Simulations on polymer nanocomposite crystallization

2.1 Simulation details of nanofiller-induced homopolymer crystallization

Since nanofillers are added into the simulation box, the interfacial interaction between polymer and nanofiller should be taken into account. Then, the potential energy change (B) for each monomer-filler pair, representing the polymer-filler interaction, is introduced. In this condition, for MC simulations, the values of B/E_c can be used to reflect the strength of the interfacial interaction. Besides, in order to systemically study the effect of the nanofillers on polymer crystallization, the number of nanofillers, the shape, or aspect ratio of nanofillers can also be changed.

2.2 Simulation details of nanofiller-induced copolymer crystallization

For MC simulations of copolymer crystallization, the crystallizable and the non-crystallizable beads can be distinguished by setting different values of E_p. Namely, the value of E_p for the parallel packing of two bonds both belonging to the crystallizable beads is larger than zero, while the value of E_p for the parallel packing of two bonds containing at least one bead belonging to the non-crystallizable beads is set to zero. Based on the definition, the non-crystallizable beads cannot crystallize. For block copolymers, another energy parameter representing the mixing interaction between crystallizable beads and non-crystallizable beads, which drives the occurrence of microphase separation can also be introduced. For homogeneous random copolymer polymers, each occupied lattice site can be defined as either a crystallizable bead or a non-crystallizable bead based on an ideal addition copolymerization process for random copolymers with a preset comonomer fraction.

2.3 Simulation details of crystallization of grafted polymers on nanofillers

For polymers grafted on the surfaces of nanofillers, the chain segments that are directly grafted on the nanofillers are not allowed to move during simulations. By changing the distribution of grafting points on the surfaces of nanofillers, the grafted polymer systems with different grafting densities can be established. In addition, the grafted polymer systems with different molecular weights can also be set up by the change of the chain length of grafted polymers.

2.4 Simulation details of flow-induced crystallization of filled polymers

There are two methods to achieve oriented chains in MC simulations. For the first method, the initial chains with extended conformation were relaxed under athermal conditions (athermal conditions correspond to an infinitely high temperature). Then, during relaxation crystallinity decreases much faster than the mean-square radius of gyration. When the crystallinity values drop to 0, the corresponding mean-square radius of gyration is still higher than that of the random coils; that is, although the crystals are melted, the polymer melts can still have a certain degree of orientation. In other words, oriented melts that have no crystalline structures but a certain degree of chain orientation can be obtained in a certain period of relaxation time.³¹

For the second method, a gradient potential E_s is introduced into the energy penalty in the conventional Metropolis sampling algorithm for a trial move of monomers in each step of the micro-relaxation process.³⁵ It was demonstrated that E_s/E_c is the external potential field of driving forces, corresponding to the driving-force aspect of shear stress in a shear field imposed along shear flow direction onto each bead.³⁵

3.1 Crystallization of polymers in nanopores, nanospheres, and near nanopatterned, flat, and curved surfaces

Müller's group performed systematically investigations on the crystallization of confined polymers.⁵⁸ In general, the increase in the confinement degree can lead to a decrease of the predominance of heterogeneous nucleation, a very large decrease of the solidification temperature, a decrease of the degree of crystallinity, and a moderate decrease in melting point.⁵⁸ In addition, surface nucleation plays a dominant role in the crystallization of polymers confined in an isolated ensemble of heterogeneity free microdomains, since surface nucleation requires lower degree of supercooling than classic volume homogeneous nucleation.⁵⁸ Wang's group observed the existence of surface freezing in microencapsulated n-alkanes, and also found that the confinement suppresses lamellar ordering and longitudinal diffusion.⁵⁹

With the help of MD simulations, Jabbarzadeh et al. studied crystallization of polymer as a drop in isolated state and on a surface.⁶⁰ They found that the crystallization rate of polymer systems decreases with the increase of the roughness ratio, but is still faster than that of the isolated polymer drop.⁶⁰

