Influence of various nanoparticle shapes on the interfacial chain mobility: a molecular dynamics simulation.

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Cite this: Phys. Chem. Chem. Phys., 2014, 16, 21372

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Influence of various nanoparticle shapes on the interfacial chain mobility: a molecular dynamics simulation† Yangyang Gao,a Jun Liu,*ab Jianxiang Shen,a Youping Wua and Liqun Zhang*ab To fully understand the polymer–filler interfacial interaction mechanism, we use a coarse-grained molecular dynamics simulation to mainly investigate the interfacial dynamic properties by tuning the polymer–filler interaction, temperature, chain length, volume fraction of filler, and size and shape of filler. The polymer beads around the filler exhibit an obvious layering behavior and a gradient of polymer dynamics is observed for systems filled with three kinds of fillers (spherical, rod-like and sheet-like). By analyzing the dynamics of the interfacial beads in the first adsorbed layer, we find that the mobility of interfacial beads becomes greater at lower polymer–filler interaction strength and higher temperature. The adsorption/desorption dynamics of interfacial beads decreases with the increase of the chain length, and then becomes nearly unchanged when the chain length exceeds the entanglement molecular weight. It is found that the influence of the different size of nanospheres on the mobility of interfacial beads is just induced by the curvature. However, for systems filled with nanorods and nanosheets, besides the curvature, the force exerted on the polymer beads also plays an important role. For systems filled with three kinds of fillers, the mobility of interfacial beads is the slowest for the nanosheet filled system and

Received 10th July 2014, Accepted 16th August 2014

only in this case the ‘‘glassy layer’’ exists for strongly attractive interfacial interaction. By comparing the

DOI: 10.1039/c4cp03019b

total force exerted on the polymer beads by the filler that determines the mobility of the interfacial beads.

dynamics of the adsorbed polymer beads for three different shapes of filler, it is concluded that it is the In short, this work could provide valuable information on the fundamental understanding of polymer–filler

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interfacial behavior, especially for systems filled with fillers of different shapes.

1. Introduction Polymer nanocomposites, that is, nanofillers (spheres, rods, plates) dispersed in an entangled matrix, have attracted substantial academic and industrial interest since the early 1990s.1–7 It is well recognized that the addition of nanofillers to polymers can result in materials that have significantly improved properties, such as rheological,8 optical,9 electrical,10,11 thermal,12,13 and mechanical properties.14,15 Polymer chains close to a filler surface often exhibited different characteristics compared to the bulk phase. To predict and control the properties of polymer nanocomposites (PNCS), it is essential to quantitatively characterize the structure and properties of the interfacial region. a

Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China b State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China. E-mail: [email protected], [email protected] † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c4cp03019b

21372 | Phys. Chem. Chem. Phys., 2014, 16, 21372--21382

In fact, some experimental and simulation research studies have been devoted to investigating this issue, but no consistent conclusions are obtained until now. For example, Kraus et al.16 found that the presence of filler does not alter appreciably the free volume in the rubbery state, and that segmental motion is little affected by the polymer–filler interaction. Roland et al.17 concluded that the glass transition and the local segmental dynamics of the chains adjacent to silica particles are basically the same as those of the unfilled system. They further pointed out that although some stiffening of the elastomer may exist in the vicinity of fillers, this effect does not translate into an appreciable effect on the segmental dynamics.18 Moreover, they claimed that the segmental dynamics and glass transition are hardly affected by the polymer–filler interaction. Meanwhile, they thought that the second transition observed by Tsagaropoulos and Eisenberg19,20 is ascribed to the terminal relaxation process (chain diffusion) of the uncross-linked polymer impeded by interaction with particles. In contrast to these viewpoints, by employing nuclear magnetic resonance (NMR) to investigate rubber–carbon black interactions, Kaufman et al.21 found that at least two distinct relaxation regions appeared for bound rubber, i.e., an immobile region

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and a relatively free region, which was also supported by results on the interfacial interactions between carbon black and cispolybutadiene through NMR.22 Chen et al.23 used dynamic mechanical analysis to reveal the existence of double tan d peaks from the glass transition of bulk poly(vinyl alcohol) and an interfacial immobilized layer. For styrene-butadiene rubber containing silica filler, a second relaxation of the tan d spectra of the composites is also detected, whose intensity increases with the filler content.24 Berriot et al.25 also found that a glass transition temperature gradient exists in the vicinity of the particles, which is further used to explain the nonlinear viscoelastic behavior in reinforced elastomers26 and supported the existence of the immobilized layer.27 Furthermore, a model based on the presence of glassy layers around the fillers is developed. It suggests that strong reinforcement will be obtained when glassy layers between fillers overlap.28 The results by Brown et al.29 indicated that the size of nanoparticles has no influence on the interphase thickness for the range of particle sizes examined. Polymer conformation and dynamics in the immediate vicinity of the interface were strongly influenced by nanoparticles30–35 and grafted polymer chains.36,37 There was a gradual change of polymer dynamics when approaching the nanoparticle surface, which can be illustrated through a ‘‘many-layer’’ dynamics model.38 By employing the molecular

Uij ðrÞ ¼

" 8 > > < 4eij > > :

s r rEV

12

s r rEV

0

dynamics simulation, it was found that polymer chain diffusivity is enhanced relative to its bulk value, when polymer–particle interactions are repulsive.39,40 However, when polymer–particle interactions are attractive,39–43 the dynamics of the interfacial polymers are strongly perturbed by the nanoparticles,38,40,44,45 so that the diffusivity of entangled polymers is reduced. The role of attractive interactions in polymer chain dynamics was explored further,43,46 showing that a weak attraction with spherical nanoparticles does not influence the chain diffusivity. Instead, above a critical value of energy gained during attraction, the chain diffusivity gradually decreases to zero.43 The effect of nanosheet filler (for example graphene) on the mobility of polymer was also explored.47 Recently, Liu et al.48 also presented an overview of the process in the investigation of the static, rheological and mechanical properties of polymer nanocomposites studied by computer modeling and simulation. Most of the aforementioned studies are focused on the effect of spherical nanoparticles on the mobility of polymer. It is recognized36,49,50 that the polymer dynamics is strongly influenced by the characteristics of nanofiller (e.g., size, shape, aspect ratio, type of nanofiller surface) and polymer (e.g., molecular weight, structure, nature of the interaction between the nanofiller and the polymer matrix). Meanwhile, from the experimental aspect, no consistent conclusion has been obtained about the polymer–filler interfacial behavior. Especially it is very important to make clear the intriguing and


controversial issue of whether ‘‘glassy layers’’ exist surrounding the filler or not. Therefore, the main goal of our work is to address this issue by systematically tuning the polymer–filler interaction, temperature, chain length and volume fraction of nanofiller for systems filled with fillers of different sizes and shapes, which we think is the most significant difference from other simulation work.

