Experimental study and molecular dynamics simulation of dynamic properties and interfacial bonding characteristics of graphene/solution-polymerized styrene-butadiene rubber composites

Abstract

Graphene/solution-polymerized styrene-butadiene rubber (SSBR) composites were prepared by using three types of SSBR matrix with different vinyl contents. The dynamic properties, interfacial bonding characteristics, and fractional free volume (FFV) of the composites were studied through a combined experimental and molecular dynamics (MD) simulation approach. We found that as the vinyl content increases in the SSBR matrix, the grapheme/SSBR interfacial interaction increases, the FFV decreases, and the graphene dispersion is improved. The interfacial interaction, which is derived from the introduction of graphene, can increase the activation energy and limit the mobility of the SSBR chains. Additionally, MD simulations of the pullout of the graphene from SSBR matrix were carried out to explore the interfacial bonding characteristics at the molecular level, which show that the interaction energy, pullout energy, and shear stress between graphene and SSBR increase with the increase of the vinyl content. The modeling results were in good agreement with the experimental results. This present study is expected to deepen the understanding of the basic physics for graphene reinforced rubber nanocomposites, especially the interfacial bonding characteristics at the molecular level.

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1. Introduction

Since its first fabrication, solution-polymerization butadiene-styrene rubber (SSBR) has attracted much attention due to its better rolling resistance and wet skid resistance than emulsion-polymerized butadiene-styrene rubber (ESBR).^1,2 SSBR is synthesized by anionic polymerization, which provides the possibility for designing the chemical structure of SSBR. Therefore, in recent years, some researchers have prepared different chemical structures of SSBR in order to obtain better properties. For instance, the end-functionalized SSBR with SnCl₄ ³ or ethoxy silyl⁴ and the in-chain modified SSBR with 3-mercaptopropionic acid⁵ are conducive to improving the filler dispersion.

Graphene, a single-atom-thick sheet of carbon atoms densely packed in a honeycomb crystal lattice, has been the subject of considerable interest and study because of its intriguing and outstanding physical properties.⁶ As expected, graphene holds promising applications in rubber composites by virtue of its potential to efficiently endow rubber with reinforcement and functional properties at very low loadings.^7,8 Xing et al.⁹ found nearly 11 folds of increase in the tensile strength of SBR is attained upon addition of 7 phr of graphene, which is comparable to the reinforcement effect of 30 phr of carbon black. Araby et al.¹⁰ revealed that the percolation threshold of electrical conductivity was observed at 16.5 vol% graphene, and the SBR thermal conductivity improved 240% at 41.6 vol% in graphene/SSBR composites. In filler/rubber composites, the filler–rubber interactions and filler dispersion are generally acknowledged to be two key factors influencing the mechanical properties and viscoelastic behavior of the rubber.¹¹ Some efforts have been devoted to the chemical functionalization of graphene to improve the graphene–rubber interactions and graphene dispersion. For example, Liu et al.¹² fabricated two series of alkylamine-modified (oleylamine and octadecylamine) graphene oxide/SBR composites and found that both modified GO improved dispersion and increased surface affinity for the SBR matrix. Tang et al.¹³ investigated the effect of graphene surface chemistry on the dispersion and interfacial adhesion of graphene/SBR composites and revealed the N-doping graphene has stronger interaction with SBR. It has been reported that the strong interfacial interaction between the filler and polymer can lead to the formation of a so-called “glass layer” close to the filler surface, and the stress transfer strongly depends on the glass layer thickness.¹⁴ The dynamic property and glass transition temperature of the polymer in the glass layer are significantly different from those of the polymer in bulk.

To our knowledge, it is difficult to devise all kinds of experiments to quantitatively study the interfacial characteristics of filler/polymer composites due to the complexity of the interface. Molecular dynamics (MD) simulation based on classical physics theory has emerged as a powerful theoretical tool to study the effect of polymer interface behaviors on the properties of materials (e.g., dynamics,¹⁵ thermal conductivity,¹⁶ and mechanical performance¹⁷). In graphene/polymer composites, many modeling studies in the past focused on the design of graphene surface chemistry for high-performance composites. These studies show that the attachment of chemical groups at reasonable concentrations to the graphene surface plays an important role in enhancing the interfacial strength.^17,18

In this study, the effect of the vinyl content in the SSBR matrix on the thermodynamics, dynamics, interfacial bonding characteristics, and fractional free volume (FFV) of graphene/SSBR composites was investigated. The surface energies of SSBR and the work of adhesion between SSBR and graphene were calculated. Strain sweep experiments were carried out to investigate the temperature-dependent, nonlinear strain dependence of storage modulus referred to as the Payne effect. Moreover, the binding energies, good indicators for the compatibility of the graphene with rubber, and the FFV from MD simulation were compared with experimental values. The dynamic properties of graphene/SSBR composites were measured by mean square displacement (MSD) and dynamic mechanical analysis. The pullout simulations of the graphene from SSBR matrix were carried out to calculate the variation of energies related to the graphene/SSBR interface during pullout.

