Molecular Dynamics Simulation Insight Into Two-Component Solubility

Article pubs.acs.org/JPCC

Molecular Dynamics Simulation Insight Into Two-Component Solubility Parameters of Graphene and Thermodynamic Compatibility of Graphene and Styrene Butadiene Rubber Yanlong Luo,† Runguo Wang,‡ Wei Wang,*,§ Liqun Zhang,† and Sizhu Wu*,†,‡ †

State Key Laboratory of Organic−Inorganic Composites, ‡Beijing Engineering Research Center of Advanced Elastomers, and §State Key Laboratory of Chemical Resource Engineering and School of Science, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China ABSTRACT: The effect of the number of layers, various defects and functional groups on solubility parameter of graphene was studied through molecular dynamics (MD) simulation. We predigested three-component Hansen solubility parameters (δD, δP, δH) to two-component solubility parameters (δvdW, δele), and the two-component solubility parameters of graphene functionalized by different groups, such as hydroxyl, carboxyl, amino, methyl and epoxy with different grafting ratios were obtained. Further, the graphene/styrene butadiene rubber (SBR) composites were constructed to investigate the effect of functional groups and grafting ratios on components compatibility. It was found that the defects and functional groups had strong impact on solubility parameter of graphene, whereas the number of layers had a negligible effect. Two-component solubility parameters were proven to be able to predict compatibility of graphene and SBR. Additionally, the common effect of multifunctional groups on solubility parameter was also investigated. The combination of multifunctional groups with a proper content can obtain lower solubility parameter than a single group. The present study is expected to provide significant insight into the relationship between solubility parameter of graphene and compatibility of graphene/SBR composites.

1. INTRODUCTION Since the first fabrication of graphene by using a micromechanical exfoliation method in 2004, the study on the potential application of graphene has made great progress in many areas, such as polymer composites, sensors, energy materials, and biomedical applications due to its intriguing and excellent mechanical, electrical, thermal, and gas barrier properties.1−3 At present the oxidation−reduction using natural graphite as raw material is the primary pathway to achieve the mass production of graphene.4 In the process of oxidation− reduction, the oxygen-containing functional groups (e.g., hydroxyl, epoxy, and carboxylic acid groups) are usually accompanied, which provide many possibilities for the chemical functionalization and functional applications of graphene or graphene oxide.5 Additionally, the defects are unavoidably present in the process of the fabrication or functionalization of graphene, and it has been found that the defect has a considerable effect on the chemical and physical properties.6,7 As expected, graphene is an ideal nanofiller to enhance the mechanical and functional properties of rubber composites at very low loading in rubber industry.8 Styrene butadiene rubber (SBR), as the largest consumption of synthetic rubber, is widely used in the production of various rubber goods due to its excellent dynamic mechanics properties, abrasive resistance, and aging resistance.9 Many studies have shown that the introduction of graphene or graphene oxide as filler into SBR © 2017 American Chemical Society

matrix can significantly improve mechanical, electrical conductivity, and gas barrier properties of SBR.10,11 On the basis of previous studies, graphene-rubber interactions and graphene dispersion are two major factors influencing the resulting properties of composites.12 The above two factors have been attempted to improve through the design of chemical structure of SBR as well as the tailor of graphene surface chemistry.12,13 From the view of thermodynamics, the compatibility of filler and rubber dominates filler dispersion and filler−rubber interactions.14 As a consequence, it is significant for us to study the compatibility of graphene and SBR. Solubility parameters including Hildebrand and Hansen solubility parameters have been widely used for predicting compatibility of materials.15−18 Basic solubility theory states that the solubility of molecular solutes is connected with the cohesive energy density, EC,T/V, where EC,T is the cohesive energy and V is the molar volume of the solvent.19 The Hildebrand solubility parameter, δT, is defined as the square root of EC,T/V. It can be shown that the cohesive energy is the sum of dispersive (D), polar (P), and hydrogen bonding (H) components20,21 Received: February 17, 2017 Revised: April 1, 2017 Published: April 17, 2017 10163

DOI: 10.1021/acs.jpcc.7b01583 J. Phys. Chem. C 2017, 121, 10163−10173

Article

The Journal of Physical Chemistry C EC,T V

=

EC,D V

+

EC,P V

+

EC,H V

the solubility parameters of defective and functionalized graphene especially for multicomponent solubility parameters. In this study, we elucidated the effect of defects and functional groups including hydroxyl (−OH), carboxyl (−COOH), amino (−NH2), methyl (−CH3), and epoxy (−CH(O)CH−) groups on solubility parameter of graphene by MD simulation. To explore the reason for the difference between simulated and experimental solubility parameters of pristine graphene, we studied the effect of the number of layers on solubility parameter further. Whether or not twocomponent solubility parameters of functionalized graphene can predict effectively the compatibility of graphene and SBR was investigated. The optimum functional group and grafting ratio for graphene/SBR composites were explored. Additionally, the common effect of multifunctional groups on solubility parameter was also investigated.

