Computer simulations of the early stages of crystal nucleation of linear and short chain branched polyethylene on carbon nanotubes

Accepted Manuscript Computer simulations of the early stages of crystal nucleation of linear and short chain branched polyethylene on carbon nanotubes K. Jerónimo, V.L. Cruz, J. Ramos, J.F. Vega, M. Trujillo, A.J. Müller, J. Martínez-Salazar PII: DOI: Reference:

S0014-3057(14)00146-3 http://dx.doi.org/10.1016/j.eurpolymj.2014.04.021 EPJ 6432

To appear in:

European Polymer Journal

Received Date: Revised Date: Accepted Date:

18 February 2014 25 April 2014 29 April 2014

Please cite this article as: Jerónimo, K., Cruz, V.L., Ramos, J., Vega, J.F., Trujillo, M., Müller, A.J., MartínezSalazar, J., Computer simulations of the early stages of crystal nucleation of linear and short chain branched polyethylene on carbon nanotubes, European Polymer Journal (2014), doi: http://dx.doi.org/10.1016/j.eurpolymj. 2014.04.021

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Computer simulations of the early stages of crystal nucleation of linear and short chain branched polyethylene on carbon nanotubes

K. Jerónimoa,b, V.L. Cruza, J. Ramosa, J.F. Vegaa,*, M. Trujillob, A.J. Müllerb,c,d and J. MartínezSalazara

a

Biophym, Departamento de Física Macromolecular, Instituto de Estructura de la Materia, CSIC, C/ Serrano 113 bis, 28006 Madrid, Spain b

Grupo de Polímeros USB, Departamento de Ciencia de los Materiales, Universidad Simón Bolívar, Apartado 89000, Caracas 1080-A, Venezuela c

Institute for Polymer Materials (POLYMAT) and Polymer Science and Technology Department, Faculty of Chemistry, University of the Basque Country (UPV-EHU), Paseo Manuel de Lardizabal 3, 20018 Donostia-San Sebastián, Spain d

IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain

*Corresponding author: e-mail: [email protected], Tel.: +34 915616800, Fax: +915 615 413

1

Abstract We have used molecular dynamics simulations to study the process of macromolecular organisation of single chain linear and branched polyethylene on the surface of carbon nanotubes. These systems can be considered as good models for the study of the mechanism of polymer folding at the early stage of crystal formation on carbon nanotubes. The mean-squared radius of gyration, the stem length, the bond orientation order parameter and the radial distribution have been used to describe the organisation process and the structure of the chains at the carbon nanotube surface. When compared to the process of organisation of isolated single chains, interesting results are observed: (i) two different mechanisms of chain organisation give rise to different morphologies; lamellar thickening and lateral crystal growth lead to mono- and multilayered structures, independently of the presence of short chain branching; (ii) lamellar thickening is however hindered, but still present, in the case of polymer chains with short chain branches; (iii) both the stem length and the order parameter increase in the nanocomposites with respect to those obtained for isolated chains under the same conditions; (iii) the reorganisation process of thickening is accelerated by the presence of the carbon nanotubes, which act as nucleating agents; and (iv) the presence of short chain branching in polymer chains delays the onset of nucleation and growth of the crystalline structure, suggesting that the process is quite sensitive to the local chain chemistry.

Keywords: Polymer crystallisation; Carbon nanotubes; Molecular dynamics; Crystal nucleation; Chain folding; Lamellar thickening

2

1. INTRODUCTION The incorporation of carbon nanotubes (CNTs) into polymeric matrices has attracted great attention in the scientific community. When CNTs are adequately dispersed, interesting polymeric nanocomposites can be prepared with enhanced mechanical properties and ease of processing [1-8]. These polymer/CNT nanocomposites are characterised by a combination of intrinsic properties associated to each of the components, but the dispersion of the CNTs and their interaction with the polymeric chains play also a key role in their final properties [9]. Indeed, there are synergistic effects that arise from this interaction, which may lead to the organisation of the long polymeric chains onto the CNT surface. This is particularly attractive in the case of crystallisable polymeric matrices. In these cases CNTs are considered as nucleating agents, as they can provide an adequate surface to promote polymer crystallisation. Notwithstanding, crystallisation behaviour of nanocomposites is sensitive to many factors, including the molecular architecture of the polymeric matrix, the dimensions and the surface features of the CNT, and the method of preparation of the nanocomposites [10]. It is very difficult to experimentally observe the dynamics of the structural changes driven by the crystallisation of polymers onto CNTs through experiments. For this reason, computer simulation can be regarded as a valuable tool for exploring the dynamics of polymers, including the crystallisation process of semicrystalline polymers. The organisation of single polymeric molecules onto CNT surfaces has been studied by some authors using computer simulations [11-16]. From these studies one can extract that the structure of a polymer on a CNT surface is determined by three main factors: the dimensions of the CNTs, the cooling program and the molecular architecture of the matrix (that eventually controls chain conformation and flexibility). Wei implemented Molecular Dynamics (MD) simulations to explore the conformational features of linear polyethylene (PE) chains on CNT and found a dependence of the wrapping angle of the polymer on the radial dimension of the CNT [11] . Kumar and co-workers have recently studied the effect of the radius of the CNT and the method of cooling [12]. They found that both absorption and arrangement of linear PE chains onto CNT are strongly affected by these two factors. The quenching process leads to a straight lamellar arrangement of the polymeric chain on the CNT surface, while the orientation is independent of its radius. However, during stepwise cooling a helical wrapping arrangement of the polymer chain is observed on the CNTs of moderate radii, while a straight lamellar arrangement is observed on the CNT with the smallest radius of around 2.0 Å. The effects of molecular architecture of the polymer matrix have also been explored. For instance, Yang and co-workers studied the organisation of linear PE molecules with different molecular weight on a fixed size CNT [13]. They cooled the systems from a high equilibrated temperature to room 3

