Sonochemical Routes

 

Sonochemical Synthesis 

1. Introduction to Sonochemistry

Sonochemistry uses ultrasound (20 kHz – 10 MHz) to drive chemical reactions through acoustic cavitation — the formation, growth, and implosive collapse of bubbles in a liquid.

Core Principle: High-intensity ultrasound → Cavitation bubbles → Localized extreme conditions → Chemical reactions

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2. Acoustic Cavitation

2.1 The Cavitation Phenomenon

When ultrasound passes through a liquid, it creates alternating compression and rarefaction cycles:

css
Pressure
   ↑
   │   Compression          Compression
   │   ┌───┐                ┌───┐
   │   │   │                │   │
   ├───┤   ├───┬───┬───┬───┤   ├───► Time
   │   │   │   │   │   │   │   │
   │   └───┘   │   │   │   └───┘
   │      │    │   │   │      │
   │      └────┘   └───┘      │
   │     Rarefaction          │
   ▼                          │

• During rarefaction, negative pressure pulls molecules apart
• If pressure drops below vapor pressure of liquid → bubble forms
• Bubble grows over several cycles
• At critical size → implosive collapse

2.2 Types of Cavitation

Type	Description	Occurrence
Stable cavitation	Bubbles oscillate around equilibrium radius	Low intensity ultrasound
Transient (inertial) cavitation	Bubbles grow rapidly and collapse violently	High intensity ultrasound (>10 W/cm²)

2.3 The Collapse — Extreme Conditions

When a cavitation bubble collapses:

Parameter	Value	Remark
Temperature	~5000 K	Hotter than surface of the sun
Pressure	~1000 atm	Equivalent to deep ocean pressure
Heating/cooling rate	>10¹⁰ K/s	Extreme non-equilibrium
Time scale	<1 μs	Ultrashort duration

The "Hot Spot" Theory:

• Bubble collapse is nearly adiabatic
• Rapid compression → enormous temperature spike
• Localized plasma may form

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3. Bubble Dynamics

3.1 Rayleigh-Plesset Equation

Describes bubble radius ($R$) as a function of time:

$$\mathrm{<span\; style="font-family:\; georgia;">R</span>}\frac{{\mathrm{<span\; style="font-family:\; georgia;">d</span>}}^{\mathrm{<span\; style="font-family:\; georgia;">2</span>}}\mathrm{<span\; style="font-family:\; georgia;">R</span>}}{\mathrm{<span\; style="font-family:\; georgia;">d</span>}{\mathrm{<span\; style="font-family:\; georgia;">t</span>}}^{\mathrm{<span\; style="font-family:\; georgia;">2</span>}}}<span\; style="font-family:\; georgia;">+</span>\frac{\mathrm{<span\; style="font-family:\; georgia;">3</span>}}{\mathrm{<span\; style="font-family:\; georgia;">2</span>}}{<span\; style="font-family:\; georgia;">(</span>\frac{\mathrm{<span\; style="font-family:\; georgia;">d</span>}\mathrm{<span\; style="font-family:\; georgia;">R</span>}}{\mathrm{<span\; style="font-family:\; georgia;">d</span>}\mathrm{<span\; style="font-family:\; georgia;">t</span>}}<span\; style="font-family:\; georgia;">)</span>}^{\mathrm{<span\; style="font-family:\; georgia;">2</span>}}<span\; style="font-family:\; georgia;">=</span>\frac{\mathrm{<span\; style="font-family:\; georgia;">1</span>}}{\mathrm{<span\; style="font-family:\; georgia;">\rho </span>}}<span\; style="font-family:\; georgia;">(</span>{\mathrm{<span\; style="font-family:\; georgia;">P</span>}}_{\mathrm{<span\; style="font-family:\; georgia;">g</span>}}<span\; style="font-family:\; georgia;">+</span>{\mathrm{<span\; style="font-family:\; georgia;">P</span>}}_{\mathrm{<span\; style="font-family:\; georgia;">v</span>}}<span\; style="font-family:\; georgia;">-</span>{\mathrm{<span\; style="font-family:\; georgia;">P</span>}}_{\mathrm{<span\; style="font-family:\; georgia;">\infty </span>}}<span\; style="font-family:\; georgia;">-</span>\frac{\mathrm{<span\; style="font-family:\; georgia;">2</span>}\mathrm{<span\; style="font-family:\; georgia;">\sigma </span>}}{\mathrm{<span\; style="font-family:\; georgia;">R</span>}}<span\; style="font-family:\; georgia;">-</span>\frac{\mathrm{<span\; style="font-family:\; georgia;">4</span>}\mathrm{<span\; style="font-family:\; georgia;">\mu </span>}}{\mathrm{<span\; style="font-family:\; georgia;">R</span>}}\frac{\mathrm{<span\; style="font-family:\; georgia;">d</span>}\mathrm{<span\; style="font-family:\; georgia;">R</span>}}{\mathrm{<span\; style="font-family:\; georgia;">d</span>}\mathrm{<span\; style="font-family:\; georgia;">t</span>}}<span\; style="font-family:\; georgia;">)</span>$$