(1)

The Hansen solubility parameter, δi (i = D, P, H), is the square of each of these components. Then the relation between Hildebrand and Hansen solubility parameters can be expressed as follows δ T 2 = δ D2 + δ P 2 + δ H 2

(2)

Previous studies on dissolving behavior of solutes indicated that as long as the Hildebrand solubility parameters of solvent and nonpolar solute are close to each other, the solute is usually soluble in solute. However, for polar solutes the good solubility can be obtained only when both Hildebrand and Hansen solubility parameters of solvent and solute are similar.15 Besides, the conclusions above have been proved to be appropriate for carbon material filled polymer systems such as carbon fiber/epoxy and carbon nanotube (CNT)/rubber composites.22,23 In most of the experiments, the Hildebrand and Hansen solubility parameters of some carbon materials (e.g., carbon fiber,22 CNT,21,23,24 and graphene20) were determined by the dissolution method using dozens of solvents with different solubility parameters, and this method is timeconsuming and costly. In addition, most of the early experimental studies were only concerned with the solubility parameters of nonmodified carbon materials. For example, graphene and the dissolution experiments using 40 kinds of solvents found that the Hildebrand solubility parameter of graphene is δT ≈ 23.0 MPa1/2, and the Hansen solubility parameters are δD ≈ 18.0 MPa1/2, δP ≈ 9.3 MPa1/2, and δH ≈ 7.7 MPa1/2.20 To the best of our knowledge, the effect of defects and functional groups on solubility parameter of graphene especially for multicomponent solubility parameters has not been reported in the literature. One possible reason is that the quantification of the defect and functional group is difficult through experimental methods because of heterogeneous structure of defective and functionalized graphene.4 With the development of computer technology, molecular simulation approaches based on classical physics or quantum physics theories have been widely used to study polymer composites.25−27 It has been reported that molecular dynamics (MD) simulation has been applied to study the solubility parameters and compatibility of materials, and the simulated results were in good agreement with the experiment results.28,29 In addition, several simplified computing methods for solubility parameters were brought forward. For example, Gupta et al.30 have used two-component solubility parameters consisting of electrostatic and van der Waals components instead of threecomponent Hansen solubility parameters to predict effectively the miscibility of pharmaceutical compounds. Most of these simulated studies centered on the solubility parameters of small molecules or polymers and their compatibility, and little attention was paid to the solubility parameters of carbon materials at the molecular level. Recent advances in the simulation method and force field provide the opportunities to calculate the detailed energy components of carbon materials as well as their solubility parameters.29,31 Compared with traditional experiment methods with which the introduction of specific defects and functional groups into graphene is difficult on account of the limitation of conditions, MD simulation is a more effective method, especially for the quantification of defects and functional groups.26,32 Therefore, MD simulation is potential as an alternative method to study

2. METHODOLOGY 2.1. Transformation of Hansen Solubility Parameters. For the MD simulations, a commercially available software Material Studio (Accelrys Inc., San Diego, CA) with condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field was utilized. In COMPASS force field, the total energy ET of the system is represented by the sum of valence and nonbond energies33 E T = E b + E0 + Eφ + Eχ + Ecross + EvdW + Eele (3) The first five terms, which correspond to the energies associated with the bond Eb, bond angle bending E0, torsion angle rotation Eφ, out-of-plane Eχ, and cross-term interaction Ecross, represent the valence energy Evalence. The last two terms consisting of the van der Waals (dispersion) term Evdw and electrostatic (coulomb or polar) force Eele represent the nonbond energy Enonbond. Therefore, the Hansen components in eq 1 derive from Enonbond. However, in COMPASS force field, Enonbond is only divided into two terms: Evdw and Eele, and EC,H cannot be obtained separately. EC,H, a strong polar force, is included in Eele in COMPASS force field as described by eqs 4 and 5 Enon‐bond = E vdW + Eele

(4)

Eele = EC,H + EC,P

(5)

Then the solubility parameters can be given by δ T 2 = δvdW 2 + δele 2

(6)

δele 2 = δ H 2 + δ P 2

(7)

