Composites Science and Technology 211 (2021) 108849

Available online 7 May 20210266-3538/© 2021 Elsevier Ltd. All rights reserved.

Molecular dynamics simulations of thermodynamics and shape memory effect in CNT-epoxy nanocomposites

Wei Jian a, Xiaodong Wang b, Haibao Lu b,**, Denvid Lau a,c,*

a Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong, China b Science and Technology on Advanced Composites in Special Environments Laboratory, Harbin Institute of Technology, Harbin, 150080, China c Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

A R T I C L E I N F O

Keywords: Carbon nanotubes Nano composites Shape memory behaviour Molecular dynamics

A B S T R A C T

Epoxy based shape memory polymers have attracted considerable attention in engineering applications. To achieve excellent thermo-mechanical performance, carbon nanotube (CNT) is used as reinforcement for epoxy matrix. The improvement of mechanical properties and shape memory effect in CNT-epoxy nanocomposites are investigated using molecular dynamics simulations in this study. The two representative systems, neat epoxy and CNT-reinforced epoxy nanocomposite are constructed, and the corresponding physical properties, such as the density and the glass transition temperature are obatained. The mechanical properties and shape memory be-haviors within the selected temperature range are characterized by applying tensile loading. The segmental dynamics are also captured during deformation process to investigate how epoxy chains are activated and changed that leads to final conformations. In addition, the free volume during recovery process is tracked to study shape recovery properties. The results can provide better understanding of the reinforcing mechanism of CNT on mechanical properties and shape memory effect of epoxy nanocomposites, which help to enrich the fundamental knowledge of shape memory epoxy nanocomposites and enlightens the design of shape memory materials.

1. Introduction

Shape memory polymers (SMPs) are novel smart materials with the ability to recover from one or more temporarily deformed shapes to their original permanent shape upon appropriate external stimuli, such as heat, humidity, light, pH, electric current, magnetic field or radio-frequency waves [1]. Due to unique structural characteristics, low cost of manufacturing and excellent physical and mechanical properties including low density, super elasticity above the glass transition tem-perature and potential biocompatibility and biodegradability, SMPs have attracted increasing interest from academia and industry [2–4]. Recent development in SMPs has led to remarkable advances in various applications from deployable space structures in spacecraft, intelligent biomedical devices or implants for surgery, smart fabrics and actuators to 4D printed architectures [5,6].

Epoxy based SMPs have been widely applied as structural materials for engineering applications because of their high thermo-mechanical endurance, satisfactory processability, good shape fixity and chemical

stability with cross-linked network. The practicability of epoxy based SMPs has been investigated in previous studies [7–11]. It is found that the shape fixity and recovery of shape memory epoxy polymers can be reached to 95–100% [7]. Highly deformable shape memory epoxy sys-tem is reported by varying the molar ratio of two components in epoxy matrix [8]. The resulting glass transition temperature (Tg) of SMP can be tuned from 40 ◦C to 80 ◦C, and the strain at break can be increased up to 111% above Tg and 212% within Tg transition [8]. The glass transition temperature of shape memory epoxy is also tuned by varying cross-linked density or chain flexibility of polymer systems [9]. The epoxy-acrylate hybrid photopolymer is applied in fabricating SMPs through three-dimensional printing techniques, which presents high shape fixity ratio, shape recovery ratio and excellent cycling stability [11]. In addition, the printed material has good thermal stability, high strength and good toughness [11]. Although epoxy based SMPs present many advantages in shape-memory properties, the low recovery stress and low deformability are the main drawbacks that become the restricting factors in potential applications. An effective approach to

* Corresponding author. Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong, China. ** Corresponding author.

E-mail addresses: luhb@hit.edu.cn (H. Lu), denvid@mit.edu (D. Lau).

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journal homepage: www.elsevier.com/locate/compscitech

https://doi.org/10.1016/j.compscitech.2021.108849 Received 6 December 2020; Received in revised form 28 March 2021; Accepted 4 May 2021

