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Due to the wide application, it is very crucial to understand the viscoelasticity of the polyurethane elastomer (PU, denoted by soft-hard block copolymer), which contains the soft segments (SS) and hard segments (HS). Thus, in this work, the effect of the content and strength of HS on the viscoelasticity of PU is explored in detail by adopting a coarse-grained model. First, the phase morphology of PU is characterized where both the single continuous phase and the bicontinuous phase are observed by varying the content of HS. Then, the viscoelasticity of PU is calculated by analyzing the storage modulus, the loss modulus, and the loss factor, which depends on the content and strength of HS. To further elucidate the mechanism for the storage modulus, the normalized interaction energy, the order parameter, and the formation probability of the HS or SS phase are characterized with the shear strain amplitude, which reflects the deformation of the phase structure. Then, the energy dissipation is quantified, which can rationalize the loss modulus well. A parameter is introduced, which considers the relative slippage and the content of HS or SS. It can explain the change in the loss factor with the content and strength of HS. In summary, this work can help to further understand how the content and strength of hard segments affect the viscoelasticity of the soft-hard block PU and structure evolution at the molecular level.

Correction for ‘Effect of the content and strength of hard segment on the viscoelasticity of the polyurethane elastomer: insights from molecular dynamics simulation’ by Yimin Wang et al., Soft Matter, 2022, 18, 4090–4101, https://doi.org/10.1039/D2SM00463A.

In this work, coarse-grained molecular dynamics simulation is adopted to investigate the effect of hybrid fillers [nanospheres (NSs) and nanorods (NRs)] on the conductive probability of polymer nanocomposites (PNCs) in the quiescent state and under the shear field. The percolation threshold gradually rises as the volume fraction ratio (α) of NSs to all the fillers increases in the quiescent state. Compared to the NSs, the greater number of beads in the NRs help them connect to other NRs to form the conductive network. Meanwhile, compared to NSs, more NRs participate in building the conductive network. A transition from the synergistic effect to the antagonistic effect occurs as the NS-NR tunneling distance is reduced. Furthermore, the shear field induces a more direct aggregation structure of NSs, which act as linkers between fillers to protect the conductive network. This result is confirmed by the fact that more NSs occupy the conductive network under the shear field. As a result, the percolation threshold declines with increasing shear rate. Finally, compared to in the quiescent state, the percolation threshold increases at α = 0.0 and remains nearly unchanged for α = 0.25 under the shear field, while it gradually decreases for α≥ 0.5. In total, the results further our understanding of how to realize the synergistic effect between NSs and NRs when forming a conductive network of PNCs.

It is very important to understand the molecular mechanism of the fracture behavior of chemically cross-linked polymer nanocomposites (PNCs). Thus, in this work, by employing a coarse-grained molecular dynamics simulation we investigated the effect of the cross-link density and the cross-link distribution on it by calculating the void formation and the chemical bond scission. Considering the fracture energy, the optimal fracture properties of PNCs are realized at the moderate cross-link density which results from the competition between the chain slippage induced voids and the bond scission induced voids. Meanwhile, more bond scission occurs on the chain backbone while a high broken percentage of the cross-link bonds appears between chains because of the higher average stress borne by one cross-linked bead than by one other bead. In addition, the number of voids is quantified which first increases and then decreases with the strain at low cross-link density. However, the number of newly formed voids increases again at high cross-link density. Finally, it decreases because of the low rate of bond scission. Furthermore, the chemical bonds are broken at a similar strain for the uniform cross-link distribution while they are broken at any strain for the nonuniform cross-link distribution. The low number of broken bonds induces the disappearance of the second peak of the number of voids with the strain for the nonuniform cross-link distribution. In summary, this work could provide a clear understanding of the fracture mechanism of the chemically cross-linked PNCs on the molecular level.

It is very important to improve the electrical conductivities of polymer nanocomposites (PNCs) as this can widen their application. In this work, by employing a coarse-grained molecular dynamics simulation, we investigated the effect of the amphiphilic diblock copolymer (BCP)-mediated nanoparticle (NP) on the conductive probability of polymer nanocomposites (PNCs) in the quiescent state and under a shear field. The conductive probability of PNCs first increases and then decreases with increasing content of BCPs while, interestingly, it exhibits an N-type dependence on the A-Block–NP interaction. Furthermore, the conductive probability shows a non-monotonic dependence on the fraction of A block (fA) in the BCPs, which reaches the maximum value at moderate fA. Under the shear field, NPs self-assemble to form the sandwich-like structures in the matrix above a critical concentration of BCPs, which leads to the anisotropic conductive probability of PNCs. In addition, the sandwich-like structures of NPs will be broken down at a high shear rate, which reduces the difference of the directional conductive probabilities. Last, the mechanism of the formation of the sandwich-like structures of NPs is discussed. In summary, this work presents a simple method to control the conductive network formation, which can help to design PNCs with high electrical conductivity, and especially anisotropy.

