Vitrimers: Dynamic Covalent Polymer Networks

• Vitrimers are permanently crosslinked polymer networks with associative bond exchange that enables topology rearrangement without loss of connectivity.
• They exhibit thermo-rheologically complex behavior, where glassy segmental dynamics and bond-exchange kinetics govern stress relaxation and material flow.
• Design strategies focus on tuning exchange chemistry, crosslink density, and phase behavior to optimize healability, reshaping, and mechanical performance.

Vitrimers are permanently crosslinked polymer networks whose covalent bonds undergo associative exchange, so the network can rearrange its topology without any significant loss of connectivity. This combination gives thermoset-like insolubility and dimensional integrity together with high-temperature stress relaxation, malleability, welding, healing, reshaping, and reprocessing (Edera et al., 2024). Contemporary vitrimer research treats these materials not as a single rheological archetype, but as a family whose behavior is jointly conditioned by exchange chemistry, segmental mobility, density, morphology, catalyst activity, and network topology, across epoxy, polyacrylate, imine, dioxaborolane, disulfide, and linker-mediated systems (Chankapure et al., 7 Sep 2025).

1. Network chemistry and defining characteristics

The defining molecular feature of a vitrimer is associative bond exchange. In the associative limit, the number of crosslinks remains fixed while partners are swapped, so the network reorganizes without transiently losing its crosslinked character (Chankapure et al., 7 Sep 2025). This distinguishes vitrimers from dissociative covalent adaptable networks, in which bond populations can decrease during exchange, and from transient physical gels, whose integrity is controlled by reversible noncovalent association. It also distinguishes vitrimer flow from thermoplastic flow: the former is enabled by topology rearrangement in a covalent network, whereas the latter follows chain disentanglement or melting.

This general principle is realized through several chemistries. Transesterification-based epoxy vitrimers use ester and hydroxyl groups in the presence of catalyst to enable exchange (Gablier et al., 2020). Dioxaborolane metathesis underlies both soft poly(methyl acrylate) vitrimers and linker-mediated vitrimer networks (Zhao et al., 5 Mar 2025). Imine vitrimers can relax through associative transimination, with free amines acting as exchange participants in at least one model system (Cheng et al., 7 Aug 2025). Disulfide exchange provides another route to topology rearrangement in vitrimer-like epoxy networks and in atomistic self-healing simulations (Singh et al., 2023).

Because the network remains covalently connected, vitrimer behavior is often discussed using both a glass transition temperature $T_g$ and a topology-freezing or vitrimer transition temperature $T_v$. The literature does not treat these as universally identical. In some analyses $T_v$ is estimated from Arrhenius extrapolation of stress-relaxation data, while in other systems the relevant practical transition is an elastic–plastic onset under load rather than a single universal thermodynamic point (Zhang et al., 2023). This terminological variability is one reason vitrimer comparisons across chemistries remain nontrivial.

2. Relaxation spectra, rheology, and time–temperature non-equivalence

A central result of recent rheology is that many vitrimers are thermo-rheologically complex rather than thermo-rheologically simple. In a zinc-catalyzed epoxy/anhydride vitrimer, the mechanical spectrum was decomposed into a glassy/segmental relaxation family and a vitrimeric, bond-exchange-controlled terminal family, with distinct activation energies,

$$E_G = 680 \pm 50\ \mathrm{kJ\,mol^{-1}}, \qquad E_V = 130 \pm 10\ \mathrm{kJ\,mol^{-1}},$$

so a single physical shift factor does not describe all modes (Edera et al., 2024). The same work emphasized the distinction between empirical time–temperature superposition and physical time–temperature equivalence: spectra can sometimes be stitched into a master curve, yet temperature still fails to accelerate all modes in the same way. In spectral form, the generalized Maxwell representation was written as

$$G'(\omega)=\sum_i H(\Omega_i)\,\frac{(\omega/\Omega_i)^2}{1+(\omega/\Omega_i)^2}, \qquad G''(\omega)=\sum_i H(\Omega_i)\,\frac{\omega/\Omega_i}{1+(\omega/\Omega_i)^2},$$

with independently shifted glassy and vitrimeric mode families.