Therefore, three-component Hansen solubility parameters (δD, δP, δH) in experiment are transformed into two-component solubility parameters (δvdW, δele) in MD simulation. In this study, the graphene/SBR composites are constructed to elucidate whether two-component solubility parameters can predict thermodynamic compatibility of SBR and graphene or not. 2.2. Model and Simulation Details. To obtain a highly computational efficiency and ensure that the grafting ratio of functional groups can be adjusted in a certain range, the size of graphene should be appropriate. The simulation single graphene sheet, which has a width of 32.666 Å and length of 42.280 Å, was used for the simulations of solubility parameters. The total number of carbon atoms in a graphene sheet is 592. The unsaturated edge configurations were terminated by 10164


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The Journal of Physical Chemistry C

of 12 Å and the electrostatic interactions were approximated by the Ewald method39 with an accuracy of 0.001 kcal/mol. To ensure the reliability of simulated results, we first calculated the Hildebrand solubility parameters of SBR and graphene, then compared simulated results with the corresponding experimental results taken from the literature,20,23 as present in Table 1. The simulated solubility parameter for SBR

adding hydrogen atoms. Generally speaking, the size of graphene in simulation is far less than that obtained by experimental method, and the boundary effect is not ignorable in simulation. Therefore, in order to maintain an electrically neutral system, the hydrotreating at the edge of graphene is essential. The defective and −OH, −COOH, −NH2, −CH3, and −CH(O)CH− groups functionalized graphene were constructed. The functionalized graphene were shown in Figure 1, and the defect types were discussed and present in detail in Section 3.2.

Table 1. Hildebrand Solubility Parameters of SBR and Graphene solubility parameters δT (MPa1/2) SBR graphene

simulated results (δMD)

experimental data (δExp)

16.91 29.16

17.2 ∼23.0

agrees well with the experimental value. However, the simulated result for graphene shows some difference from the experimental value. It is worth noting that we constructed the pristine monolayer graphene sheet without any defect and functional group in simulations. Nevertheless, in experiments20 transmission electron microscopy (TEM) images showed that both monolayer and multilayer graphene flakes exist in various solvents, and the maximum number of graphene layers was 16. Even if in N-methyl-2-pyrrolidone (NMP), the best solvent for dissolving graphene, the highest number fraction of monolayer graphene was only 29%.20 In addition, the defects and functional groups in graphene are ineluctable in practical production and application. As a consequence, we speculate the influence factors of solubility parameters and the reason for some difference between simulated and experimental values from the following three aspects: (1) number of graphene layer, (2) defect and (3) functional group.

Figure 1. Amorphous cell of composites consists of SBR chains as matrix and graphene or functionalized graphene as filler (gray atom is C, white atom is H, red atom is O, and blue atom is N).

SBR chain containing 40 repeat units was constructed. The weight content of structural unit in MD simulation is consistent with that of a commercial SBR (Nipol 1502. Styrene fraction is 23.5 wt % and 1,2-butadiene structure fraction is 11.2 wt %).23 The amorphous cells of graphene/SBR or functionalized graphene/SBR composites (see Figure 1), each with 15 SBR chains, were constructed to study the components’ compatibility by calculating the fractional free volume (FFV) of composites. Our previous work has studied the effect of particle size of graphene and SBR chain length on simulated results and demonstrated that the above models were valid.13 In a simulation, the geometry optimization procedure with energy convergence tolerance of 2 × 10−5 kcal/mol was first performed to obtain low potential energy characteristics for each cell by using Smart Minimized method. After this stage, the amorphous cell was annealed at one bar pressure from an initial temperature of 500 K to midcycle temperature of 800 K for five annealing cycles with five heating ramps per circle. Afterward, the cell was subjected to 500 ps of NVT (constant number of particles, volume, and temperature) ensemble and 500 ps of NVE (constant number of particles, volume, and energy) to maintain constant density and obtain the most stable configuration. The resulting cell was used to calculate the solubility parameters of graphene and SBR by setting the initial densities of 2.20 g/cm3 for graphene and 0.93 g/cm3 for SBR according to the literatures.34,35 The FFV of graphene/SBR composites were calculated after 1 ns of NPT (constant number of particles, pressure, and temperature) ensemble at one bar pressure. In all the simulations, the periodic boundary condition was applied. The pressure and temperature were controlled by Andersen barostat36 and Berendsen thermostat,37 respectively. The Verlet velocity time integration method38 with a time step of 1 fs was used to integrate the Newtonian equation of motion. The van der Waals interactions were calculated by the Lennard-Jones function with a cutoff distance