2. Materials and sample preparation

The pilot products of three types of SSBR (namely, S1, S2, and S3) were supplied by Qingdao Yikesi New Material Co., Ltd. These products were synthesized by anionic polymerization, and the synthetic method has been presented in the literature.¹⁹ Graphene (JLG-2710) was purchased from Sichuan Jinlu Group Co., Ltd. The graphene/SSBR composites were prepared by mixing the raw materials on a two-roll mill and vulcanized at 150 °C for a period of optimum time determined by a vulcameter. The raw materials and component content of the composite are as follows: SSBR 100 g; zinc oxide 5 g; stearic acid 1 g; N-cyclohexyl-N′-phenyl-p-phenylenediamine 1.5 g; N-cyclohexyl-2-beozothiazole sulfonamide 1.5 g; 2,2′-dibenzothiazoledisulfide 0.5 g; sulfur 1.5 g; graphene 3 g.

3. Measurements and characterization

In order to guide the modeling and guarantee the consistency of the simulations and experiments, the chemical structures of the SSBRs and graphene were firstly measured by ¹H nuclear magnetic resonance (¹H NMR), gel permeation chromatography (GPC), and X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), Raman spectroscopy and the results are given in Fig. 1 and 2 and Table 1. The results of differential scanning calorimetry (DSC), drop shape analyses, dynamic mechanical analyzer (DMA), rubber process analyzer, and positron annihilation lifetime spectroscopy (PALS) will be given and discussed in Section 5.

Fig. 1 ¹H NMR spectra of S1, S2, and S3 in CDCl₃.

Fig. 2 (a) XPS spectrum, (b) Raman spectrum and (c) tapping-mode AFM image of graphene.

Table 1 Molecular weights and weight contents of SSBRs

Sample	Styrene content (wt%)	Vinyl content (wt%)	Mn (g mol^−1)	Mw (g mol^−1)	Mw/Mn
S1	25.3	47.2	1.92 × 10^5	2.48 × 10^5	1.29
S2	25.8	56.1	2.26 × 10^5	3.25 × 10^5	1.44
S3	25.9	63.3	2.26 × 10^5	3.10 × 10^5	1.37

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The weight contents of all raw rubbers were measured by ¹H NMR on a Bruker AV600 high-resolution NMR spectrometer (Bruker Corporation, Bremen, Germany) at a frequency of 600 MHz. The raw rubbers were dissolved in CDCl₃ in a 5 mm NMR tube. Chemical shifts were given relative to a tetramethylsilane (TMS) as an internal reference. Fig. 1 shows the ¹H NMR spectra of the SSBRs, and the corresponding signal peaks are marked. According to the reported equations,²⁰ the styrene and vinyl contents were calculated. Here, the vinyl content refers to the content of 1,2-butadiene structure in SSBR.

The molecular weights and their distributions of the raw rubbers were determined by GPC on an Alliance 2690 system (Waters Corporation, U.S.A). There are three Waters Styragel columns (pore size 10², 10³, and 10⁴ Å) in series, calibrated by a monodisperse polystyrene standard. Tetrahydrofuran was used as the eluent at a flow rate of 1.0 mL min⁻¹.

Table 1 lists the molecular weights and weight contents of the SSBR samples obtained from GPC and ¹H NMR measurements, respectively. In these samples (S1, S2 and S3), the most remarkable difference is the vinyl content, which increases from S1 to S3.

XPS measurements were carried out on an ESCALAB 250 spectrometer with an Al Kα radiation source (1486.6 eV) to quantitatively determine the contents of carbon and oxygen atoms in graphene. Fig. 2a shows the XPS spectrum of graphene. Four types of carbon atoms exist in graphene: C=C (284.5 eV), C–O (286.2 eV), C=O (287.8 eV), and O=C–O (288.8 eV). The mass ratio of C/O is 17.5 : 1, so the graphene exhibits a considerable degree of reduction. Therefore, in the simulation, we constructed the pristine graphene sheet as a nano-filler.

