Relaxation and Crystallization of Oriented Polymer Melts with

Article pubs.acs.org/JPCB

Relaxation and Crystallization of Oriented Polymer Melts with Anisotropic Filler Networks Yijing Nie, Tongfan Hao, Zhouzhou Gu, Yue Wang, Yong Liu, Ding Zhang, Ya Wei, Songjun Li, and Zhiping Zhou* Institute of Polymer Materials, School of Materials Science and Engineering, Jiangsu University, 301 Xuefu Road, Zhenjiang 212013, China ABSTRACT: The coexistence of nanofillers and shear flow can influence crystallization of polymer melts. However, the microscopic mechanism of the effect is not completely revealed yet. Thus, dynamic Monte Carlo simulations were used to study the effect of the filler networks formed by one-dimensional nanofillers on relaxation and crystallization of oriented polymer melts. The filler networks restrict the relaxation of oriented polymers and impose confinement effect on the chains inside the filler networks, resulting in higher orientation and lower conformational entropy of the inside chains compared to those of the outside chains. Thus, the confined inside chains have stronger crystallizability. During crystallization, the confined chains are nucleated on the filler surface and then form nanohybrid shish−kebab structures. Furthermore, the effect of fillers and chain orientation closely depends on some factors, such as polymer−filler interaction, filler content, and filler spacing. Our simulation results are consistent with some experimental findings. Thus, these results can provide new insights into the mechanism of crystallization of filled polymers and also guide researchers to develop new polymer nanocomposites with high performance.

1. INTRODUCTION Nowadays, some nanofillers, such as carbon nanotubes (CNTs), graphene, and nanoclay, are usually added into polymer materials to improve their physical properties, such as mechanical, electrical, or thermal properties.1−5 Nanofillers can provide effective heterogeneous nucleation sites for polymer chains and reduce free-energy barriers for crystal nucleation, resulting in significant enhancement of polymer crystallizability.6 Miri et al. found that clay can induce heterogeneous nucleation in nylon 6.7 On the one hand, crystallization kinetics can be remarkably accelerated by the incorporation of nanofillers. Li et al. found that induction time for nucleation is significantly shortened in poly(L-lactide) filled with a small amount of CNTs.8,9 On the other hand, crystalline morphology is also altered by the addition of nanofillers. Li et al. first observed that CNTs induce the formation of novel nanohybrid shish−kebab (NHSK) structures in dilute polymer solutions.10 That is, CNTs act as shish, which induce the formation of polymer crystalline lamellae (kebabs), periodically decorating the surface of CNTs. A theory of soft epitaxy has been proposed by Li et al. to explain the formation mechanism of the NHSK structures.10 The anisotropic nanoparticles with small lateral size can exert a geometric confinement effect on polymer chains and force them to orient along the long axis of the nanoparticles. Some studies have been implemented to explore the microscopic details of the geometric confinement effect.11,12 Using TEM measurements, Zhang et al. and Xu et al. observed the appearance of a polymer coating on the filler surface before the formation of the NHSK structures.11,12 Besides, molecular © XXXX American Chemical Society

simulations are also used to study the formation process of the NHSK structures.13−16 Using molecular dynamics simulations, Liu et al. confirmed that two stages, adsorption and orientation, exist at the early stage of crystallization of a single polymer chain on a single CNT.13 Using dynamic Monte Carlo (MC) simulations, Hu et al. found that a single straight chain can induce the formation of shish−kebabs in polymer solutions.17 Previously, we used dynamic MC simulations to investigate the detailed nucleation process of the NHSK structures in polymer solutions and observed an anisotropic process for absorption of chain segments onto the filler surface before crystallization.18,19 Besides, we also revealed the mechanism of crystal nucleation and growth of polymer chains grafted on two-dimensional fillers by dynamic MC simulations.20 In the industrial field, a certain amount of nanoparticles is always added into the polymer matrix rather than a single nanoparticle. These nanoparticles may form filler networks in the polymer matrix. Differing from single nanoparticles, filler networks may exert some special impacts on polymer crystallization. Some studies demonstrated that filler networks impose strong confinements on the conformations or dimensions of polymer chains.21−23 In addition, chain mobility or diffusion may also be restricted by filler networks.6,24 These changes in chain conformation and mobility may further influence the polymer crystallization process. Received: December 14, 2016 Revised: January 21, 2017 Published: January 23, 2017 A

DOI: 10.1021/acs.jpcb.6b12569 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

segments formed a bond that could be oriented along lattice axes or along diagonal directions. Thus, the coordination number of each segment was 26, and each bond had 13 possible orientations.47 Several sticks representing one-dimensional nanofillers were put in the middle of the lattice box. The long axis of the fillers was in parallel with the X axis of the lattice box. As shown in Figure 1, the fillers with uniform

