REVIEW 4 major objections 5 minor 1 references
Modeling of Water Evaporation in Hydrogels from Aspect of Mechanical Analytics
T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash
Pith's one-line read Water evaporation from hydrogels is governed by a mechanical balance between stretched water and the polymer network, from which the paper derives vapor pressure and drying rate from elastic modulus alone.
desk verdict A solid mechanical model for hydrogel evaporation with a clever modulus law, but the low-water-content predictions lean on an unvalidated extrapolation of the stretched-water EOS. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is negative pressure: a metastable stretched state of liquid water in which the liquid sustains tension, described in the model by an equation of state $p_{l,\mathrm{gel}}(\varepsilon_s)$ fitted to molecular-dynamics simulations of bulk stretched water. The stretching ratio of water inside the gel is $\varepsilon_s = (1 - \Delta l/l_{w,o})/\omega$, and the mechanical balance, $p_{l,\mathrm{gel}}(\varepsilon_s) - p_e = \int_0^{\Delta l} E(\varphi_w)\,(l/l_{\mathrm{wet}})\,dl$, determines both the deformation and the water pressure. This is coupled to a series-spring constitutive model, $1/E_{\mathrm{gel}} = \varphi_p/E_p + \varphi_b/E_b(\varphi_b) + \varphi_f/E_f$ with $E_b(\varphi_b) = E_{b,o}\exp(\alpha\varphi_b)$, which reproduces the sharp rise in modulus at low water content, and to the vapor-diffusion law $J_v = k_1(p_{v,\mathrm{sat}} - p_a)$ together with a Kelvin-type relation converting water chemical potential into saturated vapor pressure.
What would settle it
Take two hydrogels designed to have the same elastic-modulus-versus-water-content curve but built from chemically different monomers, and measure their equilibrium saturated vapor pressure at several water contents. The mechanical model predicts identical vapor pressures at every water content because only modulus enters the balance; a measurable difference would refute the claim that polymer-water interactions can be neglected. A more direct check would be to measure the negative pressure of water in rigid nanopores whose size matches hydrogel mesh and compare it with the bulk stretched-water equation of state used here.
Extended reading notes
Core claim
The central claim is that the thermodynamic state of water in a drying hydrogel is set by mechanical stretching, not by polymer-water mixing. As water evaporates, the network resists shrinking, so the remaining water is pulled into tension and develops negative pressure; equilibrium is reached when the tensile stress in water equals the integrated elastic stress of the network. Because the chemical potential, and therefore the saturated vapor pressure, falls when liquid water is stretched, the same mechanical balance fixes the evaporation rate and the final water content. The paper also finds that the elastic modulus of PHEMA and PAAM follows a nearly universal curve versus water content, rising sharply below about 40 vol% water, and attributes this rise to bound/intermediate water acting as a stiff component. Fitting that modulus curve and inserting it into the mechanical balance reproduces the measured steady-state vapor pressure and dynamic drying process, and predicts that stiffer hydrogels retain more water in open air.
Load-bearing premise
The load-bearing premise is that water confined inside a shrinking hydrogel obeys exactly the same tension-versus-stretch curve as bulk water stretched in molecular-dynamics simulation; if nanometer-confined water in a polymer network resists stretching differently, the predicted negative pressures, vapor pressures, and drying rates no longer follow.
Editorial extensions
If this is right
- Two hydrogels with the same modulus at the same water content should show the same saturated vapor pressure and the same drying curve, regardless of monomer chemistry or crosslinker type.
- Raising hydrogel stiffness through denser crosslinking, reinforcement, or double networks should improve water retention at fixed ambient humidity, giving a mechanical design rule for open-air applications.
- A measured modulus-versus-water-content curve plus one mass-transfer coefficient is sufficient to predict the full dynamic drying curve and equilibrium water content, so drying tests can often be replaced by mechanical characterization.
- The sharp modulus rise below about 40 vol% water, attributed to bound/intermediate water, drives the steep drop in vapor pressure and sets the dehydration endpoint.
- Flory-Rehner polymer-solution thermodynamics is inadequate at low water content because it overestimates mixing entropy; the mechanical-stretching model is offered as the replacement in that regime.
Reading between the lines
- The same mechanical balance should apply to any deformable porous material containing water, not only polymer hydrogels; comparing the model's predictions against drying curves of cellulose or silica gels would test how far the universality claim extends.
- The authors use a mass-transfer coefficient measured for pure water evaporation; an obvious extension is to measure $k_1$ directly over a drying gel, since surface roughness, skin formation, or enrichment of polymer at the interface could change the vapor boundary layer.
- Because the model assumes one-dimensional, homogeneous drying in thin films, extending it to thick samples would require coupling the mechanical balance to internal water transport, which the present experiments deliberately avoid by using 50-100 μm slices.
