Next-Generation Vitrimers Design through Theoretical Understanding and Computational Simulations

Abstract

Vitrimers are an innovative class of polymers that boast a remarkable fusion of mechanical and dynamic features, complemented by the added benefit of end-of-life recyclability. This extraordinary blend of properties makes them highly attractive for a variety of applications, such as the automotive sector, soft robotics, and the aerospace industry. At their core, vitrimer materials consist of crosslinked covalent networks that have the ability to dynamically reorganize in response to external factors, including temperature changes, pressure variations, or shifts in pH levels. In this review, the aim is to delve into the latest advancements in the theoretical understanding and computational design of vitrimers. The review begins by offering an overview of the fundamental principles that underlie the behavior of these materials, encompassing their structures, dynamic behavior, and reaction mechanisms. Subsequently, recent progress in the computational design of vitrimers is explored, with a focus on the employment of molecular dynamics (MD)/Monte Carlo (MC) simulations and density functional theory (DFT) calculations. Last, the existing challenges and prospective directions for this field are critically analyzed, emphasizing the necessity for additional theoretical and computational advancements, coupled with experimental validation.

Keywords: Monte Carlo simulations; bond exchange reactions; density functional theory; molecular dynamics simulations; vitrimers.

Figure 1

Scheme and image illustration of computational understanding and aid design vitrimer materials. Reproduced with permission.^{[ 21c ]} Copyright 2022, American Chemical Society. Reproduced with permission.^{[ 24 ]} Copyright 2020, PNAS. Reproduced with permission.^{[ 21a ]} Copyright 2022, American Chemical Society. Reproduced with permission.^{[ 20k ]} Copyright 2022, Wiley. Reproduced with permission.^{[ 25 ]} Copyright 2022, Elsevier. Reproduced with permission.^{[ 20a ]} Copyright 2022, American Chemical Society.

Figure 2

Simulation methods. Computational accuracy versus simulation time and length scale. MLMD emerging as a potential approach to address the balance between computational cost and accuracy in conventional MD simulations.

Figure 3

a) Flowchart of the bond exchange reaction process. Reproduced with permission.^{[ 76a ]} Copyright 2015, Royal Society of Chemistry. b) The radial dependence of a (normalized) typical bond potential and the associated V₃(r) potential. Reproduced with permission.^{[ 21f ]} Copyright 2017, Springer. c) Flowchart of the crosslink process. Reproduced with permission.^{[ 76a ]} Copyright 2015, Royal Society of Chemistry. d) 3D coarse‐grained network of simulated vitrimer. Reproduced with permission.^{[ 21i ]} Copyright 2023, Wiley. e) Schematic graphs of the MD simulation of the welding process. Reproduced with permission.^{[ 83 ]} Copyright 2016, Royal Society of Chemistry.

Figure 4

a) Reduced (left) specific volume and (right) thermal expansion coefficient as a function of reduced temperature T̃ (T̃ = K _B T/ε, k _B is the Boltzmann constant, ε is the well depth of Lennard–Jones potential), T̃ _g and T̃ _v denote the glass transition temperature and the topology freezing temperature, respectively. Reproduced with permission.^{[ 21b ]} Copyright 2020, American Chemical Society. b) Simulated phase diagram as a function of temperature T and bulk density (left). Distance r ₀ corresponds to the main peak of the radial distribution function g(r) as a function of vitrimer bulk density (right). Reproduced with permission.^{[ 82 ]} Copyright 2019, PNAS.

Figure 5

a) Normalized stress relaxation under the constant uniaxial strain of 300% imposed as a step at t = 0 for a range of bond swap energy barriers. b) Self‐healing efficiency for different bond swap energy barriers. c) Schematic of self‐healing. Reproduced with permission.^{[ 21c ]} Copyright 2022, American Chemical Society. d) Universal curves of the creep compliance as a function of reduced time for (left) thermoset and (right) vitrimer. Reproduced with permission.^{[ 21i ]} Copyright 2022, Wiley.