3. RESULTS AND DISCUSSION 3.1. Effect of the Number of Graphene Layers on Solubility Parameters. We calculated the solubility parameters of monolayer and multilayer graphene. The number of graphene layers were constructed from 1 to 10, and the interlayer distance is set to 3.4 Å,40 a typical graphite interlayer distance (see Figure 2). As seen in Figure 2, there is a negligible decrease in solubility parameters with increasing the number of layers (the solubility parameter decreases only 1.8% as the

Figure 2. Effect of the number of graphene layers on solubility parameter. 10165


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influence of temperature, electric field, and so forth, the graphene hexagonal lattice can be restructure to form nonhexagonal rings.7 For example, the TSW defect is formed when four hexagons are converted into two heptagons and two pentagons through rotating one of the C−C bonds by 90° without a missing atom (see Figure 3d). The lattice reconstruction can also occur in monovacancy and divacancy defects. The reconstruction of monovacancy defect leads to the formation of a pentagon and a nonagon (monovacancy 5-9), as shown in Figure 3(b1). The divacancy defect can occur three types of reconstruction by rotating C−C bonds: (1) three pentagons and three heptagons (divacancy 555-777), (2) four pentagons, a hexagon and four heptagons (divacancy 5555-67777), and (3) two pentagons and an octagon (divacancy 5-85), as shown in Figures 3c1−c3. The aforementioned atomic structures of reconstructed defects have experimentally been observed.7 The nonbond energies of pristine graphene and graphene with different types of defects were listed on Table 3. The

number of layers increase from 1 to 10), which indicates that the number of layer, at least fewer layers, is not main factor influencing solubility parameter. From the point of calculation, we take two-layered and fourlayered graphene for examples to illustrate the reason for solubility parameter change depending on the number of layers. Table 2 lists the cohesive energy and cell volume of two-layered Table 2. Cohesive Energy and Cell Volume of Two-Layered and Four-Layered Graphene number of layers

EC,T (kcal/mol)

cell volume (Å3)

2 4

1368.265 2811.081

22.4043 28.5143

and four-layered graphene. The simulation approach to determine the solubility parameter is based on eq 8, by calculating the average cohesive energy in a system δ=

EC,T V

=

EC,T NA ·V0

(8)

Table 3. Nonbond Energies of Graphene with Different Types of Defects

where EC,T is the cohesive energy, V is the molar volume of graphene, NA is Avogadro’s number, and V0 is the cell volume. Therefore, the ratio of solubility parameter of two-layered and four-layered graphene can be calculated by eq 9, and the result is slightly larger than 1. Hence, the solubility parameter of twolayered graphene is slightly larger than that of four-layered graphene. In other words, as the number of layers increases, the increase of cell volume exceeds the increase of cohesive energy, which leads to a slight decrease of solubility parameter. (δ)two‐layered (δ)four‐layered

=

EvdW (kcal/mol)

Eele (kcal/mol)

Enonbond (kcal/mol)

593.164 588.412 583.979 577.128

0 1.285 2.042 0

593.164 589.697 586.021 577.128

decrease of EvdW and the increase of Eele with increase of the number of missing carbon atom were found. The increase of Eele is attributed to the formation of dangling bond by missing carbon atom.41 However, the decrease effect is larger than the increase effect, which leads to the decrease of Enonbond. The graphene with TSW defect from lattice reconstruction also has a lower Enonbond than pristine graphene. As shown in Figure 4, the solubility parameters decrease with increasing the number of missing carbon atoms for both

(V0)four‐layered (EC,T)two‐layered (V0)two‐layered (EC,T)four‐layered

= 1.0017 >1

types of defects pristine graphene monovacancy divacancy TSW

(9)

3.2. Solubility Parameters of Defective Graphene. The vacancy and Thrower−Stone−Wales (TSW) defects, which have been experimentally observed by high-resolution TEM, are of special concern in all types of defects.7,32 For the vacancy defects, monovacancy (see Figure 3b), one carbon atom missing from the graphene lattice, and divacancy (see in Figure 3c), two adjacent carbon atoms missing from the graphene lattice, have been experimentally observed.32 Besides, under the

Figure 4. Effect of types and missing carbon atoms number on solubility parameter.

monovacancy and divacancy. Whatever the vacancy defect, as long as the same number of carbon atoms is missing, the solubility parameters are almost identical, which indicates that the solubility parameter does not depend on the type of vacancy defect, but only depends on the missing number of carbon atoms. Additionally, the effect of vacancy defects on solubility parameter is quite prominent. For example, the

Figure 3. Schematic defects: (a) pristine graphene, (b) monovacancy defect, (c) divacancy defect and (d) TSW defect (55-77). Atomic structures of reconstructed monovacancy and divacancy defects: (b1) monovacancy (5-9), (c1) divacancy (555-777), (c2) divacancy (55556-7777), and (c3) divacancy (5-8-5). 10166