Raman spectrum was collected by confocal Raman spectroscopy (Renishaw inVia, England) from 800 cm⁻¹ to 2000 cm⁻¹ at an excitation wavelength of 514 nm. As shown in Fig. 2b, two dominant peaks corresponding to the D (located at 1385 cm⁻¹) and G (located at 1580 cm⁻¹) bands were observed. The D band was attributed to sp³ hybridized carbon atoms and defects, and the G band was attributed to sp² hybridized carbon atoms in the graphite lattice. The intensity ratio of the D to G bands (I_D/I_G) was often employed to reflect the average size of the sp² domains.¹³ The fairly low I_D/I_G value of graphene (0.22) indicates low defect concentration and considerable order structure in lattice.

AFM (Nano Scope Analysis, Bruker, Germany) was employed to characterize the geometry information of graphene in tapping mode. The graphene solution at a concentration of 0.025 mg mL⁻¹ was prepared using N,N-dimethylformamide (DMF) solvent. The graphene is uniformly dispersed in the solvent by ultrasonic treatment in ultrasonic cleaner for 1 hour. The sample was prepared by dropping the dilute solution on freshly silicon wafer, and drying at room temperature. As shown in Fig. 2c, the graphene nanosheets exhibit lateral dimensions of several hundred nanometers.

Differential scanning calorimetry (DSC) measurements were carried out on a Q100 calorimeter (TA Instruments, U.S.A). All the samples were examined from −90 to 40 °C at a scanning rate of 10 K min⁻¹ under a nitrogen atmosphere.

KRÜSS DSA 100 drop shape analyses (KRÜSS GmbH, Germany) were used to measure the static contact angles of the raw rubbers and graphene. The raw rubber films 1 mm thick were obtained by compression molding at 100 °C on a PTFE surface to minimize surface contamination. A few millimeters graphene film was obtained by compression molding on powder compressing machine (769YP-15A, China). The graphene film surface was cleaned by ethyl alcohol prior to testing. The test liquids with different surface tensions were deionized water and glycerol. To ensure data accuracy and repeatability, five contact angles were measured for each sample, and the average value was taken.

A strain sweep of the graphene-filled rubber was conducted on a Rubber Process Analyzer RPA2000 (Alpha, U.S.A) at 60 °C and a frequency of 1 Hz. The dynamic strain range is from 0.7% to 400%.

The dynamic mechanical properties of the graphene/SSBR composites were determined by a VA3000 DMA (01dB-Metravib, France). The test area of a sample was 10 × 10 × 1 mm (length × wide × thickness). The testing conditions were as follows: temperatures from −90 °C to 100 °C, heating rate of 3 K min⁻¹, and frequency of 10 Hz.

The micro-morphologies of the samples were observed with transmission electron microscopy (TEM). Ultrathin sections of the specimens were prepared at −100 °C using a ultramicrotome with a diamond knife. The thin slices were put on copper grids and then submitted to TEM observation with a Tecnai G2 20 TEM (Hong Kong FEI, China) under an accelerating voltage of 200 kV.

PALS measurements were performed on a conventional fast–fast coincident spectrometer (EG&G ORTEC Co., U.S.A) with BaF₂ as detector at room temperature. A 20 μCi ²²Na positron source sealed between aluminium foils was placed between two identical pieces of the sample, and a million counts were recorded for each spectrum. The samples were in the form of small disks with a diameter of 10 mm and a thickness of 1 mm.

4. Model and simulation details

For the MD simulations, all the theoretical calculations were performed with Material Studio (MS) software and a condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field was employed. In this force field approach, the total energy E_T of the system is represented by the sum of bonding and non-bonding interactions:

E_T = E_b + E₀ + E_φ + E_χ + E_cross + E_vdw + E_q (1)

The first five terms, which correspond to the energies associated with the bond E_b, bond angle bending E₀, torsion angle rotation E_φ, out-of-plane E_χ, and cross-term interaction E_cross, represent the bonding interactions. The last two terms consisting of the van der Waals term E_vdw and electrostatic force E_q, represent the nonbonding interactions.^21,22

In order to elucidate the graphene–SSBR interfacial bonding characteristics in detail, we constructed two models for the graphene/SSBR composites: (a) the amorphous model and (b) the layer model. The two models were constructed as follows:

(1) Amorphous model. First, we constructed three types of SSBR chains (S1, S2 and S3) with different vinyl contents as given in Table 1, each chain containing forty repeat units. Single graphene sheets (see Fig. 3), which have a length of 49.200 Å and width of 36.927 Å, were used for the simulations of the graphene/SSBR composites. Then amorphous models of the graphene/SSBR composites, each with ten SSBR chains, were constructed. As an example, the amorphous model of the graphene/S1 composite is shown in Fig. 4. The binding energy (E_binding), fractional free volume (FFV), and mean square distance (MSD) were calculated with the amorphous model.

