Structure and Conformation of Stereoregular Poly(methyl methacrylate

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

pubs.acs.org/Macromolecules

Structure and Conformation of Stereoregular Poly(methyl methacrylate) Chains Adsorbed on Graphene Oxide and Reduced Graphene Oxide via Atomistic Simulations Alireza F. Behbahani,†,‡ G. Hashemi Motlagh,‡ S. Mehdi Vaez Allaei,§,∥ and Vagelis A. Harmandaris*,⊥,†

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†

Institute of Applied and Computational Mathematics, Foundation for Research and TechnologyHellas, Heraklion GR-71110, Greece ‡ Advanced Polymer Materials and Processing Lab, School of Chemical Engineering, College of Engineering, University of Tehran, Tehran 11155-4563, Iran § Department of Physics, University of Tehran, Tehran 14395-547, Iran ∥ School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran ⊥ Department of Mathematics and Applied Mathematics, University of Crete, Heraklion GR-71110, Greece S Supporting Information *

ABSTRACT: A detailed analysis of the structure and conformation of stereoregular and atactic poly(methyl methacrylate) (PMMA) chains confined between oxidized graphene sheets is provided through long-time atomistic molecular dynamics simulations. Low-molecular-weight isotactic-, atactic-, and syndiotactic-PMMA chains confined between graphene oxide (GO) and reduced graphene oxide (RGO) sheets have been simulated at different temperatures ranging from 520 to 580 K. The interfacial properties of PMMA/pristine graphene (PG) are also discussed. GO and RGO structures have been generated based on the Lerf−Klinowski structural model of graphite oxide with carbon-to-oxygen ratios of 3 and 10, respectively. The interfacial packing and adsorption of PMMA chains on PG, RGO, and GO model surfaces are studied through the calculation of interfacial mass density profiles and distribution of monomer/surface distance. Furthermore, the arrangement of PMMA atoms in the vicinity of functional groups of nanosheets and their hydrogen bond formation are investigated. The conformations of adsorbed chains, that is, chains with at least one adsorbed monomer, are analyzed in detail as trains, loops, and tails. It is observed that the number of adsorbed monomers and the average size of trains, that is, consecutive adsorbed monomers of a chain, increase with the concentration of functional groups of the nanosheets. This is related to the strength of the polymer/substrate interactions and the increase of the roughness of model nanosheets which enhances the probability of polymer/surface contacts. The tacticity-dependent adsorption of PMMA chains is also examined in detail. Isotactic-PMMA chains, compared to atactic and syndiotactic ones, exhibit a better interfacial packing and form longer trains. i-PMMA chains are stiffer and, moreover, become more extended in the vicinity of model surfaces. The formation of longer trains by isotactic stereoisomers is found to be consistent with their higher stiffness, that is, higher characteristic ratio and gyration radius. Results reported here suggest a clear correlation between chain dimensions, size of trains, and interfacial packing of the adsorbed PMMA chains.

1. INTRODUCTION

production of graphene-like materials is based on the

Graphene-based polymer nanocomposites have appeared as a promising class of materials. Pristine single layer graphene is an exceptionally strong material with a very high electrical and thermal conductivity as well as an enormous specific surface area.1,2 One of the most promising scalable synthesis routes for

exfoliation of graphite oxide.1−4 Exfoliation of graphite oxide

© XXXX American Chemical Society

in polar solvents, like water, leads to production of graphene Received: March 20, 2019

A

DOI: 10.1021/acs.macromol.9b00574 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

has been observed.5 Tacticity-dependent shift of Tg for thin films of oligomeric PMMA chains has also been reported.17 The interfacial structure of polymers has also been investigated experimentally. Motivated by the tacticity-dependent Tg of PMMA at interfaces, the density profile and local conformation of stereoregular PMMA thin films supported by SiO2 have been investigated using IR spectroscopy and X-ray reflectometry.14,18,19 The hydrogen bonding of a series of methacrylate polymers, including PMMA, adsorbed on a silica substrate has been investigated using Fourier transform infrared spectroscopy.20 The gyration radius and entanglement of PMMA chains in GO nanocomposites have been studied by use of small angle neutron scattering and rheology techniques;21 reductions in gyration radius and interchain entanglements have been reported in this work. Besides experiments, atomistic molecular dynamics (MD) simulation is a complementary tool for providing insight into the interfacial behavior of polymers, with atomic resolution, which is hardly accessible in experiments.22 There are several works concerning atomistic simulation of realistic polymer chains adsorbed on solid surfaces, including graphene-based and functionalized surfaces. For example, mentioning a few works, Pandey and Doxastakis23 investigated the structure and conformation of polyethylene (PE) chains adsorbed on a silica surface, silica nanoparticles, and fullerene, through Monte Carlo simulations. Eslami et al.24 studied the structure and dynamics of oligomeric atactic PMMA chains around bare and surface-grafted silica nanoparticles. Skountzos et al.25 reported that oxidized graphene sheets, compared to PG, lead to higher improvement of mechanical properties of syndiotactic PMMA. Bacǒvá et al.26 studied the dynamics of PE and poly(ethylene oxide) chains near edge functionalized-graphene (hydrogenated and carboxylated graphene) sheets. Karatasos and Kritikos27 studied nanocomposite hydrogels of oxidized graphene sheets and poly(acrylic acid). The layered structure of polymers near attractive flat surfaces, like PG, has been observed in many atomistic and coarse-grained simulation works.28−32 However, near functionalized graphene surfaces, which are nanoscopically rough surfaces, a detailed description of interfacial structure is missing. At the same time, the conformations of adsorbed chains, that is chains with at least one contact to the surface, are of particular importance, as they are related to the macroscopic properties of the nanostructured systems. Thus, the properties of train, tail, and loop conformations of polymer chains have been studied previously for various polymer/solid interfaces, by using atomistic or bead-spring models, through Monte Carlo and MD simulations.23,29,33−36 The effects of chain length,29 flexibility of bead-spring chains,33,34 and radius of nanoparticles23,35 on the conformation of adsorbed chains have been investigated; however, the effects of surface chemistry and tacticity have not been analyzed so far. Furthermore, the arrangement of polymer atoms near functional groups of functionalized graphene surfaces is worth attention. Recently, we have studied the structure and the dynamics of stereoregular PMMA/PG interfaces through atomistic MD simulations.32 Tacticity-dependent interfacial packing and interfacial dynamics were observed; particularly, isotactic-PMMA, compared to atactic and syndiotactic chains, showed more restricted interfacial dynamics and higher shift of apparent glass transition temperature, near PG surface. The goal of the current work is to extend this approach by providing a detailed study of the structural and conformational

