Entropy maximization underlies topology and mechanical properties in dynamic covalent hydrogels

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.

Figures (4)

• 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 variable proportions, defined by $p$, the fraction of formed bonds. b) Chemical structure of the network precursors: 4-arm PEG stars end-functionalized either with phenylboronic acid (PBA) or aminophenylboronic acid (APBA) or with gluconolactone (GL) c) Frequency sweeps of networks formed with APBA and GL at 10 wt% for temperatures ranging from 5$^{\circ}$C to 45 $^{\circ}$C. d) Normalized dynamic modulus $G'/G_{affine}$ as a function of $p$ for all conditions tested: varying temperature and concentration of network precursors for two different boronic acids, and varying concentration of a competitor small molecule and temperature for APBA. The orange line indicates the literature prediction Parada2018BrunoM.
• 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 into account network entropy maximization calculated from $P_i$. b) Calculated fraction of stars with $i$ arms bound, $i = 0 \cdots 4$ (dashed lines), compared to the simulated fraction (symbols). c) 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 into account network entropy maximization calculated from $P_i$ and from the fraction of loops. d) Normalized dynamic modulus $G'/G_{affine}$ as a function of $p$ for all conditions tested (full symbols) compared with the literature model (orange line, Parada2018BrunoM) and with our model (blue line).
• Figure 3: Triggering bond exchange leads to a persistent change in the mechanical properties of transiently reversible networks. a) Schematics of the experiment: starting with (1) permanent disulfide bonds, DBU is added (2) to trigger the exchange of the disulfide bonds (highlighted in blue). Upon degradation of DBU (3), the disulfide bonds become permanent again. Unreactive OH groups create dangling ends. b) Expected outcome based on our results and literature models depending on $p$. c) Average and standard deviation of the storage moduli for networks with $p=0.55$ and $p=0.85$ during phases (1), (2), and (3).
• Figure 4: Schematics of the graph representation used to calculate the number of accessible microstates. Left: schematic of a real network. Right: Graph representation associated with this network.