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reinforce epoxy based SMPs is to incorporate fillers into polymer matrix [12]. Different types of fillers have been used in the experiments, including microfibers [10,13,14], mineral oxide particles [15] and carbon nanotubes (CNTs) [16–18]. Among these fillers, CNT is a po-tential candidate because of its high specific strength and superb ther-mal and electrical conductivity. The shape memory epoxy nanocomposites with a small amount of CNTs present pronounced enhancement in the flexural modulus, maximum stress and strain at break with a fast recovery [17]. The incorporation of CNTs in epoxy matrix results in the improvement of reversible plasticity shape memory properties including shape fixity, response temperature and recovery speed [18]. By controlling filler content and programming condition to tailor glass transition temperature and mechanical properties, shape memory epoxy nanocomposites can be further designed into smart structures with versatile capabilities. Such modification over the mate-rial parameters in SMPs requires in-depth knowledge of how the addi-tion of CNTs affects the structure and behavior of epoxy matrix during deformation and recovery process, which is still lacking in the current stage. Various theoretical models for the working mechanism of shape memory effect in SMPs under different conditions have already been developed, which agree well with experimental findings [19–23]. However, the detailed molecular movement and the specific interactions in the material systems are not explicitly obtained.

To understand underlying structure-property relationship for the design of advanced shape memory epoxy nanocomposites, molecular dynamics (MD) simulations act as an effective and reliable method for investigation from nanoscale. MD approach enables detailed exploration at the atomistic level in material systems, and efficient prediction of material properties in polymer systems [24,25]. The predicted glass transition temperature of SMPs with varying molecular weights using MD simulations has been found in a good agreement with experimental measurement and theoretical modeling results [26]. The mechanical responses under different external loadings and environmental condi-tions are also found to be closely related to the local structures of polymer matrix [27,28]. The segmental dynamics of polymer chains under external loadings can be obtained from MD simulations, and the relationship between segmental relaxation time and dynamic hetero-geneity is found to well describe polymer behavior [29,30]. These

reported results suggest that MD simulations are conducive to better understanding of material behaviors in polymer systems from atomistic level.

The present study aims to investigate the reinforcement of CNT on mechanical properties and shape memory effect in epoxy based SMPs using MD simulations. The neat epoxy and the epoxy nanocomposite reinforced by pristine single-walled carbon nanotube (SWCNT) are constructed, and the corresponding physical and mechanical properties as well as shape memory responses are obtained. In addition, the segmental dynamics in the two epoxy systems are captured during the tensile and deform-recovery processes for the structure-property rela-tionship. The free volume is tracked for the shape recovery properties. The results can provide better understanding of the reinforcing mecha-nism of CNT in shape memory behavior of epoxy nanocomposites, which helps to enrich the knowledge of SMPs and enlightens the design of shape memory epoxy nanocomposites for special applications.

2. Simulation method

In this study, the cross-linked network with the monomer, diglycidyl ether of bisphenol A (DGEBA), and the hardener, 4,4-diaminodiphenyl-methane (DDM), is chosen as the epoxy matrix. The chemical structures and atomistic representations are displayed in Fig. 1(a). The armchair (5,5) SWCNT segment with the diameter of 6.8 Å and the length of 49.2 Å is selected as the nano-filler in the nanocomposite system. It should be noted that although the length of SWCNT is several orders of magnitude shorter than that of the bulk materials, this model can represent the interfacial structures between CNT and epoxy matrix at atomistic level [31]. The corresponding weight fraction of CNT is 5.7 wt%. Generally, the weight fraction of CNT is not exceeding 10 wt% in experiments in consideration of CNT aggregation. The precise set-up of the nano-composite can be found in our previous work [25,31]. The initial epoxy matrix consisting of 180 DGEBA and 90 DDM molecules with 11,430 atoms in total are generated by Amorphous Cell module implemented in Materials Studio [32], and the selected size is capable to reproduce the physical and mechanical properties close to bulk cases [33–35]. An equilibration process takes place initially on the uncross-linked config-urations in preparation for the cross-linking reaction. The cross-linked

Fig. 1. (a) Chemical and atomistic structures of epoxy monomer DGEBA and hardener DDM; (b) Atomistic model of neat epoxy; (c) Atomistic model of CNT-epoxy nanocomposite. The unit vector in the direction of the z-axis is along the CNT alignment.