temperature and analysed the effect of the polymer length on the crystal size and its evolution along the simulation. They found that the CNT surface offers an effective support for the crystallisation, and that the van der Waals components of the potential were identified as the driving force of the process. Gurevitch and Srebnik [14] and Tallury and Pasquinelli [15,16] carried out computer simulations to study the conformational behaviour of polymeric chains of different stiffness on CNTs at a fixed temperature. They found that the conformation of an adsorbed chain depends on its stiffness, ranging from the randomly adsorbed conformations of flexible chains to the helical conformations in the case of rigid macromolecules. Conformational features and chain flexibility can be easily modulated in PE by means of the incorporation of a comonomer, or, in other words, short chain branches (SCB). Recently, we have studied in depth by experiments and computer simulations the effect of SCB in both the conformation and dynamics in the melt [17-23], and the structure and crystallisation process [24-28] of model polyolefins and n-alkanes but in the absence of an absorbing surface. The role of SCB in the physical properties of polyolefins has been widely explored from the experimental point of view, and now simulations are giving us interesting information which is not possible to obtain experimentally [1923,26-28]. In these works, it has been shown that the SCB number and composition has considerable influence on the crystallisation process. In general, SCB is excluded from the crystal and causes a progressive reduction in crystal size and stem length. Thus, we consider of great interest to explore the role of the SCB of the polyolefinic matrix in the organisation of the chains when they are absorbed onto a CNT. In this paper, we examine the effect of SCB on the structural evolution of single chains with different molecular architecture during the crystallisation process onto a single CNT. These simulations are compared with equivalent systems in the absence of the CNT, and also with experimental data available from the literature [29-32].

2. MOLECULAR MODELS AND SIMULATION METHODS The procedures of our computer simulations were adopted from reference 13. However, we have studied not only linear but also polyolefins with SCB, as in these systems the effect of molecular architecture on the interaction between macromolecules and CNTs has not been explored either experimentally or by means of computer simulations. We have used the graphical interface of Materials Studio software package from Accelrys Inc., for the construction of all our molecular models. The single wall CNT has a length of 122.98 Å and a radius of 6.78 Å. We have also constructed a series of flexible PE backbones with a variable number of randomly placed butyl side 4

groups (ethylene/1-hexene copolymers). The polymeric chains consisted of 0, 5 and 10 butyl branches randomly distributed in a chain containing 1,000 methylene units. The polymers have been denoted as PE00, PE05 and PE10. In each molecular model, a randomly generated PE chain was placed randomly surrounding the CNT (see Figure 1). The CNT length was supposed to be much longer than the PE chain length. The structure of the CNT was made periodic along the z-axis and the positions of CNT atoms restrained to their initial values along the MD simulations. Previous studies also imposed such a limitation in the degrees of freedom of this element of the model [14-16]. Before the MD simulations, 500 steps of energy minimization have been performed to relieve unfavourable conformations. For the MD simulations, we have used a NVT ensemble at a temperature of T=325 K, using the Dreiding force field. The parameters used in the Dreiding force field are those listed in reference [33]. A united atom model with methyl (-CH3), methylene (-CH2-) and methyne (-CH-) groups represented as individual interaction sites has been used to simplify calculations. The total potential energy Etotal consists of four terms: (1) the bond stretching energy Estretch for two adjacent united atoms, (2) the bond-bending energy Ebend among three adjacent united atoms, (3) the torsion energy Etorsion among four adjacent united atoms, and (4) the 12-6 Lennard-Jones potential EvdW (van der Waals) between two non-bonded atoms. The parameters of the periodical box were a=b=160.91 Å and c=122.98 Å. The dimensions a and b were long enough to guarantee that PE chains are not affected by periodical boundary conditions. The c dimension equals the length of the CNT. We have used a time step of 1 fs and a production run time of 2 ns. All cutoff radii have been set to 12.0 Å, and a buffer length of 0.5 Å has been adopted. In addition, the same PE chains have been simulated in absence of the CNT to compare the results with those obtained in the composite models. We have performed 10 replicas of each MD simulation to better sample the conformational space and to ensure reliability. We are aware that this sampling might be incomplete due to the complexity of the system and the limitations in the computational resources available. However, the results are consistent and reproducible along the different simulation runs. The following properties have been evaluated in order to characterise the single polymeric chain early stages crystallisation process onto the CNT surface; namely, (a) mean-squared radius of gyration, Rg2 , and morphology (b) the stem length, L, (c) the global order parameter, S, and (d) the radial distribution function with respect to the CNT centre of the linear and branched PE chains, P(r). The functions are analyzed simultaneously for the PE-CNT nanocomposite and the isolated PE systems. It is possible to quantify this process of growth by means of the evaluation of the mean-squared radius of gyration of the macromolecules. Rg2 is proportional to distance between the chain segments, and then it can be obtained from the simulations as: 5