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The Journal of Physical Chemistry C solubility parameter decreases from 29.16 to 24.31 MPa1/2, a 16.6% reduction, when the number of missing carbon atoms is 30, accounting for 5% of the total number of carbon atoms. The effect of defect reconstructions on solubility parameters is shown in Figure 5. The results indicate that the pristine

Table 4. Chargers and Forced Field Types of the Atoms groups −CH3

−OH

−COOH

−NH2 −CH(O)CH−

atom

q(e)

forced field type

H1/H2/H3 C4 C5 H1 O2 C3 H1 O2 O3 C4 C5 H1/H2 N3 C4 O1 C2/C3

0.053 −0.159 0 0.41 −0.57 0.16 0.41 −0.455 −0.45 0.495 0 0.353 −0.893 0.187 −0.32 0.16

h1 c4 c44 h1o o2h c44o h1o o2c o1 c3 c44 h1n n3h2 c4 o2e c44o

O (in −CH(O)CH) > C (in −CH3). The more charges of the atoms are expected to stronger electrostatic interactions. In the calculation of solubility parameter, the grafting ratio was defined as follows n grafting ratio = × 100 (10) N where n is the total number of functional groups, and N, the total number of carbon atoms in pristine graphene lattice, is 592 as mentioned in Section 2.2. In the simulation, the maximum grafting ratio is set as 26.0%, and then the maximum oxygen content is 34.4%. On the basis of the experiments reported in the literature,42 the oxygen content of graphene oxide prepared by the modified Hummers method is from 24% to 44%. Therefore, the oxygen content in experiment can reach that in simulation. The solubility parameters of graphene functionalized by different groups as a function of grafting ratio are present in Figure 7. Interestingly, no matter what type of group, as the grafting ratio increases, the δT and δvdW first decrease, reach a minimum, and then increase, and the δele increases linearly. The cause of solubility parameter changes is speculated in three main steps as shown in Figure 8. At first the interactions between graphene sheets are mainly π−π stacking interactions. As the functional groups were introduced into graphene lattice, the sp2 hybridization of C−C bond turns into sp3 hybridization,43 and then the whole system exists in three kinds of interactions: (1) π−π stacking interactions between graphene sheets, (2) van der Waals interactions between groups as well as between groups and graphene sheets, and (3) electrostatic interactions between groups. As the grafting ratio increases in step 1, the π−π stacking interactions decrease, and the van der Waals and electrostatic interactions increase. However, the increase effect is not enough to compensate the decrease effect resulting in the decrease of nonbond energy as well as solubility parameter. When the grafting ratio increases to a certain value in step 2, the increase effect exactly compensates the decrease effect resulting in the minimum nonbond energy. As the grafting ratio continues to increase in step 3, the increase effect is greater than the decrease effect, thus leading to the increase of nonbond energy. The grafting ratios corresponding to the minimum δT and the decrease degree in comparison to of δT of pristine graphene are listed in Table 5. The minimum δT is very significant and it decides that

Figure 5. Effect of defect reconstruction on solubility parameter.

graphene, monovacancy, and divacancy reconstructions rarely affect the solubility parameter. In other words, the solubility parameter is irrelevant to the type of reconstruction but depends on the number of missing carbon atoms. 3.3. Solubility Parameters of Functionalized Graphene. To determine the effect of different types and grafting ratios of functional groups on solubility parameters of graphene, we constructed five kinds of graphene functionalized by −OH, −COOH, −NH2, −CH3 and −CH(O)CH− groups. The functional groups were randomly bonded with carbon atoms in graphene lattice, and the ball-and-stick models of functional groups are shown in Figure 6. It is well-known that if

Figure 6. Ball-and-stick models of functional groups (gray, white, red, and blue spheres stand for C, H, O, and N atoms, respectively).

the polar group exists in molecules, the intermolecular interaction depends strongly on charges of the atoms or group electronegativity. Therefore, the atoms in functional groups and the carbon atoms in graphene bonded with functional groups were first numbered in Figure 6, and then the charges of the atoms were calculated by MD simulations and supplied in Table 4. The magnitude of charges of the atoms are as follows: N (in −NH2) > O (in −OH) > O (in −COOH) > 10167


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Figure 7. Effect of (a) −OH, (b) −COOH, (c) −NH2, (d) −CH3 and (e) −CH(O)CH− groups on solubility parameters. (f) Comparison of electrostatic solubility parameters δele.

Figure 8. Schematic diagrams of the cause of solubility parameter changes.

