1 Introduction

Graphdiyne, first synthesized by Yuliang Li team in 2010 [1], is a new all-carbon nanostructure material after fullerenes [2], carbon nanotubes[3] and graphene [4]. It has abundant carbon chemical bonds, large conjugated system, wide interplanar spacing and excellent chemical stability [5,6,7]. Its monomer structure is shown in Fig. 1. Its carbon has two hybrid state of sp, sp2 at the same time. It is the most stable synthetic allotrope of diacetylenic carbon. Due to its special electronic structure and excellent semiconductor properties similar to silicon, graphdiyne will play an important role in the fields of electronics [8,9,10], semiconductors[11] and new energy [12,13,14,15]. Recently, most researches have focused on the study of graphdiyne composites [16,17,18]. Gao et al. [19] constructed the γ-graphyne/TiO2 nanotube array heterostructures for the first time, and demonstrated their excellent photoelectrochemical and photoelectrocatalytic properties. Zhang team [20] explored hydrogen adsorption on Ti-decorated graphyne under different external electric fields by first-principles calculations.

Fig. 1
figure 1

Monomer structure of graphdiyne

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Buckminsterfullerene, discovered by American chemist Robert Curl in 1985 with Smalley and Kroto and awarded the Noble Prize in 1996, is a spherical form of carbon comprised of 60 atoms [21]. The discovery opened a new branch of chemistry. Tanzi and his coworkers [22] reported a derivatization strategy and biological application of fullerene C60 to increase solubility in water using polar “active” molecules as sugars and amino acids/peptides. Heredia et al. [23] showed that the hydrophobic carbon sphere of fullerene C60 can be replaced by cationic groups to obtain amphiphilic structures. These compounds absorb mainly UV light, but absorption in the visible region can be enhanced by anchoring light-harvesting antennas to the C60 core. Currently, research on new composite materials has attracted extensive attention. Fullerenes and graphynes are new carbon materials, and the properties of their composites need to be studied urgently. Throughout the major databases, there are very few studies on fullerene/graphyne composites.

To explore the properties of fullerene/graphdiyne-like chain composites, we use a molecular dynamics simulation to study the interaction between fullerenes and graphdiyne-like chain. In all these systems, the number of fullerenes is more than six. In the beginning, all the fullerenes are neatly arranged on the graphdiyne-like chain. The final configuration changes with the number of fullerene. The more fullerenes there are, the larger the nanoclusters. The whole process goes through three steps: sliding, twisting, and reunion. Both the van der Waals potential well and the π–π stacking interaction between fullerenes and graphdiyne-like chain play a major role in the self-assemble process. Furthermore, the influence factors such as the position of fullerenes and the simulation temperature are also investigated.

2 Simulation method

In this work, all calculations were carried out by molecular dynamics (MD) simulation, and the atomic interaction was described by the force field of condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) [24, 25]. COMPASS is an ab initio force field that has been parametrized and validated using condensed-phase properties in addition to various ab initio calculations and experimental data, with a functional form that includes covalent terms as well as long-range, non-bond (van der Waals (vdW)) interactions and electrostatic forces. It aims to achieve high accuracy in prediction of the properties of very complex mixtures [26, 27].

The potential energy \(E_{{{\text{potential}}}}\) of a system can be expressed as the sum of the valence \(E_{{{\text{valence}}}}\), the cross-term \(E_{{\text{cross - term}}}\), and the nonbond interactions \(E_{{{\text{nonbond}}}}\), with the following equation [28]

$$E_{{{\text{potential}}}} = E_{{{\text{valence}}}} + E_{{\text{cross - term}}} + E_{{{\text{nonbond}}}}$$
(1)

