Jeffrey J. Schwartz

The viscoelastic response of phase-separated polymers systems may deviate from bulk values at the nanoscale. However, current measurement techniques lack the resolution to unmask local variations. We previously demonstrated the advantages of using a focused, pulsed infrared (IR) laser to photothermally heat a sample locally during nanomechanical measurements with an atomic force microscope (AFM), with heating controlled by varying the laser repetition rate. Herein, we demonstrate this IR heating coupled with nano-Dynamic Mechanical Analysis (nDMA). First, we measured the storage and loss modulus of a homogenous copolymer at varying IR repetition rates (i.e., at varying sample temperature), demonstrating a viscoelastic modulus response that is typical near the glass transition temperature. Further, we varied the IR laser repetition rate while modulating the AFM probe between 5 Hz and 100 Hz. With time-temperature superposition, modulus master curves were constructed through the Williams-Landel-Ferry relation, and the shift factors of IR heating-coupled nDMA curves were used to estimate the relation between IR repetition rate and surface temperatures. Lastly, this technique was applied to a phase-separated polymer blend to demonstrate the utility of the technique to decouple the viscoelastic behavior of different phases by leveraging the high spatial resolution of AFM.

By transducing a sample’s photothermal expansion and contraction, the photothermal induced resonance technique (PTIR, also known as AFM-IR) enables characterization of light absorption at scales (≈10 nm) well below the limits imposed by far-field diffraction. However, AFM-IR depth sensitivity on heterogeneous samples remains poorly understood, making quantitative analyses challenging. Here, we examine stratified, three-dimensionally printed, polymer heterostructures engineered to elucidate the AFM-IR signal dependence on detection frequency, light polarization, and measurement modality (i.e., on- or off-resonance). Results show that the signal intensity, derived from absorption in the topmost layer (here, an epoxy-based prism), increases nearly linearly with its thickness regardless of detection frequency or resonance condition, aligning with previous observations in homogeneous (non-stratified) samples. However, the signal from the bottom layer (here, an acrylic photopolymer resin disk beneath the epoxy prism) can be amplified, attenuated, or remain unchanged, depending on the detection frequency and measurement modality. On-resonance, the signal coming from absorption in the bottom, acrylic layer always decays approximately exponentially with the thickness of the top, epoxy layer, with a frequency-dependent decay rate. Notably, absorption from the acrylic layer was detected even beneath the thickest epoxy region (here, ≈440 nm) for all measurement conditions, highlighting the considerable subsurface sensitivity of AFM-IR. We propose adopting a ≈95% signal decay as a convention to describe a practical AFM-IR measurement depth sensitivity (probed depth), as opposed to the previously suggested ≈63% decay. This work advances AFM-IR-based nanoscale chemical imaging by elucidating the relationship between signal attenuation and sample stratification, which represents a critical step toward more-quantitative and three-dimensional compositional analyses.

Photothermal induced resonance (PTIR), also known as atomic force microscopy-infrared (AFM-IR), enables nanoscale IR absorption spectroscopy by transducing the local photothermal expansion and contraction of a sample with the tip of an atomic force microscope. PTIR spectra enable material identification at the nanoscale and can measure sample composition at depths >1 μm. However, implementation of quantitative, multivariate, nanoscale IR analysis requires an improved understanding of PTIR signal transduction and of the intensity dependence on sample characteristics and measurement parameters. Here, PTIR spectra measured on three-dimensional printed conical structures up to 2.5 μm tall elucidate the signal dependence on sample thickness for different IR laser repetition rates and pulse lengths. Additionally, we develop a model linking sample thermal expansion dynamics to cantilever excitation amplitudes that includes samples that do not fully thermalize between consecutive pulses. Remarkable qualitative agreement between experiments and theory demonstrates a monotonic increase in the PTIR signal intensity with thickness, with decreasing sensitivities at higher repetition rates, while signal intensity is nearly unaffected by laser pulse length. Although we observe slight deviations from linearity over the entire 2.5 μm thickness range, the signal's approximate linearity for bands of sample thicknesses up to ≈500 nm suggests that samples with comparably low topographic variations are most amenable to quantitative analysis. Importantly, we measure absorptive undistorted profiles in PTIR spectra for strongly absorbing modes, up to ≈1650 nm, and >2500 nm for other modes. These insights are foundational toward quantitative nanoscale PTIR analyses and material identification, furthering their impact across many applications.

Hyperbolic phonon polaritons (HPhPs), hybrids of light and lattice vibrations in polar dielectric crystals, empower nanophotonic applications by enabling the confinement and manipulation of light at the nanoscale. Molybdenum trioxide (α‐MoO ₃ ) is a naturally hyperbolic material, meaning that its dielectric function deterministically controls the directional propagation of in‐plane HPhPs within its reststrahlen bands. Strategies such as substrate engineering, nano‐ and hetero‐structuring, and isotopic enrichment are being developed to alter the intrinsic dielectric functions of natural hyperbolic materials and to control the confinement and propagation of HPhPs. Since isotopic disorder can limit phonon‐based processes such as HPhPs, here we synthesize isotopically enriched ⁹² MoO ₃ ( ⁹² Mo: 99.93 %) and ¹⁰⁰ MoO ₃ ( ¹⁰⁰ Mo: 99.01 %) crystals to tune the properties and dispersion of HPhPs with respect to natural α‐MoO ₃ , which is composed of seven stable Mo isotopes. Real‐space, near‐field maps measured with the photothermal induced resonance (PTIR) technique enable comparisons of in‐plane HPhPs in α‐MoO ₃ and isotopically enriched analogs within a reststrahlen band (≈820 cm ⁻¹ to ≈972 cm ⁻¹ ). Results show that isotopic enrichment (e.g., ⁹² MoO ₃ and ¹⁰⁰ MoO ₃ ) alters the dielectric function, shifting the HPhP dispersion (HPhP angular wavenumber × thickness vs. IR frequency) by ≈−7 % and ≈+9 %, respectively, and changes the HPhP group velocities by ≈±12 %, while the lifetimes (≈3 ps) in ⁹² MoO ₃ were found to be slightly improved (≈20 %). The latter improvement is attributed to a decrease in isotopic disorder. Altogether, isotopic enrichment was found to offer fine control over the properties that determine the anisotropic in‐plane propagation of HPhPs in α‐MoO ₃ , which is essential to its implementation in nanophotonic applications.