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networks are constructed through a dynamic cross-linking algorithm, which comprises several key steps including energy minimizations, structural relaxation and bond breaking and formation between reactive atoms [24]. This algorithm can produce highly cross-linked epoxy network with cross-linking density over 80%, which approaches the range of the synthesized epoxy in the market [24]. The final cross-linked structures of neat epoxy and CNT-epoxy nanocomposite are shown in Fig. 1(b) and (c). After the construction, the two epoxy systems are equilibrated in canonical (NVT) ensemble at a constant temperature of 300 K for 100 ps, and another equilibration process is carried out in the isothermal and isobaric (NPT) ensemble with a constant pressure of 1 atm for 10 ns. The initial cell size of the model is 50 × 50 × 50 Å3. After equilibrium, the cell sizes are 47.2 × 47.4 × 50.9 Å3 in neat epoxy and 49.4 × 49.8 × 49.8 Å3 in CNT-epoxy nanocomposite respectively. The root mean squared displacement (RMSD) of the atoms are measured to ensure the models are properly equilibrated.

The MD simulations involving the determination of glass transition temperature, tensile deformation and shape memory behavior are per-formed in the Large-scale Atomic/Molecular Massively Parallel Simu-lator (LAMMPS) software package [36]. The polymer consistent force field (PCFF) [37] is employed to calculate the potential energy of the two material systems, which has been extensively used in epoxy related nanocomposites and yields a good agreement with experimental results [25,31]. The long-range electrostatic interaction is computed using the Particle-Particle Particle-Mesh (PPPM) solver [38]. Periodic boundary conditions are implemented in all three dimensions. To determine the glass transition temperatures of the two epoxy systems, the models are firstly heated up to a high temperature of 450 K for the rubbery state. Then the system is cooled down to 250 K in steps of 10 K every 1 ns, and the corresponding cooling rate is 1 × 1010 K/s. The change of the density is used to calculate the glass transition temperature. Similar simulation method is used to obtain the glass transition temperature in shape memory polymers with good accuracy [39,40].

In the tensile tests, the simulation cell of the system is deformed in a step-wise manner along z direction while keeping the pressure along the other two directions constant. The unit vector in the direction of the z- axis is along the CNT alignment as a reference. It is noted that the most effective load transfer from epoxy matrix to CNT is achieved along the CNT alignment in the nanocomposite. The periodic boundary conditions are set for the three directions of the systems, and the tensile deforma-tion is performed in the isothermal and isobaric (NPT) ensemble at the temperature of 300 K and the pressure of 1 atm. This setting is to allow the lateral dimensions to adjust the deformation based on the relaxation of the system structures to mimic the actual longitudinal deformation profile. The applied strain rate is 1 × 108 s− 1, which is typical for polymer systems [41]. In the simulations, the stress is calculated in the form of virial stress, which is expressed as [42]:

σ(r⇀)=1V

∑

i

[12∑

i∕=j

r⇀ij ⊗ f⇀

ij − mi v⇀

i ⊗ v⇀i

]

(1)

where V is the total volume; (i,j) covers the values taken from x, y and z

directions; r⇀i is the position vector of atom i and r⇀ij means r⇀j − r⇀i; f⇀

ij is

the interatomic force of the atom j acting on the atom i; mi and v⇀i are the mass and velocity of atom i, respectively; the symbol ⊗ represents the cross product operator. The virial stress is monitored during the entire uniaxial tensile deformation process. The Young’s modulus is calculated through fitting the linear portion of the stress-strain curves, and aver-aged from ten replicas for each of the two systems. The microstructural change of epoxy chains during deformation is captured by calculating segmental dynamics of the two systems.

To investigate the shape memory behaviors of the two systems, a thermomechanical cycle is applied [43]. The thermomechanical cycle includes 4 steps: (1) a uniaxial tensile loading is performed at the tem-perature above Tg; (2) a cooling step to the temperature lower than Tg

with tensile deformation maintained; (3) a stress release step with the temperature kept below Tg; (4) a reheating step to observe the shape recovery. In the simulation, the thermo-mechanical cycle is covered as shown in Fig. 2. In the first step, the relaxed systems are heated to the temperature above Tg (i.e., 442 K for neat epoxy and 458 K for CNT-epoxy nanocomposite respectively), and then stretched uniaxially by the strain of 0.3 along z direction. Under this deformed strain, chain movements including chain extension and chain sliding are clearly visible. The shape memory behaviors including both the shape fixity and recovery are consistent with experimental observations. The deformed structures are subjected to a 5 ns relaxation to obtain the equilibrated states. Secondly, the systems are cooled down to the temperature of 300 K in the NVT ensemble with a cooling rate of 5 × 1010 K/s. The internal stress is released subsequently by equilibrating the systems in the NPT ensemble for 5 ns. The systems are finally heated to the original tem-perature above Tg for the recovery behavior. The changes of the strains in the cycle are recorded, and the segmental dynamics is also analyzed for the shape memory responses. Shape memory polymers generally take seconds to recover at experimental timescale, which is larger than the timescale in conventional MD simulations. To overcome the time limitation, metadynamics approach that can enhance the sampling of free energy landscape is applied. In the metadynamics approach, the penalty potential is added to the Hamiltonian of the system on a selected number of degrees of freedom. The system evolves towards the nearest equilibrated configuration during metadynamics simulation. In this study, the distance between the atoms at the two ends of the systems is selected as the collective variable as the distance reflects the state of recovery of the shape memory polymer systems. The elapsed time for the structural evolution is defined using transition state theory [44]:

t=[

υ0 exp(

−ΔEkBT

)]− 1

(2)

where ΔE is the energy barrier between the initial state and the state with highest energy, υ0 is the characteristic frequency factor, which is generally taken to be 10 THz, kB is the Boltzmann constant, and T is the temperature. In addition, the free volume is the driving force for the relaxation of segments, which is related to shape memory properties. Therefore, the molecular-sized free volume is tracked during shape re-covery process.

3. Results and discussion

3.1. Glass transition temperature

The glass transition temperature is an important parameter for shape memory polymers as the shape fixity and the recovery response of polymer chains take place at different temperature levels related to Tg [45]. In order to determine Tg for neat epoxy and CNT-epoxy nano-composite, the evolution of the density of the two systems with tem-perature is calculated from MD simulations as shown in Fig. 3. As the temperature decreases, the density increases. However, this change is not steady within the entire temperature range, which is indicated by the change of slope in the curves from rubbery state to glassy state. In the rubbery state, epoxy chains are flexible and can slide against each other. The volume of epoxy matrix is reduced with decreasing temperature, leading to the increase of density in a greater slope. As the system continues to be cooled down, the epoxy chains become more packed and closed to each other. In this state, the epoxy chains are less flexible and cannot move easily. The density starts to increase more slowly, indi-cating the transition to glassy state. The change from glassy state to rubbery state can be observed from the change in the slope of the curve. The value of Tg is given by the temperature at the intersections of two linear fitting lines in the rubbery and glassy regions with the coefficient of determination R2 > 0.97 or greater, and then takes average from three cases with different initial equilibrated structures for each of the two

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systems. The obtained Tg of CNT-epoxy nanocomposite is 408 K, which is 16 K higher than that of neat epoxy. The results are in a good agree-ment with experimental measurement [46,47]. The increase of glass transition temperature is caused by the change of the structural network due to the addition of the nano-filler. It is speculated that CNT has an essential effect on the density and atomic motion of epoxy matrix. From the simulation results, the density of CNT-epoxy nanocomposite is higher than that of neat epoxy. In addition, the glass transition

phenomenon exhibits a slight difference in the two systems. The change in the slope of the curve from glassy state to rubbery state is more modest in CNT-epoxy nanocomposite than that in neat epoxy. Similar observation has been reported in previous study [33], which have stated that the change in properties during the glass transition of the reinforced system becomes more gradual. The mean-squared displacement (MSD), which measures the deviation of a target to a reference trajectory of coordinates, can be used to characterize the local mobility of epoxy atoms. The MSD of the central carbon atoms, which are considered as the most mobile heavy atoms in the epoxy monomers [48], is measured as a function of time at the glass transition temperature for the two systems as shown in Fig. 4. At the glass transition temperature, the epoxy

Fig. 2. Schematic diagram of thermomechanical cycle in MD simulations to reveal shape memory effect.

Fig. 3. The change of density as a function of temperature in neat epoxy and CNT-epoxy nanocomposite. The glass transition temperature is obtained by the intersection of the two linear fittings in the rubbery and glassy regions as shown by red dash lines. The values of Tg are indicated by arrows with 392 K for neat epoxy and 408 K for CNT-epoxy nanocomposite. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 4. The mean squared displacement of the central carbon atoms on the epoxy monomers in epoxy matrix at glass transition temperature.

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matrix is experiencing the transition to a more flexible state. The chain mobility is accelerated under this condition and reflected on the mobile heavy atoms, i.e., carbon atoms on the epoxy chains. The results are consistent with previous simulation work in that the values of MSD are of the same order of magnitude for DGEBA-based epoxy systems [48]. Generally, polymer system with higher Tg presents slower molecular mobility. From the simulation results, the change of local mobility in the two systems is analogous at the beginning, then the dynamics of the system with CNT presents a slower trend. This can be explained by the increased Tg and density in CNT-epoxy nanocomposite. The cross-linking density is another factor that affects the local mobility in epoxy matrix, which can be influenced by the addition of CNTs with different weight fractions. Therefore, the Tg of shape memory epoxy nanocomposites can be tuned with a wide range by changing the content of CNTs and curing agents [17].