In addition to nanofillers, the presence of shearing or stretching can also considerably promote polymer crystallization.25−30 During shearing or stretching, polymer chains are extended along the shearing or stretching direction and conformational entropy decreases significantly, resulting in the increase of degree of supercooling and the reduction of free-energy barrier for nucleation.28,31,32 Thus, the crystallization kinetics is accelerated and the final crystalline morphology is changed.33 Up to now, research studies are mainly focused on shear-induced polymer crystallization of neat polymers.25−27 However, the coexistence of chain orientation and nanofillers may result in the appearance of some new effects. Fu et al. observed that the NHSK structures can be formed even in polymer melts containing anisotropic fillers because of the presence of shear flow.34−37 Phillips et al. found that the presence of anisotropic fillers leads to the increase of the amount of shish in sheared isotactic polypropylene.38 However, the detailed microscopic mechanism of polymer crystallization induced by the coexistence of shear flow and nanofillers is still a matter of uncertainty. Several studies revealed that the contribution of nucleating agents or particles and shear flow to crystal nucleation is additive;39,40 that is, the nucleating agents or particles dominate the contributions at low shear rates; the shear flow (chain orientation) plays a more important role at high shear rates. However, some works argued that the effect of shear flow and fillers is synergistic rather than additive.41−44 Because of the synergistic effect of fillers and shear flow, polymer crystallization kinetics is remarkably accelerated and crystallization rate is much faster compared to those of polymers containing fillers in the quiescent state or sheared neat polymers. On the contrary, some reports even stated that the effect of nucleating additives is negative for crystallization of sheared polymers.45 Naudy et al. found that the sheared polymers with nucleating agents exhibit a slower crystallization rate and lower crystalline orientation compared to those in the sheared neat ones.45 Thus, these different findings encourage researchers to carry out more in-depth investigations on the microscopic mechanism of crystallization of sheared polymers filled with nanofillers. There are many factors that may influence polymer crystallization in filled polymers, such as filler content, polymer−filler interaction, or filler spacing. For instance, Zhong et al. observed that a change in polymer−substrate interaction can induce a change in the morphology and crystal orientation of PA6 thin films.46 The combined effect of shear flow and fillers should be dependent on these factors. However, in experiments, it is difficult to separate the individual contributions of these different factors to polymer relaxation or crystallization. Thus, in the present article, we preformed dynamic MC simulations to investigate the microscopic mechanism of the relaxation and crystallization of oriented polymers with filler networks formed by one-dimensional fillers. Furthermore, to reveal comprehensively the mechanism of the combined effect of orientation and filler networks, we systematically studied the effect of various factors, such as polymer−filler interaction, filler content, and filler spacing, on the relaxation and crystallization of oriented polymers.

Figure 1. Snapshots of the chains with fully extended conformation under different observation directions, i.e., observed from the direction along the Y axis (a) and along the X axis (b); the red strips represent the fillers, and the yellow cylinders, the polymer bonds.

orientation could be treated as the aligned anisotropic filler networks. The lattice sites occupied by fillers could not be occupied by segments again. The rest vacancy sites were considered as free volume for polymer motion. The length, width, and thickness of the fillers were 64, 2, and 2 lattice sites, respectively. In the simulation box, the chain motion obeyed a microrelaxation mode,48 that is, a segment could move from an occupied site to a neighboring vacancy site or a local chain section could slide along the chain. The presence of volume exclusion of chains would reject double occupations and bond crossings during simulations. The conventional Metropolis sampling algorithm was used to decide the segmental motion for each step of microrelaxation with the potential energy penalty E = cEc + pEp + bE b +

∑ fi Ef i

(1)

where Ec is the potential energy change caused by noncollinear connection of two consecutive bonds, which is used to reflect chain flexibility; Ep is the energy change correlated with a pair of nonparallel-packed bonds, which is the driving force for polymer crystallization;47 Eb is the energy change due to the presence of one segment−filler pair, reflecting the strength of polymer−filler interaction; Ef is the sliding-diffusion barrier caused by neighboring parallel-packed bonds, which is used to reflect the chain mobility in crystals;49 c is the net change of noncollinear connection of bonds; p is the net change of pairs of nonparallel-packed bonds; b is the net change of pair contacts between segments and fillers; and ∑i f i is the sum of parallel-packed bonds along the local sliding segments. In this work, Ep/Ec was fixed at 1 and Ef/Ec was set at 0.02 for a high sliding mobility of chain segments in crystals. In the simulations of the effect of polymer−filler interaction on polymer crystallization, we put 16 fillers into the lattice box and Eb/Ec was varied from 0 to −1 and −2, reflecting variable strengths of the interactions between polymers and fillers (the minus sign indicates that attractive interactions exist between polymers and

