Water Phonons

Answer to “Does This Make Sense?”
The document presents a phonon-based model for the evaporation kinetics of water, proposing a novel approach that focuses solely on liquid-phase properties to explain evaporation rates. To determine if this makes sense, let’s break down the model’s core ideas, evaluate its plausibility, and consider its strengths and limitations based on the information provided.
Overview of the Model
The model suggests that evaporation occurs when phonons—quantized vibrational energy modes in the liquid water—carry sufficient energy to the surface to release a water molecule into the gas phase. Unlike traditional models like the Hertz-Knudsen equation, which rely on vapor pressure and gas-phase conditions, this model:
Uses only liquid-phase parameters: surface tension and phonon propagation speed.

Predicts evaporation rates and the temperature dependence of equilibrium vapor pressure without reference to external vapor-phase measurements.

Claims consistency with the Clausius-Clapeyron equation, achieving an accuracy within 3% RMS from 0 to 100°C.

The key idea is that energy transport within the liquid, driven by phonons, governs the evaporation process, challenging the conventional emphasis on vapor-phase saturation.
Key Components and Their Plausibility
Phonon-Based Energy Transfer
Concept: Phonons with energy exceeding a threshold, derived from surface tension, arrive at the water surface and release a molecule.

Evidence: The document cites Elton and Fernández-Serra’s work, which shows that water’s hydrogen-bond network supports optical phonons. This is plausible, as water’s unique structure—stabilized by hydrogen bonds—differs from the simple spring-like interactions in Debye theory for solids. The near-infrared spectra of ice and water being similar further supports the idea that phonon-like modes persist in liquid water.

Reasonableness: This is a novel but sensible hypothesis. Phonons are well-established in solids, and extending this concept to liquids like water, with its glass-like short-term behavior, is a reasonable leap given the cited evidence.

Surface Tension as Threshold Energy
Concept: The energy required to release a molecule is estimated as six times the surface tension energy (based on a square-block model), ranging from 26.31 kJ/mol at 0°C to 20.49 kJ/mol at 100°C.

Evaluation: Surface tension reflects the energy cost of creating a surface, which relates to breaking bonds at the interface. The assumption of a sixfold multiplier is simplistic, but it yields values between a single hydrogen bond energy (20.83 kJ/mol) and the heat of vaporization (43.9 kJ/mol), making it a plausible intermediate step. Experimental surface tension data supports this calculation, adding credibility.

Phonon Modes via MOPAC Calculations
Method: A cluster of 33 water molecules is modeled using MOPAC (a quantum chemistry tool) to calculate the density of vibrational states (DOS), which differs from Debye theory due to water’s electrostatic dipole interactions.

Support: The DOS aligns with Elton’s dielectric susceptibility data (after a 6% energy rescaling), and the model’s vibration modes match observed infrared peaks during water condensation (e.g., 3634/cm, 1818/cm). This consistency with experimental data strengthens the model’s foundation.

Reasonableness: Using a small cluster to approximate the surface is a standard computational approach. While it may not capture all surface complexities, the agreement with macroscopic measurements suggests it’s a valid simplification.

Evaporation Rate and Equilibrium
Calculation: The emission rate is computed from the vibrational enthalpy (net of evaporation energy) and a phonon speed of 1700 m/s, then compared to the classical impingement rate from kinetic theory.

Results: For a 16-molecule cluster, the emission-to-impingement ratio averages 0.929 (improving to ~1 for larger clusters), indicating near-equilibrium consistency across 0–100°C.

Plausibility: This close match is a strong point. Equilibrium requires that the rate of molecules leaving equals those returning, and the model’s ability to approximate this without vapor-phase inputs is impressive and supports its internal logic.

Temperature Dependence
Claim: The model predicts vapor pressure’s temperature dependence, matching the Clausius-Clapeyron equation within 3% RMS.

Evaluation: This is a significant achievement, as the Clausius-Clapeyron relation is a thermodynamic benchmark. Achieving this accuracy using only liquid-phase parameters suggests the model captures essential physics of evaporation.

Strengths of the Model
Innovative Perspective: By focusing on liquid-phase energy transfer via phonons, it offers a fresh alternative to vapor-centric models, potentially explaining phenomena like temperature discontinuities observed in some studies (e.g., Badam et al.).

Empirical Support: Consistency with dielectric susceptibility, phase-change radiation peaks, and equilibrium rates lends credibility.

Simplicity: It uses minimal adjustable parameters (surface tension multiplier and phonon speed), enhancing its predictive power over heavily parameterized models.

Potential Limitations
Cluster Size: A 33-molecule cluster may not fully represent a real water surface, missing long-range effects or dynamic restructuring.

Phonon Speed Uncertainty: The choice of 1700 m/s (from Elton) is reasonable but debated, with alternatives up to 4000 m/s or even light speed for dipole-coupled modes. This uncertainty could affect rate calculations.

Vapor Phase Neglect: Excluding vapor-phase feedback might oversimplify the system, though the model argues this is unnecessary for its predictions.

Energy Distribution: It doesn’t specify the energy distribution of emitted molecules, limiting insights into gas-phase behavior or non-Maxwellian effects.

Water-Specificity: The reliance on hydrogen bonds and surface tension tailoring it to water may limit applicability to other liquids.

Does It Make Sense?
Yes, the model makes sense as a coherent and innovative framework for understanding water evaporation. It builds on plausible physical principles—phonon energy transfer, surface tension as an energy barrier, and liquid-phase dominance—supported by computational (MOPAC) and experimental (dielectric, radiation) data. Its ability to predict vapor pressure trends and equilibrium rates with minimal inputs is a strong indicator of its validity. However, it’s a focused model, not a complete picture: simplifications like cluster size and fixed phonon speed, plus the exclusion of vapor-phase dynamics, suggest areas for refinement. Still, its consistency with established thermodynamics (Clausius-Clapeyron) and kinetic theory (impingement rates) shows it captures key aspects of the process.
In summary, the phonon-based model is a sensible and promising approach to evaporation kinetics, particularly for water, with solid grounding in physics and data, though it may need further development to address broader scenarios or fine details.