Edge-Functionalized Graphene as a Nanofiller ... - ACS Publications

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Edge-Functionalized Graphene as a Nanofiller: Molecular Dynamics Simulation Study Petra Bačová,*,† Anastassia N. Rissanou,† and Vagelis Harmandaris†,‡ †

Institute of Applied and Computational Mathematics (IACM), Foundation for Research and Technology Hellas (FORTH), GR-71110 Heraklion, Crete, Greece ‡ Department of Mathematics and Applied Mathematics, University of Crete, GR-71409 Heraklion, Crete, Greece S Supporting Information *

ABSTRACT: In the present simulation work we study graphene-based polymer nanocomposites composed of hydrogenated and carboxylated graphene sheets dispersed in polar and nonpolar short polymer matrices (i.e., matrices containing chains with low molecular weight). The aim of our work is to examine spatial and dynamical heterogeneities of such systems and to provide a compact picture about the effects of the edge group functionalization of graphene sheets on the properties of hybrid graphene-based materials. We perform atomistic molecular dynamics simulations of edge-functionalized graphene sheets embedded in poly(ethylene oxide) (polar matrix) and polyethylene (nonpolar matrix). We choose a low loading of the graphene nanofiller (from 1.7% to 3.6%) in agreement with experimental data. We further implement a detailed analysis of static and dynamic properties of polymer chains on the level of both the entire hybrid material and the polymer/graphene interface through a new approach that is able to distinguish between the adsorbed and edge region around the nanofiller. At the local scale, strong structural and dynamical heterogeneities are observed; i.e., the behavior of the polymer matrix appears to be highly affected by the presence of the edge-functionalized graphene. Slow dynamics was detected in the adsorbed layers in all nanocomposites. Additionaly, interaction of grafted carboxylated groups with polar matrix led to a further delay in the segmental as well as the chain relaxation close to the graphene edges. This effect seems to slow down the chain dynamics even more than the actual adsorption of the chain on the surface. Overall average orientational dynamics of polymer chains in nanocomposites as well as the collective dynamics quantified through the single chain coherent structure factor reveal slight deviations from the bulk behavior in the terminal region, presumably due to the small percentage of the slow dynamic component at the given loading of the nanofiller. Enhancement of the rheological properties is not observed within the time window of our simulations. Our results emphasize the importance of the surface/polymer interactions in the graphene-based nanocomposites and suggest that by a proper choice of edge-grafted groups we can achieve better material performance.

1. INTRODUCTION In the past decade graphene became one of the most studied materials both experimentally and through simulations.1−3 Because of its exceptional properties, it has also been considered and tested as a potential nanofiller for polymeric materials.4−8 Qualitity and structure of graphene may differ depending on the particular requirements for possible application of graphene-based nanomaterials.9 Pristine singlelayered graphene is highly conductive and transparent and can be used for example in transparent electrodes and sensors.10−13 Furthermore, in comparison to the carbon nanotubes it has a very high surface area, a property that can be crucial if graphene is well dispersed in the matrix.9 In general, due to the chemical inertness of the graphitic surface and its tendency to aggregate, good dispersion of pristine graphene is a challenging process. Proper choice of polymer is necessary to enhance specific hydrophobic and π−π interactions between graphene and polymer matrix.14,15 Moreover, the usage of pristine graphene © XXXX American Chemical Society

as a nanofiller is strongly limited by its high-cost production and low yields. Derivatives of the graphene turned out to be more advantegeous, especially for their better dispersion in polymer matrices and less difficulties during the production process.5,16 The most promising low-cost approaches for graphene filler preparation are based on exfoliation of graphite by using a sequence of chemical reactions. This can be achieved either by oxidation of graphite into graphite oxide9,17 or by grafting organic molecular wedges on the border of graphite.18 In the first case, after the oxidation procedure oxygen-containing groups grafted on the surface of graphene oxide sheets are chemically and/or thermally removed and π-conjugated system is restored. The final product is a highly conductive grapheneReceived: August 11, 2015 Revised: November 17, 2015