R g2 =

1 N

N

∑ (r

i

i =1

− r0 )

2

(1)

where N is the number of particles (united atoms) and ri and rOi are the position vectors of the ith particle and the centre of mass of the polymeric chain, respectively. This function provides information about the macromolecular packing and its global shape; the higher the Rg2 value the more expanded the shape of the macromolecule. The global bond-orientation order parameter of the whole chain along the z-axis can be calculated using the equation [36]: 1 N 3 cos 2 (ϕ i ) − 1 S= ∑ N − 2 i =3 2

(2)

Where N is the number of particles and ϕi is the angle between the vector bi and the z-axis. The vector bi=(ri-ri-2)/2 is the one formed by the midpoint of two adjacent bonds i and i-1. A polymer chain with the bi perfectly parallel to z-axis assumes a value of S=1, whereas values of S=0 and S=-0.5 go with a perfectly random polymer chain and a perpendicular polymer chain to z-axis, respectively. The branches have been excluded from the calculation of the order parameter [26].

6

3. RESULTS AND DISCUSSION 3.1. Radius of gyration and morphological features The equilibrated PE chains at 325 K have been placed near the CNT and the systems left to evolve in time. Snapshots at different times of representative simulation runs showing the nucleation and organization processes of PE00, PE05 and PE10 chains onto the surface of the CNT are shown in Figures 1 and 2. The Van der Waals energy evolutions and the final energies for PE00, PE05 and PE10 are shown as Supplementary Material (Figure S1 and Table S1).

Figure 1. Snapshots of the organisation process for PE00-CNT nanocomposite at different simulation times: (A) Mechanism I gives rise to the formation of a crystal monolayer and (B) Mechanism II gives rise to the formation of a crystal multilayer. During the first stages of the simulation, in all the cases randomly folded domains (baby nuclei) emerge [34] followed by the chain collapse in which the closest segments to the CNT surface start to be 7

adsorbed on it. Within about 50 ps, entire macromolecules have collapsed onto the CNT surface. This is reflected by a sharp decrease of energy (Figure S1). However, great differences have been found in the dynamics of the process depending on the macromolecular architecture. In the three systems, two different mechanisms have been identified. In the first type (mechanism I in Figure 1A), some segments are adsorbed along the CNT surface, and subsequently the chain continues extending along the z-axis of the CNT by a diffusion mechanism to form a monolayer with a thickened lamellar-like structure. In the second type (mechanism II in Figure 1B), oriented domains of the chain are first formed and then collapse together. In a subsequent step, the globule as a whole is adsorbed onto the surface of the CNT; in this case the diffusion along the z-axis is absent, and lateral growth of the crystal segments takes place forming a multilayered structure. In all cases, the potential and Van der Waals energies are lower in the mechanism I respect to the mechanism II as it can be seen in Figure S1 and Table S1.

8

Figure 2. Snapshots of the organisation process for PE05-CNT and PE10-CNT nanocomposites at different times: (A) Mechanism I for PE05-CNT gives rise to the formation of a crystal monolayer and (B) Mechanism II for PE10-CNT gives rise to the formation of a crystal multilayer.