2. Models and simulation methods Each polymer chain is represented by using a bead-spring model developed by Kremer and Grest.51 In our simulation, the idealized polymer model consists of one hundred beads with the bead diameter equal to s. The total number of simulated polymer beads is 24 000 in all systems. Although these chains are rather short, they already show the static and dynamic behavior characteristic of long polymer chains. In our systems we use three kinds of fillers with different shapes (nanosphere, nanorod and nanosheet). The mass of the polymer bead is equal to m and the density of the filler is the same as that of polymer. Similar to the literature,52,53 here we used the modified LJ interaction to model the polymer–polymer, polymer–filler, and filler–filler interactions, as follows: 6 # U ðrcutoff Þ;

0 o r rEV o rcutoff

(1)

r rEV rcutoff where rcutoff stands for the distance (r rEV) at which the interaction is truncated and shifted so that the energy and force are zero. Here we offset the interaction range by rEV to account for the excluded volume effects of different interaction sites. For polymer–nanosphere and nanosphere–nanosphere interactions, rEV is Rn s/2 and 2Rn s, respectively (Rn is the radius of the nanosphere), and for the other pairs of interactions, rEV becomes zero. The polymer–polymer interaction parameter and its cutoff distance are epp = 1.0 and rcutoff = 2 21/6, and the filler–filler interaction parameter and its cutoff distance are enn = 1.0 and rcutoff = 21/6, while the polymer–filler interaction strength enp and its cutoff distance rcutoff are changed to simulate different interfacial interaction strengths and ranges. For better characterizing the interfacial behavior between polymer and filler, the filler is immobilized when the number of nanofiller is just one. At the same time, the nanofiller could move as a function of time when we investigated the systems with high filler loading. Additionally, the interaction between the adjacent bonded monomers is represented by a stiff finite extensible nonlinear elastic (FENE) potential: " 2 # r VFENE ¼ 0:5kR02 ln 1 (2) R0 e where k ¼ 30 2 and R0 = 1.5s, guaranteeing a certain stiffness of the s bonds while avoiding high-frequency modes and chain crossing.

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Since it is not our aim to study a specific polymer, we used the LJ units where e and s are set to unity. It means that all calculated quantities are dimensionless. To generate the initial configurations, we placed the polymer chains and fillers in a box to keep the number density of polymers around r* = 0.85, which corresponds to a dense molten state. Periodic boundary conditions are employed in all three directions. The velocityVerlet algorithm is used to integrate the equations of motion, with a time step dt = 0.001, where the time is reduced by LJ time (t). The NVT ensemble is adopted, where the temperature is fixed at T* = 1.0 by using the Nose–Hoover temperature thermostat. All structures were equilibrated over a long time so that each chain has moved at least 2Rg (Rg is referred to as the root-mean-square radius of gyration). All MD runs were carried out by using the large scale atomic/molecular massively parallel simulator (LAMMPS) developed by Sandia National Laboratories.54

3. Results and discussion Here our main goal is to investigate how the shape and size of fillers influence the mobility of the interfacial polymer. So we explore this issue by tuning polymer–filler interaction, temperature, chain length, filler size and volume fraction of fillers in the systems filled with three kinds of fillers. 3.1.

Nanosphere

For a better understanding, seven different systems are examined as shown in Table 1. The diameter of the nanosphere is 4s. Firstly, the density profiles of polymer beads around the nanosphere are plotted in Fig. 1 for several interfacial strengths, which have been normalized by the bulk density. It is observed that polymer chains are distributed in four interfacial layers, which are denoted as L1, L2, L3, and L4. Repulsive nanospheres induce a weaker layering of polymer beads. In the case of the

Table 1 Parameters of each simulated system: polymer–nanoparticle interaction strength enp, the cutoff distance represented by rcutoff and simulation temperature T*

System

Filler

Glassy system I II III IV V VI VII (1) (2) (3) (4) (5) (6) (a) (b) (c) (d) (e) (f)

No Nanosphere Nanosphere Nanosphere Nanosphere Nanosphere Nanosphere Nanosphere Nanorod Nanorod Nanorod Nanorod Nanorod Nanorod Nanosheet Nanosheet Nanosheet Nanosheet Nanosheet Nanosheet

enp 1.0 1.0 2.0 3.0 5.0 8.0 10.0 1.0 1.0 2.0 3.0 5.0 10.0 1.0 1.0 2.0 3.0 5.0 10.0

rcutoff

T*

1.12 2.5 2.5 2.5 2.5 2.5 2.5 1.12 2.5 2.5 2.5 2.5 2.5 1.12 2.5 2.5 2.5 2.5 2.5

0.3 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0


Fig. 1 Density profiles of polymer beads around the nanosphere for various interfacial strengths.