The effect of the functional groups on δele are as follows: −CH(O)CH− > −OH > −COOH > −NH3 > −CH3, as shown in Figure 7f. Note that the δele is related not only to the group electronegativity but also to the group size. That is, the δele is related to the charge per unit volume, or charge density. The electronegativity of oxygen in epoxy group is low (see Table 4), but the introduction of an epoxy group requires to

how much the solubility parameter of graphene is close to the solubility parameter of SBR. The detailed analysis is present in section 3.4. Besides, we found that the effect of the functional group on solubility parameters of graphene is remarkable. For example, the δT of −CH3 functionalized graphene decreases from 29.16 to 14.80 MPa1/2, a 49.0% decrease at grafting ratio of 10.1%. 10168


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fraction, and δT,A and δT,B are the Hildebrand solubility parameters of the solute and solvent, respectively. According to eqs 12 and 13, the relation between χ and δ can be described by v χ ≈ 0 (δ T,A − δ T,B)2 (14) kT

Table 5. Grafting Ratio Corresponding to the Minimum δT and Decrease Degree Corresponding to Pristine Graphene grafting ratio (%)

groups −OH −COOH −NH2 −CH3 −CH(O)CH− SBR

δT (MPa1/2)

δvdW (MPa1/2)

δele (MPa1/2)

20.81 17.19 15.93 14.88 26.94 16.91

17.99 14.14 13.51 13.50 23.60 16.24

5.04 5.06 2.80 1.50 10.71 2.17

10.1 19.1 11.8 10.1 8.4

decrease degree (%) 28.6 41.0 45.4 49.0 7.6

Thus, solubility is completely determined by the magnitude of χ which is related to δT,A and δT,B. The closer δT,A and δT,B, the smaller χ and ΔGmix indicating the better solubility. In other words, mixtures of components with similar solubility parameter values are thermodynamically compatible. On the basis of eq 14, Hansen wrote the Flory−Huggins parameter by replacing the Hildebrand solubility parameters with Hansen solubility parameters as19

bond with two carbon atoms. Therefore, the charge density of epoxy group is high, and the δele is large. Another point that should be noted is that the δele of −CH(O)CH− group functionalized graphene is greater than the δvdW when the grafting ratio exceeds 19.1%, whereas to other functionalized graphene, the δele is far lower than the δvdW at any grafting ratio. The results above indicate that when the grafting ratio exceeds 19.1%, the electrostatic interaction is the major component of the nonbonded energy and provides a major contribution to the solubility parameter of −CH(O)CH− group functionalized graphene. For −OH, −COOH, −NH2, and −CH3 groups, the grafting ratios corresponding to the minimum δT and δvdW are the same. However, for −CH(O)CH− group, the grafting ratios corresponding to the minimum δT and δvdW are not the same, which is attributed to the faster increase of δele. Returning to Table 1, we found that the simulated solubility parameter shows some difference from the experimental value.20 The analyses above show that the δT decreases 1.8% as the number of layers increase from 1 to 10, the δT decreases 16.6% when the number of missing carbon atom is 5%, and the effect of functional groups on the δT is more remarkable as shown in Table 5. Therefore, we speculate that the difference contributes from defects and functional groups, and the effect of the number of layers, at least fewer layers, on solubility parameter is negligible. 3.4. Compatibility of Functionalized Graphene and SBR. In Section 3.3, we obtained two-component solubility parameters of functionalized graphene, then whether or not the two-component solubility parameters can be effectively applied to predict the compatibility of graphene and SBR is the focus of our attention. In basic solubility theory, the Gibbs free energy of mixing (ΔGmix) dominates the dissolution behavior of solute in solvent and is related to both enthalpic and entropic components ΔGmix = ΔHmix − T ΔSmix

+ (δ H,A − δ H,B)2 ]

R0 =

or the Hildebrand-Scratchard equation ΔHmix ≈ (δ T,A − δ T,B)2 ϕ(1 − ϕ)

(δ D,A − δ D,B)2 + (δ P,A − δ P,B)2 + (δ H,A − δ H,B)2 (16)

R0 is the distances from solute, as the origin of the spherical coordinate, to solvent Hansen solubility parameters. Therefore, the smaller R0 represents the closer Hansen solubility parameters and better compatibility. Similarly, the difference, R, of two-component solubility parameters between graphene and SBR is given by R=

(δvdW,graphene − δvdW,SBR )2 + (δele,graphene − δele,SBR )2 (17)

where δgraphene and δSBR represent the solubility parameters of graphene and SBR, respectively. We used the free volume theory to study the compatibility of graphene and SBR. The FFV of graphene/SBR composites with various grafting ratios were determined by a grid scanning method and can be given by FFV =