Both mechanisms have been also observed in the case of PE05 and PE10 chains. In fact the probability of both mechanisms is similar for PE00 and PE05 chains. However, the extent of the thickening process (mechanisms I) is weaker in the chains with SCB than in PE00 at least within the time frame explored, as we will see later. We have quantified the thickening process given by mechanism I in following sections, using the time evolution of both the stem length and the radial distribution. As examples of both mechanisms in the SCB PE-CNT nanocomposites, Figure 2 shows selected simulation snapshots for PE05 and PE10 chains next to CNTs in which mechanism I (Figure 2 A) and II (Figure 2B) are observed.

Figure 3. Evolution of the mean-squared radius of gyration, Rg2, with the simulation time in the different systems studied. (A) PE00, (B) PE05 and (C) PE10. Solid lines correspond to PE-CNT mechanism I; dotted lines correspond to PE-CNT mechanism II and dashed lines correspond to PE isolated chain. Horizontal thin solid lines have been drawn to indicate the extent of the thickening 9

process. The arrows indicate the beginning of the thickening process. Each curve is an average of 5 simulation runs.

As it can be observed in Figure 3, the three model chains in the PE-CNT systems collapse during the first 50 ps of the simulations, to Rg2 values around 500 Å2, and two average structures with different Rg2 values are found. For chains that follow mechanism I (solid lines in Figure 3), after the initial collapse and for a simulation time higher than 50 ps, the values of Rg2 starts to increase and a clear transition to a more elongated structure is observed. This mechanism is independent of the presence of SCB, but it starts at different times depending of the SCB content, as indicated by the arrows in the Figures 3A, 3B and 3C. In addition, there is a gradual decrease in the relative change of the chain size along this process, as the transition is sharper in the case of the linear chain (PE00) than in the case of the branched ones (PE05 and PE10), as indicated by the thin solid lines in the same figures. These facts indicate that some chains can initially collapse in a non stable conformation, but they are able to explore the configurational space depending on local chain mobility. After this initial collapse, driven by the interaction with the CNT, these systems evolve in time and diffuse along the z-axis of the CNT. The extension of the process is also dependent on SCB. In the case of PE05 and PE10 the process is clearly slowed down, as the folded chain segments are fixed and the chain dynamics hindered due to the presence of SCB. For the chains that follow mechanism II (dotted lines in Figure 3), the collapse and adsorption is not followed by the thickening process, and the value of Rg2 remains almost constant until the end of the process, independently of the presence of SCB. Additionally, it has been observed than the chains following mechanism I have a slightly higher trans population than those following the mechanism II (Table S2 in Supplementary Material). There are also differences between the PE-CNT nanocomposites and the isolated chains. The time evolution of Rg2 of the isolated chains is also included in Figure 3. At first sight it is seen that the presence of the CNT affects the process from the initial stages. In fact the CNT surface acts as an effective nucleus, speeding up the structuring process of the chains. It is also observed that the isolated chains sharply evolve to ordered structures from the beginning of the process, reaching lower values of Rg2 than in the case of the PE-CNT nanocomposites. Table 1 compares the values of Rg2 obtained at the end of the simulation runs for the PE-CNT nanocomposites and the isolated systems. The effect of the macromolecular architecture is clearly observed. As the number of SCB increases, the values of Rg2 of the isolated systems and of the chains in PE-CNT nanocomposites that follow mechanism II 10

also slightly increase. However, those chains that follow mechanism I finally reach a very high value of Rg2 after the thickening process, being the effect more pronounced in the case of the linear PE00 chain. In all the cases, the values of Rg2 are quite higher than those found for the isolated PE chains, pointing towards the strong nucleating effect of the CNT. Table 1. Mean-squared radius of gyration, Rg2 , global order parameter, S, and lamellar stem length, L, for each system at the end of the simulation runs. Averaged values over 10 simulation runs are reported in each case. The standard error of the mean is within the range ±3-6 %. PE-CNT nanocomposites Sample

Rg2 (Å2)

Isolated chain

L (Å)a

S (-)

Rg2 (Å2)

S (-)