Fig. 3 Schematic of graphene.

Fig. 4 Amorphous model of graphene/S1 composite.

(2) Layer model. We constructed layer models (see Fig. 5), each with forty SSBR chains, to carry out the pullout MD simulations. More SSBR chains were used in a layer model than in an amorphous model to ensure a close chain packing. The interaction energy, pullout energy, interfacial binding energy, and interfacial shear stress were calculated with the layer model.

Fig. 5 Layer model of graphene/S1 composite after 1000 ps of NVT ensemble.

In a simulation, the energy of each cell was first minimized to less than 1.0 × 10⁻⁵ kcal mol⁻¹ Å⁻¹ by using the Smart Minimizer method to relax the state of minimal potential energy. After this stage, the simulation cell was annealed from 300 K to 500 K for four cycles with five heating ramps per circle by using the temperature cycle protocol. Subsequently, in the amorphous model, the system was subjected to 1000 ps of NPT ensemble (constant number of particles, pressure, and temperature) at 0.1 MPa to obtain the most stable system. In the layer model, the system was subjected to 1000 ps of NVT ensemble (constant number of particles, volume, and temperature) to fix the cell size and obtain the most stable system. In all the simulations, the Andersen barostat for pressure control²³ and Berendsen thermostat²⁴ for temperature control were utilized. The Newtonian equation of motion was integrated by the Verlet velocity time integration method²⁵ with a time step of 1 fs. The electrostatic interactions were calculated by the Ewald method²⁶ with an accuracy 0.001 kcal mol⁻¹ and the van der Waals interactions were approximated by the Lennard-Jones function with a cut-off distance of 9.5 Å. All the theoretical calculations were performed on the basis of the most stable polymer configuration.

5. Results and discussion

To clearly express the effect of vinyl content on the microstructure, thermodynamics, and dynamics of materials, we present all experimental results in Section 5.1–5.3 and discuss the relationship between structure and properties in Section 5.4. The results of the pullout simulation are given and discussed separately in Section 5.5.

5.1 Compatibility and dispersion of graphene in composites

It is well accepted that filler–rubber interactions and filler dispersion are two critical factors influencing the mechanical properties and viscoelastic behavior of rubber composites. From a thermodynamic point of view, the two factors strongly depend on the physicochemical surface properties of the filler and rubber. As described by Heinrich and Natarajan, the thermodynamics contribution to the dispersibility and interfacial interactions can be quantified in terms of surface energies.^27,28 Therefore, to gain insight into the dispersion of graphene and interfacial interactions in different SSBR matrices, we use Fowkes' model²⁹ to calculate the surface energies of graphene and SSBR by measuring the contact angles of two liquids—water and glycerol, as described in eqn (2) and (3):

γ_L = γ^d_L + γ^p_L (3)

where γ^p_L and γ^d_L are the polar and dispersive components of the surface energies of the liquid, γ^p_S and γ^d_S are the polar and dispersive components of the surface energies of the solid, and γ_L and γ_S are the total surface energies of the liquid and solid expressed as the sum of the polar and dispersive components. The γ^p_L and γ^d_L values for water are 51 and 21.8 mJ m⁻², and the γ^p_L and γ^d_L values for glycerol are 30.0 and 34.0 mJ m⁻².¹³ The surface energies of SSBRs and graphene are listed in Table 2. S3 with the highest vinyl content possesses the lowest values of γ^d_S and γ_S and the highest value of γ^p_S.

Table 2 Contact angles and surface energies of SSBRs and graphene

Samples	Contact angle (°)		γ^dS (mJ m^−2)	γ^pS (mJ m^−2)	γS (mJ m^−2)
	Water	Glycerol
S1	75.0 ± 1.1	98.9 ± 1.5	37.7 ± 2.7	5.9 ± 1.5	43.6 ± 4.2
S2	81.7 ± 1.8	99.3 ± 1.9	18.0 ± 3.3	9.4 ± 2.1	27.4 ± 5.4
S3	95.9 ± 1.4	99.2 ± 1.3	0.3 ± 0.1	20.1 ± 1.2	20.4 ± 1.3
Graphene	83.4 ± 1.4	84.9 ± 1.0	1.0 ± 0.3	25.4 ± 0.9	26.4 ± 1.2

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The interfacial interactions between the two materials were determined by their surface energies. The adhesive energy (W_rf), characteristic of the interfacial interaction between the filler and rubber, can be given by³⁰

where the subscripts r and f denote the rubber and the filler, respectively. Thus, γ^p_r and γ^d_r are the polar and dispersive components of the surface energies of SSBR; γ^p_f and γ^d_f are the polar and dispersive components of the surface energies of graphene.