Where:

• $\rho$ = liquid density
• $P_g$ = gas pressure inside bubble
• $P_v$ = vapor pressure inside bubble
• $P_{\mathrm{\infty }}$ = ambient pressure (including ultrasound)
• $\sigma$ = surface tension
• $\mu$ = viscosity

3.2 Resonance Radius ($R_r$)

$${\mathrm{<span\; style="font-family:\; georgia;">R</span>}}_{\mathrm{<span\; style="font-family:\; georgia;">r</span>}}<span\; style="font-family:\; georgia;">=</span>\frac{\mathrm{<span\; style="font-family:\; georgia;">1</span>}}{\mathrm{<span\; style="font-family:\; georgia;">2</span>}\mathrm{<span\; style="font-family:\; georgia;">\pi </span>}\mathrm{<span\; style="font-family:\; georgia;">f</span>}}\sqrt{\frac{\mathrm{<span\; style="font-family:\; georgia;">3</span>}\mathrm{<span\; style="font-family:\; georgia;">\gamma </span>}{\mathrm{<span\; style="font-family:\; georgia;">P</span>}}_{\mathrm{<span\; style="font-family:\; georgia;">0</span>}}}{\mathrm{<span\; style="font-family:\; georgia;">\rho </span>}}}$$

Where:

• $f$ = ultrasound frequency
• $\gamma$ = heat capacity ratio ($C_p\mathrm{/}{C}_v$)
• $P_0$ = ambient pressure

At 20 kHz, $R_r\approx 150$ μm; at 500 kHz, $R_r\approx 6$ μm

3.3 Factors Affecting Cavitation

Factor	Effect on Cavitation
Frequency	Higher $f$ → shorter rarefaction cycle → harder to form bubbles → less intense collapse
Temperature	Higher $T$ → lower viscosity, higher vapor pressure → easier cavitation but less violent collapse
Vapor pressure	High $P_v$ → more vapor inside bubble → "cushions" collapse (lower $T_{max}$)
Dissolved gas	More gas → more nucleation sites → less violent collapse
Solvent viscosity	Higher $\mu$ → damps bubble motion → less intense collapse

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4. Chemical Effects of Ultrasound

The chemical effects of ultrasound are based on the phenomenon of Acoustic Cavitation (It is the formation, growth, and implosive collapse of microscopic bubbles in a liquid due to ultrasonic waves).

When ultrasonic waves pass through a liquid, they create alternating:

• Compression cycles
• Rarefaction cycles

During rarefaction, microscopic cavities (bubbles) form.

These bubbles:

• Grow over successive cycles.
• Become unstable.
• Collapse violently.

The collapse produces:

• Extremely high local temperatures.
• Very high pressures.
• Shock waves.
• Microjets.
• Free radicals.

These conditions initiate chemical reactions.