Effect of chemical structure of elastomer on filler dispersion and interactions in silica/solution-polymerized styrene butadiene rubber composites through molecular dynamics simulation

Abstract

The dynamic properties, filler–rubber interactions, and filler dispersion in silica/solution-polymerized styrene butadiene rubber (SSBR) composites with various chemical structures of SSBR were studied through molecular dynamics (MD) simulation. The structures of SSBR studied were non-modified, star-shaped, and in-chain modified by different contents of 3-mercaptopropionic acid. The mean square displacement (MSD), binding energy, glass transition temperature (T_g), and radial distribution function g(r) of filled SSBR models were investigated. We found that there was an optimum modifier content (14.2 wt%) at which the silica/SSBR composite had the lowest self-diffusion coefficient, the highest binding energy, and the best silica dispersion. The competing effects of hydrogen bonds, steric hindrance of 3-mercaptopropionic acid and rubber–rubber interactions led to the existence of this optimum modifier content of 14.2 wt%. Furthermore, the star-shaped SSBR as well as in-chain modified SSBR had strong interactions with the silica dispersed uniformly in the rubber matrix. The modeling results were in good agreement with our previous experimental results.

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1. Introduction

Since the first fabrication of butadiene styrene rubber (SBR) by using a solution polymerization method, the structural design of solution-polymerized 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 With excellent properties such as low energy dissipation and environmental friendliness, nanosilica is widely applied to prepare green tire treads in the rubber industry.^3–5 Based on previous studies,^6,7 filler–rubber interactions and filler dispersion are two major factors influencing the mechanical properties and viscoelastic behavior of rubber. However, too many silanol groups on the surface of silica particles usually result in high surface tension, easy self-aggregation, and poor affinity with the rubber matrix, especially for non-polar rubbers.⁸ Therefore, the improvement of silica dispersion is always the focus of the designation and development of high performance composites, and the problem has been attempted to solve through the choice of appropriate particle sizes,⁹ the use of silane coupling agents,¹⁰ and the surface modification of silica.¹¹ Besides, the rational design of rubber structure has been demonstrated to be a feasible method for the improvements of silica dispersion and filler–rubber interaction. For instance, the end-functionalized SSBR with SnCl₄ ¹² or ethoxy silyl¹³ and the in-chain modified SSBR by introducing –COOH¹⁴ into the rubber chains are conducive to improving the silica dispersion. Especially for in-chain modified SSBR, many varieties that have excellent wet skid resistance and rolling resistance have been synthesized in recent years. Therefore, it is highly recommended for us to study the structure and the performance relations of in-chain modified SSBR.

With the development of computer technology, molecular simulation approaches based on classical physics or quantum physics theories have been widely used to study polymer nanocomposites, and great achievement and progress have been made.^15–17 Compared with traditional experiment methods with which the design of a macromolecular structure is difficult on account of the limitation of conditions, computer simulation is a more effective method, especially for the design of complex structures. Molecular dynamics (MD) simulation has emerged as a powerful theoretical tool due to its capability of providing direct quantitative relationships between the microstructure and macroscopic properties of materials. It has been reported in the literature that MD simulations were used to study different polymer systems (e.g., polyethylene,¹⁸ polyimide,¹⁹ poly(vinyl alcohol),²⁰ and elastomers²¹) filled by silica. Several simulation studies in the past explored the model of silica from the point of view of both atomistic and coarse-grained simulations, and the simulated results were in good agreement with the experiment results.^22,23 However, most of the early MD simulation studies were concerned with the particle size and surface chemistry of nanoparticles, and the reinforcement mechanism.²⁴ How the chemical structure of the polymer affects the filler dispersion and interfacial bonding from microcosmic point of view was rarely reported.

In this study, we elucidated the effect of non-modified, in-chain modified by 3-mercaptopropionic acid, and star-shaped SSBR on silica dispersion and filler–rubber interactions at the molecular level. The reason for the existence of an optimum modifier content was investigated. Additionally, the modeling results were compared with the results from our previous experimental analyses including differential scanning calorimetry (DSC), static contact angle measurements, rubber process analyzer (RPA) measurements, dynamic mechanical analysis (DMA), and transmission electron microscopy (TEM).²