oxide (GO). It is commonly assumed that GO is a graphenelike sheet, which is heavily doped with oxygen containing functional groups like hydroxyl, epoxied, and carboxyl.1−4 Attachment of oxygen atoms to basal carbon atoms of graphene changes their hybridization from sp2 to sp3. Therefore, the perfect conjugated structure of pristine graphene (PG) is disturbed by oxidization and as a result GO has orders of magnitude lower conductivity than PG. By thermal annealing or chemical reduction, GO is reduced to a nearly graphene-like conjugated structure which is called reduced graphene oxide (RGO).1−4 Usually the complete reduction of GO is not achieved and hence RGO has some remaining oxygen-containing functional groups. The degree of oxidization of GO and RGO is usually expressed by their carbon-to-oxygen ratios (C/O ratio). The C/O ratios for GO and RGO are commonly around 2−4 and 9−12, respectively.1,2,4,5 Polymer/nanofiller interfacial interaction plays a significant role in controlling the properties of nanocomposites.1,2 For example, it is expected that polar polymers would exhibit stronger interfacial bonding with GO and RGO, due to the presence of functional groups, compared to PG. Moreover, controlling the interfacial interaction is a crucial factor to improve the dispersion of nanofillers.1,6 The latter is of particular importance for graphene-like nanofillers, in order to take advantage of the large surface area of graphene for improving the performance of polymer nanocomposites.1 The importance of interfacial interactions has been demonstrated in several works. For example, employing neutron reflectivity, Choi et al.7 reported a large reduction of diffusion coefficient for poly(methyl methacrylate) (PMMA) chains as a result of confinement between single-layer GO sheets; however, for PS chains a significantly smaller reduction was observed. The difference between PMMA and PS is related to the stronger interaction of PMMA with GO.7 In another work the formation of hydrogen bonds between GO and carbonyl groups of poly(ethyl methacrylate) (PEMA) was assumed to be the reason for a relatively large increase (about 15 K) in Tg of PEMA with the addition of only 0.12 vol % of GO.8 Similarly, concerning thin films, a reduction in Tg from bulk value has been observed for PMMA films supported by a gold substrate;9 on the contrary, because of strong interfacial interactions, an increase in Tg of PMMA films on a SiO2 substrate has been reported.9 The adsorption of stereoregular PMMA chains on various substrates is also of interest. First, note that tacticity has a great impact on various bulk properties of PMMA, such as chain dimensions, glass transition temperature, Tg, and local conformations.10−13 Tg increases from 50 °C for isotactic to about 130 °C for syndiotactic high−molecular-weight PMMA.10 Additionally, isotactic-PMMA has a larger characteristic ratio and gyration radius and a lower population of backbone bonds in trans state.11−15 Grohens et al.16 investigated the influence of tacticity on Tg of thin PMMA films casted on SiO2 and Al2O3 substrates. For both substrates, an increase in the Tg of isotactic and atactic PMMA and a decrease in Tg of syndiotactic PMMA, relative to that of bulk polymer, have been reported.16 Liao et al.5 studied the influence of graphene on Tg of isotactic and (syndiotactic-rich) atactic PMMA. For nanocomposites of isotactic PMMA with solvent-blended PG and RGO, an increase in Tg, relative to bulk value has been reported, while for atactic PMMA, no shift B


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configurations are illustrated, using different colors for the oxidized and graphitic regions.

properties of PMMA chains adsorbed on oxidized graphene nanosheets. PMMA is a polar polymer that can interact with the functional groups of the GO and RGO sheets. To provide information about the effects of both tacticity and concentration of functional groups, isotactic-, atactic-, and syndiotactic-PMMA (i-, a-, and s-PMMA) chains close to RGO and GO model surfaces (which have different C/O ratios) are studied at different temperatures. As reference systems, stereoregular PMMA/PG interfaces are also examined. The structure of the paper is as follows: in Section 2, we provide information about the studied model systems and simulation procedure. In Section 3, interfacial packing is studied through the calculation of mass density profiles, distribution of monomer/surface distance, and radial distribution function (RDF) between surface atoms and polymer atoms. In Section 4 the conformation of adsorbed chains are investigated, whereas in Section 5 the shape and dimension of PMMA chains are analyzed. Finally, a summary of the results is provided in Section 6.

2. MODEL AND METHOD 2.1. Generation of GO and RGO Model Structures. The chemical structure of GO and RGO has been the subject of various experimental investigations.3,37−40 Here, we have constructed model GO and RGO nanosheets based on the Lerf−Klinowski structural model of graphite oxide.37,38 According to this approach, GO, which is produced by exfoliation of graphite oxide, consists of unoxidized aromatic sp2 islands which are separated by 6-membered oxidized rings containing hydroxyl and epoxied groups and carbon double bonds. Such structural features of GO have been approved by more recent experimental investigations.3,39,40 Similarly, for RGO, the islands of oxidized carbon atoms distributed between graphitic sp2 regions have been observed.3,39 Note that in the edges of GO and RGO, there are also carboxyl groups;26,37 here, we consider periodic GO and RGO models, imposed by the periodic boundary conditions, to model largescale macroscopic GO and RGO systems, so there are no edge groups. The presence of structural defects (e.g., holes) in GO and RGO has also been reported in some experimental works.3,39 Here, such defects have not been considered in the model configuration. Model GO and RGO structures have been generated via a Monte Carlo algorithm, which preserves the above-mentioned structural features: starting with PG, sp2-carbon atoms of graphene are sequentially and randomly selected for possible functionalization, with a probability Pox. A selected sp2-C is always accepted for functionalization (Pox = 1) if it has an oxidized carbon neighbor, whereas if it does not have an oxidized neighbor, it is accepted with a much smaller probability; here, we have used Pox = 0.02. The latter value was chosen by comparing the resulting configurations with available experimental microscopic images of GO and RGO.3,39 The occurrence of unphysical situations, such as creating a single sp2-C that all of its neighbors are sp3-C, is prevented in the algorithm. For both GO and RGO, the functional groups were randomly attached to both sides of the layer. The difference between our model GO and RGO structures is their carbon-to-oxygen (C/O) ratios. For GO, C/ O ratio is 3 and for RGO is 10; these selected C/O ratios are directly correspond to typical experimental values of C/O ratio for GO and RGO.1,2,4,5 The ratio of epoxied to hydroxyl groups is equal to 1. In Figure 1, the model GO and RGO

Figure 1. Top and side view snapshots of the GO and RGO model sheets. These structures were generated based on the Lerf−Klinowski model for graphite oxide. Oxidized carbons of GO and RGO are shown with yellow color, whereas graphitic carbons are blue. Also, a snapshot of the simulation box containing a periodic GO surface is presented; in the simulation box, all PMMA atoms are shown with a green color.

