Photochemical Synthesis 

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1. Introduction to Photochemical Synthesis

Photochemical synthesis uses light energy (photons) to drive chemical reactions for the synthesis of nanomaterials, organic molecules, and advanced materials. Light provides an activation energy that initiates reactions under mild conditions (room temperature, ambient pressure) that would otherwise require high temperatures or harsh reagents.

Core Principle: Molecule + $h\nu$ → Excited state → Chemical transformation

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2. Fundamental Photochemistry

2.1 Light Absorption & Excitation

A molecule absorbs a photon only if:

$${\mathrm{<span\; style="font-family:\; georgia;">E</span>}}_{\mathrm{<span\; style="font-family:\; georgia;">p</span>}\mathrm{<span\; style="font-family:\; georgia;">h</span>}\mathrm{<span\; style="font-family:\; georgia;">o</span>}\mathrm{<span\; style="font-family:\; georgia;">t</span>}\mathrm{<span\; style="font-family:\; georgia;">o</span>}\mathrm{<span\; style="font-family:\; georgia;">n</span>}}<span\; style="font-family:\; georgia;">=</span>\mathrm{<span\; style="font-family:\; georgia;">h</span>}\mathrm{<span\; style="font-family:\; georgia;">\nu </span>}<span\; style="font-family:\; georgia;">=</span>\frac{\mathrm{<span\; style="font-family:\; georgia;">h</span>}\mathrm{<span\; style="font-family:\; georgia;">c</span>}}{\mathrm{<span\; style="font-family:\; georgia;">\lambda </span>}}<span\; style="font-family:\; georgia;">\ge </span>\mathrm{<span\; style="font-family:\; georgia;">\Delta </span>}{\mathrm{<span\; style="font-family:\; georgia;">E</span>}}_{\mathrm{<span\; style="font-family:\; georgia;">g</span>}\mathrm{<span\; style="font-family:\; georgia;">a</span>}\mathrm{<span\; style="font-family:\; georgia;">p</span>}}$$

Where:

• $h$ = Planck's constant ($6.626\times {10}^{-34}$ J·s)
• $c$ = speed of light ($3\times {10}^8$ m/s)
• $\lambda$ = wavelength (nm)
• $\mathrm{\Delta }{E}_{gap}$ = energy gap between ground and excited state

Molar absorptivity ($\epsilon$): Measures how strongly a molecule absorbs at a given wavelength (Beer-Lambert Law):

$$\mathrm{<span\; style="font-family:\; georgia;">A</span>}<span\; style="font-family:\; georgia;">=</span>\mathrm{<span\; style="font-family:\; georgia;">\epsilon </span>}\mathrm{<span\; style="font-family:\; georgia;">c</span>}\mathrm{<span\; style="font-family:\; georgia;">l</span>}$$

Where $A$ = absorbance, $c$ = concentration, $l$ = path length

2.2 Jablonski Diagram — Photophysical Processes

rust
Singlet States               Triplet States
S₂ ──────┐
          │ Vibrational
          │ Relaxation
S₁ ──────┤─────────────→ T₁ ──────┐
   │     │     ISC           │     │
   │     │                    │     │
   │  Fluorescence            │  Phosphorescence
   │  (10⁻⁹ s)                │  (10⁻⁶ to 10² s)
   ▼     ▼                    ▼     ▼
S₀ ────────────────────────────────────── Ground State

Process	Timescale	Description
Absorption	${10}^{-15}$ s	$S_0+h\nu \to S_n$
Vibrational relaxation	${10}^{-14}$ to ${10}^{-11}$ s	Loss of excess vibrational energy
Internal conversion (IC)	${10}^{-11}$ to ${10}^{-9}$ s	$S_n\to S_1$ (non-radiative)
Fluorescence	${10}^{-9}$ to ${10}^{-7}$ s	$S_1\to S_0+h{\nu }^{\mathrm{\prime }}$
Intersystem crossing (ISC)	${10}^{-10}$ to ${10}^{-6}$ s	$S_1\to T_1$ (spin flip)
Phosphorescence	${10}^{-6}$ to ${10}^2$ s	$T_1\to S_0+h{\nu }^{\mathrm{\prime }\mathrm{\prime }}$