3.2. Tensile deformation

How the addition of nano-filler affects the mechanical properties of shape memory epoxy is investigated through tensile deformation. The stress-strain curves for the two systems in simulations are depicted in Fig. 5. The results show that CNT has a reinforcing effect on the me-chanical properties. The Young’s modulus is increased from 3.20 ± 0.17 GPa in neat epoxy system to 3.53 ± 0.19 GPa in CNT-epoxy nano-composite system. The reinforcement on the tensile properties have been observed from experiments, and the obtained Young’s modulus are in a good agreement with the experimental measurement which is about 3.49 GPa for neat epoxy [49]. To investigate the tensile deformation, the microstructural evolution and the change of free volume in the two systems are captured using OVITO [50]. From the initial states of the two systems in Fig. 6, it is found that the CNT-epoxy nanocomposite has a more compact structure compared to the neat epoxy. In addition, it can be clearly seen that neat epoxy suffers from larger deformation at the same deformed strain. The movements of epoxy chains are restricted in the glassy state as the energy barrier for torsional transition of chain structure is relatively high [51], and the free volume inside epoxy matrix is affected by the external loading during tensile process. More free volume is generated randomly inside the neat epoxy system when the epoxy chains are stretched or sliding, indicating more severe deforma-tion and the initiation of void nucleation. The interfacial interactions between CNT and epoxy matrix leads to the more compact system, and the results echo with the higher density situation discussed in the pre-vious section. The extension and sliding movement of epoxy chains triggered by the tensile loading take place mainly in the area away from the CNT-epoxy interfacial area, causing the deformed structure in the

surrounding boundary. To further understand the structural evolution during tensile defor-

mation, the segmental dynamics is calculated by measuring the bond autocorrelation functions in the two systems. The bond autocorrelation is defined as [52,53]:

Cb(t)= ⟨P2[u(0) ⋅ u(t)]⟩ (3)

Here, P2 is the second Legendre polynomial. u(0) and u(t) represent the unit vectors aligned along the bonds connecting the end carbon atom to the central carbon atom in epoxy monomer at the initial state and the running time t respectively. The angular brackets denote that an average is taking over all the bonds in the systems. This function has been applied to characterize the change of chain mobility during deformation process [31]. The results of segmental dynamics are shown in Fig. 7. The chain mobility is lowered with the addition of CNT, which can be seen by the slower decay of Cb(t) during the tensile process. The free volume generated inside epoxy matrix during deformation provides room for the movement of epoxy chains, which induces higher chain mobility. The chain mobility is enhanced by more free volume in the neat epoxy, while the chain mobility is found to be significantly restricted in the CNT-epoxy nanocomposite.

The molecular origin of material behavior is related to the activation of molecular mobility. To further quantify the measured segmental dy-namics and relaxation time, the bond autocorrelation function is fitted to Kohlrausch-Williams-Watts (KWW) stretched exponential relaxation function, which is expressed as [52,54]:

Cb(t)=C0 exp[−(t/

τeff)β] (4)

where C0 and τeff are the pre-exponential factor and the characteristic relaxation time respectively. β is the stretching exponent that describes the distribution of molecular relaxation time with the range between 0 and 1. By fitting the bond autocorrelation Cb to the KWW function as shown by the gray lines in Fig. 7, the pre-exponential factor, charac-teristic relaxation time and stretching exponent are obtained for the two systems. The CNT-epoxy nanocomposite exhibits a higher τeff of 29.8 ns compared to that of 10.6 ns in the neat epoxy, suggesting that the chain mobility in the neat epoxy matrix is enhanced more dramatically when it is exposed to the external tensile stress. This is because the larger deformation have a great influence on the chain mobility [30]. The stretching components also change slightly, with the value of 0.79 in the neat epoxy and 0.77 in the CNT-epoxy nanocomposite, which indicates the heterogeneity in the distribution of relaxation times. Echoed with the deformed states in different regions containing CNT, the CNT-epoxy nanocomposite is more heterogeneous compared to the neat epoxy.