L (Å)a

I

II

I/II

I

II

PE00

1063.8

331.1

0.66

46.1

27.0

179.1

0.62

16.7

PE05

922.9

383.1

0.63

40.6

22.9

183.1

0.50

15.6

PE10

683.2

385.1

0.60

32.3

22.0

186.5

0.37

15.1

a) Values obtained at the end of the simulation runs, as explained in 3.2.1

In Figures 4 and 5, final snapshots for some representative simulations of each PE-CNT nanocomposite and isolated chain are shown. For a more complete picture of the morphological features of the systems, the final states of all the trajectories can be visualized in Supplementary Material (Figures S2 to S4). A few qualitative observations can be made regarding the morphology reached at the end of the simulation protocol. All three PE-CNT systems show chains adsorbed onto the CNT forming an ordered structure. In a number of simulation runs PE chains tend to form a monolayer with the long axis of the lamella parallel to the z-axis of the CNT, which is in agreement with the results obtained by Kumar et al. in quenching processes of linear PE onto CNTs [12]. However, some of the simulations show a chain that grows with a tilt angle of around 60º with respect to the CNT z-axis (see for example PE10-CNT system case in Figure 4E). The tilted chain arrangement seems to be a preferred configuration in the SCB systems, and they have been mostly observed in the simulation runs performed for the PE10-CNT system. In some cases the tilted chains appear also in the initial stages of the structuring process for the PE00-CNT and PE05-CNT composites. This result is in close agreement with morphological observations performed by Transmission Electron Microscopy on isothermal crystallized PE-CNT nanocomposites [29]. The micrographs have shown that the lamellar morphology of these systems is almost like a bottle brush with the centre being the CNT. Since the chain direction is 11

generally perpendicular to the lamellae, the general orientation of the chains is close to parallel to the CNT axis, although some many form an angle that varies between 30 to 80 º. Local rigidity and slower dynamics brought by the chain lateral defects are possibly related to the preferred arrangement of the segments found on the CNT surface. In fact some authors have reported that semiflexible and rigid chains are allowed helical disposition as a consequence of additional optimization of the adsorbed chain conformations to maximize chain entropy and van der Waals interactions between the segments [14]. However, in our case it is difficult to give a proper quantitative statement about the effect of the conformational features and flexibility of the chains on their organisation, as in order to increase the computational performance the force field used in the simulations introduces an extra contribution to the rigidity of the systems [35].

Figure 4. Snapshots of the PE-CNT systems at the end of selected trajectories. (A,B) PE00-CNT; (C,D) PE05-CNT and (E,F) PE10-CNT

Additionally to the distribution of the chains on the CNT surface, two different packing morphologies can be observed in the systems studied. For example, in Figures 4A, 4C and 4E the polyolefin chain is adsorbed almost completely on the CNT surface forming a monolayer (mechanism I). The other adsorption type is seen, for example, in Figure 4B, 4D and 4F. It can be observed that a small fraction of the PE chain is adsorbed on the CNT surface. The remaining chain segments packs on the adsorbed 12

fragment and the crystal grows up laterally on one side of the CNT, forming a multilayer (mechanism II). This multilayer type of lamella has been observed in simulations due to an insufficient number of contacts between the chain and the surface of CNTs of small radius, which results in a kinetically trapped collapsed state [12], as it is also suggested by the relatively higher values of the energy obtained for these structures at the end of the simulation runs (see Table S2 in Supplemental Material).

Figure 5. Snapshots of the PE isolated chains at the end of selected trajectories.

Regarding the SCB systems, it can be observed in Figure 4C to 4F that the branches, represented as blue coloured balls, are in general located in the amorphous folded segments of the chains far from the most ordered regions. For comparison purposes, representative final snapshots of the MD simulation after 2,000 ps for the isolated chain systems are presented in Figure 5. It can be observed that these isolated systems reach a more compact and globular aspect than those of the composite counterparts. In the isolated chain systems it can also be observed that branches are usually found in the amorphous folded regions, in agreement with reported results on similar cases [26-28].

3.2. Organisation of the macromolecular structure

3.2.1. Stem length of the crystalline structure It is possible to follow the growth of the stem length, L, with simulation time. Classically, a crystalline stem is defined as the all-trans (straight) chain segment pertaining to the lamella, but we can alternatively use the definition given by Lacevic and co-workers [36]. In brief, the orientation of a chord vector with other chord vectors along the polymer chain can be compared. The chord vector is defined as the one formed by the middle point of the ith bond and that of the i+1th bond. If the average 13

angle between a selected chord vector and the five chords on either side of the chain is less than 15°, it is considered ordered. A minimum of 20 consecutively ordered chord vectors are needed to form a stem. The smooth random fluctuations can be removed as explained in reference [36]. This procedure has allowed us to obtain the time evolution of L for the different systems, as it can be observed in Figure 6.

Figure 6. Time evolution of the stem length, L, in the systems studied. (A) PE00, (B) PE05 and (C) PE10. () PE-CNT mechanism I; () PE-CNT mechanism II; and () PE isolated chains. The error bars indicate the standard error of the mean from the different trajectories (±3-6 %).