full LJ potential, the layering is enhanced due to the attractive part of the potential. So layering close to the filler strongly depends on the interfacial interaction. The width of the L1 layer is around 1.0s in our systems. In fact, the width of the L1 layer is the same for other systems. Next, we mainly study the dynamics of interfacial beads in the L1 layer for different interactions and temperatures. To explore the mobility of the interfacial beads, we calculated the mean-square displacement (MSD) for a short time of 50t. For better comparison, the MSD of the beads normalized by that of bulk beads is used to stand for the mobility for different distances from the center of filler, which is plotted in Fig. 2(a) for different interfacial interactions. It can be found that the chain mobility decreases in the vicinity of the nanosphere for strongly attractive cases (epn = 5.0, 8.0 and epn = 10.0), while it is nearly unchanged for the weakly attractive case (II). The mobility of interfacial beads increases for the purely repulsive case. This indicates that there is a mobility transition region from the bulk to the interface, but the mobility of interfacial beads is still maintained even at high interaction strength epn = 10. Fig. 2(b) shows the mean square displacement (MSD) of the interfacial beads in the L1 layer and glassy polymer beads. It can be found that the mobility of the beads in the L1 layer is hindered, which is attributed to the nanoscale confinement and interfacial interaction. The polymer beads in the glassy layer are almost completely immobilized and the MSD is almost zero. In comparison with the glassy state, the interfacial beads still maintain some mobility, and undergo the adsorption–desorption process, even in the case of strongly attractive interaction. To gain insight into the effect of the nanosphere surface on the polymer dynamical behavior, the local orientation mobility of polymers located in different layers has been characterized through the autocorrelation function (ACF): P1(t) = hcos(y(t))i

(3)

where y(t) is the angle between the bond vector at time t and the vector at time t = 0, and the bond vector is referred to as the vector between two connected beads in the polymer chains. The effect of the interfacial interaction on the bond orientation dynamics has been analyzed in the L1 layer as shown in Fig. S2(a) (ESI†) and in different layers defined above for the


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Fig. 2 (a) Mobility of the polymer beads as a function of distance from the center of the nanosphere for different polymer–nanosphere interactions. (b) Mean square displacement (MSD) averaged for polymer beads in the L1 region. For comparison, the MSD of polymer beads in the glassy state (T o Tg) is also shown.

case of epn = 10 in Fig. S2(b) (ESI†). The bond dynamics in the L1 layer gradually decreases with the increase of interfacial strength. From Fig. S2(b) (ESI†), the bond dynamics gradually becomes slower when approaching the nanosphere surface. However, the polymer beads in the L1 layer can still move. The characteristic relaxation time is obtained when the value of P1(t) decays to 0.5. Fig. S2(c) and (d) (ESI†) shows the change of the characteristic relaxation time as a function of interaction strength between the polymer and nanosphere and various layers. Then we explored the intrinsic dynamics of the population of the interfacial polymer beads. This population is continually exchanging beads with the rest of the polymer melt. To characterize the dynamics, we calculated the correlation functions, given by Gbead(t) = hnL1-layer(t)/nL1-layer(0)i

(4)

in which nL1-layer(t) is the number of polymer beads in the first layer at time t. In particular, we are interested in the evolution of beads in the L1 layer. First, the beads are labeled when they are in the L1 layer at t = 0. The label is removed if the beads leave the surface at time t. Thus, Gbead(t) is a measure of the fraction which have not left the surface at time t, which describes the adsorption/desorption kinetics. The effect of the interfacial interaction on the adsorption/ desorption dynamics of the interfacial beads has been analyzed in Fig. 3(a). For weak interfacial interaction, the beads can


Fig. 3 Decay of Gbead(t) (a) for different polymer–nanosphere interaction strengths and (b) for different temperatures at epn = 10.0.

easily desorb from the nanosphere surface, while the dynamics shows a decreasing trend with increasing interaction. However, the beads in the L1 layer could move even in the strongest attractive case of epn = 10, which indicates that the beads in the L1 layer are not immobilized and the ‘‘glassy layer’’ does not exist near the nanosphere. At the same time, temperature is also a very important factor which influences the mobility of interfacial beads. The adsorption/desorption rate of interfacial beads increases with the increase of temperature (Fig. 3(b)) in the case of epn = 10. It can be understood that as temperature goes up, the mobility of interfacial beads increases, which leads to the increase of the adsorption/desorption rate. To quantify the interaction strength and temperature effects, we define an adsorption/desorption characteristic time, represented by t0.5, which is equal to the time when 50% of the initially adsorbed beads leave the surface. We have plotted the logarithm of the inverse of t0.5 as a function of interfacial strength and the inverse of temperature in Fig. S3(a) and (b) (ESI†). With the increase of the interfacial strength, the adsorption/desorption rate quickly decreases and an approximate linear relationship is observed in Fig. S3(b) (ESI†), suggesting that the adsorption– desorption process is sensitive to the interfacial strength and temperature. The chain length is also a very important factor which affects the mobility of interfacial beads because high molecular length can induce entanglements. Grest and Kremer51 found that the entanglement length (Ne) is approximately 35 beads for polymer chains described by the bead-spring model. However, to become entangled, their chain length should exceed a critical length (Nc) that is larger than Ne because at least the


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Fig. 4 Decay of Gbead(t) (a) for different chain lengths and (b) for different diameters of nanosphere in the case of epn = 3.0.

first and the last few monomers of each chain are invalid to ¨ger et al.55 entangle with each other. Using the same model, Kro performed NEMD simulations to study the rheology and structural changes of polymer melts under shear flow. It was found that Nc = 100 for the polymer chain is in accordance with the entanglement length determined by Grest and Kremer.51 At present, a better estimate of the critical chain entanglement length Ne is 75.56 Thus, herein we changed the polymer chain length from N = 10 to 400 so as to cover the crossover from the unentangled to the entangled regime. From the adsorption/ desorption dynamics in Fig. 4(a) (epn = 3), the rate decreases with the increase of chain length from 10 to 60, while the rate is almost the same when we further increased the chain length. It indicates that the entanglement will reduce the adsorption/ desorption rate. The conclusion is the same for the system with epn = 10, which is not shown here. The diameter of the nanosphere has an effect on the mobility of interfacial polymers because of different curvatures. Some snapshots of the initial state are shown in Fig. S1(a) (ESI†). The effect of nanosphere diameter on the adsorption/desorption dynamics of interfacial beads has been analyzed in Fig. 4(b) (epn = 3.0). With the decrease of nanosphere diameter, the adsorption/desorption rate becomes faster, and the difference is very evident for small nanospheres (diameter = 1s). The reason should be related to different curvatures. In practical applications, a high volume fraction of nanofiller is always used to effectively reinforce the rubber, so we investigate such a system with a high volume fraction and explore the dynamics of interfacial polymer beads. We introduce 96 nanospheres of diameter = 4s into the polymer matrix, corresponding