3.2 Formation mechanisms of NHSK structures in homopolymer solutions

As mentioned above, in order to explain the microscopic mechanisms of the formation of the NHSK structures, Li's group proposed the geometric confinement theory, which describes that the one-dimensional nanofillers with small diameters can exert confinements on the chain conformations of the interfacial chain segments, and further make them to orient along the long axis of the nanofillers.^{20, 21} However, they did not give a clear explanation about the details of the special “confinements.” Interestingly, based on molecular simulations, the formation details of the NHSK structures become clearer. Liu et al. used MD simulations to study the isothermal crystallization of one single polymer chain on one CNT, and observed that the chain is firstly adsorbed onto the filler surface, and then oriented along the long axis to form an oriented crystal.⁶¹

In order to obtain in-depth information for the formation of the NHSK structures, our group further used MC simulations to investigate the nucleation details of the NHSK structures.⁶² Figure 1A shows the variations of the monomer density and the orientational-order parameter of amorphous segments along the long axis of the filler in the polymer-filler interface at the early stage of crystallization. Both the monomer density and the orientational-order parameter of amorphous segments along the long axis of nanofiller increase fast at first and then reach a plateau, indicating the absorption of chain segments onto the filler surface with small lateral size belongs to an anisotropic process. Figure 1B displayed that the orientational-order parameter along the X-axis direction (i.e., the long axis of the nanofiller) is obviously higher than these along with the Y-axis and Z-axis directions, further confirming that chain segments prefer to orient along the long axis of the nanofiller during absorption. Using MD simulations, both Yang et al. and Zong et al. observed that absorbed chain segments are oriented along the long axis of CNTs.^{63, 64} In addition, Figure 1A also showed that the crystallinity increases much slowly than the monomer density and the orientational-order parameter, demonstrating that the adsorption and orientation processes are the prerequisite for the NHSK formation. After the adsorption and orientation processes, the adsorbed oriented segments begin to participate in crystallization based on heterogenous nucleation.⁶²

In experiments, it was demonstrated that the diameters of the nanotubes can influence the formation of the NHSK structures.¹¹ According to the dynamic MC simulations, we also found that the perfect NHSK structures can also form in the systems with the nanofillers of relatively small lateral sizes, while in the systems with the nanofillers of relatively large lateral sizes some lamellar crystals with other different orientations will also form, as illustrated in Figure 1C.⁶² The increase of the lateral sizes can cause the increase of the orientational-order parameter along the lateral-dimension direction, and then lead to the formation of some lamellar crystals with other orientations. The interfacial interactions between fillers and polymers also play an important role for the NHSK formation. Our simulation results showed that the interfacial chain segments under high polymer-filler interfacial interactions have higher orientational-order parameters along the long axis of the nanofiller that these under the low polymer-filler interfacial interactions, and thus the perfect NHSK structures prefer to form in the systems with high interfacial interactions rather than that with low interfacial interactions, as shown in Figure 1D.⁶²

In addition, we also observed that a new NHSK structure with multiple shish appears in the systems containing aligned anisotropic filler networks, illustrated in Figure 2A.⁶⁵ In this special structure, several aligned one-dimensional fillers form the multiple shish, and the polymer lamellar crystals form the kebabs. During crystallization, nuclei first form inside the filler networks, and then grow up to connect the nanofillers to form the special NHSK structure with multiple shish, as illustrated in Figure 2B.⁶⁵ Due to the confinement effect of the aligned anisotropic filler networks and the interfacial interactions, the inside polymer chains have higher degree of orientation along the long axis of the nanofillers and higher monomer density (as seen in Figure 2C,D), then resulting in stronger nucleation ability of the inside chains.⁶⁵