According to Wang's model,³¹ ΔW, described as the change in adhesive energy in the filler agglomeration process and is the driving force for filler agglomeration, is given by

ΔW is always positive unless the polar and dispersive components of the surface energies for the filler and rubber are identical. Therefore, from a thermodynamic point of view, the greater the ΔW, the larger the difference of surface energies and the higher the tendency for filler agglomeration. Table 3 lists the thermodynamic parameters for interfacial interactions and filler agglomeration.

Table 3 Thermodynamic parameters for interfacial interactions and filler agglomeration

Samples	Wrf (mJ m^−2)	ΔW (mJ m^−2)
Graphene/S1	36.8	66.5
Graphene/S2	39.4	28.8
Graphene/S3	46.1	2.6

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Strain sweep measurements were carried out to study the rubber–filler and filler–filler interactions, and the results are presented in Fig. 6. The storage modulus of the filled rubber decreases as a function of strain, and this phenomenon is known as the Payne effect.³² The storage modulus is the highest under low strains (referred to as G′₀) and rapidly decreases to a low value (referred to as G′_∞).

Fig. 6 Dependence of storage modulus on strain for graphene/SSBR composites at 60 °C.

TEM micrographs of graphene/SSBR composites at a low magnification of 5000 are present in Fig. 7.

Fig. 7 TEM micrographs of graphene/SSBR composites at a magnification of 5000: (a) S1; (b) S2; (c) S3.

E_binding, which is defined as the negative value of the interaction energy ΔE, is a measure of the compatibility between two components mixed with each other.³³ A negative E_binding represents poor compatibility between the two components, and phase separation will appear in the composite. On the contrary, a positive E_binding represents good compatibility, and the larger the positive value of E_binding the better the compatibility. From the equilibrium system at the end of NPT simulation, the total energy of the system and those of the individual components can be evaluated. The E_binding between graphene and SSBR can be obtained by the following equation:

E_binding = −ΔE = −(E_total − E_graphene − E_SSBR) (6)

where E_graphene and E_SSBR are the total energies of graphene and SSBR, respectively. E_graphene is a constant (8711.6 kcal mol⁻¹) because the graphene sheet is identical in each cell. The binding energies of the graphene/SSBR composites are listed in Table 4.

Table 4 Binding energies of graphene/SSBR composites

Samples	Etotal (kcal mol^−1)	ESSBR (kcal mol^−1)	Ebinding (kcal mol^−1)
Graphene/S1	16 320.7	7797.1	188.0
Graphene/S2	16 090.1	7595.4	216.9
Graphene/S3	15 639.8	7275.3	347.1

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5.2 FFV in composites by MD simulation and PALS

Previous research has demonstrated that interfacial interactions exert a considerable effect on the microstructure of composites.³⁴ The FFV is commonly used to characterize the efficiency of chain packing and the amount of free space in a polymer matrix. A common definition of FFV iswhere V is the specific volume, V₀ = 1.3V_w is the occupied volume, and V_w is the van der Waals volume.³⁵ In the MD simulations, a grid scanning method was used to determine the FFV.

The FFV of graphene/SSBR composites can be also determined by PALS experiments. PALS is based on the fact that a positron with the same mass as an electron but positive charge captures the electron to form two types of positronium (Ps) with a short lifetime—orthopositronium (o-Ps) and parapositronium (p-Ps).³⁶ It is generally accepted that the o-Ps is caged and annihilated in the free volume of a polymer. The o-Ps lifetime (τ₃) and o-Ps intensity (I₃) depend on the magnitude of the free volume. A two-state trapping model has been proposed, in which the free volume is known as a spherically square potential well of infinite depth with a radius of R.³⁷ In the spherically square potential well, there is an electronic shell with a thickness of ΔR. The model provides a simple relationship between τ₃ and R, which is described by the following semi-empirical equation:³⁸

where τ₃ and R are expressed in the units of ns and Å, respectively. In eqn (8), R₀ = R + ΔR, where ΔR is the fitted empirical electron layer thickness and was determined as 1.659 Å.

The τ₃ and I₃ in different SSBR matrices can be determined by PALS. The free volume radius R can be obtained from eqn (8), and thus the free volume V_h = 4πR³/3. Then, the FFV is given as follows:

where C is a constant. We cannot obtain the absolute value of FFV due to the unknown constant C. However, the relative FFV can be obtained by assigning the value 1 to C.²² The FFV by MD simulations and relative FFV by PALS experiments are listed in Table 5.