2.2. Molecular Model. Atomistic MD simulations have been performed for stereoregular (i-, s-) and a-PMMA chains confined between model PG, RGO, and GO surfaces. Model systems consist of 80 PMMA chains, containing 20 chemical repeat units. A single periodic and flexible layer of PG, RGO, or GO was located in the simulation box parallel to the xy plane and periodic boundary conditions were applied along the three directions. The simulation box dimensions for all interfacial model systems are approximately 5 × 5 × 10 nm3 along the x, y, and z directions, respectively. The applied periodic boundary conditions make our model as a multilayered film of PMMA, confined between infinite sheets with layer thickness of about 10 nm. A snapshot of the simulation box is presented in Figure 1. The layer thickness is pretty larger than the gyration radius of unperturbed PMMA model chains, Rg ≈ 1 nm, and therefore the degree of confinement is rather weak (d/(2Rg) ≈ 5, where d is the thickness of the confined film). The numbers of basal carbon atoms for the model PG, RGO, and GO surfaces are equal and they have almost similar dimensions. The weight fractions of PG, RGO, and GO in the model multilayered films are 6.98, 7.86, and 9.87 wt %, respectively, slightly larger than typical concentrations of graphene-based nanofillers in polymer nanocomposites (usually 0.1−5 wt %). The volume fractions of nanofillers, calculated using the mixing rules and the densities of bulk polymers and confined systems, are 3.92, 4.24, and 5.22 vol % for PG, RGO, and GO, respectively. Details about the model systems are given in Table 1. For PMMA, an all-atom force field has been used42−44 that fairly describes the bulk properties of stereoregular PMMA, C


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Macromolecules Table 1. Description of the Model Systemsa system

Natom

wt %

vol %

i-PMMA/PG i-PMMA/RGO i-PMMA/GO

25 408 25 559 25 912

6.97 7.86 9.87

system

lz (Å)

⟨Rg2⟩0.5 (Å)

3.92 4.24 5.22 ⟨Ree2⟩0.5 (Å)

i-PMMA/GO a-PMMA/GO s-PMMA/GO

101.8 102.1 102.2

10.6 10.4 10.2

27.7 26.4 25.7

ns) were used for equilibration. The latter was examined by calculating structural and dynamical properties of PMMA model chains at different time intervals of the simulation trajectory. Note that, to reduce equilibration time, the wellequilibrated configurations at higher temperatures were used as the initial configurations for lower temperatures.

lx × ly × lz (Å3) 52.2 × 51.6 × 102.0 52.4 × 51.7 × 101.7 52.4 × 52.0 × 101.8 Csim n

41 Cexp ∞

7.6 ± 0.3 6.9 ± 0.3 6.5 ± 0.3

9.2−10.7

3. INTERFACIAL PACKING 3.1. Mass Density Profiles. We start the analysis of the MD simulations by examining the structure of the graphenebased model nanosheets. For this, we have calculated atomic mass density profiles of the PG, RGO, and GO sheets as a function of axial distance, z, from their centers-of-mass. For calculations, the total mass of nanosheet atoms in thin slabs of 0.5 Å along the z direction of the simulation box was sampled over the trajectory. The density profiles of GO, RG, and PG sheet atoms are shown in Figure 2a. For PG, because of the conformational transitions induced by temperature (rippling), there are slight fluctuations in the distance z for each atom; however, most atoms are within 1 Å axial distance of the graphene’s center-of-mass. The density profile of RGO atoms is wider than that of PG, whereas, the density profile for the

7.3−8.4

a

Natom is the total number of atoms in the system; wt % and vol % show the weight and volume fraction of pristine and oxidized graphene sheets in the system, respectively; lx, ly, lz are the box dimensions along the x, y, z directions, respectively, at T = 580 K. ⟨Rg2⟩0.5 and ⟨Ree2⟩0.5 show the average root mean squared radius of gyration and end-to-end distance of unperturbed chains, respectively. exp Csim n and C∞ are simulation and experimental characteristic ratios of model oligomers and high-molecular-weight chains, respectively; simulation results are calculated at 580 K while experimental data are at room temperature. All systems contain 80 PMMA chains (each consists of 20 chemical repeat units).

such as density, Tg, local conformation, and chain dimension.44 For PG and sp2-carbon atoms of GO and RGO, a modified Dreiding force field that was previously used for various sp2carbon structures36,45−47 has been employed. This model describes the equilibrium spacing between graphene sheets in graphite,48 as well as the geometry and phonon structure of graphite and fullerene.47,49 For the oxidized regions of GO and RGO, we have used the Dreiding force field.50 The Dreiding and the PMMA force field exclude nonbonded interactions between first and second chemically bonded neighbors, that is 1−4 interactions are applied. In addition, we should note that the Dreiding does not provide the partial atomic charges, so we assigned the partial charges of the hydroxyl and epoxied groups based on the reported partial charges for alcohols and ethers, respectively.51 The MD simulations were conducted using GROMACS package.52 Leap-frog integration scheme53 with 1 fs time step was used for integration of equations of motion. Simulations were performed at constant temperature and constant pressure (NPT ensemble). A Nosé−Hoover54,55 thermostat and a Parrinello−Rahman barostat56 were used for controlling temperature and pressure. The relaxation times for temperature and pressure coupling were equal to 0.5 and 5 ps, respectively. Nonbonded interactions were truncated at 1.0 nm. van der Waals tail corrections were applied for energy and pressure57 and the particle-mesh Ewald method58,59 was used for the calculation of long-range electrostatic interactions. The Lorentz−Berthelot combination rule was used for calculation of nonbonded interaction between dissimilar atoms. Stereoregular (i- and s-) PMMA/RGO and PMMA/GO systems have been studied at three different temperatures: 520, 550, and 580 K, whereas a-PMMA/RGO and a-PMMA/GO systems have been studied at T = 580 K. In order to compare the above systems with adsorbed PMMA on PG, i-, a-, and sPMMA/PG interfacial systems have been simulated at 580, 550, 520, and 490 K. All of the mentioned temperatures are well above the bulk Tg of the model stereoregular PMMA oligomers (about 100−200 K higher than the bulk Tg of oligomers44). For systems consisting of RGO and GO, simulation times were from 0.4 to 1.0 μs at each temperature and a considerable amount of which (from 150 ns up to 300

Figure 2. (a) Atomic mass density profiles of PG, RGO, and GO sheets as a function of axial distance, z, from their center-of-mass. (b) Atomic mass density profiles of i-PMMA near the PG, RGO, and GO surfaces as a function of axial distance, z, from surface centers-of-mass (T = 580 K). D


