Aggregation Control of α‑Sexithiophene via Isothermal Encapsulation Inside Single-Walled Carbon Nanotubes Etienne Gaufrès,† Nathalie Y.-W. Tang,† Alexandre Favron,‡ Charlotte Allard,§ François Lapointe,† Vincent Jourdain,∥ Saïd Tahir,∥ Colin-Nadeau Brosseau,‡ Richard Leonelli,‡ and Richard Martel*,† †
Regroupement Québécois sur les Matériaux de Pointe (RQMP) and Département de Chimie and ‡Département de Physique, Université de Montréal, Montréal, Quebec H3C 3J7, Canada § Département de Génie Physique, Polytechnique Montréal, Montréal, Quebec H3C 3A7, Canada ∥ Laboratoire Charles Coulomb (L2C) UMR 5221, CNRS-Université de Montpellier, Montpellier 34090, France S Supporting Information *
ABSTRACT: Liquid-phase encapsulation of α-sexithiophene (6T) molecules inside individualized single-walled carbon nanotubes (SWCNTs) is investigated using Raman imaging and spectroscopy. By taking advantage of the strong Raman response of this system, we probe the encapsulation isotherms at 30 and 115 °C using a statistical ensemble of SWCNTs deposited on a oxidized silicon substrate. Two distinct and sequential stages of encapsulation are observed: Stage 1 is a one-dimensional (1D) aggregation of 6T aligned head-to-tail inside the nanotube, and stage 2 proceeds with the assembly of a second row, giving pairs of aligned 6Ts stacked together side-by-side. The experimental data are fitted using both Langmuir (type VI) and Ising models, in which the single-aggregate (stage 1) forms spontaneously, whereas the pair-aggregate (stage 2) is endothermic in toluene with formation enthalpy of ΔHpair = (260 ± 20) meV. Tunable Raman spectroscopy for each stage reveals a bathochromic shift of the molecular resonance of the pair-aggregate, which is consistent with strong intermolecular coupling and suggestive of J-type aggregation. This quantitative Raman approach is sensitive to roughly 10 molecules per nanotube and provides direct evidence of molecular entry from the nanotube ends. These insights into the encapsulation process guide the preparation of well-defined 1D molecular crystals having tailored optical properties. KEYWORDS: carbon nanotubes, dyes, aggregation, liquid-phase encapsulation, isotherms, α-sexithiophene, Raman spectroscopy and imaging encapsulated dyes against photobleaching16 or oxidation when exposed to a harsh chemical environment.17 In addition, we have reported the presence of giant resonances in the Raman scatterings of the dye’s vibrational modes on rod-like dyes, e.g., α-sexithiophene (6T) and β-carotene, encapsulated inside single-walled carbon nanotubes (SWCNTs).17 Importantly, a recent report on enhanced nonlinear responses in asymmetric dyes encapsulated into SWCNTs has widened the interest for nonlinear optics.18 While these studies have highlighted novel properties of these photoactive assemblies, the encapsulation process of large dyes inside SWCNTs remains mostly
T
he molecular adsorption on nanopatterned surfaces is key to a wide range of fields and provides control over molecular aggregation, which can significantly impact the chemical and physical properties of the material. Carbon nanotubes (CNT) have emerged in this context as an intriguing template for the formation of new hybrid nanostructures.1 Because of their cylindrical inner cavity, filling CNTs with small molecules, such as H2,2 N2/Ar,3 Kr/He,4 H2O,5,6 and C60,1,7 has inspired various applications, such as water filtration,8 nanotube doping,9 drug delivery,10 and so forth. More specifically, the encapsulation of large chromophores in CNTs has raised interest for optical applications. It can be used for instance to photosensitize luminescent CNTs11−13 and to enhance light− matter interaction in CNT-based light-harvesting devices,14 albeit a reduced cross section is noted in the mid-IR due to screening.15 Interestingly, the nanotube shell can protect the © 2016 American Chemical Society
Received: August 22, 2016 Accepted: October 25, 2016 Published: October 25, 2016 10220
DOI: 10.1021/acsnano.6b05660 ACS Nano 2016, 10, 10220−10226
