Covalent adaptable networks (CANs) can be classified into dissociative (Diss-CANs) and associative (Asso-CANs) networks according to the exchange mechanism of covalent bonds. We simulate the exchange reaction by the hybrid Monte Carlo–molecular dynamics (hybrid MC/MD) algorithm, aiming to discover the connection and difference between Diss-CANs and Asso-CANs in viscoelasticity behavior. In the linear regime, a major difference originating from the cross-linking density is reflected in the pre-exponential factor τs 0 of the characteristic relaxation time τs. For nonlinear rheology, Diss-CANs show a faster shear thinning behavior under steady shear, while Asso-CANs have a stronger strain hardening under the shear rate start-up. The physics behind the phenomenon results from the different chain conformations and configurations related to the exchange mechanism. Compared with Diss-CANs, the inability for sticker dissociation of Asso-CANs generates a slower relaxation under shear, leading to less chain orientation and tumbling. Meanwhile, we find that multiscale relaxation times obtained from linear viscoelasticity (LVE) can be crucial limits in nonlinear applications for associative polymers (APs). Our work strongly deepens the understanding of APs in terms of both linear and nonlinear viscoelasticities.

Polymers bearing associative groups can exhibit fascinating rheological behaviors. A modified version of the Rouse model, which is originally used in block copolymers and called the sticky Rouse model here, is proposed to describe the linear viscoelasticity (LVE) of this kind of polymers without the effect of entanglement. By replacing the lifetime of a transient bond by the effective friction on stickers, the calculation of LVE functions is turned into the eigenvalue problem of the sticky Rouse−Zimm (RZ) matrix. The results show that only two parameters, sticker concentration representing the network microstructure and association interaction strength, can understand the LVE for associative polymers. In particular, the description of LVE from previous theories can be integrated in this unified theoretical framework. From the analysis of eigenvectors, it is further inferred that the rotational motion of bridge structures should be responsible for the longest relaxation times in rheology.

Polymers bearing associative groups (APs) are characterized by their fantastic viscoelastic behaviors. In a work recently published by our group [Jiang et al., Macromolecules 53, 3438–3451 (2020)], a single chain sticky Rouse model (SRM) is proposed to describe the linear viscoelasticity of APs without the entanglement effect. In this work, equilibrium molecular dynamics simulation of an unentangled melt of an AP with uniformly distributed stickers is carried out, and the dynamic properties are simultaneously analyzed from the SRM. A chain model with capped stickers is proposed so that a well-defined association chemistry is promised in the simulation system. The relative effective frictional coefficient of stickers, which is the key parameter in the SRM, is extracted from the chain center-of-mass diffusion, and it is found to be consistent with the dynamics of associative reaction in the fully gelated network. Based on this, a linear relaxation modulus and segmental diffusion functions are predicted from the SRM without fitting parameters, and these are found to quantitatively agree with the simulation results, showing the effectiveness of the SRM in connecting the dynamic properties at different molecular levels. The change in relaxation modes and the definition of the effective chain center are found to be crucial in the scenario of the SRM. Finally, the above analysis from the SRM is successfully extended to the simulation system with asymmetric chains. All these simulation results strongly support the SRM as a molecular model for the linear rheology of AP.

Understanding the nonlinear dynamics of an unentangled polymer melt from the bead-spring chain model requires knowledge of the variation of spring stiffness, monomeric friction, and Brownian intensity. In this work, these nonequilibrium (NE) parameters are quantified in the model simulation systems of unentangled melt under steady-flow conditions. We focus on a particular version of the model with undefined NE parameters. Some expressions to relate the NE parameters with the rheological and structural properties are pointed out. The spring stiffening parameter r κ is proven to be easily accessible in the planar flows. The distribution of the stiffening effect along the polymer contour is identified. The alignment-induced reduction of monomeric friction is confirmed in the simulation systems, but the anisotropic feature of friction is also emphasized. The constraint on the cooperative variation of spring stiffness and friction is proven to be an important property of extensional flow. The variation of Brownian intensity is found to be decoupled with the variation of friction, which means the violation of the fluctuation–dissipation (FD) theorem. The NE parameters of the simulation systems are further compared with those from the experimental systems.

Dual polymer networks with stickers have a reputation for enhanced modulus and toughness. We propose a modified sticky Rouse model (SRM) from the single-chain perspective for permanent and transient dual networks, aiming to find a universal description of associative polymer dynamics. The computational complexity of obtaining the analytical relaxation spectrum is simplified by graph theory, implementing matrix reduction of the Rouse–Zimm matrix based on the symmetry. The analytical relaxation spectrum can also return to the case of linear polymers and permanent networks. The modified SRM for dual polymer networks predicts a Rouse-like scale of the linear relaxation modulus G(t) ∝ t –1/2 in sticker relaxation, consistent with the existing experimental results. In particular, the key parameter in the SRM, namely, the effective friction coefficient, can be extracted from the lifetime of sticky bonds and diffusion of chains, obtained by molecular dynamics simulations (MD). Based on that, the SRM model can predict the linear viscoelasticity of dual polymer networks, quantitatively in agreement with our MD results. Our work strongly supports the applicability of the single-chain molecular model SRM for polymer complex networks with reversible associative interactions.