The energy of the valence interactions \(E_{{{\text{valence}}}}\) is generally accounted for by the diagonal terms [29]:

$$\begin{aligned} E_{{{\text{valence}}}} &= E_{{{\text{bond}}}} + E_{{{\text{angle}}}} + E_{{{\text{torsion}}}} + E_{{{\text{oop}}}} + E_{{{\text{UB}}}} \\ &= \sum\limits_{\theta } {\left[ {K_{2} \left( {b - b_{0} } \right)^{2} + K_{3} \left( {b - b_{0} } \right)^{3} + K_{4} \left( {b - b_{0} } \right)^{4} } \right]} \\ &\quad+ \sum\limits_{\theta } {\left[ {H_{2} (\theta - \theta_{0} )^{2} + H_{3} (\theta - \theta_{0} )^{3} + H_{4} (\theta - \theta_{0} )^{4} } \right]} \\ &\quad+ \sum\limits_{\phi } {\left[ {V_{1} \left[ {1 - \cos (\phi )} \right] + V_{2} \left[ {1 - \cos (2\phi )} \right] + V_{3} \left[ {1 - \cos (3\phi )} \right]} \right]} \\ &\quad+ \sum\limits_{x} {K_{x} x^{2} + E_{{{\text{UB}}}} } \\ \end{aligned}$$
(2)

where \(E_{{{\text{bond}}}}\), \(E_{{{\text{angle}}}}\), and \(E_{{{\text{torsion}}}}\) represent the bond stretching, valence angle bending, and dihedral angle torsion, respectively. \(E_{{{\text{oop}}}}\) is the inversion out-of-plane interactions (oop) terms, which are part of the force fields for covalent systems. \(E_{{{\text{UB}}}}\) gives the Urey–Bradley (UB) term, which may be used to account for the interactions between the atom pairs. For a higher accuracy, the force field is achieved by including cross-terms to account for such factors as bond or angle distortions caused by nearby atoms [30]:

$$\begin{aligned} E_{{\text{cross - term}}} &= E_{bond - bond} + E_{angle - angle} + E_{bond - angle} + E_{end - bond - torsion} \\ &\quad+ E_{middle - bond - torsion} + E_{angle - torsion} + E_{angle - angle - torsion} \\ &= \sum\limits_{b} {\sum\limits_{{b^{\prime}}} {F_{{bb^{\prime}}} (b - b_{0} )} } (b^{\prime} - b^{\prime}_{0} ) + \sum\limits_{\theta } {\sum\limits_{{\theta^{\prime}}} {F_{{\theta \theta^{\prime}}} (\theta - \theta_{0} )} } (\theta^{\prime} - \theta^{\prime}_{0} ) \\ &\quad+ \sum\limits_{b} {\sum\limits_{\theta } {F_{b\theta } (b - b_{0} )(\theta - \theta_{0} )} } \\ &\quad+ \sum\limits_{b} {\sum\limits_{\phi } {(b - b_{0} )} } (V_{1} \cos \phi + V_{2} \cos 2\phi + V_{3} \cos 3\phi ) \\ &\quad+ \sum\limits_{{b^{\prime}}} {\sum\limits_{\phi } {(b^{\prime} - b^{\prime}_{0} )} } (V_{1} \cos \phi + V_{2} \cos 2\phi + V_{3} \cos 3\phi ) \\ &\quad+ \sum\limits_{\theta } {\sum\limits_{\phi } {(\theta - \theta_{0} )} } (V_{1} \cos \phi + V_{2} \cos 2\phi + V_{3} \cos 3\phi ) \\ &\quad+ \sum\limits_{\phi } {\sum\limits_{\theta } {\sum\limits_{{\theta^{\prime}}} {K_{{\phi \theta \theta^{\prime}}} } } } {\text{cos}}\phi (\theta - \theta_{0} )(\theta^{\prime} - \theta^{\prime}_{0} ) \\ \end{aligned}$$
(3)

The different energy terms \(E_{{{\text{bond}} - {\text{bond}}}}\), \(E_{{{\text{angle}} - {\text{angle}}}}\), \(E_{{{\text{bond - }}angle}}\), \(E_{end - bond - torsion}\),\(E_{{{\text{middle}} - bond - torsion}}\), \(E_{angle - torsion}\), and \(E_{{{\text{angle}} - angle - torsion}}\), respectively, give the stretch–stretch interaction between two adjacent bonds, the bend–bend interaction between two valence angles, the stretch–bend interaction between a twobond angle and one of the bonds, the stretch–torsion interaction between a dihedral angle and one of the end bonds, the stretch–torsion interaction between a dihedral angle and the middle bond, the bend–torsion interaction between a dihedral angle and one of the valence angles, and the bend–bend–torsion interaction between a dihedral angle and its two valence angles [31].