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Macromolecules GO surface is considerably wider than those of the PG and RGO ones; the density profile of GO atoms extends to around 5 Å. This is not surprising if we consider that the presence of functional groups, on the basal plane of RGO and GO leads to roughness and curvature of them (specially for the GO surface). Note that, unlike thermally induced roughness (rippling), functional groups and hybridization lead to a rather stable (static) curvature and roughness of RGO and GO nanolayers. To distinguish the contributions of functional groups and the curvature of the basal plane in the wide density profile of GO, the density profile for carbon atoms of GO (which constitute the basal plane of GO) is also depicted in Figure 2a. Evidently, the basal carbons of GO have a relatively wide density profile, which reveals a curvature of the basal plane. A similar behavior of the atomic mass density profiles was observed for all temperatures studied here. In the literature, the adsorption of polymer chains on a solid surface is usually examined through the calculation of the interfacial atom, or monomer, density profiles.29,30,32,60,61 To achieve this, for planar substrates, the density of polymer atoms is calculated in thin slabs parallel to the surface, whereas for substrates with a slight curvature, the position of the substrate is approximated by the position of its center-of-mass.26,30,32 Here, we have performed such an analysis through the calculation of mass density profile for PMMA atoms as a function of axial distance, z, from the center-of-mass of nanosheets, using slabs of 0.5 Å. The results for i-PMMA chains are shown in Figure 2b. Near PG, a layer of adsorbed iPMMA atoms can be seen. For RGO, there is also a sharp adsorption peak, but it is rather lower than that of PG. Near GO, a considerably lower and wider peak than those of the PG and RGO interfaces is seen. However, the lower density profile peaks near the RGO and GO surfaces should not be interpreted as a sign of their weaker adsorption of PMMA chains or of better layered structure of PMMA near the PG surface. As mentioned above, for the calculation of density profiles, the position of the model surfaces was approximated by the z component of their centers-of-mass. Because of the differences between curvature of PG, RGO, and GO sheets (see Figure 2a), density profiles (which are calculated relative to the center-of-mass of nanosheets) are not conclusive concerning the effect of surface chemistry on the interfacial structure of PMMA chains. In Section 3.2, the adsorption of chains on the PG, RGO, and GO surfaces is discussed by computing the minimum distance of monomer’s center-ofmass to the surfaces. Despite the above, interfacial density profiles can provide useful insights into the tacticity dependence of the adsorption of PMMA chains. In this case, we compare different systems containing a similar nanosheet. In Figure 3a−c, the mass density profiles for i-, a-, and s-PMMA close to PG, RGO, and GO surfaces are shown. Near PG and RGO surfaces (Figure 3a,b), the first peak of the interfacial density profile for iPMMA is higher and has larger surface area (up to the first minimum) than that of a-PMMA and, particularly, s-PMMA. Moreover, after the first peak, a small peak can be observed for the density profile of i-PMMA, whereas that of s-PMMA does not have such a peak. Concerning GO, the density profile of iPMMA has also a higher peak than s-PMMA and that of aPMMA is between the above two. The mentioned contrasts between density profiles suggest tacticity-dependent adsorption of PMMA and particularly better interfacial packing of iPMMA chains than s-PMMA. The effect of stereochemistry of

Figure 3. Tacticity dependence of interfacial mass density profiles: (a−c) shows the density profiles of PMMA stereoisomers near the PG, RGO, and GO surfaces, respectively (T = 580 K).

PMMA on its adsorption on PG, RGO, and GO sheets is further discussed in Section 4. 3.2. Distribution of Monomer/Surface Distance. Here, we provide a more detailed investigation of the adsorption of PMMA chains, by examining the distributions of (minimum) distance between monomer centers-of-mass and model surfaces, denoted as f(d). Assuming bins of size δ,f(d)δ shows the fraction of monomers for which the minimum distance, d, between monomer center-of-mass and the surface atoms (all carbons and atoms of functional groups) falls in the É ÅÄ δ δ Ñ interval of ÅÅÅÅ d − 2 − d + 2 ÑÑÑÑ; here, we have used δ = 0.5 ÅÇ ÑÖ Å. Note that the calculation of distributions based on the minimum distance from surfaces differs from the calculation of density profiles (data shown in Figure 2b); the latter has been

(

E

) (

)


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Macromolecules measured as a function of axial distance from surface’s centersof-mass. The use of minimum distance provides direct insight into the interfacial structure of PMMA chains adsorbed on the RGO and GO surfaces, despite their considerable roughness and curvature. For a more clear comparison of the different systems, f(d) curves are normalized with the values of f far from surfaces (bulk-like regime), f °. It is worth mentioning that near a periodic and perfectly flat surface, f(d)/f° curve is identical to normalized (with bulk value) interfacial monomer number density profile as a function of axial distance from the surface center-of-mass. For PMMA chains at the vicinity of PG surface, which has a very small curvature, f(d)/f ° curves are very similar to the corresponding monomer number density profiles. The calculated f(d)/f° curves for i- and s-PMMA near PG, RGO, and GO surfaces are shown in Figure 4a−c for different temperatures. First, Figure 4a shows the spatial distribution of monomers of i-PMMA around model surfaces, at T = 580 K. Near all model surfaces, a large peak can be observed which indicates the organization of an adsorbed layer of i-PMMA monomers. The height of the adsorption peak is almost similar for all model surfaces; however, the peak appears at smaller distances to the RGO and GO sheets compared to the PG one. The closer adsorption peak is related to ability of PMMA atoms to come near the functional groups, especially hydroxyl groups, of RGO and GO (see also the discussion in Section 3.3). The first peak of f(d)/f ° curves is extended up to around 7 Å. In Figure 4b, the spatial distribution of monomer centerof-mass for i-PMMA at T = 520 K is shown. The pattern of f(d)/f ° is quite similar to T = 580 K data (as shown in Figure 4a). The width and height of the first peak are equal at both temperatures and also, at both 580 and 520 K, near all model surfaces, i-PMMA exhibits a small peak after the first adsorption peak, which indicates the partial organization of a second layer of i-PMMA monomers close to the surfaces. In Figure 4c, the spatial distribution of monomer center-of-mass for s-PMMA at T = 580 K is shown. Similar to i-PMMA, a large adsorption peak can be observed near all model nanosheets. Also, the peak is closer to the RGO and GO surfaces. However, concerning the presence of a second small peak, there is a slight difference between f(d)/f ° of s- and iPMMA chains. Overall, the results concerning the spatial distribution of monomer center-of-mass, show the organization of an adsorbed layer of monomers close to GO, RGO, and PG sheets for PMMA stereoisomers (results for a-PMMA are shown in Figure 7). The adsorption peak is closer to the RGO and specially GO surfaces than the PG surface. Additionally, consistent with the density profile data (Figure 3), partial organization of a second adsorption layer is also observed for iPMMA. 3.3. Local Interfacial Arrangement. In this section, we provide a detailed picture about the organization of PMMA atoms near the functional groups of RGO and GO, through the calculation of RDF between individual atoms of nanosheets and individual atoms of PMMA; that is ga,b(r) = ρb(r)/ρb ave, where a ∈ {surface atoms} and b ∈ {PMMA atoms}; here, ρb(r) is the number density of type b atoms at a distance r around type a atoms. Atom types are defined in Figure 5, which depicts a portion of a PMMA chain and of an oxidized graphene surface. In most cases, we have considered Cb, Cm, Csm, and Oc atoms of PMMA for calculation of RDFs. Atom type Cb stands for the backbone carbon while Cm, Csm, and Oc

