[Paper Review] Entropy maximization underlies topology and mechanical properties in dynamic covalent hydrogels

Lucien Cousin, Pietro Miotti+3 more|arXiv (Cornell University)|Mar 18, 2026

Hydrogels: synthesis, properties, applications0 citations

TL;DR

The paper demonstrates that dynamic covalent networks rearrange to maximize network entropy, delaying gelation and producing a steeper modulus increase; bond exchange can reconfigure mechanics without bond loss.

ABSTRACT

Adding dynamic bonds in polymer networks enables reprocessing and recycling; however the full impact of reversible bonds on dynamic network mechanics remains unclear. We build model dynamic networks and observe substantial deviations from classic theory. We rationalize these findings by considering that bond exchange enables the networks to rearrange and adopt a topology with a higher entropy. This allows us to accurately predict the gel point and elasticity of the dynamic networks. Further, we show by controlling bond exchange that network rearrangement can dramatically alter the mechanical properties, even without loss of bonds.

Motivation & Objective

• Investigate how dynamic reversible bonds influence gel point and elasticity beyond classic permanent-network theories.
• Determine whether network entropy drives internal topology changes in DCvNs as bonds form with varying p.
• Quantify how bond exchange and resulting topology affect mechanical properties near and above gelation.

Proposed method

• Synthesize model dynamic covalent networks using 4-arm PEG stars linked by reversible boronic acid–diol bonds.
• Systematically vary p (fraction of bonds formed) by adjusting temperature, concentration, and competitive binders.
• Measure gel point and plateau modulus G_P, and relaxation time tau_M via shear rheometry across conditions.
• Characterize network topology via entropy-based counting of star connectivity and loops using a graph-theoretical framework.
• Develop an entropy-maximization model to predict P_i (distribution of bound arms per star) and resulting gel point.
• Incorporate loops into the model and validate with dissipative particle dynamics simulations and experimental data.
• Propose a phantom-network-based elasticity model incorporating defects (loops and dangling chains) to predict G' as a function of p.

Figure 1: Synthesis and mechanical characterization of dynamic covalent networks. a) General structure of the dynamic covalent networks formed by cross-linking 4-arm PEG stars end-functionalized with either a boronic acid or a diol. The formed networks incorporate reacted and unreacted bonds in vari

Experimental results

Research questions

• RQ1 How does the fraction of formed bonds p influence gel point and elasticity in dynamic covalent networks beyond classical theories?
• RQ2 Can network entropy, via the connectivity distribution P_i and loops, explain deviations from affine network predictions near gelation?
• RQ3 Do bond exchange dynamics reconfigure network topology to maximize entropy, and how does this affect mechanical properties after gelation?
• RQ4 Can a unified model incorporating loops and dangling chains capture the observed elasticity near gelation for DCvNs?

Key findings

• The observed gel point p_gel is higher (~0.6) than Flory–Stockmayer predictions (~0.33).
• Normalized modulus data collapse onto a single master curve when plotted against p, regardless of how p was varied.
• Entropy-maximized connectivity, including loop formation, better predicts p_gel and the rise of G' with p than classic models.
• Bond exchange alters network topology and elasticity even without changing bond count, evidenced by moduli changes when making bonds dynamic and then re-freezing them.
• A scaling phantom-network model incorporating loops and dangling chains captures the delayed gel point and steeper G' increase near gelation.
• Simulations corroborate the P_i distribution and loop proportions predicted by entropy-maximization theory.

Figure 2: The maximization of network entropy in dynamic covalent networks leads to a different connectivity that explains the measured gel point. a) Measured gel point in the case of 4-arm and 8-arm stars compared with the predictions from the Flory–Stockmayer model and with our prediction, taking