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Fig. 5 Decay of Gbead(t) (a) for different polymer–nanosphere interaction strengths and (b) for different chain lengths in the case of epn = 3.0 for the system filled with a high volume fraction of nanospheres.

to the filler volume fraction around 10%. Fig. S4(a) (ESI†) shows the snapshots of one system (epn = 2.0). The adsorption/ desorption dynamics is shown in Fig. 5(a). It decreases with the increase of interfacial interaction. However, some differences appear. For example, compared with the rate for the system with just one nanosphere, the adsorption/desorption rate is slower for the system with a high filler loading in the case of epn = 10.0. However, at a high filler loading the rate is faster for the repulsive case (I). The underlying reason could be explained as follows: for the many-particle system, the nanospheres will aggregate directly or become aggregated via polymer chains, which is dependent on the interfacial interaction.57 Thus, the chains will be influenced by multiple neighboring nanospheres. The effect of chain length on the adsorption/ desorption dynamics is also shown in Fig. 5(b) for systems with a high nanosphere loading (epn = 3.0). In general, a ‘‘glassy layer’’ does not appear even for strongly attractive interaction in the case of nanospheres.

3.2.

Nanorod

Similar to the above case, six different systems are examined as shown in Table 1. The bead number of each nanorod is 30 and the diameter of each bead is 1s. Here our main purpose is to compare the different effects of filler size and shape on the dynamics of interfacial beads. We focus on discussing the mean square displacement and the adsorption/desorption dynamics of the interfacial beads. The density of polymer beads around the nanorod for different interfacial interactions is


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shown in Fig. S5 (ESI†), indicating that the width of the L1 layer was also around 1s. Next the mobility of polymer beads defined above is depicted for different interfacial strengths in Fig. S6(a) (ESI†). The result is similar to that for systems filled with nanospheres. However, when we compare the results of two systems filled with nanospheres and nanorods, the mobility of beads nearby the nanorod is much slower. For example, in the case of epn = 10.0, the mobility of polymer beads near the nanosphere is 0.251, while it is 0.0344 near the nanorod, indicating that the shape of the filler has an effect on the mobility of polymer beads. The mean square displacement (MSD) of the interfacial beads in the L1 layer and glassy polymer beads is shown in Fig. S6(b) (ESI†). It can be understood that the mobility of the polymer beads in the L1 layer is significantly hindered especially in the case of epn = 10.0. However, even in the case of epn = 10.0, the mobility of interfacial beads is still faster than that of glassy polymer beads, which can undergo the adsorption–desorption process. Then the adsorption/desorption dynamics of interfacial beads is analyzed for different interactions as shown in Fig. 6(a). With the increase of the interfacial strength, the rate decreases. However, the rate does not completely cease even in the case of epn = 10. From Fig. S7 (ESI†), as temperature goes up, the adsorption/desorption rate of interfacial beads increases due to high thermal Brownian motion. The adsorption/desorption dynamics for different chain lengths is shown in Fig. S8 (ESI†) (epn = 3). It decreases when the chain length varies from 10 to 60, while the rate is almost the same with longer chain length. This result is consistent with that for the system filled with the nanosphere.

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Fig. 7 Decay of Gbead(t) for different polymer–nanorod interaction strengths for the system filled with a high volume fraction of nanorods.

Here we also investigate the effect of the aspect ratio of the nanorod on the mobility of interfacial beads. Some snapshots of initial states are shown in Fig. S1(b) (ESI†). The results are shown in Fig. 6(b) in the case of epn = 3.0. With the increase of the aspect ratio, the adsorption/desorption rate becomes slower. It indicates that the nanorod with a larger aspect ratio inhibits the mobility of interfacial beads. This effect is induced by not only the shape of the nanorod but also the different force which the nanorod exerts on the interfacial beads. Lastly we turn to examine the effect of volume faction on the mobility of the interfacial beads. The number of nanorods with the aspect ratio equal to 5 is 1200, corresponding to the filler volume fraction around 10%. In this case, an additional angle potential is added for the nanorod.52 Fig. S4(b) (ESI†) shows the snapshots of one system (epn = 2.0). The adsorption/desorption dynamics is shown in Fig. 7. The adsorption/desorption rate significantly decreases with the increase of interfacial interaction. Similar to the above results, compared with the rate for the system with just one nanorod, the adsorption/desorption rate is slower for the system with a high nanorod loading in the case of epn = 3.0. Especially, the rate is very low in the case of epn = 10.0 because of the effect of many nanorods. The effect of chain length on the adsorption/desorption dynamics is similar to that for systems with just one nanorod, which is not shown here. In general, a ‘‘glassy layer’’ still does not appear for strongly attractive interaction for the system with just one nanorod. However, for the system with a large nanorod loading, the interfacial layer is similar to the ‘‘glassy layer’’ because of the effect of many nanorods. 3.3.

Fig. 6 Decay of Gbead(t) (a) for different polymer–nanorod interaction strengths and (b) for different aspect ratios of nanorod in the case of epn = 3.0.


Nanosheet

In this section, we turn to the system filled with the nanosheet. Six different systems are examined as shown in Table 1. The nanosheet is 30 30 and the diameter of nanosheet beads is 1s. From the density profiles shown in Fig. S9 (ESI†), the width of the L1 layer is also around 1s. It is worth noting that five layers are formed near the nanosheet surface while only four layers appear near the nanosphere or nanorod. It indicates that more polymer layers are adsorbed nearby the nanosheet. Next, we focus on the mobility of polymer beads in the L1 layer for different interfacial strengths and temperatures.