Figure 4. Spatial distribution of monomer center-of-mass around model surfaces. f(d) is the distribution of (minimum) distance between monomer centers-of-mass and model surfaces; f ° is the value of f far from surfaces. (a−c) shows the monomer distributions for iPMMA at T = 580 K, i-PMMA at T = 520 K, and s-PMMA at T = 580 K, respectively. The assumed length scale of adsorption of monomers is shown via a dashed vertical line.

are, respectively, the α-methyl carbon, ester-methyl carbon, and carbonyl oxygen that belong to the side groups of PMMA (see Figure 5a). Excluding hydrogen atoms, Cm, Csm, and Oc can be considered as the exterior atoms of a PMMA chain. The calculated RDFs for s-PMMA atoms adsorbed on the PG and GO surfaces, at T = 520 K, are provided in Figure 6. In more detail, the RDFs for Cb, Cm, Csm, and Oc atoms of PMMA relative to the carbon atoms of PG (CGR atoms) are provided in Figure 6a. The peaks of the RDF curves for side group atoms (Oc, Cm, and Csm), compared to backbone atoms F


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in Figure 6b. Because of the high concentration of functional groups on GO, a considerable amount of CGR atoms are in the neighborhood of oxidized regions. So, because of the different environment, the pattern of the RDF curves relative to CGR atoms of GO is different from that of PG; specially those of Csm and Oc. It should be noted that, due to the rather low concentration of functional groups on the RGO surface, the RDF curves around the CGR atoms of RGO are similar to those of the PG surface (the RDF curves around atoms of the RGO surface are presented in Figure S1 of the Supporting Information). The positions of PMMA atoms around hydroxyl functional groups of GO are investigated through the calculation of corresponding RDF curves around the H atoms of hydroxyl groups; the results are presented in Figure 6c. The Oc distribution exhibits the closet peak to H atoms. The hydroxyl H atoms have a large partial positive charge and the Oc atoms have a large partial negative charge, and they stay close to each other because of the electrostatic interaction. The large and close peak of the RDF curve for Oc atoms around H atoms provides a sign of hydrogen bond formation between PMMA chains and hydroxyl functional groups of GO and RGO. The Csm, Cm, and Cb distribution curves also worth attention. Peaks of Csm and Cm curves are slightly further than that of Oc curve and Csm has a considerably larger peak than Cm. As expected, Cb has a wide distribution curve, which is located far from hydrogen atoms of GO. Relative to hydroxyl H atoms, we have also calculated RDF curve for Os atoms which are the ester oxygen of PMMA. Similar to carbonyl oxygen atoms (Oc), Os atoms have a large partial negative charge; however, it can be seen that, due to the location of Os in a PMMA chain (see Figure 5a), the peak of Os distribution is farther from H atoms

Figure 5. (a) Small portion of a PMMA chain which shows the names of different atoms of PMMA. (b) Piece of an oxidized graphene surface which contains the names of its atoms.

(Cb), are closer to the PG surface. Also, Csm shows the largest peak near PG, revealing a tendency of PMMA chains to adsorb on the PG surface via side groups, particularly, via ester-methyl groups which are located at the end of the rather large ester side groups of a PMMA chain. The RDF curves concerning the arrangement of PMMA atoms near graphitic regions (CGR atoms) of GO are depicted

Figure 6. Pair RDF curves between specific atoms of the PG and GO surfaces and of s-PMMA. (a) g(r) shows distribution of PMMA atoms near carbon atoms of the PG surface. Distribution of PMMA atoms around (b) graphitic carbons, (c) hydroxyl hydrogen, and (d) epoxide oxygen of the GO surface. (T = 520 K). G


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Table 2. Number of Hydrogen Bonds per Donor and the Polymer/Surface Interaction (Potential) Energies, Normalized with the Contact Area, at T = 580 K and T = 520 K T = 580 K NHB/Ndonor

Ed (mJ m−2)

i-PMMA/GO a-PMMA/GO s-PMMA/GO

0.17 ± 0.01 0.16 0.17

−116.4 ± 0.5 −115.9 −114.3

i-PMMA/RGO a-PMMA/RGO s-PMMA/RGO

0.21 ± 0.01 0.21 0.19

−116.8 ± 0.5 −115.3 −114.4

i-PMMA/PG a-PMMA/PG s-PMMA/PG

0 0 0

−110.9 ± 0.5 −109.5 −108.9

T = 520 K Ep (mJ m−2) (a) GO −22.7 ± 0.3 −23.5 −23.7 (b) RGO −10.5 ± 0.3 −10.7 −10.9 (c) PG 0 0 0

