
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Figure 1. Overview of the approach used for nanomechanical measurements of thin films and membranes. (a) A model system consisting of a thin rigid film or membrane on a soft elastic substrate. The bottom row represents an optical microscope (OM) image of the cross-linked aromatic polyamide (PA) active layer of a reverse osmosis membrane on a compliant substrate of poly(dimethylsiloxane) (PDMS) (see the Materials and Methods section in Supporting Information). (b,c) Schematic illustrations (top) and representative OM images (bottom) of (b) strain-induced surface wrinkling and (c) thin-film cracking. Arrows indicate the direction of applied tensile strain. (d) A representative 3D image (scan size 280 μm 210 μm) obtained using an optical profilometer (NewView 7300, Zygo).
Figure 2. Average cracking spacing (Ædæ) plotted against the applied strain after the onset of cracking (ε̅ ) for a cracked PA film (thickness ∼200 nm) on a PDMS substrate. Dark-field OM images were used to determine Ædæ. The solid line indicates Ædæ ∼ ε̅ β with β = 1. The subsequent change in fragmentation patterns is shown in the inset OM images (scale bar = 100 μm), where the arrows indicate newly formed cracks that divide the preexisting cracks into two equal pieces.
crack. A representative loglog plot of the average cracking spacing (Ædæ) as a function of the applied strain after the onset of cracking, ε̅ (= ε ε*), is shown in Figure 2, along with dark-field optical microscope (OM) images of the cracked film. The shape of the Ædæ ε̅ curve indicates that Ædæ decreases rapidly in the very early stages of fracture, then decreases with strain in a linear manner at intermediate ε̅ (i.e., Ædæ ∼ε̅ 1), and finally exhibits a weak strain dependence at high ε̅ . The fragmentation process observed in Figure 2 is a common feature of thin-film cracking that occurs during stretching and is well described by a power-law function, Ædæ = cε̅ β, where c is a constant and β is an exponent governing the rate of fragmentation.10 In general, three characteristic fragmentation regimes can be distinguished depending on the rate of fragmentation.10,11 In the first regime, multiple cracks appear at random locations along the film and exhibit a wide distribution in d due to intrinsic defects or heterogeneity in the film. The second regime involves the subsequent division of the fragments at their midpoints (Figure 2, insets), which typically occurs when Ædæ < dc. Here, dc (= 4hfEf/Es) is the critical length over which the stress distribution is uniform along the film.11 In this regime, each
fragment is divided into two subfragments when the strain is doubled (i.e., β ≈ 1), and the distribution in d is relatively narrow. The third fragmentation regime begins when the stress transferred from the substrate is insufficient to break existing fragments further. In this instance, a significant decrease in the fragmentation rate with further stretching results in a minor decrement in Ædæ (i.e., β < 1), indicative of the deviation from the straight line of β = 1 (Figure 2). In this work, we consider only the linear regime of the thinfilm cracking, where the process is well described by the bisection of crack fragments; that is, the average fragment width is inversely proportional to the strain. A schematic diagram of our experimental geometry is shown in Figure 3a. Considering the tensile stress in the thin film (σf) develops a maximum at the midpoint between cracks (x = 0), the average width of fragments is given by7,11,12 Ædæ ¼
2hf σ , when ε > ε and Ædæ < dc Es ε
ð2Þ
where σ* is the fracture strength of the film. In this model, the film is assumed to be well bonded to the substrate so that any slip at the filmsubstrate interface can be neglected. As described by eq 2, Ædæ is inversely proportional to ε̅ , corresponding to β = 1. Equation 2 allows direct estimation of the fracture strength of the film from the slope of the linear region of a plot of crack density (1/Ædæ) versus ε. In addition, extrapolation of the linear portion to zero crack density gives a reliable estimate of onset fracture strain (ε*) without knowing the exact strain at which cracks initiate (see Figure 3b). Here, fracture strength and onset fracture strain are similar to tensile strength and elongation at break determined by conventional tensile tests. These two quantities are measures of the strength and ductility of a material, respectively, which serve as meaningful parameters that are closely related to the damage and/or performance failure of thin-film materials and devices.1315 The general applicability of the thin-film cracking approach is demonstrated on three different material classes: (a) a model system comprised of a thin, amorphous polymer film—atactic polystyrene (PS), (b) a thin metal film—nanocrystalline tantalum (Ta; from literature data10), and (c) the active polymer nanolayer of a commercial RO membrane—cross-linked aromatic polyamide (PA) (see the Materials and Methods section in 3362
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Figure 3. (a) Schematic diagram of the experimental geometry, including a thin rigid film adhered to a semi-infinite soft elastic foundation. The stress field in the film (σf) is assumed to vary from zero at the edge of the film (x = d/2) to a maximum at the center (x = 0) according to σf = (2σf,max/d)(d2/4 x2)1/2. At a critical stress level (i.e., σf,max = σ*), a new crack initiates at the center. (bd) Rescaled crack density (2hf/ÆdæEs) plotted against the applied strain (ε) for (b) PS films with different thickness on PDMS, (c) Ta films with different thickness deposited on polyimide substrates, and (d) five identically prepared PA layers (hf = 203.4 ( 20.8 nm) on PDMS. Solid lines correspond to fits with the linear strain-dependent crack density model. In (c), only the data points that fall in the second regime of fragmentation were selected from ref 10. As indicated in (b,c), no obvious thickness dependence on mechanical properties of Ta and PS thin films was found in the thickness range investigated in this study. (e) Summary of the results obtained for the three material systems.