- If the mechanical picture is correct, the vapor-pressure curve is effectively a water-potential curve, so hydrogel dehydration could be described in the same terms as water movement in soils and plants, a connection the paper leaves implicit.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes a mechanical model for water evaporation from hydrogels. The model treats the hydrogel as a deformable matrix with water under tensile stress, described by a negative pressure obtained from molecular dynamics simulations of stretched bulk water. The negative pressure is balanced against the elastic force of the polymer network, whose modulus is described by a series-spring constitutive equation. Combined with a simple diffusion equation for vapor transport, the model predicts saturated vapor pressure as a function of water content and dynamic drying curves. The authors compare predictions with experiments on PHEMA and PAAM hydrogels at 25 °C and 80% RH, reporting good agreement for vapor pressure and drying kinetics. They also use the model to predict that stiffer hydrogels retain water better.
Significance. If substantiated, the model offers a simple, mechanistic alternative to Flory-Rehner-type thermodynamic descriptions for hydrogel dehydration, and it makes a falsifiable prediction connecting elastic modulus to water retention. The authors should be credited for directly comparing against experiments, for showing that the vapor pressure data were not used to fit the model's material parameter α, and for explicitly attempting to model the sharp modulus rise at low water content via bound/intermediate water. The model also reproduces the correct qualitative trend that the effective vapor pressure drops substantially at low water content. However, the central claim of a 'universal solution' is presently supported by only two materials, and a key input—the negative-pressure equation of state—is fit to a limited range of stretch ratios and may be extrapolated in the actual predictions.
major comments (4)
- [Note S3; Fig. S1; Eq. (4)] The negative-pressure equation of state pl,gel(εs) is fit to MD data only for εs between 1 and 1.15 (Fig. S1: linear for 1–1.006, quadratic for 1.006–1.15). The stretch ratio in the hydrogel is defined by Eq. (S6) as εs = (1 − Δl/lw,o)/ω. At low water content (small ω), εs can exceed 1.15 unless the network stiffness restricts Δl sufficiently. The manuscript does not report the maximum εs reached in Fig. S8, nor does it restrict predictions to the fitted domain of the EOS. Because Eq. (4) converts this εs directly into a negative pressure and hence, via Eq. (3), into a vapor pressure, the low-water-content portion of Fig. 4a may rest on an unvalidated extrapolation of the quadratic fit. The authors should either show that εs remains ≤1.15 across the whole range of water contents used, or provide additional MD or experimental data that validate the EOS beyond εs=1.15.
- [Note S3; Fig. S1] The model assumes that water confined in hydrogel nanopores behaves identically to bulk stretched water, as computed from MD simulations of a homogeneous water box. This is a strong assumption because water near polymer chains and in nanometer-scale confinement can have altered hydrogen-bonding and thermodynamic properties. No evidence in the manuscript supports transferability of the bulk EOS to the gel environment, nor is the sensitivity of the final predictions to this EOS tested. The authors should justify this assumption, for example by comparing with an independent measurement of water activity in hydrogels or by performing MD simulations of water in a slit pore with hydrophilic walls.
- [Figs. 3a, 4a, 4b; Fig. S7] The experimental data supporting the central quantitative comparisons are presented without error bars or replicate statistics. In Fig. 3a, the modulus versus water content curve is a key input to the model, and in Fig. 4a the vapor-pressure predictions are compared to scattered data points. Without uncertainty estimates, the claim that the model 'agrees well with experiments' is not quantitatively substantiated. The authors should report the number of independent samples, the scatter or confidence intervals, and ideally a measure of goodness-of-fit (e.g., RMS error) for the key comparisons.
- [Abstract; Fig. 5] The abstract states that the model provides a 'universal solution' for evaporation in different hydrogels, but the experimental validation is limited to PHEMA and PAAM. The elasticity model has one fitted parameter α (determined from the combined modulus data of these two materials), and the predictions for other hydrogel types in Fig. 5 are not tested against any independent data. This claim of universality is therefore premature. The authors should either temper the wording to indicate a framework that requires material-specific modulus inputs, or provide additional validation on hydrogels with substantially different chemistries or network structures.
minor comments (5)
- [Main text, Eqs. (1)–(5)] The equations in the main text appear poorly typeset or garbled in the submitted PDF, which makes it difficult to follow the derivations. In particular, Eq. (4) is not rendered legibly. The authors should ensure all equations are clear in the final version.
- [Figure 1] The caption of Figure 1 uses '(b)' for both the vapor pressure plot and the chemical-potential contributions plot, which is confusing. Please re-letter the panels.
- [Section 2.1] The Flory-Rehner comparison sets the polymer-solvent interaction parameter χ to 0.5 for both hydrogels without reporting a sensitivity analysis. Since χ strongly affects the predicted vapor pressure at low water content, a brief sensitivity check would strengthen the claim that the Flory-Rehner model fails even for other reasonable choices of χ.
- [Eq. (1)] The mass transfer coefficient k1 = 1.6×10⁻⁵ g s⁻¹ m⁻² Pa⁻¹ is extracted from a pure-water evaporation experiment, but no uncertainty is given and its dependence on humidity and temperature is not discussed. Given that k1 directly scales the vapor pressure, the authors should state its precision or at least discuss how its variation would affect the extracted vapor-pressure curves.