The influences of filler dimension and size on the crystallization of polymer systems have been widely reported in experiments. The effects of one-dimensional CNTs and two-dimensional graphene nanosheets on polymer crystallization are often compared. For example, Xu et al. found that compared with graphene, CNTs with a larger aspect ratio exhibit a higher ability to induce polymer crystallization.²² Based on MD simulations, this phenomenon was also discovered and confirmed in the crystallization processes of alkanes induced by nanotubes and graphene.⁶³ Ning et al. comprehensively summarized the crystalline structures induced by nanofillers of different dimensions (including one-dimension, two-dimension, and three-dimension).¹¹

In our previous work, the crystallization behaviors of polymers filled with the nanofillers with different dimensions (i.e., zero-dimensional nanofillers, one-dimension nanofillers, and two-dimension nanofillers) were studied by dynamic MC simulations.⁶⁶ It was found that the one-dimensional nanofiller has the strongest ability to induce polymer crystallization, while the zero-dimensional nanofiller has the weakest ability. The crystalline morphology of polymer composite systems will also be affected by the filler dimension. Differing from the one-dimensional nanofiller that can induce the formation of the NHSK structures, the two-dimensional nanofiller can only induce the formation of the crystals with stem orientations parallel to the nanofiller surface, as shown in Figure 3A.⁶⁶ In the system containing the zero-dimensional nanofiller, the three-dimensional crystal growth happens, resulting in random crystal orientations. This difference of the crystalline morphologies in these systems containing nanofillers with different dimensions can be attributed to the different ability to induce the orientation of interfacial segments. As shown in Figure 3B,⁶⁶ the orientational-order parameters of interfacial amorphous bonds along with X-axis, Y-axis, and Z-axis directions are almost the same, indicating that the zero-dimensional nanofiller cannot induce segmental orientation in the interfacial regions. As shown in Figure 3C,⁶⁶ the values of the orientational-order parameters of interfacial amorphous bonds along the X-axis direction are obviously higher than these along with Y-axis and Z-axis directions. That is, the interfacial segments are inclined to align along the long axis of the nanofiller. As shown in Figure 3D,⁶⁶ the values of the orientational-order parameters of interfacial segments along X-axis and Y-axis directions are nearly the same, both of which are higher than these along Z-axis direction. Under the effect of the polymer-filler interaction interfacial segments prefer to “lie” on the filler surface (XY plane), and chain conformations are unfolded in interfacial regions, resulting in the higher orientational-order parameters along with X-axis and Y-axis directions. Wang et al. also detected that graphene platelet can induce the orientation of absorbed segments based on MD simulations.⁶⁷

Nowadays, the precise morphology control is paramount among many challenges as polymer nanocomposites move beyond commodity plastic applications.^68-71 In general, the semi-crystalline polymers with uniform crystal orientation exhibit high mechanical properties.¹¹ However, the crystals induced by the two-dimensional nanofillers, such as graphene, exhibit random orientations.^{11, 72} Then, to achieve the polymer crystals with uniform orientation (similar to the NHSK structure) in polymers containing the two-dimensional nanofillers is a very interesting topic.⁷³ Nowadays, applying shear flow field is the most commonly used method for the improvement of polymer crystal orientation.^{72, 73} The oriented chains in sheared systems can induce the formation of oriented crystals or shish-kebabs.^{72, 73} From another point of view, if oriented chains are fixed on the filler surface, oriented crystals may be obtained even without shear flow. In our previous work, using dynamic MC simulations, we modified the two-dimensional nanofiller with two-end grafted oriented chains (loops, as seen in Figure 4A),⁷⁴ and then successfully obtained the crystal structure with uniform orientation in polymer solutions, as shown in Figure 4B.⁷⁴ These simulation findings provide a new method to control polymer crystal orientation.