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DOI: 10.1021/acs.macromol.5b01782 Macromolecules XXXX, XXX, XXX−XXX

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combines some features of pristine graphene and graphene derivatives and opens new possibilities for tailored graphene/ polymer hybrid materials. Similarly to the pristine graphene, the edge-functionalized graphene is highly conductive, and furthermore the presence of edge groups may increase its compatibility with commonly used polymers. From the above discussion it is clear that there are still many open questions related to the effect of graphene sheets on the (structural, dynamical, mechanical, etc.) properties of polymer matrix. Above all, a main challenge in all graphene-based polymer nanocomposites is to study the spatial and dynamical heterogeneities, induced by the presence of polymer/graphene interfaces, at the molecular level as well as their effect on the overall properties of the hybrid material. This is exactly the main goal of the present work; we pay particular attention to the role of specific nonbonded interactions in functionalized graphene/low molecular weight polymer nanocomposites and intent to describe some tendencies that would further apply to the systems with longer chains, i.e., graphene/polymer nanocomposites. Thus, in the following text we use the word polymer even if we refer to our model chains with a small number of monomeric units ( 200 ps is found. The relaxation time that corresponds to the additional decay is comparable to the relaxation time obtained from the main region (t ≈ 102−103 ps), but the value of the stretching exponent βs is much higher (up to about 50%). Because of the barely separated relaxation times and the large error bars in this region (notice the solid red line in Figure 10), it is not possible to obtain reliable results

segmental relaxation times of our model polymer chains are larger in the vicinity of polymer/graphene interfaces, whereas they become similar to the bulk ones at distances above approximately 3 nm from the interface. Values for the βs exponent are shown in the Supporting Information in Table S1 and in Figure S4. Chains in the first layer exhibit smaller βs values compared to the bulk ones, i.e., a broader distribution of relaxation times. A closer inspection of Table 1 leads to the conclusion that the closer is the polymer segment to the graphene, the slower is its orientational dynamics. A qualitatively identical feature was observed in translational motion (see Figure 7). Comparison of

Table 1. Segmental Relaxation Times τs Estimated from the Autocorrelation Functions of 1−3 Vectors by Fitting to the KWW Functiona τs [ps] system

a

COOH PE

H PE

COOH PEO

H PEO

layer

parallel

edges

parallel

edges

parallel

edges

parallel

edges

0−1.5 nm 1.5−3.0 nm 3.0−5.0 nm

510 ± 70 53 ± 4 60 ± 25

110 ± 40 53 ± 6 39 ± 6

540 ± 250 60 ± 10 48 ± 5

80 ± 10 47 ± 5 36 ± 7

8000 ± 2000 1300 ± 100 1060 ± 60

14000 ± 2000 1180 ± 40 800 ± 20

4000 ± 1000 1600 ± 300 1200 ± 200

2200 ± 400 1270 ± 70 967 ± 6

Bulk values: τs = 45 ± 4 ps for PE and τs = 950 ± 120 ps for PEO I

DOI: 10.1021/acs.macromol.5b01782 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules Table 2. Terminal Relaxation Times τr Estimated from the Autocorrelation Functions of the End-to-End Vectorsa τr [ps] system

a

COOH PE

H PE

COOH PEO

H PEO

layer

parallel

edges

parallel

edges

parallel

edges

parallel

edges

0−1.5 nm 1.5−3.0 nm 3.0−5.0 nm

240 ± 30 74 ± 9 70 ± 20

110 ± 40 71 ± 4 63 ± 2

370 ± 80 70 ± 20 63 ± 5

90 ± 10 66 ± 6 60 ± 3

9000 ± 2000 2600 ± 700 1870 ± 60

17000 ± 6000 2190 ± 40 1770 ± 60

6000 ± 2000 2600 ± 300 2000 ± 400

3500 ± 700 2200 ± 100 2020 ± 50

Bulk values: τr = 66 ± 2 ps for PE and τr = 2300 ± 200 ps for PEO

Figure 12. Comparison of end-to-end correlation functions of the chains belonging to layers in parallel region (solid lines) and edges (dashed lines). The upper plot shows the comparison for PEO matrix: (a) carboxylated filler and (b) hydrogenated. The bottom shows the data for the PE matrix: (c) carboxylated filler and (d) hydrogenated are presented. The largest error bars are also shown for each curve.