V − V0 V

(18)

where V is the total volume, V0 = 1.3Vw is the occupied volume, and Vw is the van der Waals volume. The schematic diagrams of FFV are shown in Figure 9. FFV is commonly used to characterize the amount of free space and the efficiency of chain packing in a polymer matrix. Many previous studies have demonstrated that FFV can be used to evaluate the

(11)

χϕ(1 − ϕ)kT v0

(15)

Then, a simple parameter, R0, was proposed by defining the expression in brackets square in eq 1515

where ΔHmix and ΔSmix are the enthalpy and entropy of mixing, respectively, and T is the absolute temperature. In general, a negative ΔGmix value for the solute−solvent mixture indicates that the solute is soluble. The ΔSmix term is usually positive and, hence, ΔHmix is the determining factor.15 ΔHmix is usually expressed in terms of either the Flory−Huggins equation44,45 ΔHmix =

V0 [(δ D,A − δ D,B)2 + (δ P,A − δ P,B)2 kT

χ≈

(12) 44,45

(13)

where χ is Flory−Huggins parameters, k is boltzmann constant, v0 is the solvent molecular volume, ϕ is the solute volume

Figure 9. Schematic diagrams of FFV. Blue and gray areas represent the free and the occupied volume, respectively. 10169


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Figure 10. Curves of R and FFV with grafting ratio (a) −OH; (b) −COOH; (c) −NH2; (d) −CH3; (e) −CH(O)CH−.

components compatibility for filled polymer system, and the lower the FFV, the better the compatibility.33,46,47 Therefore, if R is proportional to FFV, then it turns out that the twocomponent solubility parameters can be applied to predict the compatibility of graphene and SBR, but the opposite is not. The FFV and R values were compared, and the results are presented in Figure 10. We found that the FFV results were in good agreement with R values indicating that two-component solubility parameters can be effectively applied to predict the compatibility of graphene and SBR. Besides, for −OH, −COOH, and −CH(O)CH− groups’ functionalized graphene systems, the R or FFV first decreases, reaches a minimum, and then increases as the grafting ratio increases. However, for −NH2 and −CH3 groups’ functionalized graphene systems, the variation of R along the grafting ratio is of “W” shape, and there are two minimum R values. The reason for the above results is that the minimum δT of −OH, −COOH, and −CH(O)CH− groups’ functionalized graphene is greater than δT of SBR, but the minimum δT of −NH2 and −CH3 groups’ functionalized graphene is less than δT of SBR (see Table 5). Then the grafting ratio corresponding to the least value of R or FFV is the optimum grafting ratio at which the best compatibility of graphene and SBR can be obtained. We found that all

functional groups have an optimum grafting ratio, and the optimum grafting ratio is listed in Table 6. Table 6. Optimum Grafting Ratios of Various Functional Groups groups

optimum grafting ratio (%)

−OH −COOH −NH2 −CH3 −CH(O)CH−

10.1 19.1 10.1 19.1 2.5

In polymer solution theory, Flory−Huggins parameter, χ, reflects the change in polymer−solvent interactions when two components are mixed.48 Besides, the magnitude of χ is a semiquantitative criterion for good or poor solvent. Generally speaking, if χ < 1/2, polymer and solvent have good compatibility, and if χ > 1/2, polymer and solvent are incompatible. Similarly, the magnitude of χ can also be used as a criterion for good or poor interactions in graphene-SBR system. The χ was calculated by eq 15, and the grafting ratios corresponding to good and poor interactions between graphene and SBR were present in Table 7. For − OH and − 10170


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modified graphene and poly(styrene-b-ethylene-co-butylene-bstyrene) (SEBS) increased. Zhang et al.50 introduced octadecylamine into graphene oxide and found that the good dissolvability of modified graphene oxide was obtained in chloroform. Therefore, our simulated results can be expected to provide the theoretical supports for some experimental results. 3.5. Effect of Multifunctional Groups on Solubility Parameter of Graphene. To meet real conditions as far as possible, we further investigate the effect of multifunctional groups on solubility parameter of graphene. Compounded with the principle of functionalization of graphene as mentioned in Section 3.4, we constructed four kinds of functionalized graphene with less than grafting ratio of 10.1%. The grafting ratio of each group is listed in Table 8. The high content of

Table 7. Grafting Ratios Corresponding to Good and Poor Interactions groups

good interactions (χ < 1/2)

poor interactions (χ > 1/2)

