Polymer crystal nucleation with confinement-enhanced orientation dominating the formation of nanohybrid shish-kebabs with multiple shish

Abstract

Nanofillers with small lateral size can induce the formation of nanohybrid shish-kebab (NHSK) structures in polymer solution, which have a variety of potential applications. We performed dynamic Monte Carlo simulations to investigate polymer crystallization behaviors induced by aligned anisotropic filler networks. An unexpected NHSK structure with multiple shish is observed. The aligned fillers act as multiple shish and the polymer crystal lamellae form kebabs. Further detection reveals that crystal nucleation firstly occurs inside the filler networks due to the high polymer density and segmental orientation. Then, the nuclei grow to connect the fillers to finally form the NHSK structure with multiple shish. The presence of filler networks imposes confinement effects on the conformations and dimensions of chains inside, forces those chains to orient along the long axis of the fillers, reduces the conformational entropy, thus resulting in stronger nucleation ability of the chains inside. The nucleation mechanism can be also applied to interpret the formation process of the shish-kebab structure with multiple shish formed in sheared polymer melts, which was observed by Hsiao et al. (Phys. Rev. Lett. 2005, 94, 117802).

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I. Introduction

The addition of a small amount of nanofillers can dramatically improve mechanical properties of polymer materials.^1–4 One of the reasons causing this remarkable improvement is that the nanofillers significantly affect crystallization behaviors of polymers, if the polymers are crystallizable.^5–8 On the one hand, polymer crystallizability can be markedly improved due to the inclusion of only a few nanofillers.^1,9,10 The fillers can act as heterogeneous nucleation agents, inducing the decrease of free energy barriers for crystal nucleation and accelerating crystallization kinetics.^11,12 On the other hand, crystalline morphology is also changed owing to the incorporation of low-dimensional nanofillers.^13–17 Li et al. firstly observed the formation of a novel nanohybrid shish-kebab (NHSK) structure in polymer solution with carbon nanotubes (CNTs) serving as the shish and polymer crystal lamellae forming the kebabs.^13,18 The formation of the NHSK structure endows polymer materials with excellent mechanical properties.^1,19,20 In addition, polymer materials with this unique hybrid structure have a variety of potential applications, such as catalyst supports or templates for nanofiller functionalization.¹⁴

Up to now, various works have been carried out to investigate nucleation mechanism of the NHSK structure.^13,21–25 Li et al. proposed a new theory of soft epitaxy (geometric confinement) to interpret the nucleation details of the NHSK structure in polymer solution containing nanofillers with very small diameters.¹³ Namely, the fillers with very small diameters affect conformations of chains near them and force chain segments to arrange in parallel with their long axis, thus resulting in the formation of the NHSK structure.¹³ Then, more and more works including experiments and molecular simulations were performed to supplement this theory, and more details of the nucleation process have been found.^21–27 In our previous studies, an anisotropic absorption process of chain segments onto the filler surface prior to crystallization was observed.²⁸ Thank to those excellent works, the formation mechanism of the NHSK structure becomes increasingly clear now.

Generally, physical properties of polymer nanocomposites depend on the volume fraction of nanofillers. When the volume fraction of nanofillers exceeds a percolation threshold, physical properties of polymers will be improved dramatically.²⁹ In this condition, nanofillers may be close to each other, resulting in the formation of nanofiller networks.²⁹ The effect of nanofiller network on polymer crystallization should be different from that of single nanofiller. Unfortunately, nowadays how the nanofiller networks influence the nucleation mechanism of polymers is still unknown. It has been demonstrated that the nanofiller networks could also efficiently improve the nucleation ability of polymers.^30,31 Nevertheless, the microscopic mechanism of polymer crystal nucleation induced by the nanofiller networks should be different from that induced by single nanofiller. Some works have revealed that nanofiller networks exert strong impacts on the conformations or dimensions of polymer chains.^32,33 For example, Karatrantos et al. detected that the conformations of a few polymer chains which have contacts with two neighboring CNTs are restricted due to the confinement effect.³⁴ The changes of the chain conformations or dimensions may further influence the nucleation process.