3.3 Differences in crystallization behaviors between cyclic and linear polymer nanocomposites

Cyclic polymers belong to fascinating materials due to the unique topology. Compared with linear polymers, cyclic polymers differ only in that their lack of chain ends. However, owing to this difference in topological structure, cyclic polymers exhibit some special microscopic structures and macroscopic physical properties.^{75, 76}

Based on molecular simulations, extensive researches have been performed on the crystallization behaviors of cyclic polymers and their linear analogs.^{77, 78} Previously, Sommer and coworkers found that the crystallization temperature, melting point, stem length, crystallinity, and latent heat of melting/crystallization of cyclic polymer melts are significantly higher than their linear counterparts subjected to the same thermal history.⁷⁷ In contrast, Iyer and Muthukumar investigated the crystallization behaviors of cyclic polymers by Langevin dynamics simulation, and observed that cyclic polymers melt at a lower temperature compared to linear counterparts.⁷⁸ These controversial conclusions have also been reported in some experimental researches. For instance, Pérez et al. reported that under the same crystallization conditions, cyclic poly(ε-caprolactone) (PCL) exhibits faster nucleation rate and higher crystallization rate compared to the analog linear PCL.⁷⁵ Similar phenomena are also observed for cyclic poly(ethylene oxide),⁷⁶ and cyclic poly(l-lactide) (PLLA).⁷⁹ However, completely opposite results have been reported for cyclic poly(tetrahydrofuran)^{80, 81} and PE.⁸² Pérez and coworkers summarized these opposite research conclusions and conducted the theoretical analysis.⁸³ The above contrastive behavior between cyclic polymer melts and linear polymer melts could be interpreted from the following two viewpoints: kinetic factors determined by diffusion and thermodynamic factors controlled by different supercooling.^{84, 85}

The addition of nanofiller also affects the crystallization behaviors of cyclic polymers. Nucleating effect has been found in cyclic PCL systems incorporating single-walled CNTs functionalized with octadecylamine.⁸⁶ In addition, it was also found that adding graphene oxide nanosheets to cyclic ultrahigh-molecular-weight PE helps to form crystals with high melting temperatures.⁸⁷ Previously, with the help of dynamic MC simulation, our group comparatively studied the crystallization behaviors of cyclic and linear polymer nanocomposites, and found that the filled cyclic polymers exhibit higher melting temperature, higher crystallization temperature, and faster crystallization rate, especially in the systems with relatively short chains.⁸⁸ In other words, the nanofiller exhibits the same promotion effects on the crystallization process of cyclic and linear polymers. Moreover, it is also observed that the NHSK structure can be formed in both the systems (as shown in Figure 5A), indicating that the chain topology has little influence on the final crystal morphology.⁸⁸

According to the famous Thomson–Gibbs equation, Su et al. deduced the modified Thomson–Gibbs equation for the cyclic polymers, which can be expressed as follows⁸⁹:

()

where T_mC is the melting temperature of the cyclic polymers, is the equilibrium melting temperature of the linear polymers (which refers to the melting temperature at which the crystal thickness is infinite), ΔS_cyc is the cyclization entropy difference between the cyclic and linear polymers, which is susceptible to chain length, is the difference in equilibrium melting enthalpy, σ_e is the fold surface free energy, and l is the lamellar thickness. Then, we further derived the cyclization entropy difference between the cyclic and linear polymers, and established the relationship between the melting point of the cyclic polymers and that of its linear analog under different chain lengths:

()

where Q/N is the number of chains, k is the Boltzmann's constant. Figure 5B displays the nonlinear fitting results between the simulated data and Equation (2). It can be seen that the fitted curves of the filled polymer systems and the unfilled polymer systems are almost coincident, confirming the rationality and reliability of Equation (2).

4.1 Crystallization behaviors of block copolymer nanocomposites

Block copolymers have been widely investigated because of their fascinating ability to self-assemble into different sophisticated structures. As we all know, in block copolymers, the repulsive interaction between chemically different blocks will cause sequence separation, while the chemical bonds connecting the sequences hinder the macroscopic phase separation as in the blend.^87-92 In the delicate balance of these two effects, microphase separation will occur between different blocks. For the crystalline-amorphous diblock copolymers, the final crystal morphology is mainly governed by the crystallization process and microphase separation, resulting in more complex, and richer structures.^93-95