2. SIMULATION DETAILS First, we established a 64×64×64 cubic lattice box and then regularly constructed 8064 model chains of 30 segments with fully extended conformation. In the simulation box, one segment could only occupy one lattice site. Two consecutive B


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The Journal of Physical Chemistry B fillers). kT/Ec (k is the Boltzmann constant, and T is the temperature) was the reduced system temperature in the current simulations (hereafter referred to as T*). In the simulations of the effect of filler spacing, the distance between two neighboring fillers along the Y and Z axes of the box was changed from 3 lattice sites to 5 and 10 lattice sites. In the simulations of the effect of filler content, the number of fillers was varied from 4 to 16 and 36.

bonds can be treated as the crystalline bond, whereas the rest can be considered as amorphous bonds. Then, polymer crystallite can be defined as the aggregation of parallel-packed crystalline bonds. In a real polymer crystal, crystalline bonds in one crystallite are just parallel to each other. It should be noted that the crystallinity defined here is a relative value rather than an absolute one. However, in the current simulations, we focused on the microscopic mechanism of polymer crystallization rather than the absolute values of crystallinity; thus, our definition of crystallinity is reasonable. It can be seen in Figure 2a that crystallinity decreases much faster than the ⟨R2g⟩ during athermal relaxation. When the crystallinity values drop to 0, the corresponding ⟨R2g⟩ is still higher than that of the random coils (about 12 lattice sites); that is, although the crystals are melted, the polymer melts can still have a certain degree of orientation. In other words, oriented melts can be obtained in a certain period of relaxation time, which have no crystalline structures but a certain degree of chain orientation. By a similar simulation process, the oriented melts have also been obtained by Hu et al.50 Apparently, the oriented melts can be treated as sheared polymer melts at high temperatures above the melting point, in which polymer chains are oriented due to shearing but have no crystalline structures.50 Then, the relaxed state at 50 MC cycles (1 MC cycle was defined as the step in which each monomer had one attempted move on average) was selected, as marked by vertical dashed lines in Figure 2a. Figure 2b shows the comparative distributions of the R2g of polymer chains in the oriented melts and in the relaxed random coils. It can be seen that the distribution curves of the oriented melts exhibit a wide single peak located at the intermediate values of R2g. Hu et al. stated that this result demonstrates the cooperative nature in the relaxation of bulk polymers, which is consistent with the reported cooperativity in the long-chain components of blends for the precursor formation under shear flow.50 Thus, we believe that the relaxed state at 50 MC cycles can be used to reflect the sheared polymer melts at high temperatures. Then, the corresponding oriented melts (the relaxed state at 50 MC cycles under athermal conditions) were quenched to two different states with T* = 4.7 and 4.5, respectively, to observe the relaxation and crystallization process. Figure 3 shows the evolutions of crystallinity with simulation time at T* = 4.7. It can be seen that crystallinity does not increase during simulation, indicating that polymer crystallization does not

3. RESULTS AND DISCUSSION The system containing 16 fillers with filler spacing of 5 lattice sites and interfacial interaction of Eb /Ec = −1 was selected as a typical example. First, the initial chains with extended conformation (the crystals with extended conformation, as seen in Figure 1) were relaxed under athermal conditions (athermal conditions correspond to an infinitely high temperature). During athermal relaxation, the evolutions of both the crystallinity and mean-square radius of gyration (⟨R2g⟩) are traced, as shown in Figure 2a. Crystallinity is defined as the fraction of bonds containing more than 12 parallel neighboring bonds. Tiny crystallites caused by thermal fluctuation can be excluded according to this definition of crystallinity. Furthermore, the bond that has more than 12 parallel neighboring

Figure 2. (a) Evolutions of crystallinity (left axis) and the mean-square radius of gyration (right axis) for polymer chains with extended conformation during athermal relaxation. The dashed lines indicate the state where the oriented melts were selected. (b) Distributions of the square radius of gyration for the selected oriented melts at 50 MC cycles and the relaxed coil state.