2.3 Quantum Yield ($\mathrm{\Phi }$)

The efficiency of a photochemical process:

$$\mathrm{<span\; style="font-family:\; georgia;">\Phi </span>}<span\; style="font-family:\; georgia;">=</span>\frac{\text{<span style="font-family: georgia;">Number of molecules transformed</span>}}{\text{<span style="font-family: georgia;">Number of photons absorbed</span>}}$$

• ${\mathrm{\Phi }}_{reaction}$ = quantum yield for product formation
• ${\mathrm{\Phi }}_{fluorescence}$ = quantum yield for fluorescence
• $\mathrm{\Phi }+\text{non-radiative losses}=1$ (energy conservation)

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3. Types of Photochemical Reactions

3.1 Photoreduction

Light-induced reduction of metal ions to form nanoparticles:

$${\mathrm{<span\; style="font-family:\; georgia;">M</span>}}^{\mathrm{<span\; style="font-family:\; georgia;">n</span>}<span\; style="font-family:\; georgia;">+</span>}<span\; style="font-family:\; georgia;">+</span>\text{<span style="font-family: georgia;">electron donor</span>}\stackrel{\mathrm{<span\; style="font-family:\; georgia;">h</span>}\mathrm{<span\; style="font-family:\; georgia;">\nu </span>}}{<span\; style="font-family:\; georgia;">\to </span>}{\mathrm{<span\; style="font-family:\; georgia;">M</span>}}^{\mathrm{<span\; style="font-family:\; georgia;">0</span>}}<span\; style="font-family:\; georgia;">+</span>\text{<span style="font-family: georgia;">oxidized donor</span>}$$

Typical mechanism:

1. Photoexcitation of a photosensitizer or photoreducing agent
2. Electron transfer to metal ions
3. Nucleation and growth of metal nanocrystals

3.2 Photooxidation

Light-induced oxidation:

$$\text{<span style="font-family: georgia;">Molecule</span>}\stackrel{\mathrm{<span\; style="font-family:\; georgia;">h</span>}\mathrm{<span\; style="font-family:\; georgia;">\nu </span>}}{<span\; style="font-family:\; georgia;">\to </span>}{\text{<span style="font-family: georgia;">Molecule</span>}}^{<span\; style="font-family:\; georgia;">+</span>}<span\; style="font-family:\; georgia;">+</span>{\mathrm{<span\; style="font-family:\; georgia;">e</span>}}^{<span\; style="font-family:\; georgia;">-</span>}$$

3.3 Photocatalysis

A photocatalyst (e.g., TiO₂, ZnO) absorbs light and generates electron-hole pairs that drive reactions:

$$\text{<span style="font-family: georgia;">Photocatalyst</span>}<span\; style="font-family:\; georgia;">+</span>\mathrm{<span\; style="font-family:\; georgia;">h</span>}\mathrm{<span\; style="font-family:\; georgia;">\nu </span>}<span\; style="font-family:\; georgia;">\to </span>{\mathrm{<span\; style="font-family:\; georgia;">e</span>}}^{<span\; style="font-family:\; georgia;">-</span>}<span\; style="font-family:\; georgia;">+</span>{\mathrm{<span\; style="font-family:\; georgia;">h</span>}}^{<span\; style="font-family:\; georgia;">+</span>}$$

• $e^{-}$ reduces species (e.g., $H^{+}\to H_2$, $M^{n+}\to M^0$)
• $h^{+}$ oxidizes species (e.g., $H_{2}O\to \cdot OH$, organics $\to C{O}_2$)

3.4 Photoinduced Electron Transfer (PET)

When a molecule absorbs light, an electron is promoted from its highest occupied molecular orbital (HOMO) to its lowest unoccupied molecular orbital (LUMO). This excited state dramatically changes the molecule's redox properties. The efficiency and rate of PET are governed by the Marcus theory of electron transfer, which calculates the reaction's kinetics based on the distance between the donor and acceptor, the surrounding solvent polarity, and the overall thermodynamic driving force (Gibbs free energy change)