_{1}

^{*}

Context and Background: Recent research has shown that the amount of energy conserved in light-matter interaction is given by the product of light’s power
*P* times its period
*τ* ,
*i.e.*
*Pτ*. To date, evidences of the validity of such finding are restricted to the interaction of light with capacitors, infrared spectroscopy, and vision in vertebrates.
Motivation: In this article, we want to explore the validity of the role of
*Pτ* in a broader range of phenomena.
Hypothesis: We assume that the photothermoelectric (PTE) effect and photoredox catalysis reactions (PCRs) are manifestations of light-matter interaction and therefore have
*Pτ* conserved in the process.
Method: We take the data published in two articles, one on the PTE effect and the other on PCRs and revisit the data analysis of the authors of the original articles considering
*Pτ* as the energy conserved.
Results: In the case of the PTE effect, we unveil that the size of the light’s beam cross-sectional area impinging on the photodetectors plays a major role in defining the performance of the photodetectors. With our analysis, the photodetector responsivities actually turn out to be higher than those reported in the original article. In the case of the PCRs, we find that the magnitude of
*Pτ* involved in successful PCRs is independent of the type of light used, whether near-infrared or blue. In addition, the involvement of
*Pτ* in the description of PCRs helps to clarify the role of the law of conservation of energy, which was neglected by the authors of the original article.
Conclusions: From this study, we infer that the hypothesis that
*Pτ*
that the hypothesis that represents the amount of energy conserved in light-matter interaction is valid and general, useful to measure device performance, and predict alternative processes to achieve desired outcomes.

Recently, experimental evidences regarding the interaction of visible and infrared (IR) light with capacitors [

With our own experiments, we have achieved the evidence that P τ as the energy conserved in light-matter interaction is capable of precisely explaining the numerical outcome of voltage from capacitors illuminated by IR light. This result led us to the inquiry whether the validity of P τ might be extended to phenomena other than the interaction of light with capacitors. Since there exist numerous experiments based on light-matter interaction published in the scientific literature, we decided to make use of them to test the hypothesis on P τ . As we find that the energy P τ efficiently captures the orders of magnitude of the outcomes from both our experiments and those of other authors, we conclude that the concept of photon is not necessary in the analysis of light-matter phenomena. Our review of the literature on light-matter interaction, specifically on the photothermoelectric (PTE) effect [

We assess the ability of P τ to capture the amount of energy conserved in light-matter interaction by revisiting the analysis to experiments on light-matter interaction performed by other authors. We have chosen two experiments, one related to the PTE effect [

The paper by Lu et al. [_{3} (r-STO) based PTE photodetectors, producing high photovoltage responsivity ( π V , i.e. the ratio between the photovoltage produced and the power of the impinging light) and broadband spectral response from 325 nm to 10.57 μm. The authors ascribe the enhanced responsivity to the existence of a Ti-O phonon mode in the long-wavelength infrared region (LWIR), in agreement with findings in the interaction of IR light with thin films [

The data provided by Lu et al. [

The main characteristics of the laser beam used by Lu et al. [

With the assumptions that P τ is the total energy in light-matter interaction, and treating the r-STO PTE photodetector as a capacitor with capacitance C, we use the equation P τ ≅ 1 2 C Δ V 2 to evaluate the energy transferred from the light’s

beam to the photodetectors such that a photovoltage Δ V is produced. This equation agrees with Equations (2a) and (2b) in [

λ (nm) | τ (fs) | P (mW) | r (μm) | ΔV (mV) | π_{V} (V/W) | C (pF) |
---|---|---|---|---|---|---|

325 | 1.08 | 2.3 | 2.5 | 2.6 | 1.13 | 0.74 |

532 | 1.77 | 3.4 | 3 | 2.9 | 0.85 | 1.43 |

785 | 2.62 | 5.1 | 5 | 3.1 | 0.61 | 2.78 |

1550 | 5.17 | 100 | 100 | 57 | 0.57 | 0.32 |

10,570 | 35.23 | 11.6 | 15 | 11 | 0.95 | 4.36 |

expression for P τ given above, and assuming the beam sizes given in [

by Lu et al. [

To achieve our goal of finding a correlation between light’s characteristics and r-STO PTE photodetector outcome in the experiments performed by Lu et al. [

we exploit the direct proportionality between C and A given by C = κ ε 0 A d ,

where ε 0 = 8.854 × 10 − 12 F / m is the permittivity in vacuum, κ is the dielectric constant varying between 1 to 10^{3}, A = π r 2 is the cross-sectional area of the beam hitting the photodetector, and d is the distance between the electrodes, or plates, of the capacitors. The rescaled capacitances are reported in

capacitances C and using Δ V = 2 P τ C , we rescale also the photovoltage Δ V

λ (nm) | τ (fs) | P (mW) | r (μm) | ΔV (mV) | π_{V} (V/W) | C (pF) |
---|---|---|---|---|---|---|