than those of Oc, Cm, and Csm and hence they do not participate in the formation of hydrogen bonds. To obtain information about the arrangement of PMMA atoms around epoxide groups, in Figure 6d the correlation between PMMA atoms and epoxide oxygen atoms, OE, is presented. OE atoms have relatively large partial negative charges. The closest and largest peak belongs to Csm and the smallest belongs to Oc, which has repulsive electrostatic interaction with OE atoms of GO. Relative to OE, we also have measured RDF for Cs atoms of PMMA. The Cs atoms have partial positive charges, but due to geometric limitation (see Figure 5a) they cannot come close to the GO surface. As discussed above, gH,OC(r), which shows correlation between hydrogen atoms of surfaces and carbonyl oxygen atoms (Oc) of PMMA (see Figure 6c), reveals the formation of hydrogen bonds between PMMA and GO. Here, we estimate the number of hydrogen bonds between PMMA stereoisomers and the model RGO and GO surfaces. A geometric criterion was used for counting the hydrogen bonds: H···O distance should be less than 3 Å and O···H−O angle should be larger than 130°.24 The calculated number of hydrogen bonds, normalized with the number of donors (hydroxyl groups of surfaces), at 580 and 520 K, is provided in Table 2. At both temperatures, the number of hydrogen bonds per donor is higher for RGO than GO; however, because of its larger number of donors, GO, as compared to RGO, has higher (absolute) number of hydrogen bonds (the number of donors on the model GO surface is around 3 times more than that of the RGO model surface). On the GO surface, the presence of many hydroxyl groups close to each other leads to a limitation of space for PMMA chains to interact with all hydroxyl groups. Because of the increase of density and decrease of mobility of polymer chains, the number of hydrogen bonds increases with reducing temperature for both GO and RGO surfaces. Concerning the effect of tacticity, only near the RGO sheet, a slight increase of number of hydrogen bonds from s-PMMA to i-PMMA can be observed; however, the differences are within the error bars of our calculations. For accurate calculation of polymer/surface interaction energies, ab initio calculations is required. However, for the characterization of our model systems, at the end of this section, we provide the interaction (potential) energies between PMMA stereoisomers and model nanosheets. The intermolecular PMMA/PG potential energy is solely due to dispersion (van der Waals) interactions, whereas for the

NHB/Ndonor

Ed (mJ m−2)

Ep (mJ m−2)

0.19 ± 0.01

−124.3 ± 0.5

−26.2 ± 0.3

0.19

−122.2

−28.0

0.25 ± 0.01

−122.3 ± 0.5

−12.1 ± 0.3

0.24

−119.4

−12.7

0 0 0

−117.1 ± 0.5 −115.2 −114.3

0 0 0

PMMA/RGO and PMMA/GO systems, due to the presence of functional groups, both dispersion and polar (electrostatic) interactions are present. The dispersion, Ed, and polar, Ep, interaction energies normalized with the contact area, which is twice of nanosheet surface area, are reported in Table 2. As expected, from PG to GO, with increasing concentration of functional groups, Ep increases. However, for both RGO and GO model nanosheets (that contain equivalent concentrations of hydroxyl and epoxide functional groups), Ep is considerably smaller than Ed. The ratio of Ep/Ed is around 0.1 and 0.2 for RGO and GO model surfaces, respectively. In addition to polar energy, Ep, it can be seen that the RGO and GO model surfaces have a slightly larger dispersion energy, Ep, than the PG surface. Overall, well above glass transition temperature, total interaction potential energy, Ep + Ed, for the PMMA/GO interface is about 9 and 27% larger than those of PMMA/RGO and PMMA/PG interfaces, respectively. As temperature decreases, interfacial density and absolute value of polymer/ substrate interaction energies increase.

4. CONFORMATION OF ADSORBED CHAINS 4.1. Spatial Extension of Trains, Loops, and Tails. Based on the analysis of spatial distribution of monomer center-of-mass, we have provided a line of evidence about the organization of an adsorbed layer of PMMA monomers close to all model surfaces (Section 3.2). Here, we continue our investigation by analyzing the conformation of chains that have at least one adsorbed monomer, usually defined as adsorbed chains.29 We have considered a monomer adsorbed on a model surface, if the minimum distance between its center-of-mass and the surface atoms is less than 7 Å. This distance corresponds to about the width of the first peak of f(d)/f ° curve for monomers of PMMA chains, shown in Figure 4. Following Scheutjens and Fleer,62,63 the monomers of an adsorbed chain can be classified as belonging to: (a) trains (consequent adsorbed monomers), (b) loops (sequences of monomers connecting two trains), (c) tails (monomers between a train and a chain end), and (d) bridges (in the case that a chain connects two different surfaces) (see Figure 7a). The train monomers are, by definition, the adsorbed monomers and the first adsorption peak of the f(d)/f ° curve shows their contribution. Figure 7b,c presents the spatial distribution of tails and loops (f tail(d)/f ° and f loop(d)/f °), together with the total monomer distribution, for PMMA stereoisomers near the PG and GO surfaces at 580 K (the H


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tails and loops for PE chains of different lengths (C40 up to C400) on graphite as calculated using MD and Monte Carlo simulations,29 as well as those of long polyamide-6,6 chains (100-mer) on graphene and oligomeric PMMA (20-mer) in contact with a silica nanoparticle as determined using coarsegrained and atomistic MD simulations.24,31 The length scale of extension of tails is the largest (structural) interphase thickness in the model systems. 4.2. Statistics of Trains. As mentioned above, trains are defined as sequences of adsorbed monomers of a chain. Thus, valuable insights into the interfacial structure can be gained by analyzing the statistics of trains. First, in Figure 8a the average

Figure 7. (a) Schematic representation of an adsorbed chain. Train, loop, and tail are also specified. (b,c) shows the spatial distribution of monomers belonging to tails and loops, together with the spatial distribution of all monomers, as a function of minimum distance between monomer center-of-mass and surfaces, d, for PMMA stereoisomers near the PG and GO surfaces, respectively (T = 580 K). In (b) subplot, the length scale of extension of trains, loops, and tails are illustrated. Rm, Rg, and Ree are monomer size, gyration radius, and chain end-to-end distance, respectively.

Figure 8. (a) Fraction of train monomers, and (b) weighted average number of monomers that belong to a train, for i-PMMA, s-PMMA, and a-PMMA adsorbed on the different (PG, RGO, and GO) surfaces (T = 580 K).

fraction of monomers belonging to trains, f tr, is shown. f tr is the ratio of number of train monomers, that is adsorbed monomers, to total monomers in the system; for the current model systems, f tr varies between 0.11 and 0.14. It is clear that (i) for the PG, RGO, and GO surfaces, from s-PMMA to iPMMA, the fraction of train monomers slightly increases (f i‑PMMA > f a‑PMMA > f s‑PMMA ). f i‑PMMA is about 2 and 4% larger tr tr tr tr a‑PMMA s‑PMMA than f tr and f tr , respectively. (ii) For all PMMA stereoisomers, the values of f tr increase with the concentration RGO GO of functional groups (f GO > f PG tr > f tr tr ). f tr is around 9 and PG 20% larger than f RGO and f , respectively. This dependence of tr tr f tr on surface chemistry can be seen in relation with the change of polymer/surface interactions, mainly because of the presence of hydroxyl groups, and higher roughness of the

results for the RGO surface are provided in Figure S2 of the Supporting Information). Qualitatively tail and loop spatial distributions are similar for all PMMA stereoisomers and surfaces. The length scale of extension of loops is approximately 1 nm from surfaces, which is almost equal to the Rg of unperturbed chains. Tails extend deeply to about 2.5 nm, which corresponds to the end-to-end distance (Ree) of unperturbed chains. Also, most monomers that are located up to around one Rg from surfaces, belong to trains, loops, or tails. The length scales of the extension of tails and loops for our model systems are comparable to the reported length scales of I