Supporting Information for details). The data in Figures 3bd show 2hf/ÆdæEs versus ε for each of the case studies. In all cases, the data collapse on a single straight line as predicted by eq 2. From these data, we can calculate the fracture strength (σ*) and onset fracture strain (ε*) for each material, and the results of the analysis are provided in Figure 3e along with the modulus (Ef) obtained from the wrinkling wavelength at low strains. For PS, the measured values compare well to bulk values for PS [tensile strength = (30 to 42) MPa, elongation at break = (1 to 2) %, Ef = (3.0 to 4.5) GPa].16,17 For nanocrystalline Ta, the value of σ* is considerably higher than that reported for bulk Ta (tensile strength ∼350 MPa).18 Recent nanoindentation measurements on such Ta films, however, reveal that the hardness of the thin film is as much as ten times higher than the bulk value (due to finer grain size for the sputter deposited thin films).19 This result, along with the analysis that hardness correlates linearly with tensile strength,20 suggests that the deduced value is reasonably accurate. Such enhanced tensile strengths in metal nanostructures have also been observed in ultrathin metal nanowires.21 For PA, the value of σ* is in a fair agreement with other work, where the rupture strength of cross-linked aromatic PA layers possessing similar chemistry was estimated to be ∼40 MPa using a pendant drop technique.22 Armed with this new measurement capability, we extend our approach to a practical challenge found in membrane technologies. Most engineered membranes must maintain performance over many years and under harsh conditions, such as oxidizing chemical environments, thermal cycling, and mechanical loading.3,2325 For example, desalination/water purification and sustainable power generation technologies based on composite membranes, such as NF, RO, forward osmosis, and
pressure retarded osmosis, rely on a thin polymer active layer (commonly made of PA having thickness typically less than 200 nm) to block the passage of dissolved salts and other impurities while permitting water to pass through.2528 During use, this active layer can undergo chemical degradation due to the introduction of chlorine to prevent membrane fouling.29 In particular, chlorine is known to attack PA through N-chlorination of the amide NH bond and potentially through subsequent chlorination of the aromatic ring via Orton rearrangement.30,31 These reactions can disrupt internal hydrogen bonding and lead to changes in the structure and transport properties of the membrane layer.32,33 However, research has been limited to direct performance measurements aided by chemical analysis using spectroscopic techniques, while mechanical changes in the membrane material have been largely ignored.3,4,25 Figure 4a,b displays dark-field OM images of strained PA nanolayers after treatment with acidic hypochlorite solution (chlorine concentration = 1000 μL/L, pH = 4) at an exposure time (texp) of 6 and 53 h, respectively (see Supporting Information for experimental details). These images indicate that the initiation and growth of fracture cracks under mechanical loading occurs more readily for longer texp. We investigated the mechanical behavior of chlorine-treated PAs for a wide range of time scales (up to 240 h). Figure 4c shows the wrinkling wavelength (normalized by film thickness) as a function of texp, providing a relative measure of the change in stiffness of the membrane layer. Figure 4d shows representative plots of the normalized crack density (2hfσ0*/ÆdæEs) as a function of strain for the PAs treated at four different texp, where σ0* is the fracture strength of the untreated PA. It is evident from Figure 4d that both crack density and onset 3363
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Figure 4. Effects of exposure time (texp) on mechanical properties of chlorine-treated PA nanolayers. (a,b) Illustrative OM images taken at different strains for (a) texp = 6 h and (b) texp = 53 h. The insets shown in the second column represent small-angle light scattering images used to determine wrinkling wavelength (see Supporting Information Figure S1). (c) Wrinkling wavelength, normalized by film thickness, as a function of texp. (d) Representative comparison of the normalized crack density of the chlorine-treated PAs plotted against the applied strain at four different texp. The solid lines represent fits with the linear strain-dependent crack density model given by eq 2.
Figure 5. Change in the three key mechanical properties of PA active nanolayers as a function of chlorine exposure time (texp). (a) Normalized plane-strain modulus, which was calculated from eq 1 for the data shown in Figure 4c. (b) Normalized fracture strength. (c) Normalized onset fracture strain. The subscript 0 refers to the value for the untreated PA (i.e., texp = 0).
fracture strain exhibit a strong texp dependence. Furthermore, the crack density shows a fairly linear variation with strain as given by eq 2. Figure 5 summarizes the measured values of elastic modulus, fracture strength, and onset fracture strain (normalized by each value of the untreated PA) for the chlorine-treated PA nanolayers as a function of texp. As is evident from Figure 5, the extent of chlorine exposure is directly correlated with changes in the three key mechanical properties. Interestingly, the modulus remains fairly constant in the early stage of chlorination (