Table 5 FFV by MD simulations and relative FFV by PALS experiments

Composite	FFV (%)	Relative FFV (%)
Graphene/S1	0.428	2.3942 ± 0.0140
Graphene/S2	0.425	2.3412 ± 0.0096
Graphene/S3	0.419	2.2439 ± 0.0130

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5.3 Dynamic properties

We studied the changes in dynamic mechanical properties of graphene/SSBR composites by DMA measurements. Of the DMA results, the loss factor (tan δ) reflects the internal friction and expresses the ratio of the dispersed energy in one deformation cycle to the energy accumulated.³⁹ A higher value of tan δ indicates a greater internal friction of the material. In Fig. 8a, the tan δ values of the composites are plotted against temperature. The glass transition temperature (T_g), taken as the temperature of maximum tan δ(tan δ_max), and the tan δ_max of the graphene/SSBR composites are listed in Table 6.

Fig. 8 Temperature dependence of (a) tan δ and (b) E′ for graphene/SSBR composites.

Table 6 Dynamic property parameters and E_a from DMA for graphene/SSBR composites

Samples	Tg (°C)	tan δmax	Ea (kJ mol^−1)
Graphene/S1	−19.6	1.60	1.23
Graphene/S2	−12.4	1.74	3.60
Graphene/S3	−5.7	1.76	5.08

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To quantify the internal friction, we calculated the activation energy (E_a) needed to mobilize one mole of rubber chains according to the storage modulus (E′)–temperature curves presented in Fig. 8b. The E_a was calculated by the following Arrhenius-type equation:⁴⁰

where E′ is the storage modulus at temperature T, E₀ is the storage modulus at reference temperature T₀, and R is the universal gas constant. According to eqn (10), the logarithm of the storage modulus is linear with the inverse temperature, and the linear relation is shown in Fig. 9. The E_a is proportional to the slope of the straight line, and the results of the E_a are listed in Table 6.

Fig. 9 Logarithm of storage modulus against inverse temperature for graphene/SSBR composites.

The dynamic properties of polymer chains can also be characterized by the MSD from MD simulation. The MSD were calculated by⁴¹

MSD = 〈[r_i(t) − r_i(0)]²〉 (11)

where r_i(0) is the initial position coordinate of atom i and r_i(t) is the position coordinate of atom i at time t. The brackets 〈 〉 denote the average over all atoms as well as over all times. The MSDs of SSBR chains with different vinyl contents are presented in Fig. 10.

Fig. 10 Mean square displacements of SSBR chains.

5.4 Discussion on structure and properties

Here a radar map is introduced to elucidate the effect of vinyl content on the microstructure, thermodynamics, and dynamics of materials. The parameters including structural parameters, thermodynamic properties, and dynamic properties were normalized and are presented in Fig. 11.

Fig. 11 Radar map of relationship between structure and properties for graphene/SSBR composites.

We found that the downward trend of the relative FFV (see Table 5) is rather similar to that of the FFV with increasing vinyl content. Thus, both MD simulation and PALS experiment demonstrate that there is less FFV in the composite with higher vinyl content.

From a thermodynamic point of view, the increase in W_rf and E_binding and the decrease in ΔW (see Table 3) indicate that a higher vinyl content is more conducive to improving graphene–SSBR compatibility, interfacial interaction, and graphene dispersion. In filled rubber composites, the filler exists in the form of network. At low strain, the filler network cannot be broken so that the composites have high storage modulus (referred to as G′₀). As the strain increases, the storage modulus decreases to a low value (G′_∞) because the filler network is broken. Therefore, the Payne effect (G′₀ − G′_∞) is attributed to the break of filler network. The greater the Payne effect indicates more obvious filler agglomeration and higher modulus at low strain. The smallest Payne effect in graphene/S3 (see Fig. 6) also corresponds to the best graphene dispersion in the S3 matrix. TEM micrographs support the results from thermodynamic analysis and strain sweep measurements. It is obvious that large graphene agglomerates exist in SSBR matrix with low vinyl content, indicating relatively poor graphene–SSBR interactions. The graphene dispersion is somewhat improved with increasing vinyl content. As far as S3 with the vinyl content up to 63.3 wt% is concerned, graphene shows a relatively uniform dispersion. Thus, it is reasonable to infer that the lowest FFV in the graphene/S3 composite is attributed to the best compatibility between graphene and the S3 matrix, leading to the closest chain packing.