In addition, the nonbond energy \(E_{{{\text{nonbond}}}}\), containing the L-J 9–6 potential function for the van der Waals interaction term \(E_{{{\text{vd}}W}}\), a Coulombic term for the electrostatic interaction,\(E_{{C{\text{oulomb}}}}\), and the hydrogen bond energy, \(E_{{H - {\text{bond}}}}\), accounts for the interactions between the nonbond atoms:

$$\begin{aligned} E_{non - bond} &= E_{vdW} + E_{Coulomb} + E_{H - bond} \\ &= \sum\limits_{i > j} {\varepsilon_{ij} } \left[ {2\left(\frac{{r_{ij}^{0} }}{{r_{ij} }}\right)^{9} - 3\left(\frac{{r_{ij}^{0} }}{{r_{ij} }}\right)^{6} } \right] + \sum\limits_{i > j} {\frac{{q_{i} q_{j} }}{{r_{ij} }} + E_{H - bond} } \\ \end{aligned}$$
(4)

where

$$r_{ij}^{0} = \left( {\frac{{\left( {r_{i}^{0} } \right)^{6} + \left( {r_{j}^{0} } \right)^{6} }}{2}} \right)^{\frac{1}{6}}$$
(5)

In the simulation, considering the nanoscale effect, the x, y, and z directions were applied by nonperiodic boundary conditions, and the COMPASS interatomic force field was selected. In practical systems, molecular chains exist in stable conformations; That is to say, it is in a lower energy conformation. For the structural optimization before MD simulation, the initial model was first simulated using molecular mechanics (MM) and "Smart Minimizer" methods, with convergence criteria and maximum interaction set at 1000 kcal/mol/Å and 5000, respectively.

All the simulations are done in the constant temperature and constant volume canonical ensemble (NVT). The equations of motions were integrated using Verlet algorithm with integration time step of 1 fs. Temperature set to 100 K, and controlled by a Nosé–Hoover thermostat [29]. The simulation system was equilibrated for 5000 ps to stabilize the interaction. After this stage, the total intermolecular interaction energy was recorded for 5000 ps with an interval of 2 ps. Finally, averages were computed to get rid of the fluctuation during the simulation.

3 Results and discussion

3.1 Condensation of eighteen fullerenes via graphdiyne-like chain

Carbon has three hybrid states of sp, sp2 and sp3, and various carbon allotropes can be formed through different hybrid states [32]. For example, sp3 hybridization can form diamond, and sp2 hybridization can form carbon nanotubes, rich carbon fullerene and graphene, etc. [33] Because the carbon–carbon triple bond formed by sp hybrid state has the advantages of linear structure, no cis–trans isomers and high conjugation, It is believed that this type of carbon material has excellent electrical, optical and optoelectronic properties and becomes the key material for the next generation of new electronic and optoelectronic devices. In this part, the graphdiyne-like chain is a straight line, set to 276.776 Å. Molecular dynamic snapshots of fullerenes/graphdiyne-like chain system over time are shown in Fig. 2a. Initially, eighteen fullerenes lined up on top of the graphdiyne-like chain. With the simulation time goes on, the graphdiyne-like chain starts to fluctuate, just like the graphene ribbons [25] and polymer chains [34, 35] discussed earlier. The eighteen fullerenes are divided into three parts, two of which are gathered at the ends of the graphdiyne-like chain, respectively, and the other part is concentrated in the middle of the graphdiyne-like chain. It is worth noting that the numbers of the three-part fullerenes are not the same, with the most in the middle part and less in the two ends. This can be clearly seen in the first 40 ps. Over time, the graphdiyne-like chains begin to twist. The end containing more fullerenes twists faster, and quickly polymerizes with the fullerene in the middle, and then the graphyne-like chains are coiled together. In addition, the other end of fullerenes starts to aggregate at this time. During this process, fullerene polymerization and graphdiyne-like chain coiling proceed simultaneously until 202 ps, completing the process. After that, this state was maintained until 1070 ps, and finally, the structure was fine-tuned to 1225 ps, and the structure of the composite material no longer changed. Throughout the whole process, it can be seen that there are three main processes of sliding, twisting, and reunion. Time evolution of potential energy (Ep) and Van der Waals energy (EvdW) for eighteen fullerenes/graphdiyne-like chain system is shown in Fig. 2b. The two curves have the same trend of change. It means that the van der Waals potential well and the π–π stacking interaction between fullerenes and graphdiynes-like chain play a major role in the whole process. The curve can be divided into four segments with nodes at 202 ps, 1070 ps, and 1225 ps, respectively. After 1225 ps, both curves appear in the form of horizontal straight lines, indicating that the reaction has reached an equilibrium state. This is consistent with the results discussed in Fig. 2a. The interaction energy (Einteraction) between fullerenes and graphdiyne-like chain with simulation time is displayed in Fig. 2c. The interaction energy increased rapidly to − 395.4 kcal/mol within 202 ps and remained unchanged until 1020 ps. After 1020 ps, the interaction energy continued to increase, and the curve did not change until after 1225 ps, at which time the interaction energy was − 440.6 kcal/mol.