By adopting coarse-grained molecular dynamics simulations, the effect of polymer functionalization on the relationship between the microstructure and the electric percolation probability of nanorod filled polymer nanocomposites has been investigated. At a low chain functionalization degree, the nanorods in the polymer matrix form isolated aggregates with a local order structure. At a moderate chain functionalization degree, the local order structure of the nanorod aggregate is gradually broken up. Meanwhile, excessive functionalization chain beads can connect the isolated aggregates together, which leads to the maximum size of nanorod aggregation. At a high chain functionalization degree, it forms a single nanorod structure in the matrix. As a result, the highest percolation probability of the materials appears at the moderate chain functionalization degree, which is attributed to the formation of the tightly connected nanorod network by analyzing the main cluster. In addition, this optimum chain functionalization degree exists at two chain functionalization modes (random and diblock). Lastly, under the tensile field, even though the contact distance between nanorods nearly remains unchanged, the topological structure of the percolation network is broken down. While under the shear field, the contact distance between nanorods increases and the topological structure of the percolation network is broken down, which leads to a decrease in the percolation probability. In total, the topological structure of the percolation network dominates the percolation probability, which is not a necessary connection with the contact distance between nanorods. In summary, this work presents further understanding of the electric conductive properties of nanorod-filled nanocomposites with functionalized polymers.

By adopting coarse-grained molecular dynamics simulation, we investigate the effects of end-functionalization and shear flow on the destruction and recovery of a nanorod conductive network in a functionalized polymer matrix. We find that the end-functionalization of polymeric chains can enhance the electrical conductivity of nanorod filled polymer nanocomposites, indicated by the decrease of the percolation threshold. However, there exists an optimal end-functionalization extent to reach the maximum electrical conductivity. In the case of steady shear flow, both homogeneous conductive probability and directional conductive probability perpendicular to the shear direction decrease with the shear rate, while the directional conductive probability parallel to the shear direction increases. Importantly, we develop a semi-empirical equation to describe the change of the homogeneous conductive probability as a function of the shear rate. Meanwhile, we obtain an empirical formula describing the relationship between the anisotropy of the conductive probability and the orientation of the nanorods. In addition, the conductivity stability increases with increasing nanorod volume fraction. During the recovery process of the nanorod conductive network, it can be fitted well by the model combining classical percolation theory and a time-dependent nanorod aggregation kinetic equation. The fitted recovery rate is similar for different nanorod volume fractions. In summary, this work provides some rational rules for fabricating polymer nanocomposites with excellent performance of electrical conductivity.

Designing a multiple-network structure at the molecular level to tailor the mechanical properties of polymeric materials is of great scientific and technological importance. Through the coarse-grained molecular dynamics simulation, we successfully construct an interpenetrating polymer network (IPN) composed of a flexible polymer network and a stiff polymer network. First, we find that there is an optimal chain stiffness for a single network (SN) to achieve the best stress–strain behavior. Then we turn to study the mechanical behaviors of IPNs. The result shows that the stress–strain behaviors of the IPNs appreciably exceed the sum of that of the corresponding single flexible and stiff network, which highlights the advantage of the IPN structure. By systematically varying the stiffness of the stiff polymer network of the IPNs, optimal stiffness also exists to achieve the best performance. We attribute this to a much larger contribution of the non-bonded interaction energy. Last, the effect of the component concentration ratio is probed. With the increase of the concentration of the flexible network, the stress–strain behavior of the IPNs is gradually enhanced, while an optimized concentration (around 60% molar ration) of the stiff network occurs, which could result from the dominant role of the enthalpy rather than the entropy. In general, our work is expected to provide some guidelines to better tailor the mechanical properties of the IPNs made of a flexible network and a stiff network, by manipulating the stiffness of the stiff polymer network and the component concentration ratio.