In the present work, we preformed dynamic Monte Carlo (MC) simulations to directly probe the early nucleation process of polymers induced by aligned anisotropic nanofiller arrays (nanofiller networks). It was found that nuclei are firstly formed inside the filler arrays, and then grow up to connect the fillers to form a NHSK structure with multiple shish. Filler networks provide heterogeneous nucleation sites for polymer chains, exert confinement effects on the conformations of chains inside, and strengthen their orientation along the long axis of the fillers.

II. Simulation details

We regularly put 1024 polymer chains, each containing 32 units with extended conformation, into a 64³ cubic lattice box with periodic boundary conditions. In the lattice model, each unit of a chain occupied one lattice site. The bonds were oriented either along lattice axes or along diagonals, and the coordination number of each unit was 26 (summed over six axes, eight body diagonals, and 12 face diagonals).^35–38 Thus, each bond contained maximum 13 possible orientations. The occupation density was 0.125 to mimic a dilute polymer solution. In experiments it has been demonstrated that polymer density influences the crystalline morphology. Namely, NHSK structures cannot be formed in the polymer systems with high polymer density without shearing, such as polymer melts. Previously, we found that no typical NHSK structures can be observed in the systems with polymer density higher than 0.375.²⁸ Thus, currently, we set the polymer density in the current simulation as 0.125. The vacancy sites played the role of solvent. The interaction between polymer and solvent was negligible. Subsequently, four strips representing one-dimensional nanofillers were placed in the middle of the simulation box. As shown in Fig. 1, the four fillers are in parallel with each other to form the aligned anisotropic filler arrays (filler networks), and the distances between two neighboring fillers along the Y-axis and Z-axis of the box are 3 lattice sites. To explore the effect of filler spacing on polymer crystallization, the systems with other distance (4 lattice sites, 5 lattice sites and 6 lattice sites) were also studied. The long axis of the fillers was parallel to the X-axis of the box. The length, width and thickness of the fillers were 64 lattice sites, 1 lattice site and 1 lattice site, respectively. For comparison, we also put single filler with the same size into the box to explore its effect on polymer crystallization. Furthermore, we ignored the surface details of the filler, and thus no lattice orientation was added into the current system. In our former paper, we have demonstrated that lattice matching is not the premise of the formation of NHSK structure.²⁸ Polymer chains could move in the lattice space via a micro-relaxation model,^35–38 which allowed a unit jumping from an occupied site to a neighboring vacancy site, or with local sliding diffusion along the chain. Double occupations and bond crossings were forbidden attributed to the volume exclusion of polymer chains. The initially extended chains were relaxed for 10⁶ MC cycles to obtain an equilibrium state under athermal conditions (each MC cycle was defined as the step when all monomers moved once on average. In thermodynamic sense, the athermal condition corresponds to an infinitely high temperature). Then, the relaxed amorphous polymer chains were further quenched to a relatively low temperature to observe isothermal crystallization.

Fig. 1 Snapshots of the four strips observed from different directions.

The conventional Metropolis sampling algorithm was employed for each step of micro-relaxation with the potential energy penalty

where E_c is the potential energy change for non-collinear connection of consecutive bonds along the chain, reflecting the chain flexibility,³⁵ E_p is the potential energy change for each pair of nonparallel packed bonds, reflecting the molecular driving force for polymer crystallization,³⁵ B is the potential energy change for each monomer–filler pair, representing the polymer–filler interaction, E_f is a kinetic energy barrier for each pair of parallel-packed bonds, to represent a frictional hindrance of chain sliding diffusion in the crystal;³⁹ c is the net number of non-collinear connection pairs of bonds along the chain, p is the net number of nonparallel packed pairs of bonds, b is the net number of pair contacts between monomers and filler, and is the sum of parallel-packed bonds along the path of local sliding diffusion. In the present simulation, E_p/E_c was fixed at 1 to allow a proper flexibility of chains at crystallization temperature, E_f/E_c was chosen as 0.02 for a high mobility of chain sliding in crystals, B/E_c was set to −1 (the minus means that attractive interaction exists between polymer and fillers), and kT/E_c (k is the Boltzmann's constant and T the temperature) representing the reduced system temperature was set to 2.5. In order to study the effect of polymer–filler interactions on polymer crystallization, the systems with B/E_c of −0.5, −0.8 and −5 were also simulated. It should be noted that we have performed three times for each set of conditions. It was found that each simulation of the same condition shows similar results. For clarity, we only show the results of one simulation for each condition.