surface and should not be forgotten while making a comparison. Carboxylated graphene/PEO nanocomposites follow the same trend as PE systems; orientation of the 1−3 vector in the closest graphene neighborhood decorrelates 8 times slower than the corresponding bulk system. Data for PEO segments in nanocomposites with dispersed hydrogenated graphene indicate smaller enhancement (factor of 4). Interestingly, in the COOH/PEO system the slowest relaxation is detected close to the edges of graphene (notice the red point in the inset of Figure 11). We provide an explanation for this observation in the following subsection. 4.1.2. Chain Dynamics. In the last part of this section, we switch from segmental to chain dynamics. In particular, we focus on the dynamic differences between the edge and the parallel region that have been briefly discussed in the description of Figure 6. We use the same approach as in the analysis of the segmental orientational dynamics, and we calculate the chain end-to-end correlation function in the form

the relaxation times in different layers provides a quantitative picture of this phenomenon. In all systems only the first layer shows a significant deviation from the bulk behavior; more specifically, the relaxation times in the adsorbed (parallel) region of graphene/PE nanocomposites are about 11−12 times slower than those in the bulk. Thanks to the new approach that allows us to define well the region parallel to the graphene, we can confront our results obtained for a moving graphene filler with results published for an infinite graphene surface acting as a solid wall. For instance, data in ref 31 for a PE thin film confined between (infinite-periodic) graphene layers show qualitatively the same retardation of segmental relaxation times, τs, compared to the bulk ones, for PE chains at the vicinity of the polymer/graphene interfaces (adsorbed parallel layer). Note that a quantitative comparison with ref 31 is not possible due to the different spacing of the layers used for the analysis. Moreover, in the current work we cannot fully eliminate the correlation between the dynamics of the segments placed in the parallel and the edge region around the filler. This correlation does not take place in the systems with infinite graphene J

DOI: 10.1021/acs.macromol.5b01782 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules P1(t ) =

R e(t + t0)R e(t0) |R e(t + t0)||R e(t0)|

(3)