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For these systems, the trend in change of the mobility is the same as for the above two cases as a function of interfacial strength (Fig. S10(a), ESI†). However for the case of epn = 10.0, the mobility of interfacial beads completely ceases, which indicates that the ‘‘glassy layer’’ exists near the nanosheet surface. Obviously, the nanosheet exerts a strong confinement on the mobility of interfacial beads. The mean square displacement (MSD) of the beads in the L1 layer and glassy beads is shown in Fig. S10(b) (ESI†). When the interfacial strength is epn = 5.0 and 10.0, the mobility of the interfacial beads is lower than that of glassy polymer beads. Accordingly, we believe that the ‘‘glassy layer’’ can be formed near the nanosheet for strongly attractive interaction. Then the intrinsic dynamics of the population of interfacial beads in the L1 layer is calculated. From Fig. 8(a), with the increase of the interfacial strength, the rate decreases. For the case of epn = 1.0, the beads can desorb from the nanosheet surface, while the beads in the L1 layer almost do not move for the case of epn = 10.0, resulting in the value of G(t) nearly equal to 1, which reconfirms that the beads adsorbed in the L1 layer are fully immobilized. High temperature can improve the mobility of the interfacial glassy beads due to the high thermal Brownian motion. From Fig. S11 (ESI†), the adsorption/ desorption rate is nearly zero if the temperature is lower than 2.5. When the temperature further increases, the interfacial beads begin to desorb from the nanosheet surface. Meanwhile for the case of both epn = 3.0 and epn = 10.0, the adsorption/desorption rates are low. So we investigated the effect of chain length on the dynamics in the case of epn = 1.0 which is shown in Fig. S12 (ESI†). The result is consistent with the above result. Here we continue to investigate the effect of filler size on the mobility of interfacial beads for the case of epn = 3.0. Some snapshots of initial states are

Fig. 8 Decay of Gbead(t) (a) for different polymer–nanosheet interaction strengths and (b) for different sizes of nanosheet in the case of epn = 3.0.


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Fig. 9 Decay of Gbead(t) for different polymer–nanosheet interaction strengths for the system filled with a high volume fraction of nanosheets.

shown in Fig. S1(c) (ESI†). From Fig. 8(b), the result is also similar to that presented above. The reason is related to the shape of nanosheet and the force, which will be discussed later. Lastly we turn to the effect of volume faction on the mobility of the interfacial beads. The number of nanosheets with 5 5 is 1200 in the systems, corresponding to the filler volume fraction around 10%. In this case, two additional angle potentials are added for the nanosheet.58 Fig. S4(c) (ESI†) shows the snapshots of one system (epn = 2.0). The adsorption/desorption dynamics is shown in Fig. 9. The conclusion is similar to that presented above. In general, the ‘‘glassy layer’’ appears for strongly attractive interaction. 3.4. Comparison of three cases (nanosphere, nanorod, nanosheet) First, we establish our simulation systems with experimental systems. When mapping the coarse-grained model to real polymers, the interaction parameter e is set to be about 2.5– 4.0 kJ mol1 for different polymers,51 indicating that the value of 10 (in units of e) for the polymer–filler interaction is about 25–40 kJ mol1. It has been reported that the interaction strengths of saturated hydrocarbon elastomers with the adsorption sites on the silica surfaces can vary from 27 to 35 kJ mol1, which are mainly attributed to van der Waals force.59 Hence, the simulated interfacial interaction strength is within realistic ranges according to those experimental examinations. For systems filled with three kinds of fillers, we compare the mean square displacement (MSD) and intrinsic dynamics of the population of interfacial beads in the L1 layer in Fig. 10(a) and (b). We found that the nanosheet exerts the strongest confinement on the mobility of interfacial polymer beads and the nanosphere produces the weakest confinement on the mobility. The snapshots give a better intuitive understanding in Fig. S13 (ESI†). Then we calculated the total force exerted on the interfacial polymer beads by the filler. The result is shown in Fig. 11. The distance from the beads position and the filler center is defined as shown in Fig. S14 (ESI†). From Fig. 11, we find that the interfacial beads are adsorbed by the nanosheet strongly, because the force is the greatest. The nanosphere exerts the smallest force on the interfacial polymer beads. So this is the reason why the filler shape leads to different mobility


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Fig. 10 (a) Mean square displacement (MSD) averaged for polymer beads in the L1 region and (b) decay of Gbead(t) for three systems filled with the nanosphere, nanorod and nanosheet in the case of epn = 10.0.

Fig. 11 The total force exerted on the interfacial beads by fillers as a function of distance from the filler center.

of interfacial beads. When the distance between the polymer bead and the nanosphere surface is the same, the force exerted on the polymer bead is exactly the same. So the effect of nanosphere diameter on the interfacial bead mobility is just induced by different curvature. On the other hand, for the systems filled with nanorods and nanosheets, the force also plays a role. For example, for the aspect ratio of nanorod equal to 10, the force exerted on the polymer beads in the L1 layer is different depending on the position of polymer beads. From Fig. S15(a) (ESI†), the blue bead and yellow bead are all near the nanorod, but the force exerted on the blue bead is higher than that exerted on the yellow bead. This is because there are more nanorod beads exerting force on the blue bead. Hence, the mobility of the blue bead is slower than that of the yellow bead.