III. Results and discussion

(A) Formation of NHSK structure with multiple shish

Fig. 2a shows the evolution of crystallinity of polymer containing the filler networks with the filler spacing of 3 lattice sites during isothermal crystallization. For comparison, the crystallinity variation of unfilled polymer is also shown. Compared with the unfilled polymer, the induction period for crystal nucleation of the filled polymer is much shorter, attributed to the presence of the heterogeneous nucleation of polymer chains induced by the filler networks. In addition, the inclusion of the filler networks also leads to the significant improvement of the maximum crystallinity of polymer. Namely, polymer crystallizability is strongly improved due to the incorporation of the filler networks. Those findings are consistent with the corresponding experimental results, which also show that the addition of nanofillers can remarkably increase the nucleation rate and final crystallinity of polymers.^5,9 The nanofillers can provide effective nucleating sites for polymer crystallization, and thus more chain segments can be involved in crystallization, resulting in the increase of ultimate crystallinity.

Fig. 2 (a) Evolutions of crystallinity of polymer containing filler networks and unfilled polymer, respectively, during isothermal crystallization. The crystallinity was defined as the fraction of bonds containing more than five parallel neighbors. (b) The snapshots of crystalline morphology of polymer containing filler networks formed at different MC cycles. The red strips denote the fillers, and the blue cylinders represent the crystalline bonds.

In addition, we found that the polymers containing the filler networks can crystallize at temperatures below 3.1, while the unfilled polymers can only crystallize at temperatures below 2.7. Namely, the highest crystallization temperature for the filled polymers is higher than that for the unfilled ones, demonstrating that the filled polymers have higher degree of supercooling and stronger nucleation ability.

Then, in order to obtain the micro-structural information about the effect of the aligned filler networks on polymer crystallization, the snapshots of crystalline morphology of the filled polymer at different MC cycles are directly draw, as shown in Fig. 2b. Surprisingly, a special NHSK structure with multiple shish is observed, in which the four aligned fillers act as the multiple shish and induce the formation of polymer crystal lamellae (kebabs) periodically decorating the surface of shish, connecting the multiple shish and aligning perpendicular to the long axis of shish. Hsiao et al. have observed a similar unexpected shish-kebab structure with multiple shish in sheared polyethylene melt, in which stretched chain sections form multiple shish and coiled chain sections form kebabs.⁴⁰ Herein, for the first time, the NHSK structure with multiple shish is detected in polymer solution. The current findings suggest that the special NHSK structure with multiple shish can be designed and fabricated with the help of the aligned anisotropic fillers with small spacing. In experiments, by regulating the number and orientation of neighboring CNTs and the spacing between them, researchers may also fabricate the NHSK structure with multiple shish. The polymer material containing the NHSK structure with multiple shish may have some better physical properties compared with that containing the conventional NHSK structure with only single shish. Thus, we hope that the current simulation results could inspire researchers to carry out further experimental investigations on the fabrication, physical properties and applications of the polymer nanocomposites containing the NHSK structure with multiple shish in the future.

Previously, we have used dynamic MC simulations to investigate the nucleation details of the conventional NHSK structure in polymer solution, and an anisotropic absorption process prior to crystallization has been observed.²⁸ Namely, the anisotropic filler absorbs chain segments, which simultaneously orient parallel to the long axis of the filler, resulting in the formation of a polymer coating with some local oriented segments on the filler surface. Subsequently, the local oriented segments participate in the heterogeneous nucleation on the filler surface, and eventually develop into kebabs with uniform orientation.²⁸ However, the formation mechanism of the NHSK structure with multiple shish induced by the aligned anisotropic filler networks may be different from that of the conventional NHSK structure.