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ACS Nano unexplored and calls for the development of sensitive methods that can quantitatively determine and control the filling, orientation, and aggregation states of the dyes. The confinement effects induced by the inner cavity of a SWCNT influence molecular adsorption through spatial and energetic constrains. For small molecules, e.g., Ar and Kr, relative to the size of the CNT cavity, the encapsulation studies have shown evidence of capillary condensation and multilayer formation, giving a nearly ideal two-dimensional (2D) adsorption behavior.19,20 For large molecules, however, higher confinement and van der Waals interactions further restrain molecular motions and force the encapsulation to become onedimensional (1D). While the crossover from 2D to 1D has been extensively studied theoretically and in bulk samples,21,22 the high aspect ratio of the CNT nanotemplate generates various energetically favorable adsorption sites located on the inner or outer interfaces that complicate the specific investigation of the encapsulation process.23 Here, we address this issue using individualized and isolated SWCNTs filled with various amounts of α-sexithiophene. Thanks to the giant Raman cross-section of 6T inside SWCNT (6T@SWCNTs),17 the filling fraction of 6T in a SWCNT can be measured experimentally from individual nanotubes at different temperatures and concentrations, providing quantitative data to examine in detail the encapsulation isotherms in the liquid phase. Our results show that 6T molecules encapsulate by the nanotube ends and form well-aligned rows of molecules aggregated inside SWCNTs, starting from the ends toward the middle. The encapsulation vs concentration proceeds in two sequential stages before maximum filling is reached. The first stage is a spontaneous 1D adsorption process of a singleaggregate of molecules aligned head-to-tail inside the nanotube. The second is an endothermic process that produces a pairaggregate of 6T inside the SWCNT. From the bathochromic shift in the Raman resonance profile of the pair-aggregate, we argue that the pairing process forms long and well-ordered Jaggregates of 6T molecules.
Figure 1. Schematics of a single unit of pair-aggregate and a typical Raman spectrum of 6T@SWCNTs at an excitation wavelength of 532 nm. The intensity is normalized with the signal of the G-band of the SWCNTs.
oriented along the nanotube axis.13,25 These studies have also indicated as much as two 6T molecules stacked side-by-side in a ∼1.3 nm diameter SWCNT. Hence, the encapsulation considered here and depicted in Figure 1 (top panel) proceeds according to a limited number of possible adsorption pathways illustrated in Figure 2. The first is a “two by two” entering/ stacking process of 6T molecules associated with the kinetic constant Kpair‑direct, which leads to the direct formation the pair-
RESULTS AND DISCUSSION Figure 1 shows a typical Raman spectrum of 6T@SWCNTs taken with an excitation wavelength of λex = 532 nm. Most of the experiments discussed below are carried out using laser ablation SWCNTs as templates for encapsulation, and hence the nanotubes diameters are between 1.1 and 1.5 nm.24 The intense peaks at 1450 and 1590 cm−1 arise from the C−C stretching mode of encapsulated 6T molecules and the tangential vibrational modes (G-band) of the semiconducting carbon nanotube, respectively. From our past study,17 we hypothesize that the Raman spectrum can be used to estimate quantitatively the relative filling factor (R6T) of 6T inside a SWCNT. This is done using the ratio R6T = I6T/IG, where I6T is the 6T-band intensity at 1450 cm−1 and IG is the G-band intensity at 1590 cm−1, from many individualized and resonant SWCNTs in a given condition of encapsulation. This approach is justified by two main arguments: (i) Encapsulated 6T molecules are well aligned along the nanotube axis, which is evidenced by the maximum polarization dependency of the 6T signal when the laser polarization is parallel to the nanotube axis; and (ii) the Raman cross-section from the 6T is comparable to that of SWCNT. Previous experiments with high-resolution transmission electron microscopy (HRTEM) have shown that the 6T molecules inside SWCNTs form head-to-tail assemblies
Figure 2. Possible encapsulation pathways for single and paired aggregates of 6T into SWCNTs. The four processes are controlled by the equilibrium constant Kpair‑direct, Ksingle, Kpair, and Ksingle‑pair. 10221
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Figure 3. Color-coded hyperspectral Raman images at 532 nm of aligned SWCNTs transferred onto SiO2/Si substrates. Intensity of the SWCNT G-band at 1590 cm−1 (Green) and of the 6T vibrational mode at 1450 cm−1 (Red) measured after partial (a,b) and full (c) encapsulation experiments.
