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Stress-Strain Relationships in Hydroxyl Substituted Polyethylene Gourav Shrivastav, and Manish Agarwal J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b05275 • Publication Date (Web): 05 Jul 2016 Downloaded from http://pubs.acs.org on July 8, 2016

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The Journal of Physical Chemistry

Stress-Strain Relationships in Hydroxyl Substituted Polyethylene Gourav Shrivastav† and Manish Agarwal∗,†,‡ †Department of Chemistry, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India 110016 ‡Computer Services Center, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India 110016 E-mail: [email protected] Phone: +91 11 26597170

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Abstract Stress-strain relationships in semicrystalline hydroxylated polyethylene are studied using all-atom molecular dynamics simulations. Chain sizes ranging from 50 to 2000 carbons are gradually cooled from melt in order to obtain semicrystalline samples for pure, 4% and 8% hydroxylated chains. Local orientational order of the polymer backbone and hydrogen bonding behaviour is studied. The effects of −OH substitution and chain length on stress-strain relationships are examined at 300 K. Number of hydrogen bonds are found to be independent of the chain length. Stress-strain relationships are generally unaffected by 4% of hydroxyl substitution in long chain polyethylene. Presence of 8%−OH tends to increase elastic limit of the material. A method for comparing semicrystalline samples of substituted and unsubstituted polymeric chains is presented by eliminating differences in alignment, distribution and extent of crystallization.

Introduction Polymeric materials are most often prepared as semicrystalline solids. The combination of ordered and disordered domains affords a wide range of mechanical and thermal properties desirable in materials of a wide variety. The tensile strength of the crystalline domains gives the material durability while its brittle nature is offset by the amorphous regions. The disordered domains are composed of an interphase region existing at the boundaries of the crystalline and the amorphous domains. 1 The lamellar structure seems counter-intuitive since fully extended chains have the lowest free energy. 2 However, kinetics of crystallization tends to grow crystals in directions perpendicular to chain direction, leading to the representative semicrystalline set. Semicrystalline polyethylene has been studied in great detail both in experiments and simulations. 3–12 In general, semicrystalline moities of polyethylene have been generated from solution 4 and melt 5–8,13 using molecular simulations. The arrangement of lamellar stacks into spherulites, hedrites and other related morphologies have also been studied recently. 9 Crystallization has also been studied using uniaxial extension and 2


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compression of chains which results in mostly aligned crystals along the strain direction. 10,11 During crystallization, molten chains undergo chain relaxation and inter chain ordering simultaneously. A considerable number of experiments and simulations have been used to understand polymeric crystallization at the microscopic level. Almost all simulations have used the united atom models, 8,11,14–19 with notable exceptions. 20,21 United atom models are able to capture majority of the underlying physics of nucleation in polyethylene. 7,8 However, in order to better account for the effect of strong polar groups such as hydroxyls all-atom force fields afford a better description, especially with respect to electrostatics. There are many force fields which are successful in reproducing properties of alkane based polymers, specifically the explicit hydrogen “all-atom” variants based on the TraPPE, CHARMM and OPLS formulations. 22–24 One of these is the optimized potentials for liquid systems all-atom (OPLS-AA), 24,25 which is used in this study. Mechanical properties of amorphous and semicrystalline polyethylene have been studied under various conditions such as effect of temperature, deformation rates, chain length etc. using molecular simulations. 26–29 Stress-strain behaviour is strongly effected by amount and distribution of amorphous content, since each of them have a widely different response. In sequence, a typical uniaxial strain causes stretching of amorphous chains in the pulling direction, along with reorientation of crystalline domains, crazing, and failure. Different strain rates may result in varied stress response. 29 Stress-Strain behaviour of polymeric materials also differs from other materials since deformations result from a series of continuous processes where all phases must deform concurrently and consistently. 30 Pure and substituted semicrystalline polyethylene form a variety of thermoset and thermoplastic materials which are used as resins, membranes etc. Among the many uses of semicrystalline polymeric substances such as polyethylene and its derivatives like polypropylene is in the field of dielectrics. Recent experimental and simulation studies have shown that introduction of polar groups in polyethylene and polypropylene considerably improves their dielectric properties. 31–34 When subjected to electric fields, such as charging-discharging cy-