This paper deals with molecular-dynamics simulations of the mechanical properties of prestretched double network filled elastomers. To this end, we firstly validated the accuracy of this method, and affirmed that the produced stress-strain characteristics were qualitatively consistent with Lesser's experimental results on the prestretched tri-block copolymers with a competitive double network. Secondly, we investigated the effect of the crosslinking network ratio on the mechanical properties of the prestretched double network homopolymers under uniaxial tension. We found that the prestretched double network contributes greatly to the enhanced tensile stress and ultimate strength at fracture, as well as to the lower permanent set (the residual strain) and dynamic hysteresis loss, both parallel and perpendicular to the prestretching direction. Notably, though, an anisotropic behavior was observed: in the parallel direction, both the first and the second crosslinked networks bore the external force; whereas in the perpendicular direction, only the second crosslinked network was relevantly effective. Finally, the polymer nanocomposites with a prestretched double network exhibited tensile mechanical properties similar to those of the studied homopolymers with prestretched double networks. Summing up the results, it can be concluded that the incorporation of prestretched double networks with a specified crosslinking network ratio seems to be a promising method for manipulating the mechanical properties of elastomers and their nanocomposites, as well as for introducing anisotropy in their mechanical response.

To systematically study the effect of functionalized chain groups on polymer nanocomposites, we perform our simulation work in the following two ways. In the case of dilute loading of nanoparticles (NPs) with different geometries (spherical, sheet-like, rod-like NPs), we adopt coarse-grained molecular dynamics simulation to study the structural, dynamic and mechanical properties of polymer nanocomposites influenced by the terminal groups of linear polymer chains. We observe that the terminal groups have more probability to be adsorbed onto the surface of NPs with decreasing temperature, chain molecular weight and increasing chain stiffness. For all NPs with different geometries, more terminal groups segregate into the surface of NPs with increase in the interaction energy εf-n between the terminal groups and the NPs. We also notice that the attractive interaction between the terminal groups and the sheet-like NPs induces the appearance of a gradient of translational dynamics of polymer chains, and the relaxation at the chain length scale is evidently different for various adsorbed layers, whereas the segmental relaxation only becomes slightly slower nearby the sheet-like NPs. For both pure and filled systems with spherical NPs, it is found that the stress-strain curves and bond orientations are significantly enhanced with increase in the interaction strength between the terminal groups as well as terminal groups and NPs. In the case of concentrated loading of NPs, we construct the atomistic models of C60, CNT and graphene to accurately account for the "many body effect." We explore the influence of the functionalization position along the chain backbone on the dispersion kinetics, realizing that the end-functionalization is more effective. The end-groups effect on the chain configuration, chain packing and graphene equilibrium dispersibility is examined. The translational and rotational (segmental and terminal relaxation) dynamics influenced by the interactions between the end groups and graphene are probed by tuning εf-n and the volume fraction of graphene ϕ. Moreover, the shift in the glass transition temperature influenced by εf-n and ϕ is quantitatively estimated by fitting the temperature dependence of the relaxation time using the Vogel-Fulcher-Tammann (VFT) equation. This work is hoped to provide a deep understanding of the polymer nanocomposites with functionalized polymer chains.

By setting up a coarse-grained model of polymer nanocomposites, we monitored the change in the elastic modulus as a function of the strain, derived from the stress-strain behavior by determining uniaxial tension and simple shear of two typical spatial distribution states (aggregation and dispersion) of nanoparticles (NPs). In both these cases, we observed that the elastic modulus decreases non-linearly with the increase of strain and reaches a low plateau at larger strains. This phenomenon is similar to the so-called "Payne effect" for elastomer nanocomposites. Particularly, the modulus of the aggregation case is more sensitive to the imposed strain. By examining the structural parameters, such as the number of neighboring NPs, coordination number of NPs, root-mean-squared average force exerted on the NPs, local strain, chain conformations (bridge, dangle, loop, interface bead and connection bead), and the total interaction energy of NP-polymer and NP-NP, we inferred that the underlying mechanism of the aggregation case is the disintegration of the NP network or clusters formed through direct contact; however, for the dispersion case, the non-linear behavior is attributed to the destruction of the NP network or clusters formed through the bridging of adsorbed polymer segments among the NPs. The former physical network is influenced by NP-NP interaction and NP volume fraction, while the latter is influenced by NP-polymer interaction and NP volume fraction. Lastly, we found that for the dispersion case, further increasing the inter-particle distance or grafting NPs with polymer chains can effectively reduce the non-linear behavior due to the decrease of the physical network density. In general, this simulation work, for the first time, establishes the correlation between the micro-structural evolution and the strain-induced non-linear behavior of polymer nanocomposites, and sheds some light on how to reduce the "Payne effect".