Furthermore, due to the unique structural characteristics of block copolymers, block copolymer nanocomposites also exhibit special crystallization behaviors. For instance, the NHSK structure has also been observed in block copolymers filled with CNT bundles.⁹⁶ Interestingly, a novel nanohybrid epitaxial brush (NHEB) structure, which is formed by a central CNT, disc-shaped folded-chain lamellar crystals of PE blocks decorating on filler surface and random coils of amorphous polyvinyl cyclohexane (PVCH) blocks surrounding PE crystals, was found in triblock copolymers (PVCH-PE-PVCH).⁹⁷ Based on molecular simulations, similar structure has also been observed in crystalline-amorphous diblock copolymer systems filled with one-dimensional nanofiller, and the formation mechanism has also been revealed.^{98, 99} At the beginning of crystallization, due to the attractively interfacial interactions between the crystallizable blocks and the nanofiller, the amorphous chain segments (segments in crystallizable blocks that have not crystallized) are adsorbed into the interface area of the nanofiller and orient along the long axis of the filler. These amorphous segments grow into small crystallites (segments in crystallizable blocks that have crystallized) oriented along the long axis of the filler through heterogeneous nucleation, and finally form the NHSK structure. In this case, with the nanofiller as the center, the crystallizable segments are decorated on the surface of the nanofiller, while the non-crystallizable segments (segments in non-crystallizable blocks) are wrapped in the outermost layer. The formation of this hierarchical NHEB structure indicates that microphase separation occurs between the crystalline block and the non-crystallizable block. The distribution of different chain segments in the NHEB structure was also observed and counted. From Figure 6,⁹⁸ one can see that the crystallizable segments are mainly distributed on the surface area of the filler due to the interfacial interaction, while the non-crystallizable segments are mainly distributed in the area away from the surface of the filler due to microphase separation. In general, the above-mentioned research results reveal the details of the formation of NHEB structure from the molecular scale (Figure 6⁹⁸).

Microphase separation can significantly affect the crystallization behaviors of block copolymers filled with nanofillers. It is reported that the enhancement of repulsive interaction between different blocks can promote microphase separation, which in turn leads to the local stretching of crystallizable blocks.⁹⁹ Under this condition, the crystallization process through homogeneous nucleation is promoted, as shown in Figure 7A.⁹⁹ In general, the repulsive interaction between the two blocks is the main driving force for microphase separation. In addition, the different crystallizability and the different polymer-filler interactions of various blocks will also promote the occurrence of microphase separation. For crystalline-amorphous diblock copolymers, the polymer-filler interfacial interaction enhances the heterogeneous nucleation, while the local stretching of the crystallizable segments caused by microphase separation promotes homogeneous nucleation. Thus, the final crystal morphology of the system is codetermined by these two factors, as shown in Figure 7B.⁹⁹ In the systems with relatively weak repulsive interaction between blocks, the crystallizable segments preferentially crystallize through heterogeneous nucleation, and finally form a regular NHSK structure. In the systems with relatively strong repulsive interaction between blocks, the local stretching of the crystallizable segments is strengthened, and the pre-stretched crystallizable segments preferentially crystallize through homogeneous nucleation. Under this condition, homogeneous nucleation and heterogeneous nucleation compete with each other, leading to the degradation of crystal morphology.

In general, here we mainly introduce the crystallization behaviors of crystalline-amorphous diblock copolymers filled with one-dimensional nanofiller, and summarize the formation mechanism of the NHEB structure and the influence of microphase separation on the crystallization behaviors. These simulation results provide new ideas for the development and design of complex nanostructures. However, the crystallization behavior of filled crystalline–crystalline diblock copolymers and multi-block copolymers still needs further studies.