2. Model and simulation details

To ensure consistency with the grafting ratios of our previous experimental samples (M0, M1, M2 and M3),² we first constructed four SSBR models with different structures, each containing 100 repeat units: (a) g0, (b) g1, (c) g2, and (d) g3. Then additional models (e) g4, (f) g5, (g) g6, and (h) star-shaped SSBR with carbon atom coupling were computed to further analyze the effect of modifier content and macromolecular structure on filler dispersion and filler–rubber interactions. Table 1 lists the experimental modifier contents and unit contents of SSBR, and Table 2 lists the simulated modifier contents and unit contents. The chemical structure of 3-mercaptopropionic acid and g2 chain are shown in Fig. 1. The addition reaction occurs between the vinyl groups of 1,2-polybutadiene and the sulfhydryl groups.² Each cell consists of two SSBR chains and five amorphous silica particles (Fig. 1) with a diameter of 12 Å centered on a silicon atom. The unsaturated boundary effect was avoided by adding hydrogen atoms to the surface of the silica particle.²⁵

Table 1 Experimental unit contents and weight contents of modifiers of SSBR samples

Sample code	Styrene units (wt%)	1,2-Polybutadiene units (wt%)	1,4-Polybutadiene units (wt%)	Modifier (wt%)
M0	21.0	47.4	31.6	0
M1	20.7	45.6	31.3	2.4
M2	20.4	44.2	31.2	4.2
M3	20.1	40.2	30.1	9.6

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Table 2 Simulated unit contents of SSBR and weight contents of modifier

Sample code	Styrene units (wt%)	1,2-Polybutadiene units (wt%)	1,4-Polybutadiene units (wt%)	No. of modifiers	Modifier (wt%)
g0	21.0	47.4	31.6	0	0
g1	20.7	46.4	31.5	2	2.4
g2	20.4	44.3	31.0	3	4.3
g3	19.9	40.6	30.0	8	9.5
g4	17.8	36.1	28.9	10	14.2
g5	16.6	35.6	27.0	15	20.8
g6	15.5	32.2	26.4	20	26.9
Star-shaped SSBR	21.0	47.4	31.6	0	0

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Fig. 1 Models of 3-mercaptopropionic acid, SSBR chain and silica particle (grey, red, yellow, white, and blue spheres stand for C, O, Si, H, and S atoms, respectively).

In a simulation, the energy of each cell was first minimized to 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. In all the simulations, the Andersen barostat for pressure control²⁶ and Nose thermostat²⁷ for temperature control were utilized. The newtonian equation of motion was integrated by the Verlet velocity time integration method²⁸ with a time step of 1 fs. The electrostatic interactions were calculated by the Ewald method²⁹ 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 12 Å. Subsequently, the system was subjected to 500 ps of NVT ensemble (constant number of particles, volume, and temperature) and 1000 ps of NPT ensemble (constant number of particles, pressure, and temperature) at 0.1 MPa to obtain the most stable polymer configuration. All the simulations were performed with the Material Studio software, and a condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field³⁰ was employed.

3. Results and discussion

3.1. Radius of gyration of polymer chains

In MD simulation for nanoparticle/polymer composites, the nanoparticle radius R and the radius of gyration R_g of polymer chain are very significant parameters for the validity of simulation modeling. It has been found that when R_g > R, the dynamic properties of nanoparticle do not depend on the chain length, but only depend on the mass of nanoparticle.³¹ The R_g is used to characterize the size and crimp degree of polymer chains and can be calculated in MD simulation by the following expression:³²where r_i is the position vector of each atom, r_cm is the center-of-mass of the whole chain, and N is the total number of atoms. Table 3 lists the R_g of the SSBR models with various structures. It can be seen that the R_g of all polymer chains are greater than the radius of a silica nanoparticle (6 Å). Therefore, at the same mass of silica nanoparticles, the dynamic properties of nanoparticle do not depend on the chain length, but only depend on the chemical structure of SSBR, which also assures that the modeling results are related to the chemical structure of SSBR only. Meanwhile, it is easy to understand that star-shaped SSBR with the branched structure has the lower R_g compared with linear structure at the same degree of polymerization.