To obtain more microscopic details of the nucleation process, we observed the formation process of the NHSK structure with multiple shish at early stage of crystallization from the side of the simulation box, as illustrated in Fig. 3. Interestingly, nuclei (blue cylinders) firstly appear inside the filler networks, and then grow up to connect the four fillers that play the role of the multiple shish. This nucleation process indicates that the chains inside the filler networks have stronger nucleation ability than those outside. It should be noted that the crystalline bonds of nuclei are firstly formed in the inside regions of the polymer–filler interface, indicating the occurrence of heterogeneous nucleation, as shown in the snapshot at 300 MC cycles in Fig. 3. The polymer–filler interface was defined as the neighboring lattice sites of the filler surface. The formation of surface nuclei can lead to the decrease of surface free energy for nucleation, and thus is beneficial for crystallization. In addition, we are only able to see the circular end surface of the highly oriented nuclei in Fig. 3, indicating that the crystalline bonds in the nuclei are highly oriented along the long axis of the fillers.

Fig. 3 Snapshots of crystalline morphology of polymer containing filler networks formed at different MC cycles observed from the side of the simulation box. The red strips denote the fillers, and the blue cylinders represent the crystalline bonds.

Subsequently, we tried to explore the underlying mechanism controlling the formation process of nuclei inside the filler networks. It has been revealed that two processes, the adsorption and orientation of segments, play important roles in the formation of the conventional NHSK structure.^23,28 Thus, we tried to investigate how the filler networks influence those two processes. Firstly, we calculated the variations of the polymer density in the polymer–filler interface inside and outside the filler networks at the early stage of crystallization, respectively, as shown in Fig. 4 (the statistical regions in the polymer–filler interface inside and outside the filler networks were marked in the inset of Fig. 4). The polymer density is defined as the fraction of the lattice sites occupied by units of polymer in the corresponding regions. Both of the polymer densities inside and outside the filler networks increase rapidly due to the adsorption of segments into the neighborhood of the fillers under the effect of polymer–filler interactions and then level off. It should be noted that the increase of the polymer densities is faster than the evolution of crystallinity. In addition, the polymer density inside the filler networks is apparently higher than that outside. As is well known, the nucleation rate is controlled by the free energy barrier for critical nucleus formation according to the classical nucleation theory.^41,42 Moreover, the critical free energy barrier is inversely proportional to the degree of supercooling.¹² The higher polymer concentration inside the filler networks will result in the higher degree of supercooling and thus the lower critical free energy barrier. Accordingly, the faster increase of the polymer density inside the filler networks will result in the stronger nucleation ability of segments inside the filler networks. As demonstrated in Fig. 4, the crystallinity of the polymers in the polymer–filler interface inside the filler network increases faster than that outside, directly demonstrating that the segments inside have the stronger crystallizability.

Fig. 4 Evolutions of polymer densities and crystallinity of polymers in the polymer–filler interface inside and outside the filler networks during isothermal crystallization. The statistical regions in the polymer–filler interface inside and outside the filler networks are filled with diamonds and squares, respectively, and the red squares represent the fillers.