It is still feasible to distinguish between the two different mechanisms, in parallel with the changes observed in the time evolution of Rg2 . The thickening process (mechanism I) is clearly identified in all the cases, being less pronounced as the SCB content increases, in the simulation time available. As in the case of the changes observed in the chain global dimensions with time, the evolution of L is effectively faster in all the PE-CNT nanocomposites than in the isolated chains at equivalent conditions 14

because of the nucleating effect of the CNT, as it has been probed experimentally in linear PE-CNT nanocomposites [29-32]. Moreover, the values of L are higher in the PE-CNT systems (> 40 %) than in those obtained for the isolated chains, irrespective of the mechanisms (I or II) followed by the chain (see the values listed in Table 1). In fact, an immediate effect of the CNT is seen, as the values of L are higher in the nanocomposites even from the beginning of the process. The enhanced crystallisation processes suggest the strong interfacial interactions between polymer chains and the CNT being a major reason for the exceptional properties found experimentally in this type of materials. Furthermore, the enhanced values of L in PE-CNT nanocomposites point towards a remarkable higher thermodynamic stability of the crystals when compared to the case of the isolated chains. This effect has been reported by some of us in experiments for the case of linear PE growth on the surface of the CNT, for which the higher stability of the crystals is reflected in melting temperatures up to 5 ºC higher than in the case of the linear PE alone [29]. The thicker lamellae observed experimentally in linear PECNT nanocomposites is regarded as an intriguing result since the lamellar thickness produced under isothermal crystallisation conditions and the same undercooling should be the same than in the isolated chains. Even considering the nucleation effect of CNT, the expectation would be only a higher number of crystals, since nucleation is favoured, but of equivalent thermodynamic stability. Our simulations suggest that the reason why the CNT are producing more stable crystals is that the chains adsorbed to the CNT still retain the ability to diffuse along its z-axis to a more stable state, acting the CNT surface as a template of the emerging crystalline structure. Our simulations also point out that this ability is restricted by the presence of SCB, as lower values of L are obtained as SCB increases, as seen in Table 1. No experiments are available in the literature for SCB PE-CNT nanocomposites, but our results imply that the SCB first dictates the folding process, and second hinders the diffusion of the folded segments along the z-axis of the CNT, and hence the final size of the ordered segments.

3.2.2. Global bond-orientation order parameter The evolution of the averaged bond-orientation global order parameter, S, along the simulation time is plotted in Figure 7 for the PE-CNT systems and the isolated PE chains. The average result over 10 simulation runs for each case is presented, as we have not found differences in the evolution of this parameter for mechanisms I and II. The lines characterise the best-fitted sigmoidal curve to the simulation data. The parameter S for PE chains takes values of zero at short times, indicating disordered “random-coil” conformations in all cases. S increases quickly during the first stages of the simulations of PE-CNT nanocomposites, reaching a “plateau” at high times. The increase of the S 15

parameter is slower in the case of isolated chains, and the structuring process requires an induction time. Thus a clear evolution from random-coil conformations to ordered chains is observed for the three systems. A strong dependence of the SCB content in this transition is observed, as S values at the end of the simulation runs are remarkably lowered as the SCB content increases. Additionally, the growth rate of S and the transition time strongly depend on the SCB content of the simulated chains. A decrease in the growth rate in the initial stages and an increase of the transition time from coil-toordered structure as SCB increases are clearly seen in Figure 7. This is a general behaviour observed also in isolated chains, and it is a consequence of the disorder and slower dynamics introduced by the presence of SCB [21,26].

Figure 7. Time evolution of the global bond-orientation order parameter, S, in the systems studied. (A, squares) PE00, (B, circles) PE05 and (C, triangles) PE10. Closed symbols for the PE-CNT nanocomposites and open symbols for the isolated PE single chains. 16

It is worth mentioning that the increase observed in the values of S at the end of the simulation runs for the PE-CNT composites (listed in Table 1), as compared to that obtained in the isolated chains, is stronger as SCB increases, ranging from 3 % in PE00-CNT to 62 % in PE10-CNT. These results again points towards the fact that CNT surface provides an effective support for a more stable structural assembly of the macromolecules, as it has been reported experimentally in linear PE [29-32]. The enhanced values of S found in the PE-CNT nanocomposites suggest higher crystallinity degree in these systems than in the isolated PE chains, mainly in the case of the branched species. The increase of crystallinity due to the addition of CNT has not been always observed experimentally in the case of linear PE, but recently Trujillo et al. have found increased values of the crystalline content but in composites with low CNT contents. These authors assigned this increase to the nucleating effect of the CNT in polymer chains without topological confinement [30]. Enhanced crystallinities with respect to the neat polymeric matrix have been observed in nanocomposites of polyvinyl alcohol [37,38], poly(mphenylenevinylene-co-2,5-dioctyloxy-p-phenylenevinylene)

[39],

poly(3-hexylthiophene)

[40],

poly(vinylidene fluoride) [41] and polyamide-6 [42]. As judged by the results shown in Figure 7B and 7C, this effect seems to be particularly important in the SCB PE-CNT nanocomposites, but to our knowledge this fact has not been explored experimentally.