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Macromolecules RGO and GO surfaces relative to the PG surface which might increase their effective surface area (or available volume around surfaces) for the adsorption of monomers. Note that it is possible to approximately estimate a value for f tr by calculating 2 × δ , where d is the confined film thickness, δ d = 0.7 nm, is the length scale of adsorption of monomers, and coefficient 2 takes into account two sides of surfaces; for the current model systems, in all cases d ≈ 10 nm and 2 × 0.7 = 0.14 (as mentioned above actual values vary between 10 0.11 and 0.14). In Figure 8b, the weighted average train size, ⟨str⟩ (⟨str⟩ =

∑s s 2N (s) ∑s sN (s)

, where N(s) is the number of trains with

size s) is shown. ⟨str⟩ shows the weighted average number of monomers belong to a train. Values of ⟨str⟩ fall in the interval of 4−8 monomers for the current model systems. The following general trends can be observed in Figure 8b: (i) ⟨str⟩ is tacticity-dependent and increases with the population of isotactic sequences of PMMA (⟨str⟩i‑PMMA > ⟨str⟩a‑PMMA > ⟨str⟩s‑PMMA). The tacticity dependence of ⟨str⟩ is more pronounced than f tr. ⟨str⟩i‑PMMA is around 13 and 24% higher than ⟨str⟩a‑PMMA and ⟨str⟩s‑PMMA, respectively. The tacticitydependent train properties are discussed in Section 5 in connection with chain dimensions and stiffness. (ii) The size of trains depends on surface chemistry and increases from PG to GO (⟨str⟩GO > ⟨str⟩RGO > ⟨str⟩PG). On average, ⟨str⟩ for PG is about 20 and 45% less than those of RGO and GO surfaces, respectively. As mentioned above, because of the roughness of the RGO and GO surfaces, their surfaces geometry is different from that of PG surface. It has been proposed that, because of their geometries, the disordered surfaces increase the probability of contacts with chain molecules.64,65 Also, a chain can interact with a rough surface without changing its shape very much.64,65 Overall, both modification of polymer/ surface interactions and roughness of graphene based surfaces can affect the size of train conformations. It is worth noting that ⟨str⟩ exhibits a rather weak chain length dependence, whereas the average tail and loop sizes are highly chain length-dependent and monotonically increase with increasing length of polymer chains.29,63 In the case of our model systems, the weighed average tail and loop sizes are around 12 and 5 monomers, respectively. As a side note, the fraction of adsorbed chains varies around 0.29−0.34 and the average number of trains per adsorbed chain falls between 1.5 and 2.5, for the model systems studied here. More detailed information about the structure of trains can be acquired by analyzing the train size distribution. Here, we compute the weight fraction of trains with size str, W(str) (W (str) =

strN (str) , ∑s sN (s)

Figure 9. Weight fraction of trains with size str for (a) i-PMMA and (b) s-PMMA chains adsorbed on PG, RGO, and GO sheets (T = 580 K).

of W(str) curves, comparing Figure 9a,b reveals that i-PMMA, as compared to s-PMMA, has a wider curve with a lower peak and a higher concentration of large trains. Also, the peak of W(str) curve for i-PMMA is located at slightly larger str values than that of s-PMMA. Although W(str) provides information about the number of monomers that belong to small and large trains, it might hide information about the number of trains, especially number of small trains. So, it is also convenient to consider the number fraction of trains with size str, P(str). The calculated P(str) curves are provided in Supporting Information (Figure S3). Unlike W(str), in most cases P(str) shows rather large values at str = 1,2, which is partly due to the preference of chain ends to be adsorbed on the graphene-based surfaces. As shown in Figures 9 and S3, in all of the model systems studied in this work the probability of finding a train length equal to the total chain length is small. This is in contrast to the results of adsorption of linear PE chains on a graphite substrate, that for PE chains containing up to about 80 backbone carbon atoms, a rather large probability for full adsorption of a chain has been reported.29 The simulation results discussed in this section provide a basis for the explanation of experimental findings about higher shift of Tg for i-PMMA thin films and nanocomposites than those of s-PMMA,5,16 as well as recent simulation results, from

where N(s) shows the number of trains

with size s). The results of W(str) for i- and s-PMMA near PG, RGO, and GO surfaces are shown in Figure 9a,b, respectively. In all cases, W(str) has a qualitatively similar trend; W(str) begins with a rather small value at str = 1 and then increases and goes through a maximum around str = 4, 5, 6 monomers, after which it decays ultimately to zero. The dependence of W(str) on surface chemistry and tacticity is of interest. For both i- and s-PMMA chains, with increase of the concentration of functional groups, the peak height of W(str) reduces, the position of peak slightly shifts toward larger sizes, the W(str) curve become broadened, and the weight fraction of large size trains increases. Similarly, concerning the tacticity dependence J


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Macromolecules our group, reporting more restricted interfacial dynamics and higher shift of Tg for i-PMMA/PG interface, compared to sPMMA/PG one.32 i-PMMA has a slightly higher fraction of train monomers, and more importantly a larger average train size. Train properties are also linked to the better interfacial packing of i-PMMA than s-PMMA (as discussed in Sections 3.1 and 3.2). These tacticity-dependent interfacial structural properties lead to tacticity-dependent dynamical behavior and shift of Tg as well.

5. CHAIN DIMENSIONS In this section, we analyze the dimensions of PMMA chains by calculating the gyration tensor, S, as a function of distance from the model surfaces. The position of each chain, relative to the surface, was determined by the minimum distance between the chain center-of-mass and the surface atoms. Mean-squared gyration radius, ⟨Rg2⟩, has been calculated through S66 ⟨R g 2⟩ = ⟨Sxx + Syy + Szz⟩