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cles in a capacitor, such a material is expected to undergo considerable physical and thermal stresses. The main motivation for this study is to compare the stress strain relationship of hydroxylated polyethylene using molecular simulations as well as to investigate the structural costs of improving the dielectric properties. For this, we present a method to compare substituted and unsubstituted polyethylene moities while maintaining the amorphous, interphase and crystalline distributions. In this study, we examine n-alkanes with 50 to 2000 carbons, randomly substituted with hydroxyl groups (−OH) using all-atom molecular dynamics simulations. The concentration of hydroxyls is chosen to be similar to that used in previous studies, i.e. 4-8 mol% −OH per monomer i.e. per −CH2 −CH2 − unit. 34 Semicrystalline samples are subjected to a strain using non-equilibrium molecular dynamics and the corresponding stress response is measured. As far as the authors knowledge, all atom alkane chains substituted by polar groups, have not been subjected to stress-strain analysis. In the following section we describe the simulation procedure, detailing the preparation of the samples, and the method used.

System and Computational Details We have simulated the system of n-alkane chains ranging in the chain sizes both below and above the entanglement length of polyethylene, with a total of 2000 carbons (1000 ethylene monomers). The systems studied are “25mer” (25 CH2 −CH2 units) × 40 chains, “50mer” × 20 chains, “100mer” × 10 chains and a single chain of “1000mer”. Chains are terminated by an additional hydrogen i.e. by forming methyls at the ends of the chains. Each of these 4 systems were substituted with ≈4% and ≈8% hydroxyls i.e. 41 and 80 hydroxyls respectively on the backbone. The hydroxylated samples were also later dehydroxylated to provide additional 8 samples, resulting in a total of 20 systems. Details of system preparation are described below.

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Potential Energy Surface We have used all-atom model to represent the n-alkane chains in which each carbon atom has explicit hydrogen atoms. The OPLS-AA force field 24,25 is used to simulate all the systems. All bond stretch and angle bendings are represented using harmonic potential with dihedral motion governed by OPLS-AA triple cosine series potential. In non-bonded forces, van der Waals interactions are described by standard Lennard-Jones 12-6 (LJ) potential. The parameters for interactions between unlike pair of atoms i and j are calculated using the √ √ geometric mixing rules i.e. σij = σii σjj and ǫij = ǫii ǫjj where σ is LJ size and ǫ is LJ well-depth. Electrostatic interaction between two atoms is given by

UES (r) =

X X qi qj i

j

4πǫo r

(1)

and are computed using particle-particle particle-mesh algorithm as implement in LAMMPS. The complete force field parameters for bonded and non-bonded interactions are provided in the Supporting Information Table S1 and S2 respectively. We note that recently OPLS-AA has been optimized and extended for long chain molecules. 35 However, we use a combination of small and long chains, and hence use the original parameterization.

Equilibrium Molecular Dynamics Simulations All simulations were performed in the isothermal-isobaric (NPT) ensemble with orthogonal periodic boundary conditions. 34,36 Simulations were carried using GPU accelerated LAMMPS package. 37–39 Equations of motion were integrated using velocity-Verlet algorithm with the time step of 1 fs. The temperature was controlled using Nosé-Hoover thermostat with the time constant of 1 ps. Pressure of 0 atm was maintained for all simulations using the Nosé-Hoover barostat with time constant of 5 ps as implemented in LAMMPS. The barostat time constant is chosen to avoid coupling to the thermostat time constant, typically used in simulations. 5