3.3. Radial distribution function Finally we have also obtained the radial density distribution function, P(r), defined as the probability of finding a particle at a distance r from the middle tube axis. We have defined the probability of finding particles at distance r from the centre of the CNT through the radial density distribution function in a cylindrical geometry system as P(r) ≡ N(r)/2πrΔrN where N(r) is the number of particles (united atoms) lying within the cylindrical shell located between r and r + Δr and N is the total number of particles present in the polymer chain [12]. A value of 1 Å has been taken for Δr. We have calculated P(r) with respect to the central CNT axis for selected nanocomposite trajectories and represented its time evolution in Supplementary Material (Figure S5) and Figures 8 and 9. In Supplementary Material (Figure S5) we have selected the case of the radial distributions of PE00CNT composites in the whole range of distances (thus the area under the curves is 1), as an example. Again we have observed two well differentiated profiles corresponding to mechanisms I and II, which finally lead to different morphologies of the polymeric chains, i.e., mono- and multi-layer, respectively. From this figure we can appreciate that the zone of interest in which the major changes occur during 17

the process is located between 8 and 32 Å. The chain segments have a wide radial distributions when the process begins (t=1 ps, in black).

Figure 8. Radial distribution functions from the centre of the CNT at selected simulation times for PECNT systems and mechanism I. (A) PE00-CNT, (B) PE05-CNT and (C) PE10-CNT.

In the case of mechanism I (see Figure 8), as the simulation proceeds, the chain segments are adsorbed onto the CNT surface and three peaks appear at around 10, 14 and 17 Å. After 100 ps, the intensity of the peak corresponding to the closest united atoms to the CNT wall increases. However, the intensity of the 2nd and the 3rd peaks starts to decrease, which indicates the beginning of the adsorption and thickening processes process of the chains over the CNT surface [13]. At the end of the simulation most of the chain segments are adsorbed on the CNT surface. In the case of PE00-CNT composite (Figure 8A), around the 85 % of the united atoms of the chain are adsorbed at the end of the simulation run. The trend found in P(r) is similar in PE05-CNT and PE10-CNT composites (Figures 8B and 8C, respectively), but the SCB content affects the dynamics of the collapse-adsorption-thickening process. The presence of SCB slows down the adsorption of the PE chain onto the CNT surface. In general, the nearest peaks to the origin are smaller as the SCB content increases denoting the lower adsorption of 18

chain segments to the CNT wall. The closest segments to the CNT wall at the end of the simulation runs are in these cases around the 75 % and the 70 % of the united atoms of the chains for PE05-CNT and PE10-CNT composites, respectively.

Figure 9. Radial distribution functions from the centre of the CNT at selected simulation times for PECNT systems and mechanism II. (A) PE00-CNT, (B) PE05-CNT and (C) PE10-CNT.

In the case of mechanism II (see Figure 9), as the simulation proceeds the chain segments are adsorbed forming a multilayer, and up to six peaks appear in the radial distribution at around 10, 14, 17, 21, 24 and 28 Å. After 100 ps only the first peak slightly increases in intensity, and then it remains, together with the other peaks, nearly constant for the rest of the simulation run. Similar patterns have been obtained in all PE-CNT nanocomposites, but in the case of branched chains it seems that the number of layers decreases with SCB content. In all the cases the closest segments to the CNT wall represent only 40 % of the total number of united atoms in the chain.

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4. CONCLUSIONS In this work, the isothermal organisation process of semicrystalline single chain polyolefins onto carbon nanotube surface as a function of the short chain branching content is studied by computer simulations of their molecular dynamics. The time evolution of the ordered structure follows two different paths in the three cases studied. On one hand, a stepped structuring mechanism is identified; consisting in a collapse of the macromolecule followed by the adsorption and thickening of the oriented segments. This mechanism is much more pronounced in the linear sample than in the branched ones, at least in the simulation time frame explored, and it gives rise to an ordered single chain monolayer. A decrease of the adsorbed segment fraction as short chain branching increases is seen (from 85 % to 75 % of the united atoms of the chains). This is likely due to the hindered chain dynamics and the forced folding sites induced by the presence of the branches. On the other hand, a second mechanism is identified, in which a multilayer morphology is finally obtained after the collapse, adsorption and lateral growth of the chain segments. In this case a minor fraction of the chain is adsorbed on the carbon nanotube surface (40 % or lower). In parallel, the multilayer morphology shows higher energy values that the extended monolayers, suggesting that the former could be kinetically trapped structures at the selected crystallisation temperature. The presence of defects in polymer chains delays the onset of nucleation and growth of the crystalline structure, suggesting that the process is quite sensitive to the local chain chemistry in both nanocomposites and isolated chains. A lower lamellar period and chain order parameter are obtained for the branched systems as compared to their linear counterpart. However, both the lamellar thickness and the order parameter are higher in the nanocomposites than those obtained for isolated polymer chains, in agreement with the experiments. These results point towards the strong effect of the carbon nanotube surface as nucleating agent. Particularly interesting is the increase found in the stem length in the case of the linear chain nanocomposite, which is stronger than in the branched chains nanocomposites. On the contrary, the carbon nanotube seems to increase more efficiently the global order parameter (or crystallinity) in the case of the branched chains than in the linear one. Thus, the lower values of stem length in the branched samples are however parallel to an increase in the global order parameter or the crystallinity degree of these systems.