Secondly, the filler networks also affect chain conformations. In the present simulations, the four anisotropic fillers are parallel to each other, and the spacing between the neighboring fillers along the Y-axis direction (3 lattice sites) is smaller than the double of the Y-axis part of the radius of gyration (2R_gy) of random polymer coils in equilibrium (about 4.5 lattice sites). Thus, the chains inside the filler networks suffer the confinement effect of the fillers. To reveal the confinement effect of the filler networks on the chain conformations, we further focused on the chains inside the networks, which directly suffer the confinement. If more than half of the segments in a chain are located inside the filler networks, this chain is considered to be located inside the filler networks. Then, we calculated the time-evolutions of the separate X-axis (parallel to the filler) and Y-axis (perpendicular to the filler) parts of the mean square radius of gyration (R_g²) of the chains inside the filler networks, as depicted in Fig. 5a. The Y-axis part of R_g² (R_gy²) is similar to the Z-axis part of R_g², and thus we only show the results of R_gy² here. For comparison, the X-axis part of R_g² (R_gx²) of the random polymer roils in equilibrium was also shown in Fig. 5a. For the chains inside, the R_gx² is apparently higher than the R_gy², indicating that the fluctuations of the chain conformations in the Y- or Z-axis directions are restricted by the filler networks. Then, the chain conformations are thus forced to orient along the X-axis direction. As shown in Fig. 5b, the orientational-order parameter of the amorphous bonds in the chains inside the filler networks along the X-axis is much higher than that of the bonds in the random coils, further demonstrating the presence of the enhanced orientation of chains under confinement. 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 referred to the direction of the long axis of the fillers, and 〈 〉 means an average over all the corresponding bonds. In experiments, it has been found that the presence of oriented anisotropic nanofillers or filler networks favors molecular orientation of polymer chains, and enhances polymer crystallizability.^43,44 By means of MC simulations, Sharaf et al. also documented the presence of the anisotropic effects of the oriented prolate particles on chain dimensions, namely, the chain dimensions became anisotropic, with significant increases and decreases parallel and perpendicular to the direction of the particle axes, respectively.⁴⁵ Similarly, by a combination of computational and experimental methods, Meng et al. observed that polymer chain conformation becomes more extended due to confinement between the CNTs.⁴⁶ Recently, we have investigated the influence of filler network on strain-induced crystallization of natural rubber by a combination of synchrotron wide-angle X-ray diffraction measurements and molecular simulations.³¹ Improvements of segmental orientation and earliest nucleation in regions near the polymer–filler interfaces were observed.³¹ The anisotropic filler networks orient the inner chain segments, reduce the number of chain conformations, and consequently lead to a reduction in conformational entropy,^47,48 accompanied by an increase of melting point and degree of supercooling, which is beneficial for crystal nucleation. Thus, the restriction of chain conformations and improved orientation of segments inside the filler networks also contribute to the earliest appearance of nuclei inside the filler networks. Moreover, the confinement effect of shish on chain conformations may also play an important role in the formation of the shish-kebab structures with multiple shish formed in sheared polymer melts observed by Hsiao's group.⁴⁰ Namely, due to the presence of entanglements, during shear several shish are formed together in a local region. Those shish are parallel to each other, and exert confinement effect on chains existing in the middle region, resulting in the first crystal nucleation in the middle regions and final formation of the shish-kebab structures with multiple shish. In short, the chains inside the filler networks have higher polymer density and higher orientational orders compared with those outside, and thus they participate in crystal nucleation firstly. The crystal nucleation of chains inside the filler networks can be further demonstrated in Fig. 6. For clarity, only one chain (the 679th chain) that was earliest involved in nucleation was selected, and the corresponding conformational evolutions were shown in Fig. 6. At initial state, the chain is located outside the filler networks. At 500 MC cycles, the chain is absorbed into the inside of the filler networks. Then, at 1000 MC cycles, some segments oriented along the long axis of the fillers firstly participate in the secondary nucleation on the inside surface of the fillers.

Fig. 5 (a) Time-evolutions of the separate x-axis and y-axis parts of the mean square radius of gyration of the chains inside the filler networks and the x-axis part of the mean square radius of gyration of the chains in random coils; (b) time-evolutions of orientational-order parameter of amorphous bonds inside the filler networks and that of amorphous bonds in random coils.

Fig. 6 Snapshots for crystal nucleation of single chain inside the filler networks. The yellow cylinders denote the amorphous bonds, while the blue cylinders represent the crystalline bonds.