Figure 3. (a) Evolutions of crystallinity and the mean-square radius of gyration during relaxation at T* = 4.7. C


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The Journal of Physical Chemistry B occur. As shown in Figure 4a, the parallel fraction (X axis fraction) of ⟨R2g⟩ (⟨R2gx⟩, parallel to the long axis of the fillers) of the chains inside the filler networks decreases more slowly than that of the outside chains, demonstrating that the filler networks restrict the relaxation of the inside chains. The regions inside the filler networks were marked in the inset of Figure 4, whereas the other regions were considered as the regions outside the filler networks. Here, if more than 80% of the segments in a chain are located inside the filler networks, this chain is considered to be located inside the filler networks. In addition, if no segments in a chain are located inside the filler networks, this chain is considered to be located outside the filler networks. In experiments, it has been found that the sheared polymers filled with anisotropic nanofillers, such as CNTs, exhibit slower relaxation compared with the unfilled ones.43 The oriented segments can be absorbed by the filler surface due to the presence of polymer−filler interactions, and thus the chain relaxation is more difficult compared to that in the unabsorbed ones.43,51,52 As illustrated in Figure 5, the dimension of a typical inside chain along the long axis of the fillers decreases more slowly than that of the outside one. Some contact points between the chain and the fillers were marked by arrows in Figure 5. Apparently, these contacts hinder the relaxation of the oriented chain. Thus, the corresponding relaxation of the inside chains should be slower. In addition, as depicted in Figure 4a,b, compared with the outside chains, the inside chains exhibit slightly higher platform values of ⟨R2gx⟩ but lower platform values of the perpendicular fraction of ⟨R2g⟩ ((⟨R2gy⟩ + ⟨R2gz⟩)/2, perpendicular to the fillers). Therefore, the presence of filler networks exerts a confinement effect on the polymer chains inside the filler networks. The filler networks “press” the inside chains from the lateral directions and thus hinder the conformation fluctuation of the inside chains along the Y and Z axes, resulting in the decrease of the lateral dimension (lower values of (⟨R2gy⟩ + ⟨R2gz⟩)/2) and the increase of the dimension along the long axis of the fillers (higher values of ⟨R2gx⟩). The higher ⟨R2gx⟩ implies that the inside chains are slightly oriented along the long axis of the fillers due to the confinement effect. To further confirm the above findings, the evolutions of the orientational-order parameters of the amorphous bonds inside and outside the filler networks along the long axis of the fillers were also calculated, as depicted in Figure 4c. The orientational-order parameter of the amorphous bonds is defined as P = (3⟨cos2 θ ⟩ − 1)/2

(2)

where θ is the angle of the bond orientations with respect to the long axis of the fillers and ⟨ ⟩ means an average over all the corresponding bonds. Figure 4c shows that the orientationalorder parameters of the inside chains decrease more slowly than those of the outside chains, also indicating that the filler networks can restrict the relaxation process of the insideoriented chains. In addition, Figure 4c also displays that the inside chain segments exhibit apparently higher platform values of the orientational-order parameters than those of the outside segments, further demonstrating that the confinement effect of the filler networks can induce the orientation of the inside segments along the long axis of the fillers. In both experiments and simulations, some research groups have observed that the filler networks impose effective restrictions on the chain conformation or dimension of confined chains.21−23,53,54 For instance, Meng et al. observed that the inside chains are more oriented due to the confinements of the CNT networks.53 In

Figure 4. (a) Evolutions of the parallel fraction of the mean-square radius of gyration for the inside and outside chains during relaxation at T* = 4.7; for clarity, a partial section of the curves was enlarged in the inset; (b) evolutions of the perpendicular fraction of the mean-square radius of gyration for the inside and outside chains during relaxation at T* = 4.7; (c) evolutions of the orientational-order parameters of the amorphous bonds inside and outside the filler networks along the long axis of the fillers. D


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Figure 5. Snapshots of the conformation evolutions of a typical inside chain and a typical outside chain during relaxation at T* = 4.7; the red strips represent the fillers and the blue cylinders denote the chain bonds.