Acknowledgements: The authors acknowledge funding support from CSIC - Project PIE 201360E097, and from the Spanish Ministerio de Economía y Competitividad (MINECO) - Project MAT201236341. J.R. acknowledges financial support through the Ramón y Cajal program - RYC-2011-09585 contract. 20

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Supplementary Material (Tables) Table S1. Average potential and Van der Waals energies for each trajectory of the linear system. The averages are calculated in the last nanosecond. Energies are given in kcal/mol. Trajectory 2 3 4 6 7 9 Average 1 5 8 10 Average

Structure I I I I I I II II II II

-1814.5 ±26.1 -1683.5 ±39.2 -2324.5 ±28.4 -1776.3 ±30.5 -1617.9 ±29.6 -1652.9 ±45.3 -1811.6 ±33.2 -1472.7 ±21.9 -1577.4 ±25.2 -1527.2 ±26.3 -1575.8 ±35.1 -1538.3 ±27.1

-2720.5 ±13.9 -2640.9 ±16.1 -3233.9 ±16.4 -2707.1 ±18.2 -2595.5 ±15.4 -2613.9 ±25.2 -2752.0 ±17.5 -2474.3 ±16.4 -2575.0 ±15.0 -2525.1 ±13.9 -2566.2 ±18.5 -2535.1 ±16.0

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Table S2. Initial and final trans populations of the backbone for PE00, PE05 and PE10 chains. The trans populations were calculated in the first 50 ps (initial) and in the last 200 ps of each trajectory. The integration interval for trans population was chosen to be between 120 and 240 degrees. PE-00 Trajectory 2 3 4 6 7 9 1 5 8 10

Structure I I I I I I II II II II

% trans initial 83.8 83.8 84.0 78.9 76.8 79.1 83.8 84.4 79.8 79.8

% trans final 94.4 92.7 94.4 93.4 92.8 92.7 89.9 90.4 90.0 90.9

Trajectory 6 7 8 9 10 1 2 3 4 5

Structure I I I I I II II II II II

% trans initial 79.5 79.9 79.2 81.4 79.4 81.6 82.2 81.8 81.0 83.1

% trans final 92.4 93.4 94.4 93.8 93.3 89.6 89.6 91.5 92.1 88.9

Trajectory 6 7 1 2 3 4 5 8 9 10

Structure I I II II II II II II II II

% trans initial 79.3 79.6 82.0 81.1 82.6 79.9 82.6 79.6 77.2 76.9

% trans final 92.0 92.8 90.7 90.0 91.0 88.3 91.8 90.9 89.4 87.5

PE-05

PE-10

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Supplementary Material (Figures)

Figure S1. Van der Waals energy evolution of the systems following the mechanism I (left) and II (right) for a) PE00, b) PE05 and c) PE10 chains.

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Figure S2. Snapshots of the final states of all the trajectories of PE00-CNT systems studied in this work.

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Figure S3. Snapshots of the final states of all the trajectories of PE05-CNT systems studied in this work.

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Figure S4. Snapshots of the final states of all the trajectories of PE10-CNT systems studied in this work.

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Figure S5. Radial distribution functions from the centre of the CNT at selected simulation times in the whole range of distances for PE00-CNT systems (A) Mechanism I, (B) Mechanism II. The inlets show the zone of major changes within the range 8 - 30 Å.

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Computer simulations of the early stages of crystal nucleation of linear and short chain branched polyethylene on carbon nanotubes

K. Jerónimo, V.L. Cruz, J. Ramos, J.F. Vega, M. Trujillo, A.J. Müller and J. Martínez-Salazar

Graphical Abstract

30

Highlights

Computer simulations of the early stages of crystal nucleation of linear and short chain branched polyethylene on carbon nanotubes

K. Jerónimo, V.L. Cruz, J. Ramos, J.F. Vega, M. Trujillo, A.J. Müller and J. Martínez-Salazar

MD simulations of linear and branched polyethylene on carbon nanotubes. Study of the mechanism of chain folding at the early stages of crystal formation. Two types of crystal structures on the nanotube have been identified. Morphology, crystal thickness and molecular order are affected by the presence of the carbon nanotubes and short chain branching.

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