14 Scientific Article The Israel Chemist and Chemical Engineer Issue 8 · November 2021 · Kislev 5782 atomic force microscopy (AFM) in a single microscope, applicable at high pressures. Furthermore, static microspectroscopy measurements have been performed in gaseous environments with spatial resolutions of down to 20–30 nm . Notable efforts from catalysis company Haldor Topsøe include a focus on advancing high-resolution transmission electron microscopy (HR-TEM) for heterogeneous catalysis applications [20, 21]. Nevertheless, these approaches still often study model materials, such as single crystal slabs, rather than industrial catalysts, which contain mesopores, micropores and even nanopores, and are combinations of several different materials, including for example promotors. Furthermore, while temperature may be (slightly) increased, pressure is disregarded, or vice versa. The operando spectroscopy approach is an approach that is gaining more and more traction after its introduction approximately 20 years ago , particularly due to these considerations. The operando spectroscopy approach is to study a catalyst at work, under reaction conditions, and while quantifying the products in order to ensure relevance. Nevertheless, this approach is plagued (at least) by the problems 1–3 listed above. 2. Modulated excitation spectroscopy 2.1 Principles and background A possible way to overcome these limitations is by taking the working principle of lock-in amplifiers. Lock-in amplifiers are among the most widely used general tools in physics and engineering labs, generally used to measure the amplitude and phase of an oscillating electrical system or, more specifically, to extract a very small electronic measurement signal from e.g., the utility frequency of -50-60 MHz by use of a known carrier-wave frequency. The working principle is to take the input signal along with the unwanted noise, combine it with a known reference signal and put this through a frequency mixer, after which the desired frequency is filtered out using an adjustable low-pass filter. This entire principle of mixing, and filtering is called phase-sensitive detection (PSD) . This phase-sensitive detection follows the following equation [24-28]: (1) with A, the original signal as a function of energy E and time t, ФPSD the modulation phase angle, k the harmonic (k = 1, fundamental harmonic), and T = 1/ω as the demodulation period, see also Figure 2. Steps have been made to combine the methodology with relevant systems in simple heterogeneous catalytic systems, most notably by spectroscopists at the Swiss Light Source, such as Ferri and Nachtegaal [27,29]. The “phase-sensitive” phrasing stems from the principle that (aside from any component which has a different frequency than the reference signal) any out-of-phase component which has the same frequency as the reference signal is attenuated, which can mathematically be explained by the functional orthogonality of sine functions. That is, if you multiply a sine with a cosine function it is attenuated. As Fourier’s theorem states that any function can be described as the sum of sine and cosine functions, one might expect the cosine to also appear in Eq. 1. However, by the addition of the phase shift and phase angle components to Eq. 1 this Fourier property can be simulated manually and therefore manipulated. 2.2 Uses and examples in catalysis One might deduce from the explanation of the lock-in amplifier that the addition of a known reference signal to a noisy system allows for the demodulation of very small signal fractions (see point 1 in Section 1.1 above). Let the signal in this case be the convoluted spectroscopic signal from a catalytically active supported Pt nanoparticle system, and the known reference signal be a periodic excitation of this system with alternating gas pulses; O2 and CO. The frequency of the external stimulation ω and the demodulation phase angle Φk PSD (which in practice is an arbitrary input) are applied leading to the attenuation of all components of the original signal that do not follow ω , such as the contribution of “spectator” signal (the spectral species which are present but do not partake in the reaction). For example, upon the examination of this hypothetical Pt system with hard-X-rays, we can cancel the signal from inorganic atoms that comprise the bulk of the Pt nanoparticles (in the case that they do not respond to the external gas stimulation) or, by using infrared spectroscopy, we can distinguish between vibrations from active and inactive organic catalytic intermediates thereby elucidating side reactions from the main active reaction pathways (see, for example, Figure 3). Figure 2. A scheme showing the principle behind modulated-excitation spectroscopy.