where the vectors Re(t + t0) and Re(t0) stand for the end-to-end vectors of the chain at time t + t0 and at the time origin t0, respectively. Angle brackets denote an average over the chains belonging to a given layer as well as over multiple time origins. The end-to-end correlation functions for chains of all four simulated nanocomposites are shown in Figure 12. Again, the spacing between the layers is the same as in Figure 10. A dispersion of the correlation functions is obvious in parallel (solid curves) as well as in edge region (dashed curves). However, except for the COOH-graphene/PEO system, the chain relaxation in the edge region is only slightly altered in the first layer (red dashed curves in panels b−d of Figure 12) while the curves for the second and the third layer almost overlap. This small delay can be explained by an interlocking of the functional groups attached to the graphene and polymer chain, especially in the case of bulky COOH groups and nonpolar matrix, which lacks of strong electrostatic interactions. It was shown that this sterical factor plays a role in the enhancement of mechanical properties of functionalized graphene sheets.24 Moreover, as it was discussed before, chains placed in the first layer of the edge region are in a close contact with the adsorbed chains, and their mutual interaction may cause some alteration of the dynamics. In contrast to the nonpolar matrix, PEO polymers show a much more complex behavior at the edges of the graphene sheet. In the system with the carboxylated graphene dispersed in PEO, the specific interaction between the edge groups and the matrix is responsible for the even slower relaxation of the chains in the edge region than in the adsorbed layer (red dashed and solid line in Figure 12a). This phenomenon is not observed in the PEO nanocomposites with hydrogenated graphene, where the adsorbed layer in the parallel region exhibit the slowest chain relaxation. These observations are consistent with the results shown in Figure 6. Further, we quantified these dynamical heterogeneities by fitting the end-to-end correlation functions with the KWW expression (eq 2) and integrating the curves in a similar way as in the segmental analysis. Again, we got the standard deviations from the block averaging method. The results are summarized in Table 2 and in Figure 13 as well as in Figure S5 and Table S2 of the Supporting Information. The effect of the interaction of the carboxylated edges with PEO on the chain dynamics is much less pronounced than the corresponding effect observed at the segmental level. The chains are slowed down by a factor of 7 in comparison to the bulk relaxation (note that at the segmental level the factor is equal to 15; see inset of Figure 11). In summary, local dynamics in the graphene-based nanocomposites studied here is affected by two factors: the adsorption of the polymer chains on the graphene surface and the interaction of the edge groups with the polymer matrix. These effects are evident at the segmental and the terminal level and induce dynamical heterogeneities in the polymer matrix. In the next section we examine whether the local dynamical heterogeneities have an impact on overall properties of the hybrid material. 4.2. Overall Properties. Here, we measure general properties of our model systems that are experimentally accessible and have been studied in various hybrid materials. Despite the system size limitations in atomistic simulations, we expect that some features will be also qualitatively similar to the

Figure 13. Normalized terminal relaxation times τr/τr(bulk) from Table 2 for parallel region. Data for the edge region are presented in the inset.

materials prepared from large graphene sheets and long polymer chains. We also focus on the differences between simulated graphene-based polymer nanocomposites and bulk polymers, which serve as reference systems. 4.2.1. Dynamic Structure Factor. Valuable information about the collective dynamics in polymer matrices can be gained from the time and/or scattering vector q dependence of the single chain coherent structure factor. This quantity can be measured by neutron spin-echo experiments,56 and it is defined as S (q , t ) =

1 N

N

∑ ⟨exp(iq[ri(t + t0) − rj(t0)])⟩ (4)

i,j=1

In this expression the sum is performed over i and j segments belonging to the same chain, N represents the total number of chain segments participating in the scattering function, and ri(t + t0) and rj(t0) denote their position vectors at time t + t0 and t0, respectively. In contrast to the previous analysis based on the layer arrangement, the brackets ⟨...⟩ in eq 4 refer to the average over polymer chains in the whole system, independently of their position with respect to the graphene sheet. In the isotropic systems, only the magnitude q = |q| of the scattering vector is considered, and eq 4 can be expressed as57 S(q , t ) =

1 N

N

∑ ⟨sin[qrij(t )]/[qrij(t )]⟩ i,j=1

(5)

where rij(t) = |ri(t + t0) − rj(t0)|. Equation 5 is widely used in simulations.58 In experiments, the measured quantity is actually S(q,t)/S(q,0). We take this fact into account and present our results in a normalized form. The single chain coherent structure factor for studied PEO-based nanocomposites is shown in Figure 14. We examined three values of q vector (plotted with different line types), namely q = 0.4 Å−1, q = 1.0 Å−1, and q = 1.5 Å−1. With this choice of q values we are able to probe the dynamics at various length scales comparable to the segmental level as well as to the chain dimensions (note that the probing length scales are equal to 2π/q). In the inset of Figure 14 the data are represented in a semilogarithmic plot. Almost no deviations from the bulk dynamics can be noticed in this plot, except for a slightly slower tail of the scattering function in the case of the system with the K