Table 3 Radius of gyration R_g of various SSBR models

	g0	g1	g2	g3	g4	g5	g6	Star-shaped SSBR
Rg (Å)	21.5	19.5	24.0	20.4	21.9	22.3	24.5	17.8

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3.2. Energy properties of silica/SSBR composites

The binding energy (E_binding), which is defined as the negative value of the interaction energy (E_inter), is a measure of the compatibility between two components mixed with each other.³³ A negative E_binding represents poor compatibility between 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 indicates 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 silica and SSBR can be obtained by the following equation:

E_binding = −E_inter = −(E_total − E_silica − E_SSBR) (2)

where E_silica and E_SSBR are the total energies of silica and SSBR, respectively. E_silica is a constant (−6636.1 kcal mol⁻¹) because the numbers and structure of silica particles are identical in each cell. Besides, the non-bond energy (E_non-bond), which can reflect the intermolecular interactions of the whole system, can be obtained from the equilibrium configuration of the trajectory file. The energy properties of the eight SSBR systems at 298 K are listed in Table 4. A negative E_total value indicates that the interaction between the SSBR and silica is beneficial towards a lower energy and the composite is thus stable.³⁴ The compatibility between SSBR and silica is the best in the silica/g4 composite, indicating that there is an optimum modifier content (14.2 wt%). Predictably, phase separation will appear in the silica/g6 composite because of the negative E_binding. It can be seen that the non-bond energy shows the same trend as the binding energy, an indication that the silica/g4 is the most stable system.

Table 4 Energy properties of eight SSBR composites

Silica/SSBR composites	Etotal (kcal mol^−1)	ESSBR (kcal mol^−1)	Ebinding (kcal mol^−1)	Enon-bond (kcal mol^−1)
Silica/g0	−5193.7	1104.6	−337.8	−6816.6
Silica/g1	−5992.6	440.1	−203.4	−7745.1
Silica/g2	−6378.1	310.8	52.8	−7958.2
Silica/g3	−6841.7	51.9	257.5	−8287.3
Silica/g4	−6897.8	32.4	294.1	−8415.7
Silica/g5	−6966.7	−192.2	138.4	−8254.6
Silica/g6	−7238.9	−729.1	−126.3	−8199.9
Silica/star-shaped SSBR	−6616.2	245.4	225.5	−8204.7

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3.3. Dynamic properties

The dispersion of filler and filler–rubber interactions play an important role in the dynamic properties of the composite. The self-diffusion coefficient (D_s), which is related to the temperature and pressure, is one of the critical parameters in quantitatively determining the mobility of the polymer chains. The D_s of the SSBR chains can be calculated by the Einstein equation:³⁵where N is the number of atoms in SSBR chains, 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. 〈|r_i(t) − r_i(0)|²〉 is the mean square displacement (MSD) of the atoms over time t.³⁶ The brackets denote that the average is taken for all atoms as well as over all time origins. Fig. 2 shows the MSD of the silica/SSBR composites at 298 K, and Fig. 3 shows the corresponding D_s as a function of temperature.

Fig. 2 Mean square displacement of SSBR chains at 298 K.

Fig. 3 D_s of SSBR chains at different temperatures.

The results of MSD and D_s show that the mobility of the polymer chains increases as the temperature increases because the movements of the atoms are much faster at higher temperature. The gap of MSD between g0 and g1 indicates the abrupt change in the motion of the polymer chains with the introduction of 3-mercaptopropionic acid into SSBR chains. Besides, the least mobile in the eight systems is g4 at all temperatures investigated, indicating that with increasing modifier content, the D_s of the SBR chains first decreases, reaches a minimum in the g4/silica system, and then increases. To elucidate the relationship between dynamic properties and interactions, we compared the D_s with the E_binding, as shown in Fig. 4. We found that the higher the E_binding is, the lower the D_s will be.

Fig. 4 E_binding and D_s with different chemical structure of SSBR systems.

In our previous work,² the activation energy (E_a) from RPA measurements needed to mobilize one mole of rubber chains was calculated. DMA measurements were carried out to study the dynamic mechanical properties and T_gs of the SSBR/silica composites. Table 5 lists the E_a, tan δ_max and T_gs. The E_a, tan δ_max, and T_g increase with increasing modifier content (from 0 to 9.5 wt%), indicating that the higher the modifier content is, the stronger the interactions and the higher the energy dissipation will be. The results of E_a, tan δ_max, and T_g of M0, M1, M2, and M3 are consistent with the results of E_binding and D_s of g0, g1, g2, and g3.