Figure 6

a) Comparison between the defect allowing mixture (DAM) and defect free mixture (DFM) stress relaxation values. b) Histogram of the number of connections between connected stars for both mixtures. Reproduced with permission.^{[ 45 ]} Copyright 2018, American Physical Society. c) Dependence of the bond lifetime τ _b and the slow relaxation time τ _s for several E _a values. Reproduced with permission.^{[ 53 ]} Copyright 2019, Royal Society of Chemistry.

Figure 7

a) Autocorrelation function of exchangeable bonds as a function of simulation time at different temperatures (left). Average lifetime of bonds as a function of temperature (right). Reproduced with permission.^{[ 21b ]} Copyright 2020, American Chemical Society. b) Stress–strain relations of the simulated thermoset and vitrimer system for various values of α. Number of successful bond exchanges as a function of reduced time during uniaxial extension simulations of vitrimers for various α values (α is an artificial parameter, which is used to scale the energy difference between two states in the MC step). Reproduced with permission.^{[ 21g ]} Copyright 2021, Wiley.

Figure 8

a) The structures of N,O‐dimethylcarbamate and activation energy E _a as a function of the O═C(OCH₃)N(H)CH₃ dihedral angle. Reproduced with permission.^{[ 20i ]} Copyright 2015, American Chemical Society. b) Calculated free energy diagram for the reaction between methyl but‐2‐ynoate with different amines. Reproduced with permission.^{[ 7c ]} Copyright 2021, American Chemical Society. c) Bond dissociation energy (Ho‐BDE) and heterolytic bond dissociation energies (He‐BDE) of the Se─Se bond in Bn‐Se₂ with increasing solvent polarity and the polarity of the molecular groups. Reproduced with permission.^{[ 105 ]} Copyright 2022, American Chemical Society.

Figure 9

a) Illustration of the two‐step metathesis reactions, the heterogeneous dilute and homogeneous dense systems of the vitrimers. b) Entropy‐driven cross‐linking at low temperature. Reproduced with permission.^{[ 24 ]} Copyright 2020, PNAS. c) Schematic diagram of the entropy‐driven crosslinking induced sol–gel transition to form thermo‐gelling vitrimer. d) Snapshots of structural change at different temperature. e) Thermo‐gelling vitrimers, structural relaxation time, and crosslinking degree as a function of temperatures for various activation barriers. Reproduced with permission.^{[ 21a ]} Copyright 2022, American Chemical Society.

Figure 10

a) Scheme of synthetic route of the polyimine–metal complex vitrimers. Reproduced with permission.^{[ 111 ]} Copyright 2020, American Chemical Society. b) Self‐healing simulation results of GO/vitrimer and vitrimer, 370 K. c) Percentage of new disulfide bonds as the BER loop count increases and number of new disulfide bonds at the end of the BER loop in the self‐healing region and the interphase. Reproduced with permission.^{[ 118 ]} Copyright 2020, Elsevier. d) Simulating the vitrimer and its healing using MD simulation. Reproduced with permission.^{[ 73b ]} Copyright 2021, Elsevier.

Figure 11

a) Reaction energy profiles for the transesterification catalyzed by 1‐MI (blue), TBD (black), Zn(OAc)₂ (red), and DETO (green) in solution‐ and gas‐phase and solution‐phase transition‐state energies and intermediate energies plotted versus gas‐phase SN₂ enhancement indices with linear fits for each energy series. Reproduced with permission.^{[ 26 ]} Copyright 2021, American Chemical Society. b) Optimized structure and the HOMO‐LUMO gaps of the chosen catalysts. c)Free energy surface of the polymerization of ABA catalyzed by zinc acetate. Reproduced with permission.^{[ 25 ]} Copyright 2022, Elsevier.

Figure 12

a) Proposed mechanisms of the exchange reaction in neutral and acidic conditions (protic, top) and in basic conditions or in the presence of Lewis acids (aprotic, bottom). b) Potential energy surface of the exchange reaction through the protic mechanism for different vinylogous acyl compounds. X = O (black line), S (yellow line), NH (red line), and CH₂ (green line). Reproduced with permission.^{[ 20k ]} Copyright 2022, Wiley.