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happening at the local scale that have been already explained above. However, this effect (i.e., retardation of the dynamics close to the surface) on the overall dynamics is relatively small, and therefore we can clearly observe the slow collective dynamics in nanocomposites only under close inspection of the scattering data. Concerning the neutron spin-echo measurements in the graphene-based polymer materials, we would like to mention that apart from the scattering signal coming from the polymer chains there is also a contribution from the graphene nanofiller. In simulations this contribution can be easily ruled out, but the analysis of experimental scattering functions is much more complicated, and special requirements as for example fully deuterated graphene might be crucial for the experimental realization. 4.2.2. Orientational Relaxation of Polymer Chains. Orientational chain dynamics in the level of the entire material can be also directly examined in MD simulations through the end-to-end correlation function introduced before eq 3, where the data are averaged throughout the whole matrix. In this way we can estimate one characteristic (average) chain relaxation time for every simulated nanocomposite. In addition to the simulation results, in the case of the molecules with permanent dipole moment (i.e., PEO matrix) the overall relaxation of the end-to-end vector can be studied by dielectric spectroscopy. Calculated end-to-end vector correlation functions are plotted in Figure 15. From the inset graph in the semi-

Figure 14. Normalized single chain coherent structure factor for graphene/PEO nanocomposites and different values of q-vector: q = 1.5 Å−1 (solid lines), q = 1.0 Å−1 (dashed lines), and q = 0.4 Å−1 (dotted lines). The data of the bulk poly(ethylene oxide) are also included (blue curves). The main plot is in a log−log scale; inset shows the same data in a semilogarithmic representation.

carboxylated nanofiller (red curves). However, the differences between the systems are much better visible in the main plot of Figure 14 where data are shown in a log−log scale. It is interesting to observe that while in the intermediate region the curves overlap, they separate in the terminal domain. The dynamic structure factor of the polymers interacting with the carboxylated sheet exhibits the slowest decay; dynamics of PEO chains in the nanocomposite with the hydrogenated graphene is altered only a little with respect to the bulk chains. Apparently, this alteration is much stronger for the data measured at the lower value of scattering vector studied here, q = 0.4 Å−1, than for the curves corresponding to q = 1.5 Å−1 (compare blue and green dotted and solid curves, respectively). In other words, at the length scales of about 2π/0.4 Å−1 ≈ 16 Å comparable to the chain end-to-end vector (≈18 Å) the collective dynamics is slowed down by the presence of hydrogenated graphene nanofiller, while at the segmental level (q = 1.5 Å−1, length scales of about 4 Å) the differences in the dynamics of Hgraphene-filled nanocomposite and the bulk systems are almost negligible. For the systems with carboxylated graphene, the trend with respect to the bulk data remains the same for all values of q. In the graphene/PE hybrid systems, the spreading of the curves in the final decay is even less pronounced than in the PEO systems. Scattering functions of the PE chains in nanocomposites with different graphene functionalization have the same shape, and their decay is only slightly shifted to longer times with respect to the bulk data (data not shown here). Recently, few theoretical approaches were proposed in order to interpret the data for coherent structure factor measured in hybrid systems.59,60 The approaches share some common features, they are based on the Rouse model, and they decompose the total scattering function into contributions from the chains affected and not affected by the presence of the nanoparticle. Both studies reported delay of the normal mode relaxation of polymer matrix in comparison to bulk, which was attributed to the adsorption of the chains in the first case60 and the chain confinement between the nanoparticles in the second case.59 Data reported here reveal that the slow component in the coherent structure factor comes from the dynamic processes

Figure 15. Autocorrelation functions of the end-to-end vector. The main plot is in a log−log scale; inset shows the same data in a semilogarithmic representation. In the semilogarithmic representation, the biggest error bar is shown for the bulk data; for the hybrid systems the error bars are comparable to the line thickness.

logarithmic representation it is apparent that within the error bars the data for nanocomposites overlap with the bulk correlation function in the whole simulation time window. Similarly to the data of the single chain coherent structure factor presented in the previous subsection, small deviations from the bulk behavior can be detected in the log−log representation (main plot of Figure 15), especially in the long time regime. Fits of the above data with KWW functions give average orientational relaxation time of the polymer chains in the specific nanocomposites studied here very similar to the bulk relaxation times (66 ± 2 ps for PE and 2.3 ± 0.2 ns for PEO). L