our previous works, using dynamic MC simulations, we observed the presence of confinement-enhanced orientation of the chains inside the filler networks in dilute polymer solutions.19 Furthermore, the presence of filler networks leads to the decrease of conformational entropy of the inside chains55 and thus the increase of free energy. From the viewpoint of thermodynamics, to reduce the corresponding free energy, these inside chains subject to the confinement effect are preferred to diffuse out of the inside regions of the filler networks or the segments near the fillers are preferred to diffuse away from the interfacial regions. However, the filler surface can absorb chains due to the presence of attractive polymer−filler interactions, causing the decrease of the free energy of the chains that are in contact with the fillers. In this way, the chains with higher orientations can exist stably within the filler networks. However, when the relaxation temperature is changed from T* = 4.7 to 4.5, different phenomena can be observed. In this condition, as shown in Figure 6a, crystallinity increases after a critical simulation time, indicating that crystallization occurs in the oriented polymer melts containing the filler networks. For comparison, the results of the oriented unfilled polymers prepared with the same simulation process were also shown in Figure 6a. It can be seen that the unfilled polymers cannot crystallize at T* = 4.5, implying that the presence of filler networks can promote polymer crystallization. As further illustrated in Figure 6b, after the oriented filled system is quenched, some local bundles of oriented segments develop into small crystallites, with orientation along the long axis of the fillers.56 On the one hand, the filler surface retards the relaxation of the oriented segments because of the polymer− filler interactions. On the other hand, the filler networks can provide effective heterogeneous nucleation sites for these inside-oriented segments and reduce surface free energy of the small crystallites. Thus, the inside-oriented segments have stronger crystallizability compared to that of those outside. In experiments, Ezquerra et al. also found that the nuclei are formed and stably exist near the CNT surface after shearing but those far away from CNT do not.51 Figure 6b shows that the oriented crystallite inside the filler networks that has direct contacts with the fillers indeed grows up to finally form the NHSK structure, in which the fillers act as the multiple shish and the polymer crystal lamella serves as the kebab. The similar NSHK structures have been observed in sheared polymer melts containing anisotropic fillers, such as CNTs36,37 or inorganic whiskers.34,35 If no shear flow is applied to polymer melts, the NHSK structures cannot be formed.

Figure 6. (a) Evolutions of crystallinity for the filled and unfilled oriented polymers at T* = 4.5; (b) snapshots of evolutions of crystallites in the filled system with Eb/Ec = 1 formed at T* = 4.5; the red strips represent the fillers, and the yellow cylinders denote the crystalline bonds.

Previously, we have demonstrated that at the quiescent state the NSHK structures can be formed only in the dilute polymer solutions containing the one-dimensional filler.18 Thus, the appearance of NHSK structures in the current simulations E


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the inside chains have stronger crystallizability and can crystallize at T* = 4.5. The above simulation findings successfully reveal that the inclusion of the anisotropic filler networks can retard the relaxation of the inside-oriented chains and improve the crystallizability of these chains. In addition, the polymer−filler interaction, filler content, and filler spacing are the important factors that influence the relaxation and crystallization of oriented polymer melts. In the following sections, we will further investigate the effects of these factors on polymer relaxation and crystallization. 3.1. Effect of Polymer−Filler Interaction. The oriented polymer melts (the relaxed melts at 50 MC cycles under athermal conditions) with different polymer−filler interactions (Eb/Ec = 0, −1, and −2) were quenched from the athermal condition to the state at T* = 4.5. As seen in Figure 8a,

further confirms that our simulation process preparing the sheared polymer melts is reasonable. Marom et al. have observed that the sheared isotactic polypropylene melts containing short aramid fibers exhibit a significant improvement in crystallization kinetics compared with the sheared neat ones.41 Li et al. found that the crystallizability of isotactic polypropylene is dramatically improved because of the coexistence of shear flow and CNTs.43 Because of the restriction of the relaxation of the oriented segments and the confinement of the filler networks, the inside segments are inclined to maintain higher orientation, as demonstrated by the slower decrease and the higher platform values of the ⟨R2gx⟩ of the inside chains in Figure 7a and by the orientational-order

Figure 8. (a) Evolutions of crystallinity for polymers containing filler networks with different polymer−filler interactions (Eb/Ec = 0, −1, and −2), at T* = 4.5; (b) snapshots of evolutions of crystallites formed at T* = 4.5 for polymers containing filler networks with Eb/Ec = −2; the red sticks represent the fillers, and the yellow cylinders denote the crystalline bonds.

Figure 7. (a) Evolutions of the parallel fraction of the mean-square radius of gyration for the inside and outside chains, at T* = 4.5; (b) evolutions of orientational-order parameters of the amorphous bonds inside and outside the filler networks along the long axis of the fillers, respectively.

crystallization does not occur in the system without interfacial interaction (Eb/Ec = 0). However, the systems with the attractive interfacial interactions (Eb/Ec = −1 and −2) crystallize. As seen in Figures 6b and 8b, for the systems with attractive interfacial interactions, one small inside-oriented crystallite is formed after quenching and then it grows up to form a crystal lamella with orientation along the long axis of the fillers, similar to the NHSK structures observed in the sheared polymer melts filled with CNTs.36,37 These findings reveal that

parameters of the inside segments in Figure 7b. Thus, the corresponding conformational entropy and the free-energy barrier for nucleation will be reduced. In the meantime, the presence of the filler surface with the attractive interfacial interactions will also cause the decrease of the surface free energy and the free-energy barrier for nucleation. Therefore, F