Figure 4. (a) Raman ratio R6T at 532 nm of SWCNTs encapsulated vs concentration of α-sexithiophene in toluene at 30 and 115 °C. (b) Log− log plot of the data set to emphasize the behavior at low concentrations.
Interestingly, experiments produced cases of partial encapsulation at the nanotube ends and others without any noticeable encapsulation. The partial encapsulations are probably due to a clogging of the nanotube ends by polymer residues left during processing. These experiments reveal that 6T aggregates tend to cluster together from the entrance toward the middle of the nanotubes (e.g., Figure 3b). No case of encapsulation through sidewall defects is observed, which indicates that the CNTs have good structural quality. From all of these experiments, we conclude that dyes molecules encapsulate through the large openings at the nanotube ends and assemble in two segments forming long and continuous aggregate inside the SWCNT. Encapsulation isotherms (Figure 4) were acquired using a slightly different experimental protocol. Briefly, the encapsulation was carried out on a large ensemble of isolated SWCNTs deposited on a silicon oxide surface (SiO2/Si). The length and diameter distributions of the laser-ablation SWCNTs range from 0.5 and 3 μm and 1.1 and 1.5 nm, respectively. Samples of uniformly distributed SWCNTs were used to ensure good consistency between measurements. The samples are immersed in a solution of 6T in toluene at various temperatures, T, and concentrations, C, during 10 min, which corresponds to the minimum time required to reach near equilibrium (Figure S2). The procedure is further detailed in the Supporting Information and involved the preparation of roughly one hundred samples. The R6T value is averaged over three different
aggregates (Figure 2a). Another scenario is the sequential formation of a single row (Figure 2b), driven by the constant Ksingle, followed by the formation of the pair-aggregate. By itself, this second step can occur via two different routes: The first is the stacking of new molecules on top of an existing single row (Kpair, Figure 2c), and the other corresponds to an internal reorganization of the molecules from the single aggregate already formed in the SWCNT (Ksingle‑pair) (Figure 2d). Using Raman imaging, we first explored the encapsulation from major entry points, which are located at the nanotube ends or near sidewall defects. To do so, we used long, aligned, and naturally closed-end SWCNTs that were previously synthesized by CVD on quartz and transferred on a oxidized silicon (SiO2/Si) substrate.26 A section of the SWCNT array was processed by electron-beam lithography followed by plasma etching and annealed for 1 h at 800 °C in vacuum (Supporting Information A-1 and Figure S1). The liquid-phase encapsulation step was performed in toluene at 115 °C using a concentration of 2 × 10−6 M. SWCNTs were then imaged by Raman spectroscopy at a wavelength of 532 nm using a hyperspectral global imaging instrument (RIMA). Figure 3 shows multispectral Raman images extracted from the stack of the intensity plots of the bands at 1450 cm−1 (6T-band) and 1590 cm−1 (G-band), recorded after different encapsulation experiments. SWCNTs of lengths between 10 and 140 μm exhibit complete and homogeneous encapsulation (Figure 3c). 10222
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ACS Nano samples with five measurements each, taken in different areas (i.e., 15 spectra per data points) and fixed acquisition time of 60 s per spectrum using our custom-built microRaman system. This procedure was thoroughly tested to yield consistent results with a standard deviation of 5%. Note that not all SWCNTs are Raman active at 532 nm and that surface coverage may vary from one region to another (Figure S3). That is, for the laserablation SWCNTs used here, only semiconducting ones are in resonance at 532 nm, which constitutes roughly 2/3 of all available chiralities.27 Moreover, the density of deposited SWCNTs slightly influences the time needed to reach equilibrium, and the reason for that is unclear (Figure S4). Hence, we exerted careful control over the deposition density of nanotubes and systematically characterized the surface coverage by atomic force microscopy (AFM) before the encapsulation experiments (Figure S4). Considering that the laser spot of our apparatus has a diameter of ∼600 nm and that roughly 500 molecules of 6T (pair-aggregate) can physically fit inside a 600 nm-long SWCNT, the maximum value of R6T corresponds to ∼500 molecules of 6T per SWCNT. Moreover the signal-to-noise ratio obtained after 60 s of acquisition is 70, which indicates that a minimum variation