−OH −COOH −NH2 −CH3 −CH(O)CH−

16.2%∼20.5% 10.1%∼11.8% 8.4%∼19.1%

0−26.0% 0−16.2%, 20.5%∼26.0% 0−10.1%, 11.8%∼26.0% 0−8.4%, 19.1%∼26.0% 0−26.0%

CH(O)CH− groups functionalized graphene systems, graphene and SBR have poor interactions at any grafting ratio. However, for − COOH, − NH2, and − CH3 groups functionalized graphene systems, graphene and SBR have good interactions at a certain grafting ratio. To prepare high-performance graphene/SBR composites, the functionalization of graphene should comply with the following principles from the view of thermodynamics: the solubility parameter of graphene has a value as low as possible at a smaller grafting ratio. The smaller grafting ratio is to ensure the structural integrity and keep excellent properties of graphene. The solubility parameter as low as possible at a smaller grafting ratio can ensure that the solubility parameter of graphene keeps as close to that of SBR as possible and the best compatibility available. On the basis of the principle above, a smaller R is better at the same grafting ratio. Figure 11 shows R as a

Table 8. Grafting Ratio of Each Group −CH3 (%)

−NH2 (%)

−CH(O) CH− (%)

−OH (%)

−COOH (%)

total grafting ratio (%)

2.5 3.4 3.4 3.4

0.8 0.8 1.7 3.4

0.5 0.8 1.7 1.7

0.5 0.8 0.8 0.8

0.8 0.8 0.8 0.8

5.1 6.6 8.4 10.1

methyl group is maintained, which is attributed to the fact that the introduction of methyl group can dramatically decrease the solubility parameter of graphene. The combination of multifunctional groups can obtain lower solubility parameter than a single functional group at the same grafting ratio, as shown in Figure 12. Therefore, by adjusting proper content of groups we

Figure 11. R as a function of grafting ratio as well as functional group.

function of grafting ratio as well as functional group. Then the priority of the introduction of functional group into graphene is as follows from the perspective of compatibility of graphene and SBR: when grafting ratio is less than 3.7%, −CH3 > −NH2 > −COOH > −CH(O)CH− > −OH; when grafting ratio is greater than 3.7%, −CH3 > −NH2 > −COOH > −OH > −CH(O)CH−. An abrupt increase of R occurs after the introduction of a certain amount of epoxy groups because the epoxy group has a strong effect on δele. Besides, the compatibility of −CH3 group functionalized graphene and SBR is the best, which can be attributed to the nonpolarity of −CH3 group and SBR. Several experimental studies in the past also indicated that the introduction of alkane into graphene can improve the dissolution of graphene in nonpolar or weakly polar solvents and strengthen the interactions of graphene and nonpolar elastomers. For example, Salavagione et al.49 found that the graphene modified by short-chain polyethylene can dissolve in o-dichlorobenzene (o-DCB), and the interactions of

Figure 12. Effect of multifunctional groups on solubility parameter of graphene.

can obtain the solubility parameter of graphene closer to that of SBR and better compatibility of graphene and SBR at lower grafting ratio. In other words, the introduction of multifunctional groups into graphene is superior to a single group.

4. CONCLUSION The effect of the number of layers, various defects and functional groups on solubility parameters of graphene as well as compatibility of graphene and SBR were investigated by MD simulation. We found that the defects and functional groups had strong impacts on solubility parameters of graphene, whereas the number of layers, at least fewer layers, had a negligible effect. The solubility parameter is irrelevant to the 10171


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types of defects but depends on the missing carbon atoms number. The difference between simulated and experimental solubility parameters is attributed to defects and functional groups. Two-component solubility parameters of functionalized graphene were computed and proven to be able to predict the compatibility of graphene and SBR. Additionally, there is an optimum grafting ratio of functional group at which the FFV is the smallest, and the compatibility of graphene and SBR is the best. The priority of the introduction of functional group into graphene will change with grafting ratio from the perspective of compatibility of graphene and SBR. The combination of multifunctional groups can obtain a lower solubility parameter than a single functional group at the same grafting ratio. Therefore, the introduction of multifunctional groups into graphene is superior to a single group from the perspective of compatibility of graphene and SBR

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (W.W.). Tel.: 8613699106185. *E-mail: [email protected] (S.Z.W.). Tel.: +86-1064444923. Fax: +86-10- 64433964. ORCID

Sizhu Wu: 0000-0001-7863-2954 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial supports of the Major Research Plan from the Ministry of Science and Technology of China under Grant 2014BAE14B01 and the National Natural Science Foundation of China under Grant 51473012 are gratefully acknowledged.

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Molecular Dynamics Simulation Insight Into Two-Component Solubility

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