A complementary theoretical picture describes vitrimer relaxation as a competition between local exchange and polymer-mediated diffusion. In that framework, a high-temperature regime is reaction-controlled, while a low-temperature regime is diffusion-controlled, leading to

$$\tau_{\text{bond}} \cong \tau_{\text{ex}}+\tau_{\text{diff}} \cong \tau_{\text{ex}}+c\,\tau_\alpha.$$

The key point is that local exchange and long-range bond decorrelation are not the same event: nearby partners can swap recursively unless diffusion separates them (Branham-Ferrari et al., 23 Sep 2025). This directly explains why terminal vitrimer relaxation can remain Arrhenius over a wide range even when segmental $\alpha$-relaxation is super-Arrhenius.

Crosslink density itself need not strongly slow local chain dynamics, yet it can transform the viscoelastic state by changing connectivity. In a model imine vitrimer based on telechelic poly(propylene glycol), varying the ratio $r$ of aldehyde to amine groups barely altered segmental and chain relaxation once a small $T_g$ shift was accounted for, but it strongly changed the linear viscoelastic response, producing finite branched sols below gelation, a broad critical regime near $r \approx 0.7$ with $T_v$0, and rubbery plateaus above gelation (Cheng et al., 7 Aug 2025). The same study reported activation entropies

$T_v$1

showing that unusually large negative activation entropy can dominate the exchange timescale even when activation enthalpy is modest. This directly contradicts the common simplification that a single “vitrimer activation energy” suffices to characterize long-time mechanics.

3. Density, phase separation, and interfacial structure

Vitrimer physics is not limited to kinetics; the equilibrium state itself can change when dynamic crosslinks are introduced. In a coarse-grained bead-spring model where dynamic bonds were the same size as ordinary chain bonds, increasing crosslink fraction increased the saturated liquid density, decreased interfacial width, increased surface tension, left crosslinks well mixed in the bulk, and depleted them from the air/polymer interface (Karmakar et al., 2024). This was interpreted as an entropic cohesive effect: the added internal constraints altered the entropy of the liquid in a way that favored denser packing even without introducing stronger pair attractions.

That entropic densification is not universal once crosslinkers have explicit size and chemistry. In an associative-limit melt with explicit spherical bifunctional crosslinkers of diameter

$T_v$2

the packing fraction

$T_v$3

increased monotonically with $T_v$4 for chemically compatible crosslinkers and decreased monotonically with $T_v$5 for incompatible crosslinkers (Chankapure et al., 7 Sep 2025). Incompatible crosslinkers segregated to the polymer–air interface and lowered interfacial tension; for

$T_v$6

the same model reported macrophase separation. This makes explicit that dynamic crosslinkers can act simultaneously as network connectors, finite-volume fillers, and interfacially active particles.

In polyethylene/dioxaborolane maleimide vitrimers, incompatibility drives a still richer hierarchy. These materials macroscopically phase separated into graft-rich and graft-poor regions and, at smaller scales, formed dioxaborolane maleimide-rich aggregates packed in a mass-fractal arrangement that persisted in both the melt and the amorphous fraction of the semicrystalline state (Ricarte et al., 2018). SAXS analysis was consistent with an aggregate radius fixed at $T_v$7, a radius standard deviation of about $T_v$8, a fractal length scale of about $T_v$9–$T_v$0, and fractal dimension about $T_v$1–$T_v$2. The same morphology rationalized low insoluble fractions and reduced crystallinity in the graft-rich network phase.