of 7 molecules per SWCNT is needed to gain a noticeable variation of R6T. This sets roughly the sensitivity limit of our method to about 10 dye molecules per nanotube. Next, we use the R6T ratio at 532 nm to study the encapsulation as a function of 6T concentration (C6T) in toluene and temperature. We follow R6T at two different temperatures, i.e., 30 and 115 °C, and various concentrations between 1 × 10−8 M and 1 × 10−5 M. Solutions concentrations were previously monitored using well-calibrated fluorescence measurements (Figure S5). Figure 4a shows the evolution of the Raman R6T with respect to C6T at each temperature, and Figure 4b highlights the low concentration region. At 30 °C, the isotherm shows a rapid increase of R6T until 2 × 10−7 M and reaches a quasi plateau at R6T between 0.1 and 0.2. At 115 °C, the isotherm curve begins with R6T values that overlap those obtained at 30 °C until 2 × 10−7 M. After this point, a distinct kink appears, followed by a sharp increase of the R6T value which then levels off at about R6T = 0.8. The C6T = 2 × 10−7 M is particularly interesting since it marks a transition between two regimes, and we will refer to this concentration as C1. In the region below C1, the same evolution of R6T for the two temperatures indicates a direct (spontaneous) encapsulation process in this region. This spontaneous mechanism is consistent with previous simulations of encapsulation of large molecules inside carbon nanotubes.28,29 Above C1, a second step is indicative of another phase characterized by a second saturation plateau near R6T = 0.8, which appears to be thermally activated. The general form of this encapsulation isotherm suggests a sequential formation of a monolayer (single) followed by a bilayer (pair) of 6T molecules. These results suggest that simultaneous growth of single- and pair-aggregates of 6T does not occur in these conditions. To gain further insight on Ksingle‑pair (Figure 2), we devised an experiment in which we limit the number of 6T molecules in SWCNTs. Encapsulations of 6T molecules using the concentration and temperature conditions for monolayers (30 °C, 2 × 10−6 M) or bilayers (115 °C, 2 × 10−6 M) were used to prepare two separate samples consisting of singleaggregates and pair-aggregates, respectively. R6T data measured on those samples after annealing in vacuum from 50 to 500 °C with steps of 50 °C are presented in Figure 5a. For this
Figure 5. (a) Evolution of the Raman ratios (λex = 532 nm) R6T‑pair and R6T‑single vs the annealing temperature under vacuum of singleand pair-aggregates of 6T inside SWCNTs, respectively. (b) Dependence of the Raman ratio (R6T‑pair/R6T‑single) on the excitation laser wavelength.
experiment, statistics were performed as described for the previous set of results, i.e., each value of R6T is averaged over three distinct samples fabricated with the same experimental protocol. For the pair-aggregates, we observe that R6T is constant until 400 °C and decreases abruptly above that temperature, which is probably due to degradation or molecular desorption. For the single-aggregate samples, the same loss in R6T occurs at 400 °C, but an additional effect is observed between 250 and 300 °C. This feature reveals that the signal from the 6T aggregates becomes stronger after an annealing above 250 °C, while the number of 6T remains constant. To elucidate the signal enhancement effect, we measured Raman spectra on single- and pair-aggregate samples of 6T@ SWCNT at excitation energies ranging from 425 to 532 nm (Supporting Information A-2). It is important to keep in mind that the SWCNT resonances are highly sensitive to the excitation energy, so we used the ratio R6T‑single/R6T‑pair of the two aggregation states at each excitation energy (Figure 5b) to determine possible shifts in optical resonances between singleand pair-aggregated samples. The increase of the ratio with the wavelength clearly indicates that the absorption of the double occupancy state is red-shifted compared to that of single occupancy. This shift not only explains the stronger intensity for the pair-aggregate compared to the single one in Raman spectra at 532 nm but also indicates important interaction between adjacent molecules. The 1D nature of the confinement compared to the rod-like geometry of molecules and this bathochromic shift suggest a contribution from J-type aggregation. Furthermore, the redshift explains the peculiar intensity behavior in Figure 4a, i.e., the value of R6T at saturation for the pair-aggregates is about 4 times higher, while the number of 6T molecules in bilayer is only twice as many as in the monolayer, a discrepancy that can be safely