Table 5 E_a, T_g and tan δ_max of silica/SSBR

	Ea/(kJ mol^−1)	Tg/°C	tan δmax
Silica/M0	11.3	−5.9	1.07
Silica/M1	12.8	−3.9	1.11
Silica/M2	14.2	−2.7	1.19
Silica/M3	17.7	0.1	1.30

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3.4. T_g of silica/SSBR composites by MD simulation

As a rubber is cooled and turned into the glassy state, an abrupt change in its density ρ or specific volume v will occur at T_g.³⁷ Based on the change, we can use MD simulation to calculate the ρ as a function of temperature and then figure out T_g from the linear fits to the data. Fig. 5 shows the simulated T_gs of all SSBR systems. The T_g first increases, reaches a maximum for g4, and then decreases. The silica/g4 composite has the highest T_g of 256 K and the star-shaped structure has a higher T_g than the non-modified SSBR. As can be seen in Table 6, the variation of T_g with the g0, g1, g2, g3, and g4 systems exhibits the same trend as the variation of T_g with the M0, M1, M2, and M3 systems for DSC measurements.²

Fig. 5 Simulated T_gs of (a) silica/g0, (b) silica/g1, (c) silica/g2, (d) silica/g3, (e) silica/g4, (f) silica/g5, (g) silica/g6, and (h) silica/star-shaped SSBR.

Table 6 T_g of silica/SSBR composites by MD simulation and DSC measurements

MD simulation	Tg/K	DSC measurements	Tg/K
Silica/g0	241	Silica/M0	246.0
Silica/g1	245	Silica/M1	246.5
Silica/g2	248	Silica/M2	247.8
Silica/g3	253	Silica/M3	249.3
Silica/g4	256
Silica/g5	249
Silica/g6	247
Silica/star-shaped SSBR	251

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3.5. Silica dispersion in SSBR matrix

In MD simulation, the dispersion of filler can be analyzed by examining the radial distribution function g_AB(r).³⁸ The g_AB(r) gives a measure of the probability that, given the presence of an atom at the origin of an arbitrary reference frame, there will be an atom with its center located in a spherical shell of infinitesimal thickness at a distance r from the reference atom.³⁹ The g_AB(r) can be calculated by the average of the static relationship of every given pair of particles AB as follows:where 〈n_AB(r)〉 is the average number of atom pairs between r and r + Δr and ρ_AB is the density of atom pairs of type AB. Because the model of silica particle is centered on a silicon atom, the distribution of silica particles can be examined by calculating the g_Si–Si(r) between Si and Si located at the center of the silica particles. The g_Si–Si(r) results are presented in Fig. 6. The peak of g_Si–Si(r) gives the high probability for the distance between two atoms to fall within this range. The greater the abscissa value r of the peak indicates the greater the distance between silica particles and the better the dispersion. The r values of the peak of g_Si–Si(r) for all systems are listed in Table 7. The dispersion of silica increases gradually with increasing modifier content from 0 to 14.2 wt%, reaches a maximum at 14.2 wt%, and decreases with modifier content above 14.2 wt%. In addition, the dispersion of silica in star-shaped SSBR is better than in g2 but worse than in g3.

Fig. 6 Radial distribution function g_Si–Si(r) for Si and Si in silica/g0 composite.

Table 7 Abscissa r values of peak of g(r) for all systems

	g0	g1	g2	g3	g4	g5	g6	Star-shaped SSBR
r(Å)	13.7	14.1	14.8	15.5	15.7	15.0	14.3	15.0

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According to RPA, contact angle, and TEM measurements, our previous work² also found that the higher the modifier content is, the more homogeneous the silica dispersion and the narrower the particle size distribution will be. The thermodynamic parameters for filler–rubber adhesion W_rf and ΔW and the filler flocculation rate constant k_a from contact angle measurements are listed in Table 8, where W_rf is the adhesive energy between silica and rubber, and ΔW and k_a is the driving force for filler agglomeration. The value of W_rf increases and the values of ΔW and k_a decrease with increasing modifier content, indicating that the introduction of a modifier into the SSBR chains can increase the interactions between silica and rubber and improve the dispersion stability of silica.

Table 8 Thermodynamic parameters for filler–rubber adhesion and filler flocculation

Sample code	Wrf (mJ m^−2)	ΔW (mJ m^−2)	ka × 10^−3 (S^−1)
Silica/M0	51.2	13.0	3.98
Silica/M1	53.3	11.8	3.56
Silica/M2	55.8	8.1	3.12
Silica/M3	62.1	4.6	2.82

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3.6. Analysis of optimum modifier content

Through above mentioned analyses, we found that the modifier content has an optimum value of 14.2 wt%. In addition, by calculating the filler dispersion, filler–rubber interactions and T_gs, we obtained good agreements between the modeling results and the experimental results for modifier contents from 0 to 9.5 wt%. Though SSBR samples with higher modifier contents than 9.5 wt% have not been prepared at present, the good agreement for modifier contents from 0 to 9.5 wt% provides an experimental basis for further simulation at higher modifier contents.