Morphology can also become the dominant controller of relaxation. In associative vitrimers with incompatible stickers, microphase separation can make the slow step the migration of a sticker from one domain to another rather than the bare local exchange reaction (Karmakar et al., 26 Jun 2025). Related thermodynamic arguments appear in linker-mediated and protector-mediated systems: linker-mediated dioxaborolane vitrimers show a reentrant gel–sol transition with increasing linker concentration, and protector molecules can create an entropy-driven thermo-gelling vitrimer that is liquid at low temperature but gels on heating (Lei et al., 2020, Xia et al., 2022). These results place density, compatibility, and state-point thermodynamics on the same footing as exchange kinetics.

4. Modeling, simulation, and theoretical frameworks

Because vitrimer exchange changes topology rather than merely sampling bond vibrations, simulation methodology is unusually consequential. A general Monte Carlo bond-swap algorithm for dynamically crosslinked polymers was developed for multivalent and multi-species systems by enforcing detailed balance through a valency-dependent bias term (Rao et al., 2023). For a symmetric proposal scheme, the acceptance rule becomes

$T_v$3

where $T_v$4 is the number of free valences on the attacking residue and $T_v$5 is the corresponding reverse-move multiplicity. The point is not merely algorithmic convenience: naive residue-based swap selection violates detailed balance once multivalency or species competition is present.

A distinct coarse-grained route models associative exchange through an explicit three-body potential. In a star-polymer vitrimer, the swap barrier was controlled by

$T_v$6

and topological defects were shown to accelerate stress relaxation dramatically (1804.01723). In the defect-allowing mixture, primary loops accounted for about $T_v$7 to $T_v$8 of all bonds, and the estimated liquid-like relaxation time at zero barrier was about $T_v$9, compared with about $$E_G = 680 \pm 50\ \mathrm{kJ\,mol^{-1}}, \qquad E_V = 130 \pm 10\ \mathrm{kJ\,mol^{-1}},$$0 in the defect-free analogue. This identified defects as a “highway” for stress relaxation because they reduce the redundancy of load-bearing connections.

All-atom MD has been used to incorporate explicit dynamic bond exchange into cured epoxy networks. In a DGEBA/AFD vitrimer, sulfur exchange was activated when sulfur atoms came within $$E_G = 680 \pm 50\ \mathrm{kJ\,mol^{-1}}, \qquad E_V = 130 \pm 10\ \mathrm{kJ\,mol^{-1}},$$1, with a temperature-dependent sigmoidal reaction probability centered at $$E_G = 680 \pm 50\ \mathrm{kJ\,mol^{-1}}, \qquad E_V = 130 \pm 10\ \mathrm{kJ\,mol^{-1}},$$2 (Singh et al., 2020). That model was then used to simulate thermal healing of a CNT-pullout pore by heating to $$E_G = 680 \pm 50\ \mathrm{kJ\,mol^{-1}}, \qquad E_V = 130 \pm 10\ \mathrm{kJ\,mol^{-1}},$$3 for $$E_G = 680 \pm 50\ \mathrm{kJ\,mol^{-1}}, \qquad E_V = 130 \pm 10\ \mathrm{kJ\,mol^{-1}},$$4, after which the healed structure recovered the pristine elastic modulus below $$E_G = 680 \pm 50\ \mathrm{kJ\,mol^{-1}}, \qquad E_V = 130 \pm 10\ \mathrm{kJ\,mol^{-1}},$$5. The kinetics were phenomenological rather than Arrhenius, but the framework established a direct atomistic route from topology updates to dilatometric, mechanical, and healing behavior.

