[Paper Review] On the plausible nature of the size effect in heterogeneous catalysis on gold nanoparticles

Kamil A. Moldosanov, A. V. Postnikov|arXiv (Cornell University)|Aug 31, 2018

nanoparticles nucleation surface interactions3 references3 citations

TL;DR

The paper proposes that the size-dependent catalytic activity of gold nanoparticles (GNPs) in the 1.3–9 nm range arises from spontaneous terahertz (THz) emission driven by longitudinal acoustic (LA) phonons. When phonon energy is channeled into THz photons, adsorbed molecules on the GNP surface undergo resonant excitation of rotational and vibrational modes, weakening chemical bonds and facilitating surface reactions. The key result is that THz emission efficiency peaks at small sizes (D < 1.3 nm), explaining the observed size effect in catalysis, with activity declining sharply beyond 10 nm due to quasicontinuous phonon spectra that suppress photon emission.

ABSTRACT

We suggest that the size effect in heterogeneous catalysis on gold nanoparticles (GNP) of ~1.3 - 9 nm size can be related to spontaneous terahertz (THz) emission of GNPs in the process of channeling the energy of longitudinal phonons therein into THz electromagnetic radiation. Since rotational and vibrational energy levels of molecules adsorbed on the GNP surface are in the THz range, the irradiation by self-induced THz photons would engage the molecules' swing and twisting, which in its turn would weaken or break the intramolecular bonds, facilitating their entering a chemical reaction on the GNP surface.

Motivation & Objective

• To explain the experimentally observed size effect in gold nanoparticle (GNP) catalysis, where activity peaks for particles 1.3–9 nm and vanishes above 10 nm.
• To propose a novel mechanism linking longitudinal acoustic (LA) phonons in GNPs to terahertz (THz) photon emission as a driver of catalytic activity.
• To analyze how quantum confinement in GNPs affects phonon energy level spacing and its impact on electron-phonon-photon coupling.
• To connect the size-dependent catalytic efficiency to the competition between phonon emission and THz photon emission, governed by energy level quantization and uncertainty principles.

Proposed method

• Modeling GNPs as spherical particles with diameter D to analyze quantization of bulk and surface phonons using momentum and energy uncertainty principles.
• Calculating energy level spacing for bulk phonons as ΔE↔ = hv*L/D and for surface phonons as ΔE∘ = hv*L/(πD), where v*L ≈ 10⁵ cm/s is the reduced sound velocity.
• Applying the Heisenberg uncertainty relation to estimate energy uncertainty δE ≈ v*L h / (2πD) to account for size-induced broadening of energy levels.
• Evaluating the condition for suppressed phonon emission (and thus enhanced THz emission) as ΔE↔ > FWHM + δE, leading to a critical size threshold D ≲ 0.84 h v*L / FWHM.
• Using numerical estimates for D = 1.3 nm and D = 10 nm to compare ΔE↔, δE, and FWHM (≈2.8 meV) to assess the transition from discrete to quasicontinuous phonon spectra.
• Analyzing the role of Fermi-level electrons in absorbing phonon energy and relaxing via radiative (THz photon emission) or non-radiative (phonon emission) channels, with selection governed by energy and momentum matching.

Experimental results

Research questions

• RQ1 Why does catalytic activity of gold nanoparticles peak in the 1.3–9 nm size range and vanish above 10 nm?
• RQ2 How can longitudinal acoustic phonons in GNPs lead to the emission of terahertz (THz) radiation?
• RQ3 What role does quantum confinement play in determining the energy level spacing of phonons and the efficiency of THz photon emission?
• RQ4 How does the interplay between phonon emission and THz photon emission depend on nanoparticle size?
• RQ5 What is the significance of the energy uncertainty δE ≈ v*L h / (2πD) in enabling or suppressing THz emission at different sizes?

Key findings

• For D = 1.3 nm, the phonon energy level spacing ΔE↔ ≈ 3.2 meV is comparable to the FWHM of the LA phonon peak (≈2.8 meV), and with δE ≈ 0.5 meV, the discrete nature of levels suppresses phonon emission, favoring THz photon emission.
• At D = 10 nm, ΔE↔ ≈ 0.4 meV is much smaller than FWHM + δE ≈ 2.9 meV, resulting in a quasicontinuous phonon spectrum that favors non-radiative relaxation and suppresses THz emission.
• The condition D ≲ 0.84 h v*L / FWHM ≈ 1.2 nm defines the size threshold below which phonon emission is effectively blocked, maximizing THz emission and catalytic activity.
• The mechanism explains the experimentally observed size effect: catalytic activity is highest for GNPs below ~5 nm and drops sharply beyond 10 nm due to loss of energy-level quantization.
• The model predicts that THz radiation from GNPs can selectively excite molecular vibrations and rotations, weakening chemical bonds and promoting surface reactions.
• The hypothesis is consistent with experimental evidence of LA phonon peak redistribution in GNPs and supports the idea that size-dependent THz emission is a key factor in heterogeneous catalysis.