Table 6 shows that both T_g and tan δ_max increase with increasing vinyl content. The highest E_a for the graphene/S3 composite indicates that the greatest energy is required to overcome internal friction to mobilize one mole of S3 chains. The results of MSD (see Fig. 10) show that the mobility of the SSBR chains is in the other S1 > S2 > S3, in good agreement with the results of E_a from DMA experiments.

It is worth noting that there are two factors influencing the T_g of the composites. One factor is that the increase of T_g of the composites is simply due to the higher T_g of neat SSBR. The other factor is that the changes of relaxation behaviors are attributed to the interfacial interactions between graphene and SSBR. For clarifying this issue, DSC experiments were performed to measure the T_gs of the graphene/SSBR and the neat SSBRs, and the DSC curves are shown in Fig. 12. The T_gs of the graphene/SSBR composites and the neat SSBRs are listed in Table 7. Table 7 shows that there is no significant difference between the T_g of a graphene/SSBR composite and the neat SSBR involved. Therefore, we concluded that the changes in T_g are mainly due to the different SSBR matrices rather than the differences in interfacial interactions. In a previous study, similar results were obtained for graphene oxide/SSBR composites.¹³

Fig. 12 DSC curves for (a) graphene/SSBR composites and (b) SSBRs.

Table 7 T_g from DSC of neat SSBRs and graphene/SSBR composites

Samples	Tg (°C)	Samples	Tg (°C)
Graphene/S1	−35.9	S1	−36.8
Graphene/S2	−26.8	S2	−27.3
Graphene/S3	−20.5	S3	−19.1

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In MD simulation, the validity of model and whether the model constructed can represent the real system or not are the focus of most attention. The graphene exhibited lateral dimensions of several hundred nanometers by AFM measurement. With the limitation of computer hardware, the particle size of several hundred nanometers is too large for typical MD simulation. Besides, if the particle size is too large, the simulation system is difficult to reach thermodynamic equilibrium which is the premise for validity of the modeling results. Thus, the particle size of graphene in almost all of MD simulations is far less than real one. For example, Jing et al.,⁴² Zhang et al.,¹⁷ and Lv et al.¹⁸ established the particle size of graphene of 6 nm × 6 nm, 3 nm × 3 nm, and 4 nm × 6 nm. To our best knowledge, there isn't a consistent standard for the choice of particle size.

To study the effect of particle size of graphene on modeling results, we constructed additionally the amorphous cell with the particle size of graphene of 64.231 Å × 75.413 Å. The results of the comparison of E_binding and FFV were given in Table 8. We found that the E_binding increases, FFV decreases with increasing particle size of graphene. The increase of E_binding is attributed to the increase of the number of atoms as the particle size increases. Meanwhile the increase of E_binding leads to the decrease of FFV. The decrease of FFV is slight, which may be connected with the greater wrinkling of graphene as the particle size increases.⁴³ However no matter what particle size, the SSBR with higher vinyl content always has higher E_binding and less FFV. In other word, the particle size of graphene does not influence the relative magnitude of the modeling results.

Table 8 Effect of particle size of graphene on E_binding and FFV

Samples	Ebinding^a (kcal mol^−1)	Ebinding^b (kcal mol^−1)	FFV^a (%)	FFV^b (%)
a The particle size of graphene is 49.200 Å × 36.927 Å.b The particle size of graphene is 64.231 Å × 75.413 Å.
Graphene/S1	188.0	225.6	0.428	0.425
Graphene/S2	216.9	269.2	0.425	0.422
Graphene/S3	347.1	436.5	0.419	0.414

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Generally speaking, we compare the modeling results with the experimental results to estimate whether the model is valid in MD simulation. If the modeling results are in good agreement with the experimental results, the model is valid. According to the modeling results of larger size and the consistency between the modeling and experimental results, we reasonably argue that we can equate this small size in MD simulation to real one.

5.5 Interfacial bonding characteristics by pullout MD simulations

We carried out pullout MD simulations of the graphene from SSBR matrix to investigate at the molecular level the effect of vinyl content on the interfacial bonding between graphene and SSBR. Snapshots of the pullout process are shown in Fig. 13. ΔZ represents the displacement of graphene during pullout. The graphene sheet is first fully embedded in the SSBR matrix and then gradually pulled out in the pullout simulation. We calculated the energies related to the graphene/SSBR interface during pullout.

Fig. 13 Simulated snapshots of pullout of graphene (ΔZ is defined as the displacement of graphene during pullout).