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induce polymer chains to orient along the long axis of the fillers in the interfacial regions.18 Under the effect of polymer−filler interactions, the segments will be absorbed and arrange along the long axis of the fillers and thus exhibit higher orientation along the long axis of the fillers.18 First, the improvement of the segmental orientation can contribute to the enhancement of the crystallizability of the inside chains. Second, the higher interfacial interactions can efficiently reduce the surface free energy of the nuclei formed and thus are beneficial for crystallization. Third, the higher interfacial interactions can lead to the higher segment density in the interfacial regions, which also favors the nucleation process, as shown in Figure 10.

the presence of attractive interfacial interactions is beneficial for the improvement of the crystallizability of inside chains. Rastogi et al. found that shear-induced precursors are more stable in the polymers filled with CNTs (because of the presence of strong polymer−filler interactions) than in the polymers with zirconia nanoparticles (because of poor polymer−filler interactions).57 After the cessation of shear flow, the presence of the contact points between chains and fillers can hinder the relaxation of local oriented segments. Zhu et al. also proposed that the particle surface can stabilize the formation of oriented nuclei that subsequently grow up to form oriented lamellae.58 In contrast, for the system without polymer−filler interactions, the contact points have no adsorption effect; thus, chains are easier to relax after the cessation of shear flow. In addition, Figure 8a shows that the system with the interfacial interactions of Eb/Ec = −2 exhibits a longer induction period for nucleation compared to that for the system with the interfacial interactions of Eb/Ec = −1. Therefore, excessively strong interfacial interactions will lead to the decrease in the nucleation ability of the inside polymer chains. As is well known, the rate of polymer crystal nucleation (i) can be expressed as59 ⎛ ΔU ⎞ ⎛ ΔG* ⎞ ⎟ exp⎜ − ⎟ i = i0 exp⎜ − ⎝ kT ⎠ ⎝ kT ⎠

(3)

where i0 is the prefactor, ΔU is the activation energy for shortdistance diffusion of molecules, and ΔG* is the critical freeenergy barrier for crystal nucleation. Therefore, the activation energy for diffusion and the critical free-energy barrier codetermine the nucleation rate. As shown in Figure 9, at T* Figure 10. Evolutions of segment density at the interfacial regions for the systems containing filler networks with different polymer−filler interactions (Eb/Ec = 0, −1, and −2), at T* = 4.5.

However, the excessively high interfacial interactions will lead to the decrease in the mobility of segments near the fillers. Figure 11 displays the evolutions of the mean values of the probability of segment movement (PSM) of amorphous chains during relaxation at T* = 4.5 for the systems with different polymer−filler interactions. PSM that can be used to directly reflect segmental mobility was defined as the probability of

Figure 9. Evolutions of the parallel fraction of the mean-square radius of gyration for the inside and outside chains in polymers containing filler networks with different polymer−filler interactions (Eb/Ec = 0, −1, and −2), at T* = 4.5.

= 4.5, the values of ⟨R2gx⟩ of the inside chains for the systems with stronger polymer−filler interactions decrease more slowly than those for the systems with weaker polymer−filler interactions, indicating that the presence of polymer−filler interactions retards the relaxation process of oriented polymers. In addition, as shown in Figure 9, the platform values of ⟨R2gx⟩ of the inside chains for the system with no interfacial interaction are lower than those for the systems with high interfacial interactions (Eb/Ec = −1 and −2). Previously, we have demonstrated that high polymer−filler interactions can

Figure 11. Evolutions of the mean PSM of amorphous chains at T* = 4.5 for the systems with different polymer−filler interactions (Eb/Ec = 0, −1, and −2). G