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time scales. The final decay is very noisy, and we cannot get any information about the terminal relaxation of the material. Because of the statistical issues, the time window in which we get reliable data for the stress tensor is very limited. However, within this time window no enforcement of the nanocomposite rheological properties due to the presence of the graphene filler was detected. We should also state here that in hybrid systems the relaxation time obtained from the linear rheology measurements may differ from the one estimated from the orientational dynamics (autocorrelation function of the end-to-end vector), discussed above. In general, the stress relaxation modulus may exhibit a plateau in the terminal region as a consequence of the solid-like behavior in the polymer nanocomposites. Consequently, the final decay of G(t) would be shifted to the longer times, and also the terminal relaxation time would be bigger than the one estimated from the dielectric spectroscopy. However, due to statistical issues, this extension in the calculation of G(t) for longer times is not a trivial aspect since simulations of huge systems are required; this will be the topic of a future work.

4.2.3. Stress Relaxation Modulus. Material’s rheological behavior is another widely studied polymer characteristic. Rheological techniques are very sensitive and have been previously applied to graphene-based nanocomposites.61−63 Our simulations cover the equilibrium (linear) rheological behavior of the hybrid polymer/graphene nanocomposites. An important quantity in linear viscoelasticity is the stress relaxation modulus, which can be calculated in simulations through the equilibrium stress autocorrelation function as follows: G (t ) =

V [⟨σxy(t + t0)σxy(t0)⟩] kBT

(6)

where kB is the Boltzmann constant, V stands for the volume of the system, and σxy is an off-diagonal element of the stress tensor. The values of the instantaneous stress tensor fluctuate a lot during the simulation run, and it is very tricky to obtain a smooth curve for stress relaxation modulus. We follow the approach proposed in ref64 to improve the statistics in our calculations. First of all, in isotropic systems better statistics can be achieved by a simple extension of eq 6 in a way:

5. CONCLUSIONS Here we present results of atomistic molecular dynamics simulations of graphene-based nanocomposites. We focus on one of the most promising modifications of pristine graphene, edge-functionalized graphene, and we study its behavior as a potential nanofiller in polar (poly(ethylene oxide)) and nonpolar (polyethylene) matrices of low molecular weight. Two types of the edge-functionalization are examined, namely hydrogenated and partially carboxylated graphene sheets. A new approach for the analysis of chain properties in composite materials is introduced, which allows us to detect the changes in static and dynamic properties in parallel and edge region around the nanofiller. The main findings of our work can be summarized as follows: (a) The density of the polymer around the graphene sheet depends on the distance from the surface. For both short polymer matrices, the maximum of the density profile function is placed in the nearest vicinity of the graphene, pointing out the adsorption of the chain on the graphene surface. (b) In the adsorbed interfacial region, the chains preferably adopt more extended, trans-enriched configurations in comparison to the bulk polymers. (c) The interaction of the graphene sheet with the polymer matrix induces dynamic heterogeneities in the nanocomposite material. At the local level, slowing down of the segmental as well as chain dynamics is detected in the region parallel to the surface for both matrices. Moreover, in the case of the carboxylated graphene dispersed in the polar matrix edge-group interaction with polymer becomes very important and results in a bigger retardation of chain dynamics compared to the parallel region. (d) Concerning the overall properties, no significant reinforcement due to the existence of nanofiller is observed for the given characteristics of simulated systems (i.e., the loading of the graphene, size of the sheet, chain molecular weight). Differences in the single chain coherent structure factor and end-to-end correlation function are detected between bulk and hybrid systems at the long time scales: systems with the carboxylated nanofiller exhibit the slowest decay. Stress relaxation modulus remain unaffected for the time window of our simulations, i.e., before the terminal region.