325 | 1.08 | 2.3 | 5 | 1.30 | 0.57 | 2.95 |

532 | 1.77 | 3.4 | 5 | 1.74 | 0.51 | 3.97 |

785 | 2.62 | 5.1 | 5 | 3.10 | 0.61 | 2.78 |

1550 | 5.17 | 100 | 5 | 113.24 | 1.14 | 0.0008 |

10,570 | 35.23 | 11.6 | 5 | 33.01 | 2.85 | 0.48 |

and responsivity π V , both of which are reported in

We can further rescale the photovoltage Δ V and responsivity π V by assuming all r-STO PTE photodetectors to have a spot radius r = 5 μ m and a capacitance C = 2.04 ± 1.47 pF , the average value found from the data in

In

In conclusion, we have found that the use of P τ as the total energy, or the energy conserved, in light’s interaction with an r-STO PTE photodetector enables highlighting the trends in the responsivity as a function of light’s wavelength or period. First, the size of the light’s beam cross-sectional area impinging on the r-STO PTE photodetectors plays a major role in defining the performance of the photodetectors. Then, in agreement with [

λ (nm) | τ (fs) | P (mW) | r (μm) | ΔV (mV) | π_{V} (V/W) | C (pF) |
---|---|---|---|---|---|---|

325 | 1.08 | 2.3 | 5 | 1.56 | 0.68 | 2.04 |

532 | 1.77 | 3.4 | 5 | 2.43 | 0.71 | 2.04 |

785 | 2.62 | 5.1 | 5 | 3.62 | 0.71 | 2.04 |

1550 | 5.17 | 100 | 5 | 22.51 | 0.22 | 2.04 |

10,570 | 35.23 | 11.6 | 5 | 20.02 | 1.72 | 2.04 |

Wavelength λ (nm) | Intensity I (10^{5} W/cm^{2}) |
---|---|

325 | 0.117 |

532 | 0.120 |

785 | 0.065 |

1550 | 0.003 |

10,570 | 0.016 |

The article by Ravetz et al. [

To address the problem of finding the source of Δ E blue-NIR satisfying the law of conservation of energy, we assume that, in light-matter interaction, the total energy, or the energy conserved, is given by the product of light’s power P times

its period τ , i.e. P τ [

P τ as the total energy conserved in PCRs, we collect the information available on light characteristics ( λ , τ and P) of the light sources used by Ravetz et al. [

The first two rows in

The third and fourth rows in

Type | λ (nm) | τ (fs) | P (mW) | Pτ (fJ) | Location within [ |
---|---|---|---|---|---|

Laser diode | 730 | 2.44 | 40 | 0.1 | |

Laser diode | 450 | 1.5 | 1600 | 2.4 | |

LED | ~750 | 2.5 | 15,000 | 37.5 | |

LED | ~460 | 1.53 | 35,000 | 53.55 | |

Laser diode | 730 | 2.44 | 16.8 | 0.041 | |

Laser-diode | 450 | 1.5 | 37.2 | 0.056 |

Finally, the fifth and sixth rows in

The actual values of P τ calculated in reviewing the analysis by Ravetz et al. deserve some comment. Let us pick from _{3}]^{2+}-catalyzed reaction and blue light. First, if the whole amount of 0.056 fJ is needed for the activation of one enone molecule, then we estimate that ≈80 Mcal/mole would be required for enones. This is an enormous amount of energy compared to the standard reaction activation energies, which are of the order of about tens of kcal/mole! Perhaps a mechanism exists that reduces the energy of the absorbed blue light by, e.g.: 1) emission of light at a different wavelength, as mentioned in [

To summarize, we use the characteristics of the light used to activate PCRs by Ravetz et al. [

The evidence so far that the product of light’s power P times its period τ , i.e. P τ , is the amount of energy conserved in light-matter interaction is provided by experiments examining the outcome from capacitors illuminated by light. As such, P τ plays a primary role in the analysis of light-matter interaction because it competes with photons with energy given by Planck’s constant h times light’s frequency ν. Indeed, both P τ and the photon are called into play when conservation of energy is considered in light-matter interaction. However, as the energy P τ and the energy of the photon hν are different in the orders of magnitude, it appears necessary to shed light on which one of the two energies truly satisfies the energy balance in light-matter interaction.

Our research shows results clearly in favor of P τ . Indeed, from the study of the photothermoelectric effect and of photoredox catalysis reactions, we infer that the hypothesis that P τ represents the amount of energy conserved in light-matter interaction is generally true. In addition, through P τ , in the case of the photothermoelectric effect, we unveil that the size of the light’s beam cross-sectional area impinging on the photodetectors plays a major role in defining the performance of the photodetectors. With our analysis, the photodetector responsivities actually turn out to be higher than those reported in the original article. In the case of the photoredox catalysis reactions, we find that the magnitude of P τ involved in successful photoredox catalysis reactions is independent of the type of light used, whether near-infrared or blue. In addition, the involvement of P τ in the description of photoredox catalysis reactions helps to clarify the role of the law of conservation of energy, which was neglected by the authors of the original article.

The hypothesis that P τ represents the amount of energy conserved in light-matter interaction was revealed to be also effective in the interaction of light with capacitors [

The author thanks the Department of Physics and Astronomy of the James Madison University for supporting the research that results in this article.

The author declares no conflicts of interest regarding the publication of this paper.

Scarel, G. (2019) The Role of Pτ in the Photothermoelectric Effect and in Photoredox Catalysis Reactions. World Journal of Condensed Matter Physics, 9, 91-101. https://doi.org/10.4236/wjcmp.2019.94007^{ }