In order to make it clear that the optimum modifier content is 14.2 wt%, we calculated the hydrogen bonds, interactions between SSBR chains, and g_Si–C(r) between Si located at the center of the silica particle and C in the backbone of SSBR.

Intermolecular interactions include hydrogen bonding and van der Waals forces. Hydrogen bonding, though weaker than chemical bonding, is the strongest physical force among intermolecular interactions. We can calculate the type and number of H-bonds by MD simulation.³⁴ Due to the 3-mercaptopropionic acid in SSBR chains and the hydroxyl groups on the surface of silica particles, three types of H-bonds can form in silica/SSBR composites. The first H-bond is between silica particles and modified SSBR chains. The second H-bond is between silica particles. The third H-bond is between modified SSBR chains. Here, we were only concerned on the first H-bond presented in Fig. 7, and Table 9 lists the number of H-bonds.

Fig. 7 H-bonds in amorphous cell of silica/SSBR (the black dotted lines represent H-bonds. Grey, red, yellow, green, and blue sticks stand for C, O, Si, H, and S atoms, respectively).

Table 9 Number of H-bonds in silica/SSBR composites

	Silica/g0	Silica/g1	Silica/g2	Silica/g3	Silica/g4	Silica/g5	Silica/g6
No. of H-bonds	0	0	1	3	4	4	4

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The g_Si–C(r) results are presented in Fig. 8. The peak of the g_Si–C(r) gives the high probability for the distance between silica particle and the backbone of SSBR to fall within this range. The greater the abscissa value r of the peak indicates the greater the distance between silica particle and the backbone of SSBR.

Fig. 8 Radial distribution function g_Si–C(r) for Si (silica) and C (SSBR) in silica/SSBR composites.

The interactions between SSBR chains (E_inter-SSBR) were determined as follows:

E_inter-SSBR = −(E_SSBR − E_SSBR1 − E_SSBR2) (5)

where E_SSBR1 and E_SSBR2 are the total energies of separate SSBR chains, and E_SSBR are the total energies of two SSBR chains. The E_inter-SSBR of various SSBR systems is listed in Table 10.

Table 10 E_inter-SSBR of various SSBR systems

	g0	g1	g2	g3	g4	g5	g6
Einter-SBR (kcal mol^−1)	−386.7	−200.7	−125.4	−2.0	114.9	372.9	501.8

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As modifier content increases, the number of hydrogen bonds first increases, reaches a maximum in silica/g4, and then stays constant. The maximum in the number of hydrogen bonds indicates the strongest interactions between modifier and silica particles. However, from the g_Si–C(r), we found that as modifier content increases, the backbone of SSBR is increasingly remote from the silica surface because of the steric hindrance of modifier, which leads to a decrease in interactions between backbone of SSBR and silica particle. In addition, the increase of E_inter-SBR also indicates closer chain packing. The competing effects of hydrogen bonds, steric hindrance of modifier and rubber–rubber interactions led to the existence of this optimum modifier content of 14.2 wt%.

4. Conclusions

Silica/SSBR composites with different modifier contents (0, 2.4, 4.2, and 9.5 wt%) were first constructed to investigate the filler dispersion and filler–rubber interactions. The introduction of the polar groups (3-mercaptopropionic acid) into SSBR chains can limit the chains motion, enhance the silica–SSBR interactions, and improve silica dispersion. The modeling results of g0, g1, g2, and g3 were in good agreement with the experimental results of M0, M1, M2, and M3. Further MD simulations of SSBR with higher modifier contents (14.2, 20.8, and 26.9 wt%) and star-shaped SSBR showed that the modifier content in SSBR has an optimum value (14.2 wt%) at which the strongest silica–SSBR interactions and the best silica dispersion are obtained. Therefore the SSBR with modifier content of 14.2 wt% is an optimum structure for silica filler. Additionally, from the perspective of binding energy and filler dispersion, the star-shaped SSBR is also a considerable structure. The present study is expected to provide significant insight into the relationships between the chemical structure of SSBR and silica dispersion as well as interactions. This insight provides a foundation for the preparation of high-performance silica/SSBR composites from the perspective of rational design of macromolecular structures.

Acknowledgements

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

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