(B) Effect of polymer–filler interactions

In our pervious paper, we have demonstrated that the strength of polymer–filler interactions directly influences the formation of NHSK structure.²⁸ Thus, we further investigated the effect of polymer–filler interactions on polymer crystallization in the presence of filler networks. As shown in Fig. 7a, the systems with higher polymer–filler interactions (B/E_c = −0.5 to −1) exhibit shorter induction period for crystal nucleation and faster crystallization kinetics. The presence of higher polymer–filler interactions reduces the free energy barrier for the formation of nuclei, and thus favors the crystal nucleation process. However, the very strong polymer–filler interaction (B/E_c = −5) leads to the slowing down of crystallization kinetics, since the chain movements near the fillers are restricted. Fig. 7b illustrates the crystalline morphology of polymers containing filler networks with different polymer–filler interactions formed at the late stage of crystallization. The crystals formed in all the systems exhibit uniform orientation along the long axis of the fillers. Namely, the NHSK structure can be formed in the systems with high and low interactions.

Fig. 7 (a) Evolutions of crystallinity of polymers containing filler networks with different polymer–filler interactions during isothermal crystallization. (b) The snapshots of crystalline morphology of polymers containing filler networks with different polymer–filler interactions formed at the late stage of crystallization.

For comparison, the simulation results of the systems containing single filler were also shown here. The corresponding crystalline morphology is displayed in Fig. 8. In the systems with the high interactions (B/E_c = −0.8 and −1), the typical NHSK structure with the filler acting as shish and the lamellae as kebabs can be observed. However, when the interaction was decreased to −0.5 (B/E_c = −0.5), the orientation of crystal formed on the filler surface is perpendicular to the direction of the long axis of the filler, indicating that no NHSK structure was formed. In this case we observed strong fluctuations of the crystal orientation. Several independent simulations were carried out, and we found that the crystals exhibit different orientations in different simulations. Then, we selected one sample and showed the crystalline morphology in Fig. 8. In short, the NHSK structure can be only formed in the polymers filled with single filler in the presence of high polymer–filler interactions, but it can be formed in the systems containing filler networks with relatively weak polymer–filler interactions. Namely, the confinement effect of filler networks is beneficial for the formation of the NHSK structure.

Fig. 8 The snapshots of the crystalline morphology of polymer composites containing single filler under different polymer–filler interactions.

Then, we focused on the details of crystal nucleation process in the systems filled with filler networks with different polymer–filler interactions. Fig. 9 shows the nuclei formed at the early stage of crystallization in those systems. Interestingly, for all the systems, the nuclei with orientation along the long axis of the fillers firstly appear inside the filler networks. In other words, the chains inside the filler networks that have suffered the confinement of filler networks have stronger nucleation ability. As mentioned above, the presence of filler networks exerts confinement effect on chain conformations, forcing the chain segments inside the filler networks to orient along the long axis of the fillers. Fig. 10a further reveals that the segmental orientation is influenced by the polymer–filler interactions. The segments of chains inside the filler networks exhibit higher orientational orders in the systems with higher polymer–filler interactions. That is, the high polymer–filler interaction is beneficial for the orientation of segments under confinement. Then, the chains inside the filler networks with higher orientational orders have lower conformational entropy, and thus stronger nucleation ability.

Fig. 9 The snapshots of crystalline morphology of polymers containing filler networks with different interactions formed at the early stage of crystallization.

Fig. 10 (a) Time-evolutions of orientational-order parameters of amorphous bonds inside the filler networks with different interactions and (b) of those in the polymer–filler interface in the polymer containing single filler.

Fig. 10b comparatively shows the time-evolutions of orientational-order parameters of amorphous bonds of chains inside the filler networks and those in the polymer–filler interface of the system filled with single filler with a same polymer–filler interaction (B/E_c = −0.5). The segments inside the filler networks have higher orientational-order parameters compared with those near the single filler. Namely, the segmental orientation along the long axis of the fillers is enhanced due to the confinement of filler networks, leading to the formation of the NHSK structure.