Thermal fluctuations often impose both fundamental and practical measurement limits on high-performance sensors, motivating the development of techniques that bypass the limitations imposed by thermal noise outside cryogenic environments. Here, we theoretically propose and experimentally demonstrate a measurement method that reduces the effective transducer temperature and improves the measurement precision of a dynamic impulse response signal. Thermal noise–limited, integrated cavity optomechanical atomic force microscopy probes are used in a photothermal-induced resonance measurement to demonstrate an effective temperature reduction by a factor of ≈25, i.e., from room temperature down as low as ≈12 K, without cryogens. The method improves the experimental measurement precision and throughput by >2×, approaching the theoretical limit of ≈3.5× improvement for our experimental conditions. The general applicability of this method to dynamic measurements leveraging thermal noise–limited harmonic transducers will have a broad impact across a variety of measurement platforms and scientific fields.

Photothermal induced resonance (PTIR), also known as AFM-IR, enables nanoscale infrared (IR) imaging and spectroscopy by using the tip of an atomic force microscope to transduce the local photothermal expansion and contraction of a sample. The signal transduction efficiency and spatial resolution of PTIR depend on a multitude of sample, cantilever, and illumination source parameters in ways that are not yet well understood. Here, we elucidate and separate the effects of laser pulse length, pulse shape, sample thermalization time (τ), interfacial thermal conductance, and cantilever detection frequency by devising analytical and numerical models that link a sample's photothermal excitations to the cantilever dynamics over a broad bandwidth (10 MHz). The models indicate that shorter laser pulses excite probe oscillations over broader bandwidths and should be preferred for measuring samples with shorter thermalization times. Furthermore, we show that the spatial resolution critically depends on the interfacial thermal conductance between dissimilar materials and improves monotonically, but not linearly, with increasing cantilever detection frequencies. The resolution can be enhanced for samples that do not fully thermalize between pulses (i.e., laser repetition rates ≳ 1/3τ) as the probed depth becomes smaller than the film thickness. We believe that the insights presented here will accelerate the adoption and impact of PTIR analyses across a wide range of applications by informing experimental designs and measurement strategies as well as by guiding future technical advances.

By combining capabilities of atomic force microscopy (AFM) with infrared (IR) spectroscopy, AFM-IR resolves nanoscale compositional details. This tutorial reviews technical breakthroughs, working principles, best practices, and future prospects of AFM-IR.

Hyperbolic phonon polaritons (HPhPs) enable strong confinements, low losses, and intrinsic beam steering capabilities determined by the refractive index anisotropy—providing opportunities from hyperlensing to flat optics and other applications. Here, two scanning-probe techniques, photothermal induced resonance (PTIR) and scattering-type scanning near-field optical microscopy (s-SNOM), are used to map infrared (6.4–7.4 µm) HPhPs in large (up to 120 × 250 µm2) near-monoisotopic (>99% 10B) hexagonal boron nitride (hBN) flakes. Wide (≈40 µm) PTIR and s-SNOM scans on such large flakes avoid interference from polaritons launched from different asperities (edges, folds, surface defects, etc.) and together with Fourier analyses (0.05 µm−1 resolution) enable precise measurements of HPhP lifetimes (up to ≈4.2 ps) and propagation lengths (up to ≈25 and ≈17 µm for the first- and second-order branches, respectively). With respect to naturally abundant hBN, we report an eightfold improved, record-high (for hBN) propagating figure of merit (i.e., with both high confinement and long lifetime) in ≈99% 10B hBN, achieving, finally, theoretically predicted values. We show that wide near-field scans critically enable accurate estimates of the polaritons’ lifetimes and propagation lengths and that the incidence angle of light, with respect to both the sample plane and the flake edge, needs to be considered to extract correctly the dispersion relation from the near-field polaritons maps. Overall, the measurements and data analyses employed here elucidate details pertaining to polaritons’ propagation in isotopically enriched hBN and pave the way for developing high-performance HPhP-based devices.

Hyperbolic phonon polaritons (HPhPs) are hybrid excitations of light and coherent lattice vibrations that exist in strongly optically anisotropic media, including two‐dimensional materials (e.g., MoO ₃ ). These polaritons propagate through the material’s volume with long lifetimes, enabling novel mid‐infrared nanophotonic applications by compressing light to sub‐diffractional dimensions. Here, the dispersion relations and HPhP lifetimes (up to ≈12 ps) in single‐crystalline α‐MoO ₃ are determined by Fourier analysis of real‐space, nanoscale‐resolution polariton images obtained with the photothermal induced resonance (PTIR) technique. Measurements of MoO ₃ crystals deposited on periodic gratings show longer HPhPs propagation lengths and lifetimes (≈2×), and lower optical compressions, in suspended regions compared with regions in direct contact with the substrate. Additionally, PTIR data reveal MoO ₃ subsurface defects, which have a negligible effect on HPhP propagation, as well as polymeric contaminants localized under parts of the MoO ₃ crystals, which are derived from sample preparation. This work highlights the ability to engineer substrate‐defined nanophotonic structures from layered anisotropic materials.