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So when the aspect ratio of nanorod decreases, the ratio of interfacial beads like blue beads and total interfacial beads decreases, and therefore the mobility of interfacial beads increases. The reason is the same for the system filled with the nanosheet in Fig. S15(b) (ESI†). For a better understanding, for example, for the aspect ratio of nanorod equal to 10 and size of the nanosheet 10 10, the adsorption/desorption rate of the interfacial beads on the edge of filler like yellow bead was faster than that on the center of filler like blue bead from Fig. S16(a) (ESI†), which agrees with our analysis. The snapshots further confirm the results in Fig. S16(b) (ESI†). Now we can understand why the mobility of beads decreases with the increase of the size of nanosheet. In fact, for the system filled with a high filler loading, the force exerted on the polymer beads in the L1 layer is larger than that for the system with just one filler because of the effect of many particles. So the mobility of interfacial beads in the L1 layer decreases. In total, it is the force which is exerted on the polymer beads by the filler that determines the mobility of the interfacial polymer beads. It also determines whether the ‘‘glassy layer’’ in the proximity of the filler exists or not. Thus by using the common measure t0.5 (the adsorption/desorption characteristic time), we can obtain three ‘‘equivalent’’ systems, namely nearly the same t0.5 if we tuned the parameters (interfacial interaction, chain length, size of filler, volume fraction and temperature). From Fig. S17(a) (ESI†), t0.5 is nearly the same for three different systems although the curves do not completely collapse. In addition, the values of the t0.5 of the two different systems approach to be equal as shown in Fig. S17(b)(ESI†). The adsorption/desorption rate is dependent on the mobility of beads (which is affected by the temperature) and the confinement introduced by the nanoparticles (which is affected by the interfacial interaction, chain length, size of filler nanoparticle, volume fraction and so on). We can tune these parameters to get similar mobility of interfacial beads for different systems. From Fig. S18 (ESI†), the effect of various parameters on the mobility of interfacial beads is the greatest for systems filled with the nanosheet and the lowest for systems filled with the nanosphere. Lastly, we compared our results with the work carried out by Li et al.60,61 The graphene sheet has the strongest interaction with the polyethylene (PE) matrix and the interaction between nanodiamonds (ND) and their PE matrix is the smallest due to their truncated octahedron shape. Both the interaction energy and polymer chain packing follow the same trend of the surfacearea-to-volume ratio of filler. The PE/graphene and PE/Xjunction have the largest bulk entanglement density, while PE/ND has the smallest. This result is consistent with our observation that the nanosheet-like filler exerts the greatest force on the interfacial beads. Meanwhile, there exists a critical volume fraction fc equal to 31%. When below fc, the polymer chain relaxation accelerates upon filling, while above fc, the situation reverses: polymer dynamics becomes geometrically constrained upon adding nanoparticles (NP). In our work, we just use one system with the filler volume fraction around 10%. The mobility of interfacial polymer beads accelerates or slows down which is dependent on the interfacial strength. Meanwhile, they also found that the attractive polymer–NP interaction slows down the relaxation,


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while the non-attractive polymer–NP interaction leads to an increased rate of relaxation. This is also consistent with our findings.


4. Conclusions By changing the polymer–filler interaction, temperature, chain length, volume fraction of filler and size and shape of filler, we use MD simulation to systematically investigate dynamic properties of the interfacial polymer melts for systems filled with three kinds of fillers (nanosphere, nanorod and nanosheet). The beaddensity profiles near the filler surface show that the polymer beads exhibit an obvious layering behavior, which depends on the polymer–filler interaction and filler shape. For the dynamic analysis, the mobility gradient of polymer beads is clearly observed for different polymer–filler interactions and different filler shapes. By analyzing the mean square displacement (MSD) and adsorption/desorption dynamics of the interfacial beads in the L1 layer, we find that the mobility of the interfacial polymer increases with decreasing interfacial interaction and increasing temperature. The adsorption/desorption dynamics of interfacial beads will decrease with increasing chain length and then nearly does not change when the chain length exceeds the entanglement molecular weight. The mobility of interfacial beads increases with the decrease of filler size. It is found that the influence of the different size of nanospheres on the mobility of interfacial polymer beads is just induced by curvature. However, for systems filled with nanorods and nanosheets, besides the curvature, the force exerted on the polymer beads by the filler also plays an important role. Meanwhile the mobility of interfacial polymer beads is the slowest for the nanosheet filled system and only in this case the ‘‘glassy layer’’ exists for strongly attractive interfacial interaction. The mobility of the interfacial beads will be slower for systems with high filler loading compared to that for systems with just one filler because of the effect of many particles. It is the total force which is exerted on the polymer beads by the filler that determines the mobility of the interfacial polymer beads. The results obtained here could provide some insights into the polymer–filler interfacial behavior, especially for systems filled with fillers of different shapes.

Acknowledgements This work is supported by the National Natural Science Foundation of China (51333004 and 21274011), the National High Technology Research and Development Program of China (863 Program) (2009AA03Z338), the Foundation for Innovative Research Groups of the NSF of China (51221002), and the National Basic Research Program (2011CB706900) and the ‘‘Chemical Grid Project’’ and Excellent Talents Funding of BUCT.

References 1 R. Krishnamoorti and R. A. Vaia, Polymer nanocomposites, J. Polym. Sci., Part B: Polym. Phys., 2007, 45(24), 3252–3256.


Paper

2 M. Maiti, M. Bhattacharya and A. K. Bhowmick, Elastomer Nanocomposites, Rubber Chem. Technol., 2008, 81(3), 384–469. 3 M. Moniruzzaman and K. I. Winey, Polymer nanocomposites containing carbon nanotubes, Macromolecules, 2006, 39(16), 5194–5205. 4 D. R. Paul and L. M. Robeson, Polymer nanotechnology: Nanocomposites, Polymer, 2008, 49(15), 3187–3204. 5 L. Schadler, Nanocomposites – Model interfaces, Nat. Mater., 2007, 6(4), 257–258. 6 Z. H. Wang, J. Liu, S. Z. Wu, W. C. Wang and L. Q. Zhang, Novel percolation phenomena and mechanism of strengthening elastomers by nanofillers, Phys. Chem. Chem. Phys., 2010, 12(12), 3014–3030. 7 L. Zhang, Y. Wang, Y. Wang, Y. Sui and D. Yu, Morphology and mechanical properties of clay/styrene-butadiene rubber nanocomposites, J. Appl. Polym. Sci., 2000, 78(11), 1873–1878. 8 M. E. Mackay, T. T. Dao, A. Tuteja, D. L. Ho, B. Van Horn, H. C. Kim and C. J. Hawker, Nanoscale effects leading to non-Einstein-like decrease in viscosity, Nat. Mater., 2003, 2(11), 762–766. 9 W. Caseri, Nanocomposites of polymers and metals or semiconductors: Historical background and optical properties, Macromol. Rapid Commun., 2000, 21(11), 705–722. 10 G. Polizos, E. Tuncer, A. L. Agapov, D. Stevens, A. P. Sokolov, M. K. Kidder, J. D. Jacobs, H. Koerner, R. A. Vaia, K. L. More and I. Sauers, Effect of polymer-nanoparticle interactions on the glass transition dynamics and the conductivity mechanism in polyurethane titanium dioxide nanocomposites, Polymer, 2012, 53(2), 595–603. 11 V. V. Zuev and Y. G. Ivanova, Mechanical and electrical properties of polyamide-6-based nanocomposites reinforced by fulleroid fillers, Polym. Eng. Sci., 2012, 52(6), 1206–1211. 12 C. Y. Jiang, S. Markutsya, Y. Pikus and V. V. Tsukruk, Freely suspended nanocomposite membranes as highly sensitive sensors, Nat. Mater., 2004, 3(10), 721–728. 13 J. Zhu, F. M. Uhl, A. B. Morgan and C. A. Wilkie, Studies on the mechanism by which the formation of nanocomposites enhances thermal stability, Chem. Mater., 2001, 13(12), 4649–4654. 14 V. M. Boucher, D. Cangialosi, A. Alegria, J. Colmenero, I. Pastoriza-Santos and L. M. Liz-Marzan, Physical aging of polystyrene/gold nanocomposites and its relation to the calorimetric T-g depression, Soft Matter, 2011, 7(7), 3607–3620. 15 S. P. Delcambre, R. A. Riggleman, J. J. de Pablo and P. F. Nealey, Mechanical properties of antiplasticized polymer nanostructures, Soft Matter, 2010, 6(11), 2475–2483. 16 G. Kraus and J. T. Gruver, Thermal expansion, free volume, and molecular mobility in a carbon black-filled elastomer, J. Polym. Sci., Part A-2, 1970, 8(4), 571–581. 17 R. B. Bogoslovov, C. M. Roland, A. R. Ellis, A. M. Randall and C. G. Robertson, Effect of silica nanoparticles on the local segmental dynamics in poly(vinyl acetate), Macromolecules, 2008, 41(4), 1289–1296. 18 C. G. Robertson, C. J. Lin, M. Rackaitis and C. M. Roland, Influence of particle size and polymer-filler coupling on