ascribed to a red-shifted resonance profile of the pair-aggregate. Finally, no fluorescence emission is measured with up to 420 nm light excitations, which contrasts with previous reports of photoluminescence from 6T@SWCNTs in solution.13 From the annealing experiment, we conclude that a rearrangement from single-aggregate into pair-aggregate takes place above 250 °C. Hence, this internal reorganization occurs at a temperature that is much higher than for the direct pairaggregate formation in toluene, which is observed at a temperature as low as 115 °C (Figure 4). The difference between these two processes implies that Kpair rather than Ksingle‑pair governs the liquid-phase encapsulation of pairaggregates in toluene. Interestingly, the double occupancy 10223
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ACS Nano occurs only when the first layer reaches saturation. Furthermore, we note from Figure 4 that the number of pairaggregates at a given concentration above 10−6 M is higher at 115 °C than at 30 °C, indicating that the pair-aggregates formation is endothermic. To model this encapsulation isotherm, our first approach is to consider the nanometer-sized diameter of the nanotube and a sequential formation of the single- and pair-aggregates in Figure 2. A suitable approximation for the adsorption of 6Ts inside SWCNTs is given by a dual-site Langmuir isotherm (DSL, also called S-shaped isotherm).30 The important parameters of this model are the equilibrium constants Ksingle and Kpair (Figure 2). This model is adapted to our system by adding a Heaviside function, H, which requires a fully formed single layer before the onset of the formation of a pairaggregate:
Figure 6. Evolution of the R6T at 532 nm of encapsulated SWCNTs at the concentration C1 = 2.10−7 M and C2 = 2.10−6 M vs the temperature. Inset: Plot of ln(Kpair) as the function of inverse temperature. The red line is a fit to obtain the formation enthalpy ΔHpair of the pair-aggregate of 6T@SWCNTs.
R 6T = R 6T ‐ single + R 6T ‐ pair =
1 K singlec 1 K pairc +H(C6T ‐ single ‐ sat) A1 1 + K singlec A 2 1 + K pairc (1)
−En = H0 + H1 ∑ εi1 + H2 ∑ εi2 + i
, where c is the concentration, R6T‑single and R6T‑pair are the Raman ratios of single- and pair- aggregations, respectively, and A1 and A2 are constants. As described above, Ksingle is spontaneous in those conditions, while Kpair relies on the formation enthalpy, ΔH:
K pair ∝ e−ΔH / kBT
i
∑
hi , jεiαεjα −
i≥j
∑ Giεi1εi2 i
α = 1,2
(3)
, where H0, H1, and H2 are the free energies of the nanotube sidewall in solution, of the 6T molecules in the single- and pairaggregation states, respectively, hi,j is the interaction energy between two adjacent 6Ts in the same configuration (6Tsingle− 6Tsingle and 6Tpair−6Tpair), and Gi is the formation enthalpy between the single- and pair-aggregates. For nondissociative adsorbates, the expression of H1 and H2 follows the expression Hi = kBT ln(kP), where k is the reaction rate constant and P is the pressure. Figure S7 shows the fit of the Ising isotherms for different temperatures. This interaction model gives a formation enthalpy value ΔH pair = (260 ± 20) meV (Supporting Information B-3), which is close to the ones obtained from the previous isotherm model.
(2)
, where kB is the Boltzmann constant. Fits of the experimental data to eq 1 are shown in Figure 4: The monolayer in gray (dashed line), the pair-aggregate at 30 °C in blue, and the pairaggregate at 115 °C in red. The upper gray dashed curve simulates encapsulation at 200 °C, which is difficult to reach experimentally due to the boiling point of toluene at 120 °C. It nevertheless indicates that the endothermic character of the bilayer formation would induce a saturation of the signal at even lower 6T concentration in this case. The value of Kpair from the fit of the experimental isotherms in Figure 4 gives ΔHpair = (330 ± 100) meV per molecule (Supporting Information B-2 and Figure S6). A more direct measurement of Kpair can be obtained by varying T at a constant concentration using ln(Kpair) = Cte + −ΔH/kBT (from eq 2). To validate the enthalpy obtained through the fits, we measure R6T of various samples encapsulated at the fixed concentrations C1 and C2 as a function of the temperature (Figure 6). From this data set, the slope of ln(Kpair) vs 1/T provides another experimental measure of a formation enthalpy at ΔHpair = (280 ± 50) meV for the pair-aggregates (Supporting Information B-1). This simple model is however incomplete and suffers from the fact that the H function was arbitrarily included for convenience rather than from a direct evidence. Hence, we turn to the Ising model to calculate the total energy of the system by considering all of the interactions between individual 6T molecules and the nanotube. The energy of the system consists of the sum of the Hamiltonians corresponding to the monolayer and bilayer configurations coupled with interaction terms between 6T molecules as described below:
CONCLUSIONS We present, using quantitative Raman spectroscopy, an exhaustive account of the liquid-phase encapsulation of 6T molecules inside isolated SWCNTs and highlight the main paths to control the aggregation state. We have measured two sequential isothermal encapsulation stages of α-sexithiophene molecules in toluene. The filling takes place from the opened ends of the nanotubes and involves first the spontaneous formation of a single row of 6T inside the SWCNT. After or near the saturation of the single row, a second row of 6T molecules assemble with a formation enthalpy of (260 ± 20) meV in toluene. Our study shows that this final state consists of a pair-aggregate of 6T exhibiting a red-shifted resonance profile that is consistent with a collective molecular coupling and suggestive of J-type aggregation. While the physical adsorption of molecules on surfaces is generally described by the Langmuir isotherm or by its derivatives, such as the Brunnauer−Emmett− Teller multilayer or the empirical Dubinin−Radushkevich equations, the two-step adsorption isotherm found here is peculiar and delves itself into the complex nature of molecular interaction in highly confined space. Its sequential feature is interesting because it allows to readily prepare a large quantity 10224
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well as additional results and figures (Raman hyperspectral images, Raman signal with encapsulation time, reproducibility of encapsulation protocol, effect of SWCNT density, calibration of 6T concentration by fluorescence) (PDF)
of long and well-defined aggregates of dyes, e.g., single, paired, or more, using control over the experimental parameters: concentration and temperature.
METHODS The SWCNTs used were produced by laser ablation.24 The SWCNTs were purified using concentrated nitric acid wet chemical oxidation and then thoroughly washed with water filtered on a PTFE filter (1.2 μm pore size). The nanotube residue was then dispersed in dimethylformamide (DMF) (∼0.1 mg SWCNT in 1 mL of DMF), sonicated (cup) for 30 min, and centrifuged at 7000 rpm for 1 h. The supernatant was diluted to obtain a good deposition of SWCNTs and subsequently used for SWCNTs deposition by spin coating onto aminopropyltriethoxysilane-coated (APTES) SiO2/Si substrates. 4‑Aminopropyltriethoxysilane (99%) and α-sexithiophene (6T) (Sigma-Aldrich) were used without further purification. All solvents were reagent grade and used as received. Ultralong SWCNTs were prepared using stripes of iron catalyst nanoparticles deposited on stable temperature-cut (ST-cut) quartz wafers by patterning a layer of S1818 photoresist loaded with a methanol solution of FeCl3, followed by development and calcination steps. Long and aligned SWCNTs were then grown on the ST-cut quartz by catalytic chemical vapor deposition using ethanol as carbon precursor, hydrogen as reducing agent, and argon as gas vector. Transfer of SWCNTs from quartz to SiO2/Si substrates was carried out by a polymeric water-based method using cellulose acetate butyrate (CAB). Electron beam lithography (RAITH e-line at 20 kV) was used to define selected areas on the sample for nanotube opening. After development, the SCWNTs were cut using a reactive ion etching by oxygen plasma (RIE at 100W, 100 mTor, 30 s). The liquid encapsulation of 6T was performed directly on SWCNTs deposited on the Si/SiO2 substrates. The substrate was first annealed under vacuum at 500 °C for 1 h to remove the water inside SWCNTs. Each substrate was cut into 9 small squares of 5 × 5 mm and immediately used for encapsulation. The appropriate concentration of 6T in toluene was prepared, and each solution concentration quantitatively determined by fluorescence (10 mm Quartz cuvette, Horiba Jobin-Yvon Fluorolog-3). The encapsulation was carried out in closed vials with 20 mL of solution at the desired temperature and specified time. The encapsulated sample was then rinsed with toluene and IPA and nitrogen dried before characterization by AFM and Raman spectroscopy. Encapsulation time for ultra-long SWCNTs is 24 h. The AFM images were obtained using a Dimension 3100 scanning probe microscope, and height images were acquired using an intermittent-contact mode using silicon probes of nominal spring constants of 42 N m−1, resonance frequency of ∼320 Hz, and tip radius curvature