- [Section 2.2] The sentence 'the model neglect the mass transfer resistance of water in PHEMA' contains a grammatical error and should read 'the model neglects'. Also, the explanation that the initial evaporation rate is overestimated because of neglecting mass-transfer resistance is plausible but not quantified; a brief discussion of the magnitude of this resistance would be useful.
Circularity Check
No significant circularity: target vapor-pressure and evaporation data are never used to fit model inputs; the in-house MD equation of state and the fitted modulus curve are external material inputs, not restatements of the predicted outputs.
full rationale
The derivation chain is: (1) measure hydrogel mass loss and use Eq. 1 with k1 from pure-water evaporation to obtain experimental pv,sat; (2) independently measure modulus versus water content (Fig. 3a) and fit the series-spring constitutive law (Eq. 5) with α=18.6 and Eb,o=3.2 GPa; (3) take the negative-pressure equation of state for stretched water from ref. 33 (Fig. S1), a prior MD study by the same group; (4) solve the mechanical balance Eq. 4 to obtain negative pressure and strain, then convert to vapor pressure via the Kelvin relation Eq. 3. The reported vapor-pressure and dynamic evaporation data are not used in any fit: α is fitted to modulus data, and Eb,o is set from ice modulus, while pv and mass-loss data are reserved for comparison. The cited prior MD EOS and the claimed modulus-dominance of vapor pressure (ref. 15) are external inputs from published work, not derivations from this paper's fitted values, so they do not constitute circularity under the stated rules. The agreement between calculated and measured vapor pressure is therefore a genuine cross-validation rather than a tautology. The only notable weakness is that the MD EOS is fitted only up to εs=1.15 and low-water-content predictions may extrapolate beyond that range; that is a correctness and extrapolation risk, not a circularity, and it does not affect the verdict here.
Assumptions & free parameters
free parameters (4)
- alpha (α) =
18.6
- Eb,o (bound water modulus anchor) =
3.2 GPa
- Negative-pressure EOS coefficients for pl,gel(εs) =
Piecewise linear and quadratic fit parameters from Fig S1
- Mass transfer coefficient k1 =
1.6e-5 g s^-1 m^-2 Pa^-1
assumptions (4)
- domain assumption Water in hydrogel behaves like bulk stretched water, with a negative-pressure equation of state fitted from MD simulations (Fig S1).
- domain assumption Mixing entropy and polymer-water mixing enthalpy are neglected; only mechanical stretching and elastic deformation determine the water chemical potential.
- ad hoc to paper Hydrogel modulus follows a series-spring combination of polymer, bound/intermediate water, and free water, Eq 5, with Eb rising exponentially until free water appears.
- standard math Kelvin equation (Eq 3) and a Fickian mass-transfer law (Eq 1) connect the computed pressure to vapor pressure and evaporation flux.
Cite this review
Pith. "Pith review of Modeling of Water Evaporation in Hydrogels from Aspect of Mechanical Analytics." pith.science (2026). https://pith.science/paper/PR2ABIM7
@misc{pith2026250521075,
author = {Pith},
title = {Pith review of: Modeling of Water Evaporation in Hydrogels from Aspect of Mechanical Analytics},
year = {2026},
howpublished = {\url{https://pith.science/paper/PR2ABIM7}},
note = {Machine review of arXiv:2505.21075}
}
read the original abstract
Water evaporation is critically important for hydrogels in open-air applications, but theoretically modeling is difficult due to the complicated intermolecular interactions and sustained deformation. In this work, we construct a simplified model to describe the state of water inside the hydrogel by only considering mechanical stretching. We employ "negative pressure" to bridge the stretching force in water and elastic force generated by the polymer network. Combined with a constitutive equation of elasticity for hydrogels and classic diffusion equation, this model gives a universal solution to calculate the saturated vapor pressure, dynamic evaporation rates and real-time deformation of different hydrogels. The calculated results agree well with experiments results both in steady state and dynamic process for commonly used poly 2-hydroxyethyl methacrylate and polyacrylamide hydrogels with diverse components. In addition, the model predicts that, hydrogels with high modulus shows stronger ability to retain water in open environment.
Figures
Figures from the paper (2 more)
Reference graph
Works this paper leans on
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[1]
(1) Y. Liu, X. Liu, B. Duan, Z. Yu, T. Cheng, L. Yu, L. Liu, K. Liu, Polymer-water interaction enabled intelligent moisture regulation in hydrogels. J. Phys. Chem. Lett. 2021, 12 (10), 2587-2592. (2) X. Liu, W. Wei, M. Wu, K. Liu, S. Li, Understanding the structure and dynamical properties of stretched water by molecular dynamics simulation. Mol. Phys. 20...
work page 2021
Reviewed August 7, 2026 · model on record in the stance chip above.
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