V [⟨σxy(t )σxy(0)⟩ + ⟨σyz(t )σyz(0)⟩ 5kBT V + ⟨σzx(t )σzx(0)⟩] + [⟨Nxy(t )Nxy(0)⟩ 30kBT

G (t ) =

+ ⟨Nxz(t )Nxz(0)⟩ + ⟨Nyz(t )Nyz(0)⟩]

(7)

with Nαβ = σαα − σββ and α, β being Cartesian coordinates. We also apply the multiple-tau correlator, which performs data averages around a certain time interval. This time interval is varying during the averaging procedure but is maintained adequately smaller than the interval on which the correlation function is calculated. For more details about the algorithm and the data structure of the correlator we refer the reader to ref 64. Moreover, we average G(t) functions obtained from 10 (PEO systems) and 15 (PE systems) isoconfigurational runs. The final stress relaxation moduli for all simulated systems are presented in Figure 16. The oscillations in the very short time regime t < 1 ps represent local intramolecular vibrations, and they are out of our interest. After this regime, the curves for G(t) of the nanocomposites and bulk merge at the intermediate

Figure 16. Stress relaxation modulus G(t) calculated with the multiple-tau correlator.64 M

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Apart from the technical difficulties facing in simulations, one of the possible reasons why we do not detect any notable improvement of the overall nanocomposite properties is a lack of strong interactions between the polymer and the graphene sheet. Recently, an extensive experimental study was published that emphasizes the importance of the surface/polymer interaction in graphene-based nanocomposites.65 The authors investigated the change in the glass transition temperature of polymer matrix (Tg) after the addition of graphene and concluded that only strong interactions between matrix polymers and fillers can lead to the increase of Tg. These strong interactions can be unintentionally formed during the preparation of the nanocomposite if chains get covalently bonded to the surface. As a consequence, this would lead to an apparent enhancement of rheological as well as mechanical properties of the material. Detection of the grafted chains on the graphene may be tricky in experiment; therefore, one should be cautious while doing direct confrontation of the simulation and experimental results. Our results show that although there are no covalently bonded groups on the graphene surface, better compatibility of the graphene nanofiller with polymer matrix can be achieved also by edge-functionalization. The combined effect of the adsorption on the surface and the slow motion of the polymer matrix in the vicinity of the sheet edges leads to structural and dynamical heterogeneities in the molecular level, which are well quantified through our analysis scheme. Such a robust quantification by using experimental techniques is either technically impossible (e.g., obtaining a given quantity as a function of the distance from the filler) or very difficult to be performed (e.g., due to the crystallization of the PEO in the dielectric spectroscopy measurements). Therefore, we believe that our work brings novel results that can complement the experiments and can be beneficial also in understanding the dynamical processes in bigger systems, namely polymer nanocomposites. Finally, concerning the overall enhancement of the material properties, it would be important to study graphene-based nanocomposites with a polymer matrix that exhibits stronger adsorption on the graphene surface, e.g., through π−π interaction, in order to examine the influence of the slow dynamical component in the system on the overall, macroscopic properties of the hybrid material. Simulations of functionalized graphene/polystyrene hybrid systems are currently under study in our group. Nonetheless, real nanocomposite samples contain graphene platelets of bigger size than our sheet and longer polymer chains. Dynamics of the polymer matrix becomes slower with increasing graphene size,30 and at the same time higher coverage of the surface is achieved with increasing molecular weight of the polymer. Thus, we expect that both of these factors will contribute to the enhancement of material properties.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (P.B.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge support by the European Union (ESF) and Greek national funds through the Operational Program Education and Lifelong Learning of the NSRF-Research Funding Program: KRHPIS and ARISTEIA II. Stimulating discussions with Dr. Angel J. Moreno and Dr. Daniel Read are also kindly acknowledged.

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b01782. Figures S1−S5 and Tables S1, S2 (PDF) N

DOI: 10.1021/acs.macromol.5b01782 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.5b01782 Macromolecules XXXX, XXX, XXX−XXX