3.3. Shape memory behavior

As the nano-filler plays an important role in the mechanical prop-erties of epoxy matrix, the effect on the shape memory behavior is investigated to unveil the reinforcing mechanism for tuning mechanical performance of epoxy based SMPs. The changes of strain in the two epoxy systems during shape recovery process at the same temperature above Tg are recorded as shown in Fig. 8. The two systems show fast strain recovery rate at the very beginning, then a slow recovery process with increasing simulation time is followed in the neat epoxy. The re-covery response keeps in a fast manner in the CNT-epoxy nano-composite. The recovery time calculated using Eq. (2) is about 14.5 ns for neat epoxy and about 3.5 ns for CNT-epoxy nanocomposite. The results indicate that the addition of CNT can remarkably increase the rate of shape recovery, and such enhancement has been found in the previous experiment [17].

The shape deformation and recovery of shape memory polymers are related to the segmental dynamics in the systems [23,51]. Fig. 9 presents the bond autocorrelation function of the two material systems during the shape recovery process based on Eq. (3). At the temperature above Tg, Fig. 5. The stress-strain curves for neat epoxy and CNT-epoxy nanocomposites.

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more free volume is available for the movements of epoxy chains, which causes the increase of chain mobility. From the calculation results, the CNT-epoxy nanocomposite has a faster decay in the bond autocorrela-tion function, which indicates higher segmental dynamics. The higher segmental dynamics reflects faster movement of the epoxy chains, which results in faster recovery response in CNT-epoxy nanocomposite. By fitting the bond autocorrelation functions to KWW function, the corre-sponding relaxation times are 4.8 ns for the neat epoxy and 4.3 ns for CNT-epoxy nanocomposite. It is speculated that the conformational states of epoxy chains are changed more easily with the addition of CNT,

resulting in the fast recovery in CNT-epoxy nanocomposite. In addition, the stretching exponents are 0.93 for the neat epoxy and 0.88 for CNT-epoxy nanocomposite, demonstrating the dynamic heterogeneity in the system with the addition of CNT. Similar to the state during tensile deformation, the segmental dynamics in CNT-epoxy nanocomposites displays heterogeneity in shape recovery process as the deformation is more severe in the area away from the interfacial zone. The stretched epoxy chains in the loose part are affected by the parts of cross-linked epoxy chains that are suffered from the interfacial adhesion between CNT and epoxy, and are recovered in a faster rate during the relaxation

Fig. 6. The snapshots of the deformation process for (a) neat epoxy and (b) CNT-epoxy nanocomposite at initial state and the deformed strain of 0.15 and 0.3. The voids generated inside epoxy matrix are presented in purple. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 7. The segmental dynamics of the two systems during tensile deformation.

Fig. 8. The change of strain as a function of time in the two systems during recovery process.

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time. However, the addition of CNTs with higher weight fraction can cause CNT aggregation and limitation of chain mobility. The limited dynamics in the epoxy matrix leads to the reduced rate of shape re-covery, and as a result, poor shape recovery behavior of nano-composites. The weight fraction of CNT is an important factor in the fabrication and application of CNT-epoxy shape memory nano-composites, which will be the focus in future investigation of epoxy based SMPs.

Free volume is critical for the relaxation of polymer chains in SMPs [55]. The changes of free volume in the two systems are tracked as shown in Fig. 10. In the neat epoxy, the free volume decreases rapidly at the beginning, and the voids in the deformed structure are filled by the reunion of epoxy chains. The reunion of epoxy chains is realized through chain movements as shown in Fig. 11. In this process, the epoxy chains are relaxed from the stretched conformation and become active under the temperature above Tg. Some chains reorient themselves in random manner, and some chains rearrange their structures. In addition, some active chains can also slide towards each other, leading to the reunion. The reduction slows down at the second stage, reflecting the slow decrease of strain in the strain-time curve. However, the free volume changes slightly in the CNT-epoxy nanocomposite during the shape re-covery process. Compared to neat epoxy, CNT-epoxy nanocomposite has a more compact structure. During tensile deformation, the load is not directly applied on the CNT. Instead, the stress is transferred from soft epoxy matrix to hard CNT with high tensile strength and toughness

through the interface, dissipating the effect of the applied tensile load. Therefore, epoxy chains are not deformed as much as those in neat epoxy, and the voids generated inside the epoxy matrix during tensile deformation are less compared to those of the neat epoxy, as shown in Fig. 6. During the shape recovery, the epoxy chains around the CNT mostly align themselves on the surface of CNT due to the π-π stacking interactions between aromatic rings from CNT and epoxy molecules. Such alignment causes the restriction of chain movement in the direc-tion normal to the surface of CNT. The anisotropic chain dynamics can generate free volume while the voids are being filled, leading to slight change in free volume. A theoretical model has been proposed that applies free volume as a parameter to predict the shape memory prop-erties [51]. The results of free volume from MD simulations can be further used as input in the model.