4.2 Crystallization behavior of random copolymer nanocomposites

Another type of copolymer that has been studied extensively is random copolymer composed of crystallizable monomers and non-crystallizable comonomers. Compared with homopolymers, the sequence regularity of the molecular chains of statistical random copolymers is destroyed, which makes it difficult to form thicker lamellae structure, resulting in a decrease in the melting point of the system. Based on the assumption that the non-crystallizable comonomers are uniformly distributed in space, Flory¹⁰⁰ deduced the theoretical formula for equilibrium melting point of statistical random copolymers. Subsequently, Colson and Eby¹⁰¹ further derived the melting point formula under the condition that the non-crystallizable copolymer unit can enter the crystal region, and found that the decrease in melting point is proportional to the content of non-crystallizable comonomers. In addition, in random copolymers, the addition of non-crystallizable comonomers can hinder the crystallization process and reduce the crystallization rate.¹⁰² Furthermore, the crystal morphology will also be significantly affected due to the presence of non-crystallizable comonomers. As the content of non-crystallizable comonomers increases, the crystal morphology gradually degenerates from spherulites formed in homopolymer bulks to granular-based morphology or even small crystallites, which has been confirmed in experimental studies and computer simulations.^103-105 In fact, the addition of a small amount of non-crystallizable copolymerization units can significantly reduce the melting point and the crystallinity of the random copolymer system, which is often used in industry to control the semi-crystalline structure of polymers and improve the toughness of materials.¹⁰⁶

The crystallization behavior of random copolymer nanocomposites is also an interesting research topic. Similar to homopolymer nanocomposites, the addition of nanofillers in random copolymers can also promote the crystallization process and accelerate the crystallization rate.^107-109 For example, Verma and Choudhary¹⁰⁷ investigated the crystallization process of PP random copolymers under isothermal conditions in presence of multiwalled carbon nanotubes (MWCNT), and found that MWNT lowers the nucleation barrier, thereby accelerating the crystallization process. In addition, for the random copolymer nanocomposite systems, the crystallization behavior and crystal morphology also depend on the content of non-crystallizable comonomers. Based on molecular simulations, the isothermal crystallization process of a series of random copolymer nanocomposites with different contents of non-crystallizable comonomers has been studied.¹¹⁰ The simulation results indicate that increasing the comonomer content will slow down the nucleation rate and reduce the final crystallinity. Moreover, the crystalline morphology is also affected by the comonomer content. In the random copolymer nanocomposites with lower contents of non-crystallizable comonomers, the one-dimensional nanofiller can induce the formation of the NHSK structures.¹¹⁰ However, in the random copolymer nanocomposites with very high contents of non-crystallizable comonomers, the presence of a large number of comonomers with no ability of parallel arrangements hinders the formation of the NHSK structures. Under this condition, the formed crystallites usually exhibit different orientations.

5.1 Effect of grafting density on polymer crystallization

Grafting density can affect the crystallization process of grafted polymer systems. Previously, our group systematically investigated the crystallization behaviors of polymers grafted on the surface of nanofillers with different dimensions based on dynamic MC simulations, and found that a higher grafting density can result in a shorter nucleation induction period and a higher final crystallinity.^122-131 This phenomenon can be attributed to the decreased conformational entropy of the grafted chains and the decreased critical free energy nucleation barrier caused by the increased segment density in the regions near the grafting points and the chains with highly stretched conformations.¹²³

Second, grafting density also affects the nucleation mode and the orientation of chain segments, which in turn changes the crystalline morphology. It has been reported that the crowding effect of molecular chains is relatively weak for the polymer systems with lower grafting density, which leads to the tendency of molecular chains to participate in the nucleation and growth of crystals in the form of intramolecular chain-folding nucleation.^123-125 However, for the polymer systems with higher grafting density, the crowding effect of molecular chains is very strong and the degree of conformational extension is high, which results in the preferential crystallization of the molecular chains through intermolecular fringed-micelle nucleation. Due to the different nucleation modes, the systems with different grafting densities exhibit different crystal morphologies. The final crystal morphologies of the polymer systems grafted on two-dimensional nanofillers with different grafting densities were shown in Figure 8.¹²³ It can be seen that the crystalline stems tend to crystallize parallel to the filler surface when the grafting density is low, and the crystalline stems prefer to crystallize perpendicular to the filler surface when the grafting density is high.