(C) Effect of filler spacing

Subsequently, we further investigated the effect of filler spacing on the formation of the NHSK structure. Fig. 11 illustrates the crystal nucleation process in the systems containing filler networks with different spacing. For the systems with relatively small spacing (3 and 4 lattice sites, <2R_gy of polymer random coils in equilibrium), it can be seen that most of the nuclei firstly appear inside the filler networks. For the system with the filler spacing of 5 lattice sites, during nucleation process part of nuclei are formed only on the surface of one filler, while part of nuclei are formed inside the filler networks. When the filler spacing is further increased to 6 lattice sites, all the nuclei are directly formed on the surface of one filler. Conclusively, the fraction of nuclei formed inside the filler networks decreases with the increase of filler spacing.

Fig. 11 The snapshots of crystalline morphology of polymer containing filler networks formed at the early stage of crystallization.

This change of nucleation sites is caused by the weakening of confinement effect of filler networks on chain segments with the increase of filler spacing. Namely, the restriction of chain conformations inside the fillers will be weakened due to the increase of filler spacing, thus resulting in the weakening of confinement effect. For the system with the filler spacing of 3 lattice sites, the filler spacing is smaller than the 2R_gy of random coils, and thus chains inside the filler networks suffer confinement. Herein, the chains near the fillers are considered to be composed of two kinds of chains: the chains inside the filler networks and those outside. If a chain has more than one segment but less than half of the segments located inside the filler networks, it is treated as the one outside the filler networks. As shown in Fig. 12, the orientational-order parameters of chains inside the filler networks are obviously higher than those outside due to the confinement effect. For the system with filler spacing of 4 lattice sites (still smaller than the 2R_gy of random coils), the orientational-order parameters of chains inside the filler networks are still higher than those outside, but the difference between them is reduced due to the weaker confinement effect. Thus, for those two conditions the nuclei were mainly formed inside the filler networks due to the higher orientational orders of the chains inside. For the systems with filler spacing of 5 lattice sites (larger than the 2R_gy of random coils), the difference between orientational orders of the chains inside and outside the filler networks was further reduced (the confinement effect was weakened), and thus more nuclei are preferred to be formed only on the surface of one filler. When the filler spacing is further increased to 6 lattice sites, the chains inside no longer suffer confinement of fillers, and thus all the nuclei are formed only on the surface of one filler.

Fig. 12 Time-evolutions of orientational-order parameters of amorphous bonds inside and outside the filler networks with different filler spacing: (a) spacing of 3, (b) spacing of 4, (c) spacing of 5 and (d) spacing of 6.

IV. Conclusion

In conclusion, by means of dynamic MC simulations we successfully observed a new NHSK structure with multiple shish, in which the fillers form the multiple shish and the polymer crystal lamellae form the kebabs. During crystallization, the surface nuclei first appear inside the filler networks and then grow up to connect the fillers to form the NHSK structure with multiple shish. On the one hand, in the polymer–filler interface the polymer density inside the filler networks is apparently higher than that outside. On the other hand, the chains inside the filler networks suffer the confinement of the filler networks, resulting in the enhancement of segmental orientation and the reduction of conformational entropy. Thus, the chains inside the filler networks participate in crystal nucleation first.

In addition, we found that the NHSK structure can be formed in the systems containing filler networks with high and low polymer–filler interactions, but the NHSK structure can be only formed in the polymers filled with single filler in the presence of high interactions. The filler spacing directly affects the nucleation mechanism of the NHSK structure. For the systems with relatively small filler spacing (smaller than the 2R_gy of random coils), the nuclei firstly appear inside the filler networks. The increase of filler spacing will result in the appearance of fewer nuclei formed inside the filler networks.

This special NHSK structure may endow polymer materials with more excellent physical properties. We hope that our current simulation findings will inspire researchers to carry out further experimental works in the future to investigate the fabrication and properties of polymer materials with the NHSK structures with multiple shish.

Acknowledgements

The financial supports from the National Natural Science Foundation of China (No. 21404050 and 21174057) are 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.

Notes and references

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