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(16 and 36 fillers). As illustrated in Figures 6b and 12b, the nuclei that have contacts with several fillers are formed inside the filler networks and then grow up to form the NHSK structures in the systems with more fillers. As also seen in Figure 12a, the system filled with 16 fillers exhibits a shorter induction period for nucleation compared to that of the system filled with 36 fillers. In addition, the system filled with four fillers cannot crystallize. Therefore, the system with proper filler content has the strongest crystallizability. It is significant to reveal the underlying mechanism of the effect of filler content on the crystallization of oriented polymers. For the system with the lowest filler content (four fillers), first, the number of chains inside the filler networks suffering from the confinement effect is lowest among the three systems, as shown in Figure 13a. At T* = 4.5, the orientational-order parameters of the segments inside the filler networks for the system with the lowest content of fillers are slightly lower than those of the other two systems with more filler content, as depicted in Figure 13b. In addition, it can be found that the values of the orientational-order parameters for the system with the lowest content of fillers fluctuate much more intensely compared to that for the other two systems. This fluctuation of the orientational-order parameters implies that the conformation fluctuation of the inside chains is stronger in the system filled with four fillers. Then, the inside chains may diffuse more easily out of the interior region of the filler networks in the system with a weaker confinement effect. Figure 13c quantitatively shows the evolutions of the fraction of the chains staying inside during relaxation. The fraction of the chains staying inside can be defined as the ratio of the number of chains staying inside the filler networks and the initial number of the inside chains before relaxation at T* = 4.5. It can be clearly seen that the fraction of chains staying inside the system with the lowest filler content decreases much faster compared with that in the other two systems, demonstrating that the inside chains are exposed to the weakest confinement effect in the system with the lowest filler content. The overall entropy reduction is codetermined by the number of chains suffering from the confinements and the entropy reduction of the single inside chain. The smallest number of the inside chains, the lowest degree of orientation, and the most intense fluctuations of the inside chains in the system with the lowest filler content lead to the lowest overall entropy reduction caused by the confinement effects. Thus, the nucleation ability of polymer chains in this system is lowest and crystallization cannot occur at T* = 4.5. However, as shown in Figure 12a, the induction period for nucleation decreases as the number of fillers is increased from 16 to 36 fillers, suggesting a decrease in the nucleation ability. In the system with the highest filler content, there exists the largest polymer−filler interface; thus, more segments will be absorbed by the fillers. In other words, the number of segments with low mobility in the system with the highest filler content is largest. Thus, the activation energy for short-distance diffusion will be increased, resulting in the increase of nucleation energy barrier and the decrease of nucleation ability. In experiments, Huang et al. have found that the nanofiller networks with a high concentration of graphene oxide significantly restrict the mobility and diffusion of polymer chains, thus resulting in the decrease of crystallization rate.6 Besides, Wang’s group also detected that the filler networks with a high concentration of CNTs can provide restriction to mobility and diffusion of polymer chains.24

movement of one segment by moving into its neighboring empty sites or partial sliding diffusion in one MC cycle60 ⎡ PSM = min⎢1, ⎢⎣

n

⎛ −ΔEij ⎞⎤ ⎟⎥ ⎝ kT ⎠⎥⎦

∑ exp⎜ j=1

(4)

where n is the number of neighboring empty sites around the corresponding segments, ΔEij is the energy change of the system caused by the movement of a segment from sites i to j. It can be seen in Figure 11 that the segments in the systems with higher interfacial interactions exhibit lower mean PSM. This reduction of segmental mobility in the systems with highest interfacial interactions (Eb/Ec = −2) will lead to the increase in the activation energy for chain diffusion and thus the drop of the nucleation ability and the increase of the induction period for nucleation. 3.2. Effect of Filler Content. To investigate the effect of filler content on the relaxation and crystallization of oriented polymers, other two systems with different filler content (one contains 4 fillers and the other contains 36 fillers in a box) were also established. Figure 12a shows the evolutions of crystallinity for the three systems with different filler content at T* = 4.5 after quenching from the athermal state. It can be seen that crystallization does not occur in the system with the lowest content of fillers (four fillers), whereas crystallinity increases after a critical simulation time in the systems with more fillers

Figure 12. (a) Evolutions of crystallinity for polymers with different filler content (4, 16, and 36 fillers, at T* = 4.5; (b) snapshots of evolutions of crystallites formed at T* = 4.5 for polymers containing 36 fillers; the red sticks represent the fillers, and the yellow cylinders denote the crystalline bonds. H


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3.3. Effect of Filler Spacing. We further investigate the effect of filler spacing on the relaxation and crystallization of oriented polymers. Here, three systems containing 16 fillers with respective filler spacings of 3, 5, and 10 were investigated. As shown in Figure 14, the crystallinity for the systems with the

Figure 14. Evolutions of crystallinity for polymers with different filler spacings (10, 5, and 3 lattice sites), at T* = 4.5 (the data for the systems with filler spacings of 10 and 3 lattice sites overlap).