The evolution of microstructures including chain extension, chain sliding or conformation change of epoxy chains is captured as shown in Fig. 12. In the neat epoxy, epoxy chains are mostly stretched along the tensile direction under the deformed state. During shape recovery, epoxy chains go through the conformation changes, including reor-ientation and rearrangement into a more relaxed state as shown by the orange and green chains in Fig. 12. In addition, the separate chains in the vicinity are sliding towards each other. As there are aromatic rings on both the epoxy monomer DGEBA and the cross-linker DDM, some chains become parallel and interact with each other through the π-π stacking interactions. Such arrangements between chains are not com-mon due to the amorphous and cross-linked structure in epoxy matrix. However, epoxy chains around CNT in the nanocomposite are rear-ranged and adhere to the surface of CNT through the π-π stacking in-teractions between aromatic rings on both CNT and epoxy molecules as shown by the purple chains in Fig. 12. The interfacial interactions be-tween CNT and epoxy can restrict the movement of epoxy chains in the vicinity of CNT surface, indicating the inhibition effect of CNT on epoxy chain mobility.

4. Conclusions

In this study, the thermal and mechanical properties of shape memory epoxy polymers are investigated using MD simulations. The glass transition temperature and Young’s modulus of neat epoxy and CNT-reinforced nanocomposite are obtained. The results show that the addition of CNT in epoxy matrix can cause the increase in glass transi-tion temperature. The Young’s modulus of CNT reinforced epoxy nanocomposite is 33.9% higher than that of neat epoxy. In addition, the chain mobility of epoxy matrix in the two epoxy systems correlated to the change of free volume is strongly affected by the nano-filler. Furthermore, the shape memory behaviors in the two material systems are studied. It is found that the addition of CNT increases the rate of

Fig. 9. The segmental dynamics of the two systems during shape recov-ery process.

Fig. 10. The free volume of (a) neat epoxy and (b) CNT-epoxy nanocomposite during shape recovery process. The gray lines are used for guidance of the trend.

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Fig. 11. Schematic diagram of the voids in the deformed state filled by the reunion of epoxy chains. The reunion is mainly due to the reorientation, the rear-rangement of single chain and the chain sliding between chains.

Fig. 12. Molecular details of epoxy chains under deformed and recovered states in (a) neat epoxy and (b) CNT-epoxy nanocomposite. The same chains at the two states are in the same color. The stretched epoxy chains along the tensile loading direction are reoriented and rearranged in the recovered state of the two systems, as captured by the orange and green chains. Some separated chains in the vicinity slide towards each other, as shown by the yellow chains. In the neat epoxy system, some epoxy chains become parallel due to the π-π stacking interactions between the aromatic rings on epoxy molecules during shape recovery, as captured by the purple chains. In the CNT-epoxy nanocomposite, most of the epoxy chains are reoriented or rearranged and adhere to the surface of CNT through π-π stacking interactions during shape recovery. The aromatic rings on epoxy molecules are highlighted in red hexagon for the purple chains. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

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shape recovery. The segmental dynamics is further captured to reveal the mechanism of shape memory effect and the reinforcement of CNT on the mechanical properties of epoxy. The results of free volume from MD simulations can be further used in theoretical model to predict the shape memory properties and help to understand how the addition of CNT affects free volume at the nanoscale that changes the shape recovery behavior in macroscale. This study helps the tailoring for material properties of shape memory nanocomposites in the design process.

Credit author statement

Wei Jian: Conceptualization, Methodology, Software, Formal anal-ysis, Writing - Original Draft.

Xiaodong Wang: Formal analysis, Writing - Review & Editing. Haibao Lu: Conceptualization, Supervision, Writing - Review &

Editing. Denvid Lau: Funding acquisition, Project Administration, Concep-

tualization, Supervision, Writing - Review & Editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU11255616], and the support from Shenzhen Science and Technology Innovation Committee under the grant JCYJ20170818103206501.

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