View Article Online

Paper


19

20

21

22

23

24

25

26

27

28

29

30

31

32

viscoelastic glass transition of particle-reinforced polymers, Macromolecules, 2008, 41(7), 2727–2731. G. Tsagaropoulos and A. Eisenberg, Dynamic Mechanical Study of the Factors Affecting the Two Glass Transition Behavior of Filled Polymers. Similarities and Differences with Random Ionomers, Macromolecules, 1995, 28(18), 6067–6077. G. Tsagaropoulos and A. Eisenburg, Direct observation of two glass transitions in silica-filled polymers. Implications to the morphology of random ionomers, Macromolecules, 1995, 28(1), 396–398. S. Kaufman, W. P. Slichter and D. D. Davis, Nuclear magnetic resonance study of rubber–carbon black interactions, J. Polym. Sci., Part A-2, 1971, 9(5), 829–839. J. O’Brien, E. Cashell, G. E. Wardell and V. J. McBrierty, An NMR Investigation of the Interaction between Carbon Black and cis-Polybutadiene, Macromolecules, 1976, 9(4), 653–660. L. Chen, K. Zheng, X. Tian, K. Hu, R. Wang, C. Liu, Y. Li and P. Cui, Double Glass Transitions and Interfacial Immobilized Layer in in-Situ-Synthesized Poly(vinyl alcohol)/Silica Nanocomposites, Macromolecules, 2009, 43(2), 1076–1082. V. Arrighi, I. J. McEwen, H. Qian and M. B. S. Prieto, The glass transition and interfacial layer in styrene-butadiene rubber containing silica nanofiller, Polymer, 2003, 44(20), 6259–6266. J. Berriot, H. Montes, F. Lequeux, D. Long and P. Sotta, Evidence for the Shift of the Glass Transition near the Particles in Silica-Filled Elastomers, Macromolecules, 2002, 35(26), 9756–9762. H. Montes, F. Lequeux and J. Berriot, Influence of the Glass Transition Temperature Gradient on the Nonlinear Viscoelastic Behavior in Reinforced Elastomers, Macromolecules, 2003, 36(21), 8107–8118. A. Papon, H. Montes, M. Hanafi, F. Lequeux, L. Guy and K. Saalwachter, Glass-Transition Temperature Gradient in Nanocomposites: Evidence from Nuclear Magnetic Resonance and Differential Scanning Calorimetry, Phys. Rev. Lett., 2012, 108(6), 065702. S. Merabia, P. Sotta and D. R. Long, A Microscopic Model for the Reinforcement and the Nonlinear Behavior of Filled Elastomers and Thermoplastic Elastomers (Payne and Mullins Effects), Macromolecules, 2008, 41(21), 8252–8266. ´le ´ and N. D. Albe ´rola, Effect of D. Brown, V. Marcadon, P. Me Filler Particle Size on the Properties of Model Nanocomposites, Macromolecules, 2008, 41(4), 1499–1511. D. Barbier, D. Brown, A.-C. Grillet and S. Neyertz, Interface between End-Functionalized PEO Oligomers and a Silica Nanoparticle Studied by Molecular Dynamics Simulations, Macromolecules, 2004, 37(12), 4695–4710. A. Ghanbari, T. V. M. Ndoro, F. Leroy, M. Rahimi, ¨hm and F. Mu ¨ller-Plathe, Interphase Structure in M. C. Bo Silica–Polystyrene Nanocomposites: A Coarse-Grained Molecular Dynamics Study, Macromolecules, 2011, 45(1), 572–584. A. Karatrantos, R. J. Composto, K. I. Winey and N. Clarke, Structure and Conformations of Polymer/SWCNT Nanocomposites, Macromolecules, 2011, 44(24), 9830–9838.