On the theoretical side, coarse-grained simulation combined with microscopic and schematic Mode-Coupling Theory showed that vitrimer fragility can be tuned from fragile to strong to superstrong by decreasing density, with a crossover around

$$E_G = 680 \pm 50\ \mathrm{kJ\,mol^{-1}}, \qquad E_V = 130 \pm 10\ \mathrm{kJ\,mol^{-1}},$$6

and fragility index approximately

$$E_G = 680 \pm 50\ \mathrm{kJ\,mol^{-1}}, \qquad E_V = 130 \pm 10\ \mathrm{kJ\,mol^{-1}},$$7

at and below that density (Ciarella et al., 2019). The microstructural predictor was the temperature sensitivity of the main structural peak $$E_G = 680 \pm 50\ \mathrm{kJ\,mol^{-1}}, \qquad E_V = 130 \pm 10\ \mathrm{kJ\,mol^{-1}},$$8: weak growth of $$E_G = 680 \pm 50\ \mathrm{kJ\,mol^{-1}}, \qquad E_V = 130 \pm 10\ \mathrm{kJ\,mol^{-1}},$$9 on cooling suppressed the usual packing-cage mechanism and produced strong or superstrong vitrimer behavior.

5. Mechanical response, healing, damage, and structural applications

Vitrimer mechanics span a wide range, from soft highly dissipative elastomers to structural composites. A poly(methyl acrylate) vitrimer based on dioxaboralane metathesis reached up to 8000% strain at break, about 6.5 MPa tensile strength in the strongest fully cured sample, toughness of about 20–55 MJ/m$$G'(\omega)=\sum_i H(\Omega_i)\,\frac{(\omega/\Omega_i)^2}{1+(\omega/\Omega_i)^2}, \qquad G''(\omega)=\sum_i H(\Omega_i)\,\frac{\omega/\Omega_i}{1+(\omega/\Omega_i)^2},$$0, and a loss factor $$G'(\omega)=\sum_i H(\Omega_i)\,\frac{(\omega/\Omega_i)^2}{1+(\omega/\Omega_i)^2}, \qquad G''(\omega)=\sum_i H(\Omega_i)\,\frac{\omega/\Omega_i}{1+(\omega/\Omega_i)^2},$$1 with maxima between about 2 and 3 (Zhao et al., 5 Mar 2025). In frequency space, $$G'(\omega)=\sum_i H(\Omega_i)\,\frac{(\omega/\Omega_i)^2}{1+(\omega/\Omega_i)^2}, \qquad G''(\omega)=\sum_i H(\Omega_i)\,\frac{\omega/\Omega_i}{1+(\omega/\Omega_i)^2},$$2 was maintained from about 0.001 to 100 Hz, and in temperature space the same criterion held over about $$G'(\omega)=\sum_i H(\Omega_i)\,\frac{(\omega/\Omega_i)^2}{1+(\omega/\Omega_i)^2}, \qquad G''(\omega)=\sum_i H(\Omega_i)\,\frac{\omega/\Omega_i}{1+(\omega/\Omega_i)^2},$$3 around room temperature at 1 Hz. The semi-cured low-$$G'(\omega)=\sum_i H(\Omega_i)\,\frac{(\omega/\Omega_i)^2}{1+(\omega/\Omega_i)^2}, \qquad G''(\omega)=\sum_i H(\Omega_i)\,\frac{\omega/\Omega_i}{1+(\omega/\Omega_i)^2},$$4 formulation also self-healed at $$G'(\omega)=\sum_i H(\Omega_i)\,\frac{(\omega/\Omega_i)^2}{1+(\omega/\Omega_i)^2}, \qquad G''(\omega)=\sum_i H(\Omega_i)\,\frac{\omega/\Omega_i}{1+(\omega/\Omega_i)^2},$$5: after 1 h it recovered 55% of elongation at fracture and 74% of tensile strength, and after 24 h it recovered 76% and 96%, respectively. The same system could be reprocessed both thermo-mechanically and chemically.