Fig. 2
figure 2

Molecular dynamic snapshots of eighteen fullerenes/graphdiyne wire system over time. (a) Time evolution of potential energy (Ep) and Van der Waals energy (EvdW) for eighteen fullerenes/graphdiyne wire system. (b) Interaction energy (Einteraction) between fullerenes and graphdiyne wire with simulation time (c)

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3.2 Condensation of sixteen fullerenes via graphdiyne-like chain

Molecular dynamic snapshots of sixteen fullerenes/graphdiyne-like chain system over time are shown in Fig. 3a. The graphdiyne-like chain is also set to 276.776 Å. In the first 10 ps, some of the fullerenes begin to move toward the ends as the graphyne chain fluctuates. When the time reaches 30 ps, the fullerenes mainly aggregate in three different positions, the ends and the middle. At this time, the middle position of the graphyne-like chain begins to twist under the action of fullerenes. When the time reaches 180 ps, the graphdiyne-like chains at both ends cross to form a "tadpole"-like shape. In addition, the fullerenes at both ends are still clinging to the graphyne-like chain. As the simulation time continued, the graphene-like chains at the two ends merged together, eventually (346 ps) forming a lateral "8" shape, while the fullerenes filled the gaps. Time evolution of potential energy (Ep) and Van der Waals energy (EvdW) for sixteen fullerenes/graphdiyne-like chain system is shown in Fig. 3b. In Fig. 3b, it can be seen that the two curves have only one inflection point, which is at 346 ps, indicating that after translation and torsion, the final structure is formed in one step without any adjustment.

Fig. 3
figure 3

Molecular dynamic snapshots of sixteen fullerenes/graphdiyne wire system over time. (a) Time evolution of potential energy (Ep) and Van der Waals energy (EvdW) for sixteen fullerenes/graphdiyne wire system (b)

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3.3 Different number of fullerene

The number of fullerene influences the final configuration of the composite. In this part, all graphdiyne-like chains are also set to 276.776 Å. The number of fullerene changes from twenty, eighteen, sixteen, fourteen, twelve, ten to six. The initial and final configurations of different fullerenes/graphdiyne-like chain systems are shown in Fig. 4a. Regardless of the number of fullerenes, in the final structure, they are all agglomerated, except when the number is sixteen. When the number of fullerenes is more than twelve, the graphdiyne-like chains can coil together to form a core–shell structure. However, when the number of fullerenes is relatively small, although a cluster structure is formed, the graphdiyne-like chains cannot be completely wound on its surface, and different structures are finally formed. Time evolution of the interaction energy (Einteraction) for these different fullerenes/graphdiyne-like chain systems is displayed in Fig. 4b. The interaction energies of all systems show an increasing trend. The more fullerenes there are, the greater the interaction energy, and the faster the increase rate, which can be obtained from the analysis of the slope of the curve. The interaction energy of these different fullerenes/graphdiyne-like chain systems is − 509.1 kcal/mol, − 440.6 kcal/mol, − 378.1 kcal/mol, − 352.1 kcal/mol, − 288.5 kcal/mol, − 278.1 kcal/mol, − 43.6 kcal/mol, respectively.

