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We present a theory that explains the resonance effect of the vibrational strong coupling (VSC) modified reaction rate constant at the normal incidence of a Fabry–Pérot (FP) cavity. This analytic theory is based on a mechanistic hypothesis that cavity modes promote the transition from the ground state to the vibrational excited state of the reactant, which is the rate-limiting step of the reaction. This mechanism for a single molecule coupled to a single-mode cavity has been confirmed by numerically exact simulations in our recent work in [J. Chem. Phys. 159, 084104 (2023)]. Using Fermi’s golden rule (FGR), we formulate this rate constant for many molecules coupled to many cavity modes inside a FP microcavity. The theory provides a possible explanation for the resonance condition of the observed VSC effect and a plausible explanation of why only at the normal incident angle there is the resonance effect, whereas, for an oblique incidence, there is no apparent VSC effect for the rate constant even though both cases generate Rabi splitting and forming polariton states. On the other hand, the current theory cannot explain the collective effect when a large number of molecules are collectively coupled to the cavity, and future work is required to build a complete microscopic theory to explain all observed phenomena in VSC.

This work provides the fundamental theoretical framework for few-mode cavity quantum electrodynamics by resolving the gauge ambiguities between the Coulomb gauge and the dipole gauge Hamiltonians under the photonic mode truncation. We first propose a general framework to resolve ambiguities for an arbitrary truncation in a given gauge. Then, we specifically consider the case of mode truncation, deriving gauge invariant expressions for both the Coulomb and dipole gauge Hamiltonians that naturally reduce to the commonly used single-mode Hamiltonians when considering a single-mode truncation. We finally provide the analytical and numerical results of both atomic and molecular model systems coupled to the cavity to demonstrate the validity of our theory.

Osteoarthritis is a degenerative joint disease that limits mobility of the affected joint due to the degradation of articular cartilage and subchondral bone. The limited regenerative capacity of cartilage presents significant challenges when attempting to repair or reverse the effects of cartilage degradation. Tissue engineered medical products are a promising alternative to treat osteochondral degeneration due to their potential to integrate into the patient's existing tissue. The goal of this study was to create a scaffold that would induce site‐specific osteogenic and chondrogenic differentiation of human adipose‐derived stem cells (hASC) to generate a full osteochondral implant. Scaffolds were fabricated using 3D‐bioplotting of biodegradable polycraprolactone (PCL) with either β‐tricalcium phosphate (TCP) or decellularized bovine cartilage extracellular matrix (dECM) to drive site‐specific hASC osteogenesis and chondrogenesis, respectively. PCL‐dECM scaffolds demonstrated elevated matrix deposition and organization in scaffolds seeded with hASC as well as a reduction in collagen I gene expression. 3D‐bioplotted PCL scaffolds with 20% TCP demonstrated elevated calcium deposition, endogenous alkaline phosphatase activity, and osteopontin gene expression. Osteochondral scaffolds comprised of hASC‐seeded 3D‐bioplotted PCL‐TCP, electrospun PCL, and 3D‐bioplotted PCL‐dECM phases were evaluated and demonstrated site‐specific osteochondral tissue characteristics. This technique holds great promise as cartilage morbidity is minimized since autologous cartilage harvest is not required, tissue rejection is minimized via use of an abundant and accessible source of autologous stem cells, and biofabrication techniques allow for a precise, customizable methodology to rapidly produce the scaffold.