smallest spacing and largest spacing does not increase during simulation, whereas that for the system with intermediate filler spacing increases beyond a critical simulation time. Therefore, polymer crystallization can only occur in the systems with proper filler spacing. As shown in Figure 15a, the orientationalorder parameters of amorphous bonds inside the filler networks in the systems with smaller spacing decrease more slowly compared to those in the systems with larger spacing, indicating that the filler networks with smaller spacing can exhibit stronger restrictions on the relaxation of the inside-oriented segments. In addition, the platform values of the orientational-order parameters of amorphous bonds inside the filler networks in the systems with the smallest spacing are largest among the three systems with different filler spacings. For the system with the smallest spacing, the filler networks can impose a stronger confinement effect on the inside chains, leading to higher orientational-order parameters. Thus, each confined polymer chain has a higher entropy change. However, according to the classical nucleation theory,59 polymer crystallization can only occur when critical sizes of crystal nuclei have been reached. In the system with the smallest filler spacing, the number of inside chains is smallest due to the smallest confined space, as shown in Figure 15b. Accordingly, the critical size of crystal nuclei cannot be reached within the smallest spacing and polymer crystallization cannot happen. In addition, as shown in Figure 16, the inside segments in the system with the smallest filler spacing exhibit the lowest segmental mobility; thus, the corresponding activation energy for chain diffusion will be highest, resulting in the decrease of nucleation ability. For the system with the largest spacing, the filler spacing

Figure 13. (a) Evolutions of the number of inside chains during relaxation at T* = 4.5 in polymers with different filler content; (b) evolutions of the orientational-order parameters of the amorphous bonds inside the filler networks in polymers with different filler content along the long axis of the fillers, during relaxation at T* = 4.5; (c) evolutions of the fraction of the chains staying inside the systems with different filler content, during relaxation at T* = 4.5.

along the Y axis or Z axis is much larger than 2 ⟨R g2y⟩ (the lateral size of chains); thus, the confinement effect should be weak. As shown in Figure 15a, the orientation-order parameters of the inside chains for the system with the largest filler spacing are the lowest among the three systems, demonstrating the I


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presence of the weakest confinement effect. Thus, the corresponding crystallizability should also be the weakest. In short, the combined effect of orientation (shear flow) and nanofillers closely depends on the polymer−filler interactions, the filler content, and the filler spacing. Previously, Marom et al. proposed that the origin of the synergy is the interfacial interactions between the fibers and the orientation of polymer chains.41 Obviously, in addition to the interfacial interactions, the filler spacing and the filler content also play a key role. Conclusively, the synergistic effect of orientation and nanofillers exists only in the systems with proper interfacial interactions, proper filler spacing, and proper filler content. The presence of very strong or very poor interfacial interactions, very large or very small filler spacing, and very high or very low filler content can weaken the promotion effect of orientation and nanofillers on polymer crystallization.

4. CONCLUSIONS The networks formed by one-dimensional fillers can restrict the relaxation of oriented polymers and exert a confinement effect on the inside polymer chains, thus resulting in higher orientational orders of the inside chain segments along the long axis of the fillers. At an appropriate crystallization temperature, the oriented polymer melts with filler networks exhibit a shorter induction time for nucleation and faster crystallization kinetics compared to those in the unfilled polymers. Several factors directly influence the relaxation and crystallization of oriented polymers. First, a proper interfacial interaction is beneficial for the improvement of polymer nucleation ability. If the interfacial interaction is too strong, segmental mobility will be restricted, leading to the decrease of nucleation ability. Second, optimum filler content is needed for improving the polymer crystallizability. If the filler content in the oriented polymers is too low or too high, the polymer crystallizability will be decreased. Third, the filler spacing also plays an important role in polymer crystallization. In the system with large filler spacing, the confinement effect on the polymer conformations is weak, resulting in weak polymer crystallizability. In the system with a very small filler spacing, though the confinement effects are strong, the number of chains subject to the confinements is low, also resulting in the reduction of polymer crystallizability.

Figure 15. (a) Evolutions of the orientational-order parameters of the amorphous bonds inside the filler networks in polymers with different filler spacings along the long axis of the fillers, during relaxation at T* = 4.5; (b) evolutions of the number of inside chains during relaxation at T* = 4.5 in polymers with different filler spacings.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Zhiping Zhou: 0000-0002-9550-3035 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support from the National Natural Science Foundation of China (No. 21404050) is gratefully acknowledged. The National Basic Research Program of China (973 Program, No. 2012CB821500), the Research Foundation of Jiangsu University (No. 14JDG059), the Jiangsu Planned Projects for Postdoctoral Research Funds (No. 1402019A), and the Postdoctoral Science Foundation of China (No. 2015M580394) are also appreciated. In addition, the authors want to express their gratitude to Jiangsu Province for

Figure 16. Evolutions of the mean PSM of amorphous chains at T* = 4.5 for the systems with different filler spacings.

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