The interfacial bonding was estimated from the graphene–SSBR interaction energy ΔE, which includes many molecular interactions, such as the interfacial bonding energy γ, the pullout energy E_pullout, and the shear stress τ_i. ΔE can be calculated according to eqn (6). In addition, ΔE is twice the γ normalized by the contact area A, and for graphene with a sheet structure, A is twice the surface area S of the graphene sheet:⁴⁴

E_pullout is defined as the energy difference between the fully embedded graphene sheet and the complete pullout configuration.⁴⁵ E_pullout is divided into three terms as follows:⁴⁶

E_pullout = E₂ − E₁ = (−ΔE₂ + E_graphene2 + E_SSBR2) − (−ΔE₁ + E_graphene1 + E_SSBR1) = (ΔE₁ − ΔE₂) + (E_graphene2 − E_graphene1) + (E_SSBR2 − E_SSBR1) (13)

where E, E_graphene, and E_SSBR are the total energy of the composite, graphene, and SSBR, respectively. The subscripts “1” and “2” refer to the fully embedded configuration and the complete pullout configuration, respectively. E_pullout is related to τ_i¹⁸ by the following relation:where h and L are the width and length of the graphene sheet, respectively, and x is the coordinate along the longitudinal axis.⁴⁵ Note that the graphene sheet will wrinkle after 1000 ps of NVT ensemble, as presented in Fig. 5. The wrinkling of the graphene sheet can change the bond lengths and bond angles of C–C resulting in the change of graphene surface area. It is difficult to calculate the wrinkled graphene area accurately. We can only take S as roughly twice the surface area A of the graphene sheet in eqn (15). ΔE, E_pullout, and γ are plotted against the displacement of the graphene sheet in Fig. 14–16.

Fig. 14 Interaction energy during pullout.

Fig. 15 Pullout energy during pullout.

Fig. 16 Interfacial bonding energy during pullout.

Due to the stable interfacial bonding energy (see Fig. 16) and the decrease of contact area during the pullout, the interaction energy decreases linearly toward a value of zero, as shown in Fig. 14. Fig. 15 indicates that the pullout energy of the graphene/SSBR composites increases as the graphene sheet is pulled out. Both the interaction energy and pullout energy are the highest for the graphene/S3 composite during pullout. In the simulations, the interaction energy is connected with the total number of atoms. Because of the nearly constant number of atoms in the three systems, the effect of vinyl content is smaller on the interaction energy than on the pullout energy. For example, in the graphene/S3 system, the interaction energy varies from 1657 kcal mol⁻¹ to 0, but the pullout energy varies from 0 to 4464 kcal mol⁻¹. A previous study showed that the pullout energy was mainly influenced by the wrinkling of graphene and the change of the conformation of the polymer during pullout.⁴³ Therefore, the larger effect on the pullout energy can be attributed to the wrinkling of the graphene sheet and the change in SSBR conformation.

Table 9 lists the interfacial shear stresses of the graphene/SSBR composites. The interfacial shear stress also increases with increasing vinyl content. The interfacial bonding energy determines the shear stress to some extent. In other words, the higher the interfacial bonding energy is, the higher the interfacial shear stress is.

Table 9 Interfacial shear stress τ_i of graphene/SSBR composites

Samples	τi (MPa)
Graphene/S1	15.5
Graphene/S2	22.6
Graphene/S3	25.8

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6. Conclusions

We have elucidated the effect of vinyl content on the microstructure, thermodynamics, and dynamics of graphene/SSBR composites through a combined experimental and MD simulation approach. According to the thermodynamic analysis and strain sweep measurements, a high vinyl content can improve the SSBR/graphene interactions and graphene dispersion. In addition, the high vinyl content can also improve the T_g, decrease the FFV, and limit the mobility of the SSBR chains, according to PALS, DMA, and DSC measurements. The variation in dynamic and thermodynamic properties can be attributed to the difference between graphene/SSBR compatibility and graphene dispersion. The predicted E_binding, MSD, and FFV also show good agreement with the experimental results.

The simulations on the pullout of graphene from SSBR matrix were carried out to investigate the interfacial bonding characteristics, especially the interfacial shear stress. We found that the effect of vinyl content is smaller on the interaction energy than on the pullout energy during pullout. A higher vinyl content leads to higher interfacial bonding energy and shear stress. Besides, the interfacial bonding energy is constant during the pullout.

Acknowledgements

The financial supports of the Major Research Plan from the Ministry of Science and Technology of China under Grant No. 2014BAE14B01 and the National Natural Science Foundation of China under Grant No. 51473012 are gratefully acknowledged.

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