The long-time deformation and failure of vitrimers are likewise chemistry-specific. In all-atom MD of a disulfide-exchange epoxy vitrimer, dynamic bonds preferentially aligned orthogonal to the loading axis during creep, decreasing axial stiffness during secondary creep and promoting larger creep strain than a corresponding epoxy without exchange; at longer times this increased strain led to void growth and tertiary creep (Singh et al., 2023). In tear tests on a disulfide vitrimer film, the fracture energy was decomposed as

$$G'(\omega)=\sum_i H(\Omega_i)\,\frac{(\omega/\Omega_i)^2}{1+(\omega/\Omega_i)^2}, \qquad G''(\omega)=\sum_i H(\Omega_i)\,\frac{\omega/\Omega_i}{1+(\omega/\Omega_i)^2},$$6

with strongly rate-dependent intrinsic fracture energy $$G'(\omega)=\sum_i H(\Omega_i)\,\frac{(\omega/\Omega_i)^2}{1+(\omega/\Omega_i)^2}, \qquad G''(\omega)=\sum_i H(\Omega_i)\,\frac{\omega/\Omega_i}{1+(\omega/\Omega_i)^2},$$7 and only weakly rate-dependent bulk dissipation $$G'(\omega)=\sum_i H(\Omega_i)\,\frac{(\omega/\Omega_i)^2}{1+(\omega/\Omega_i)^2}, \qquad G''(\omega)=\sum_i H(\Omega_i)\,\frac{\omega/\Omega_i}{1+(\omega/\Omega_i)^2},$$8 (Song et al., 2021). Over normalized crack velocities $$G'(\omega)=\sum_i H(\Omega_i)\,\frac{(\omega/\Omega_i)^2}{1+(\omega/\Omega_i)^2}, \qquad G''(\omega)=\sum_i H(\Omega_i)\,\frac{\omega/\Omega_i}{1+(\omega/\Omega_i)^2},$$9 to $$\tau_{\text{bond}} \cong \tau_{\text{ex}}+\tau_{\text{diff}} \cong \tau_{\text{ex}}+c\,\tau_\alpha.$$0, the reported bulk dissipation was about

$$\tau_{\text{bond}} \cong \tau_{\text{ex}}+\tau_{\text{diff}} \cong \tau_{\text{ex}}+c\,\tau_\alpha.$$1

while $$\tau_{\text{bond}} \cong \tau_{\text{ex}}+\tau_{\text{diff}} \cong \tau_{\text{ex}}+c\,\tau_\alpha.$$2 followed an Eyring-type logarithmic rate dependence. These results differ sharply from standard viscoelastic-fracture assumptions in which bulk dissipation carries most of the rate sensitivity.

Chemical kinetics alone do not determine practical processability. In transesterification-capable epoxy–thiol vitrimers, the Arrhenius activation energies extracted from stress relaxation were about 134, 92, 75, and 54 kJ/mol for EDDT, BD1, GDT, and GDMP networks, respectively, but the elastic–plastic transition under load was also strongly affected by rubbery stiffness (Gablier et al., 2020). Softer networks showed much lower vitrification temperatures even when their bond-exchange activation energies were higher. The same study found that increasing TBD concentration accelerated relaxation only up to approximately 4–5 mol%, above which the rate saturated, indicating a crossover from chemically limited to mobility- or encounter-limited exchange.

A systems-level demonstration of vitrimer mechanics is the recyclable vitrimer-based printed circuit board. Transesterification vitrimer PCBs supported functional 2.4 GHz Bluetooth IoT devices, high-speed eye-diagram testing at 2.48 Gb/s, repair of fractures and holes over more than four cycles, and shape recovery at 100 °C in 1 min (Zhang et al., 2023). The same platform achieved about 98% polymer recovery, 100% fiber recovery, and 91% solvent recovery, with storage-modulus retention of 96.9% after one recycling cycle and 94.4% after two. This established that vitrimer mechanics can be integrated with copper lamination, chemical etching, multilayer processing, and closed-loop composite recovery.