5.2 Effect of molecular weight on polymer crystallization

The molecular weight will affect the conformations of polymer chains, thus significantly changing the crystallization behaviors of grafted polymers. Jana et al. found that the increasing molecular weight of PCL grafted onto MWNT leads to higher crystallization temperature and higher crystallinity.¹¹⁶ In the PCL systems grafted onto MWNT, Zhou, and coworkers also observed that the growth of molecular weight can reduce the activation energy of crystallization.^{119, 120} The detailed microscopic mechanisms of the influence of molecular weight on the crystallization behaviors of grafted polymers have also been further revealed by molecular simulations.^{127, 128} For example, our group reported that the increasing molecular weight leads to shorter nucleation induction period and higher final crystallinity, which is consistent with the experimental results.¹²⁷ In addition, the nucleation mode and the orientation of crystalline stems are also affected by molecular weight. It has been reported that the chain segments prefer to choose the intermolecular nucleation mode in the grafted polymer systems with lower molecular weight, while the chain segments exhibit the intramolecular nucleation in the grafted polymer systems with higher molecular weight.^{127, 128} The difference in nucleation modes can be attributed to the limiting effect from grafting points. Namely, when the molecular weight is low, the limiting effect from grafting points is stronger, and then the formation and growth of crystal nuclei are mainly through the intermolecular nucleation. When the molecular weight is high, this limiting effect is weaker and the molecular chains are much easier to bend and fold, and thus the molecular chains tend to grow into crystals through the intramolecular nucleation. Furthermore, as the molecular weight increases, the crystalline bonds gradually deviate from the initial orientation perpendicular to the filler to the orientation parallel to the filler, and eventually return to the orientation perpendicular to the filler again, as shown in Figure 9. This phenomenon can be explained by the crowding effect caused by the increase of the molecular weight.¹²⁷

5.3 Effect of interfacial interactions on polymer crystallization

Polymer-filler interaction is another important factor affecting the crystallization behaviors of polymer nanocomposites. Based on molecular simulations, the crystallization process and crystal morphology of polymer systems grafted onto two-dimensional nanofillers under different conditions have been reported, as displayed in Figure 10.¹²⁹ For the systems with lower grafting density, the polymer-filler interaction plays a dominant role in the crystallization behaviors of these systems. Under this condition, the increase of the attractive interfacial interaction will cause the occurrence of heterogeneous nucleation and the shortening of the nucleation induction period, but the orientation of the chain segments will not be changed. Similar heterogeneous nucleation has also been observed in PLLA grafted on SiO₂ by Wu and coworkers.¹¹⁸ For the systems with medium grafting density, the crowding effect caused by the increasing grafting density will drive more segments to move away from the interface, while the attractive interfacial interaction will cause the filler to adsorb more segments on the surface. Due to the competition of these two effects, the crystallization behaviors of the system are more complicated. The enhanced interfacial interaction can compensate for the conformational entropy loss caused by the restriction of the nanofiller, resulting in the increasing segments density in the interface regions and the enhanced nucleation ability. Therefore, the improved interfacial interactions can also shorten the nucleation induction period, but the system does not undergo heterogeneous nucleation. Li et al. also found this phenomenon in the study on the crystallization of PLLA on the surface of CNT.¹⁵ In addition, as the polymer-filler interaction increases, the nucleation mode changes from the intermolecular nucleation mode to the intramolecular nucleation mode. Under the competition of crowding effect and attractive interaction, the increase of interfacial interaction will cause crystals to gradually change from perpendicular to the filler surface to parallel to the filler surface. For systems with higher grafting density, the excessive crowding effect controls the crystallization process, and the crystallization ability is hardly affected by the polymer-filler interaction. Under this condition, the system does not undergo heterogeneous nucleation, and the crystal orientation of all systems tends to be perpendicular to the filler surface.