PCCP

¨ger and 33 A. Karatrantos, R. J. Composto, K. I. Winey, M. Kro N. Clarke, Entanglements and Dynamics of Polymer Melts near a SWCNT, Macromolecules, 2012, 45(17), 7274–7281. 34 G. N. Toepperwein, N. C. Karayiannis, R. A. Riggleman, ¨ger and J. J. de Pablo, Influence of Nanorod IncluM. Kro sions on Structure and Primitive Path Network of Polymer Nanocomposites at Equilibrium and Under Deformation, Macromolecules, 2011, 44(4), 1034–1045. 35 G. N. Toepperwein, R. A. Riggleman and J. J. de Pablo, Dynamics and Deformation Response of Rod-Containing Nanocomposites, Macromolecules, 2011, 45(1), 543–554. ¨hm and F. Mu ¨ller-Plathe, Interface 36 T. V. M. Ndoro, M. C. Bo and Interphase Dynamics of Polystyrene Chains near Grafted and Ungrafted Silica Nanoparticles, Macromolecules, 2011, 45(1), 171–179. 37 T. V. M. Ndoro, E. Voyiatzis, A. Ghanbari, D. N. Theodorou, ¨hm and F. Mu ¨ller-Plathe, Interface of Grafted and M. C. Bo Ungrafted Silica Nanoparticles with a Polystyrene Matrix: Atomistic Molecular Dynamics Simulations, Macromolecules, 2011, 44(7), 2316–2327. 38 F. W. Starr, T. B. Schrøder and S. C. Glotzer, Molecular Dynamics Simulation of a Polymer Melt with a Nanoscopic Particle, Macromolecules, 2002, 35(11), 4481–4492. 39 T. Desai, P. Keblinski and S. K. Kumar, Molecular dynamics simulations of polymer transport in nanocomposites, J. Chem. Phys., 2005, 122(13), 134910. 40 G. D. Smith, D. Bedrov, L. W. Li and O. Byutner, A molecular dynamics simulation study of the viscoelastic properties of polymer nanocomposites, J. Chem. Phys., 2002, 117(20), 9478–9489. 41 P. J. Dionne, R. Ozisik and C. R. Picu, Structure and Dynamics of Polyethylene Nanocomposites, Macromolecules, 2005, 38(22), 9351–9358. 42 P. J. Dionne, C. R. Picu and R. Ozisik, Adsorption and Desorption Dynamics of Linear Polymer Chains to Spherical Nanoparticles: A Monte Carlo Investigation, Macromolecules, 2006, 39(8), 3089–3092. 43 J. H. Huang, Z. F. Mao and C. J. Qian, Dynamic Monte Carlo study on the polymer chain in random media filled with nanoparticles, Polymer, 2006, 47(8), 2928–2932. 44 J. Liu, Y. Wu, J. X. Shen, Y. Y. Gao, L. Q. Zhang and D. P. Cao, Polymer-nanoparticle interfacial behavior revisited: A molecular dynamics study, Phys. Chem. Chem. Phys., 2011, 13(28), 13058–13069. 45 R. C. Picu and A. Rakshit, Dynamics of free chains in polymer nanocomposites, J. Chem. Phys., 2007, 126(14), 144909. 46 M. Goswami and B. G. Sumpter, Anomalous chain diffusion in polymer nanocomposites for varying polymer-filler interaction strengths, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2010, 81(4), 041801. 47 A. N. Rissanou and V. Harmandaris, Dynamics of various polymer-graphene interfacial systems through atomistic molecular dynamics simulations, Soft Matter, 2014, 10(16), 2876–2888. 48 J. Liu, L. Q. Zhang, D. P. Cao and W. C. Wang, Static, rheological and mechanical properties of polymer nanocomposites studied by computer modeling and simulation, Phys. Chem. Chem. Phys., 2009, 11(48), 11365–11384.


View Article Online


PCCP

49 J. S. Smith, D. Bedrov and G. D. Smith, A molecular dynamics simulation study of nanoparticle interactions in a model polymer-nanoparticle composite, Compos. Sci. Technol., 2003, 63(11), 1599–1605. 50 Q. H. Zeng, A. B. Yu and G. Q. Lu, Multiscale modeling and simulation of polymer nanocomposites, Prog. Polym. Sci., 2008, 33(2), 191–269. 51 K. Kremer and G. S. Grest, Dynamics of entangled linear polymer melts: A molecular-dynamics simulation, J. Chem. Phys., 1990, 92(8), 5057–5086. 52 Y. Y. Gao, J. Liu, J. X. Shen, L. Q. Zhang and D. P. Cao, Molecular dynamics simulation of dispersion and aggregation kinetics of nanorods in polymer nanocomposites, Polymer, 2014, 55(5), 1273–1281. 53 J. Liu, D. Cao, L. Zhang and W. Wang, Time-Temperature and Time-Concentration Superposition of Nanofilled Elastomers: A Molecular Dynamics Study, Macromolecules, 2009, 42(7), 2831–2842. 54 S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J. Comput. Phys., 1995, 117(1), 1–19. ¨ger, W. Loose and S. Hess, Rheology and structural 55 M. Kro changes of polymer melts via nonequilibrium molecular dynamics, J. Rheol., 1993, 37(6), 1057–1079.


Paper

56 R. S. Hoy, K. Foteinopoulou and M. Kroger, Topological analysis of polymeric melts: Chain-length effects and fast-converging estimators for entanglement length, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2009, 80(3), 031803. 57 J. Liu, Y. G. Gao, D. P. Cao, L. Q. Zhang and Z. H. Guo, Nanoparticle Dispersion and Aggregation in Polymer Nanocomposites: Insights from Molecular Dynamics Simulation, Langmuir, 2011, 27(12), 7926–7933. 58 S. T. Knauert, J. F. Douglas and F. W. Starr, The effect of nanoparticle shape on polymer-nanocomposite rheology and tensile strength, J. Polym. Sci., Part B: Polym. Phys., 2007, 45(14), 1882–1897. 59 M.-J. Wang and S. Wolff, Filler-Elastomer Interactions. Part V. Investigation of the Surface Energies of Silane-Modified Silicas, Rubber Chem. Technol., 1992, 65(4), 715–735. 60 Y. Li, M. Kroger and W. K. Liu, Nanoparticle Effect on the Dynamics of Polymer Chains and Their Entanglement Network, Phys. Rev. Lett., 2012, 109(11), 118001. 61 Y. Li, M. Kroger and W. K. Liu, Nanoparticle Geometrical Effect on Structure, Dynamics and Anisotropic Viscosity of Polyethylene Nanocomposites, Macromolecules, 2012, 45(4), 2099–2112.


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