(1)

where Sxx, Syy, and Szz are the diagonal components of S, and ⟨⟩ indicates average over all chains whose centers-of-mass are located in an appropriate distance from graphene. Eigenvalues of S form an ellipsoidal cloud for polymer chains.66 Thus, in order to characterize asymmetries in the shape of chains, or their aspect ratio, we also calculate ⟨λ1⟩/⟨λ3⟩; here, λ1 and λ3 are the largest and smallest eigenvalues of S, respectively. The calculated values of ⟨Rg2⟩ for i-, a-, and s-PMMA chains in different regions around the PG, RGO, and GO surfaces are provided in Figure 10. First, the unperturbed dimensions (distances further than around Rg from nanosheets) are worth attention. Experimentally, it has been found that the dimension of PMMA chains (both oligomers and high molecular weight chains) is tacticity-dependent and larger for i-PMMA than aand s-PMMA.11,13,15 The simulation results capture the tacticity-dependent dimension of PMMA chains (also see Table 1). Second, concerning interfacial behavior, i-PMMA exhibits different behavior than s-PMMA. Close to all three studied surfaces, an increase in the gyration radius of i-PMMA chains can be observed while no significant alteration of gyration radius can be detected for s-PMMA. The stretching is seen for i-PMMA chains, whose centers-of-mass are located up to around 8 Å of the model surfaces. A considerable number of monomers of a chain should be adsorbed, if its center-of-mass come to such a close distance from the surface (as mentioned above the length scale of adsorption of monomers is about 7 Å). Therefore, the long adsorbed trains of i-PMMA monomers belong to these chains that their centers-of-mass are close to the surfaces. So, the increase in the dimension of i-PMMA chains might be explained as follows: the dimension of those portions of i-PMMA chains that are adsorbed (i.e., trains) increases and as the lengths of model chains are small, the increment in the size of trains is reflected in the overall dimension of chains. It is worth mentioning that similar behavior to Rg was found for end-to-end distance, Ree (see Figure S4). The ratios of the largest to smallest eigenvalues of gyration tensor ⟨λ1⟩/⟨λ3⟩ are shown in Figure 11a−c. This ratio can be considered as the (square of) aspect ratio of polymer chains. In the case of spherical symmetry in the shape of chains, the ratio equals 1.0. First, regarding unperturbed behavior (further than a distance of about one Rg from the surfaces), it can be seen that, on average, the ratio of eigenvalues is larger for i-PMMA

Figure 10. Mean squared gyration radii of i-, a-, and s-PMMA chains in different regions (see x-axis ticks) around the PG, RGO, and GO surfaces at T = 580 K. (a−c) shows the results for PG, RGO, and GO surfaces, respectively. To improve visibility, the error bars of some data are not shown; for these data, the lengths of error bars are comparable to those that are provided.

than s-PMMA and that of a-PMMA falls between the above two. This difference shows a more asymmetric shape with a higher aspect ratio for unperturbed i-PMMA chains relative to s-PMMA ones. Second, regarding interfacial behavior, at the vicinity of surfaces, an increase in the aspect ratio of all PMMA stereoisomers can be detected. The effect is more pronounced for i-PMMA; i-PMMA has a larger interfacial aspect ratio than a- and particularly s-PMMA. The parallel component of mean-squared gyration radius was also calculated at different distances from the model surfaces; the results are presented in the Supporting Information (Figure S5). The results presented in this section suggest a correlation between dimensions of polymer chains, size of trains, and interfacial packing of chains. Unperturbed i-PMMA chains, compared to a-PMMA and particularly s-PMMA, are stiffer, that is they have a larger gyration radius and characteristic ratio. Furthermore, they become more extended at the vicinity of surfaces. The formation of longer trains by i-PMMA chains is consistent with, and can be explained by, their higher stiffness. It might be worth noting that, by using of a beadspring model, Linse and Källort33 studied adsorption of K


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interfacial packing, forms longer trains, and has a slightly higher fraction of train monomers. Longer trains and better interfacial packing of i-PMMA chains can explain the simulation and experimental results of the more restricted interfacial dynamics of i-PMMA stereoisomer and its higher shift of Tg at attractive interfaces as well. (b) Unperturbed i-PMMA chains are stiffer than a- and, particularly, s-PMMA chains; on top of that, they become more extended in close vicinity of surfaces. The better packing of i-PMMA chains and their longer trains correlate with their stiffness, that is their extended chain dimension. (c) The fraction of train monomers, as well as the average train size, depends on the surface chemistry; both increase as the concentration of functional groups increases. This is related to stronger physical adsorption of PMMA chains on functionalized (GO and RG) sheets, compared to PG, both due to the interaction of PMMA chains with the hydroxyl functional groups, and to the higher surface roughness of functionalized graphene sheets which increases the probability of polymer/surface contacts. (d) For all studied PMMA model systems, tails and loops extend to around Ree and Rg from surfaces, respectively. (e) Ester-methyl carbon atoms, which are located at the end of large ester side group, have a rather high concentration at the model interfaces. Also, a direct sign of hydrogen bond formation between hydroxyl groups of nanosheets and carbonyl oxygen of both iPMMA and s-PMMA was detected. Concerning the effect of surface chemistry, the number of hydrogen bonds per donor is higher for RGO than GO surfaces. In this work, we presented the structural and conformational properties of stereoregular PMMA confined between model RGO and GO surfaces. The dynamical properties of the stereoregular confined PMMA chains will be the subject of a future work.

Figure 11. (a−c) Ratios of largest to smallest eigenvalues of gyration tensor, ⟨λ1⟩/⟨λ3⟩, as a function of distance from the PG, RGO, and GO surfaces at T = 580 K, respectively. For the sake of visibility, only the error bars of some data are presented.

■

polymers from solution. They found that stiffer chains, with higher persistence length and characteristic ratio, form longer trains and have higher fractions of train monomers, which is almost comparable to our above mentioned correlation. Concerning the effect of chain dimensions on the size of trains, one can also consider extreme cases of adsorption of rodlike and flexible polymer chains. These results propose the importance of shape and size of polymer chains in controlling interfacial structure of polymers.

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.9b00574.

6. CONCLUSIONS Atomistic MD simulations were performed to investigate the structural and conformational properties of low-molecularweight i-, a-, and s-PMMA chains confined between periodic PG, RGO, and GO surfaces at various temperatures above Tg. To properly consider the curvature and the roughness of the RGO and GO model surfaces, we investigated the structure and conformation of the adsorbed PMMA by calculating minimum distances between monomer centers-of-mass and surfaces. Our main findings are summarized as follows: (a) We found tacticity-dependent adsorption of PMMA chains on all model surfaces. i-PMMA stereoisomer, as compared to a- and s-PMMA chains, exhibits better

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RDF curves between individual atoms of RGO sheet and individual atoms of PMMA, spatial distribution of tail and loop monomers near RGO surface, number distribution of train length, end-to-end distance of PMMA stereoisomers, and parallel component of mean-squared gyration radius at different distances from the model sheets (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Vagelis A. Harmandaris: 0000-0002-9613-7639 Notes

The authors declare no competing financial interest. L


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ACKNOWLEDGMENTS S.M.V.A. acknowledges partial support from the Research Council of the University of Tehran. This work was partly supported by computational time granted from the Greek Research & Technology Network (GRNET) in the National HPC facility ARIS under HPC-Europa3 project.

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Structure and Conformation of Stereoregular Poly(methyl methacrylate

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