Fig. 4
figure 4

Initial and final configurations of different fullerenes/graphdiyne wire systems (a) Time evolution of the interaction energy (Einteraction) for these different fullerenes/graphdiyne wire systems. (The number of fullerene changes from twenty (I), eighteen (II), sixteen (III), fourteen (IV), twelve (V), ten (VI) to six (VII).)

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3.4 Different position

In this part, we put the same number of fullerenes at both ends of graphyne-like chains. The initial and final configurations of different fullerenes/graphdiyne-like chains systems are shown in Fig. 5a. When the total number of fullerenes at both ends exceeds eighteen, all fullerenes agglomerate together, and graphdiyne-like chains coat the outer surface to form a shell–core structure. When the total number of fullerenes is less than sixteen, the fullerenes at both ends are reunited, and the graphyne-like chain only wraps around once, forming a structure similar to a dumbbell with two large ends and a thin middle. Time evolution of the interaction energy (Einteraction) for these different fullerenes/graphdiyne-like chain systems is shown in Fig. 5b. With the increase of the number of fullerenes, the interaction energy gradually increases, and the rate of increase becomes faster and faster. From the slope of the curve, it can be seen that the speed of increase is slow or fast, and the greater the slope, the faster the speed. The interaction energy (Einteraction) for these different fullerenes/graphdiyne-like chain systems is − 600.4 kcal/mol, − 337.8 kcal/mol, − 285.1 kcal/mol, − 284.5 kcal/mol, − 182.8 kcal/mol, − 118.9 kcal/mol, − 26.9 kcal/mol, respectively.

Fig. 5
figure 5

Initial and final configurations of different fullerenes/graphdiyne wire systems. (a) Time evolution of the interaction energy (Einteraction) for these different fullerenes/graphdiyne wire systems. (The total number of fullerene changes from twenty(I), eighteen(II), sixteen(III), fourteen(IV), twelve(V), ten(VI) to six(VII).)

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3.5 Different temperature

The simulation temperature is also investigated. Under the same condition, we set the temperature of 1 K, 100 K, 200 K, 300 K, respectively. When the simulation temperature is 1 K, the motion speed of fullerene and graphyne-like chain is too slow to fully reflect the interaction between them, because the temperature is too low. Its final configuration shows that all the fullerenes are still aligned on the graphyne-like chains. As the temperature increases, the molecules move faster. When the temperature exceeds 200 K, part of the fullerene escapes from the surface of the graphyne-like chain. For example, when the temperature is 200 K, Three fullerenes escape, and when the temperature is 300 K, four fullerenes escape. The interaction energy (Einteraction) for fullerenes/graphdiyne-like chain systems at different simulation temperature is shown in Fig. 6b. The higher the temperature, the greater the interaction energy.

Fig. 6
figure 6

Final configurations of fullerenes/graphdiyne wire systems at different simulation temperature. (a) Interaction energy (Einteraction) for fullerenes/graphdiyne wire systems at different simulation temperature. (b) [1 K(I), 100 K(II), 200 K(III), 300 K(IV)]

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4 Conclusions

In summary, we use a molecular dynamics simulation to study the interaction between some fullerenes and graphdiynes-like chains. The result indicates that the final configuration varies with the number of fullerene. All linearly aligned fullerenes clump together to form nanoaggregates. The more fullerenes there are, the larger the nanoclusters. When the number of fullerenes increases to eighteen, all fullerenes aggregate to form a perfect core–shell structure. The entire process goes through three steps: sliding, twisting, and reunion. Both the van der Waals potential well and the π–π stacking interaction between fullerenes and graphdiynes-like chains play a major role in the self-assemble process. When fullerenes are placed at both ends of the graphdiynes-like chains, the composite material forms different configurations due to different quantities. As the temperature increases, the speed of molecular motion increases, which can also lead to differences in the final structure. The research results provide an important theoretical basis for the fabrication of high-quality carbon nanomaterials and other novel nanostructures, which have enormous potential applications in optics, hydrogen storage, and supercapacitor or battery energy storage.