6. Design principles, inverse design, and unresolved questions

The cumulative design lesson of the vitrimer literature is that no single parameter governs performance. Segmental mobility and exchange kinetics must both be favorable for self-healing, welding, and reprocessing; bond exchange alone does not guarantee practical rearrangement if chain mobility is insufficient (Edera et al., 2024). Large negative activation entropy can suppress exchange even when activation enthalpy is modest (Cheng et al., 7 Aug 2025). Crosslinker compatibility and size can reverse the sign of densification and alter interfacial activity (Chankapure et al., 7 Sep 2025). Sticker incompatibility can shift the slow step from local chemistry to inter-domain transport (Karmakar et al., 26 Jun 2025). Linker concentration and protector chemistry can, in some systems, control equilibrium crosslinking itself rather than merely the rate of rearrangement (Lei et al., 2020, Xia et al., 2022). Taken together, these studies do not support a chemistry-only or rheology-only description of vitrimer design.

Data-driven discovery has begun to formalize that multidimensional design space. An MD-informed machine-learning workflow for bifunctional transesterification vitrimers used a dataset of 8,424 labeled vitrimer $$\tau_{\text{bond}} \cong \tau_{\text{ex}}+\tau_{\text{diff}} \cong \tau_{\text{ex}}+c\,\tau_\alpha.$$3 values drawn from 1,000,000 hypothetical chemistries sampled from a space of about 2.5 billion possible combinations (Zheng et al., 26 Mar 2025). The best single model, LASSO with Mordred descriptors, achieved

$$\tau_{\text{bond}} \cong \tau_{\text{ex}}+\tau_{\text{diff}} \cong \tau_{\text{ex}}+c\,\tau_\alpha.$$4

while the best ensemble reached

$$\tau_{\text{bond}} \cong \tau_{\text{ex}}+\tau_{\text{diff}} \cong \tau_{\text{ex}}+c\,\tau_\alpha.$$5

That workflow identified DGEBA + D,L-malic acid and DGEBA + 2,6-naphthalenedicarboxylic acid as new vitrimer chemistries with measured $$\tau_{\text{bond}} \cong \tau_{\text{ex}}+\tau_{\text{diff}} \cong \tau_{\text{ex}}+c\,\tau_\alpha.$$6 values of 348 K and 395 K, respectively, while retaining healability.

An AI-guided inverse-design framework based on a graph variational autoencoder constructed a vitrimer dataset of one million chemistries, calculated $$\tau_{\text{bond}} \cong \tau_{\text{ex}}+\tau_{\text{diff}} \cong \tau_{\text{ex}}+c\,\tau_\alpha.$$7 on 8,424 of them by high-throughput MD calibrated by a Gaussian process model, and generated candidates for a target

$$\tau_{\text{bond}} \cong \tau_{\text{ex}}+\tau_{\text{diff}} \cong \tau_{\text{ex}}+c\,\tau_\alpha.$$8

(Zheng et al., 2023). Incorporating chemical intuition, it led to a synthesized vitrimer with

$$\tau_{\text{bond}} \cong \tau_{\text{ex}}+\tau_{\text{diff}} \cong \tau_{\text{ex}}+c\,\tau_\alpha.$$9

together with experimentally demonstrated healability and flowability. These results suggest that inverse design for vitrimer networks can move beyond manual chemistry selection toward latent-space search constrained by dynamic-covalent functionality.

Several issues remain unsettled. The choice between WLF and Arrhenius descriptions is still debated and can be system dependent (Edera et al., 2024). Inverse relaxation-spectrum reconstruction is mathematically ill-posed, even when fits to $\alpha$0, $\alpha$1, and $\alpha$2 are excellent (Edera et al., 2024). The large prefactor $\alpha$3 needed in reaction/diffusion descriptions of some experimental systems remains unexplained (Branham-Ferrari et al., 23 Sep 2025). More broadly, vitrimer behavior is now understood to be governed by coupled control variables—exchange chemistry, segmental dynamics, activation entropy, density, microphase separation, defects, topology, and interface thermodynamics—so the most robust descriptions are those that keep all of these variables in the same framework rather than reducing the class to a single “vitrimer timescale” or “vitrimer activation energy.”