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Initially, a single alkane chain was generated in an “all-trans” configuration. This was replicated and packed in a simple cubic arrangement with interchain spacing chosen to accommodate the van der Waal radii. These initially packed systems were heated from 100 K to 1000 K at the rate of 25 K / 100 ps in an anisotropic pressure condition, i.e. relative lengths of the simulation cell were allowed to fluctuate. At 1000 K, the respective boxes were deformed into a cubic box and further simulated for 1 ns. These systems were then cooled to 750 K under an isotropic pressure condition at the rate of 10 K / 100 ps and then up to 350 K at the rate of 5 K / 500 ps under anisotropic pressure conditions. This rapid cooling was done to obtain the approximate onset temperature range for the homogeneous crystallization. All ˚ these simulations were performed using a global cut-off of 2.5σC (σC = 3.5A). In order to obtain stable semicrystalline configurations, the next step was to determine the highest temperature having a significant crystallinity (Tonset ). For this, several simulations of 15 ns with global cut-off of 3.2σC were performed starting from the last configurations of the rapid cooling sets at temperatures near and above the approximate onset temperature. Tonset was determined to be that temperature above which there is no significant crystals present. Presence of significant crystallisation was confirmed by using end to end vector single chain order parameter (SCOP) (Eq. 3) and the local order parameter P2 (Eq. 2). Starting from the last configuration obtained at Tonset , the system was further simulated for 30 ns so as to generate a trajectory with a stable order parameter. Simulations at any higher temperature than Tonset did not undergo crystallization in 15 ns. Third step was to perform cooling from this configuration to 300 K at the rate of 5 K / 500 ps and global cut-off of 3.2σC followed by a 15 ns simulation at 300 K. Systems with 4% and 8% hydroxyl groups corresponding to every pure system were generated by randomly replacing hydrogens with hydroxyl groups in respective configurations obtained at 1000 K, ensuring that there were no geminal substitutions. This was followed by the cooling procedure described above to obtain stable trajectories at 300 K. Samples from this trajectory was used as starting configurations for the stress-strain studies. It must be noted

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that since the samples have been equilibrated at “high” temperatures, i.e. respective Tonset s, the crystalline content is expected to be higher, unlike in Ref 34. Semicrystalline morphologies and hence polymeric properties derived from molecular simulations are known to be sensitive to the scheme used to generate them, such as the rate of cooling. 15 Thus, comparison of stress-strain relationships arising due to substitution becomes difficult. In order to keep the distribution of crystalline lamellae and the amorphous chains constant, the final configurations of the substituted samples were dehydroxylated to obtain a second set of pure PE configurations. These configurations were equilibrated for 4 ns, and stress-strain analysis conducted.

Non-Equilibrium Molecular Dynamics Simulations Deformation was simulated in the NPT ensemble by extending one of the box dimensions, e.g. x(t) = x(0) exp(λdt), at the true strain 16,29 rate of λ = 109 s−1 and maintaining 0 stress along orthogonal directions using Nosé-Hoover barostat with relaxation time of 5 ps. Starting from different trajectory snapshots at 300 K, 10 independent non equilibrium molecular dynamics (NEMD) simulations were performed for 2 × 105 steps. The box was stretched in each of the three Cartesian directions. We report the data obtained from NEMD simulations along the largest box direction. The true strain rate of 109 used here is much higher than corresponding typical experimental rates. However, this is in accordance with previous simulations performed on polymeric materials where rates of 106 − 1010 have been used. 29,40,41 Another important consideration is that the compute time required for slower rates is currently inaccessible. In order to estimate the finite size effect, box sizes were doubled and the stress-strain calculations repeated. This did not change the stress-strain curves significantly.

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Order-Parameters The crystal nucleus is defined based on a local P2 order parameter. 8 The local P2,i order parameter of the ith C atom on a chain is defined as

P2,i =

n 3 cos2 (θij ) − 1 1X n j=1 2

(2)

where θij is the angle between the vector from the (i − 1)th to the (i + 1)th C atom, and the vector from the (j − 1)th to the (j + 1)th C atom. The average over P2,i in Eq. 2 is ˚ taken over all of the j neighboring i that lie within a cutoff distance rij < rP2 = 8.75A. The cutoff distance rP2 was chosen to ensure that two neighbouring shells of carbons were included in the calculation. Crystalline carbons are defined with P2,i ≥ 0.6, and are colored

Figure 1: Typical folded structure of a polyethylene chain; The snapshot shows a representative 100mer chain. Crystalline carbons are colored blue, interphase region green and amorphous is shown as red. n.b. Terminal carbons are not shown. blue, inter-phase region is defined by green color in the range of 0.6 > P2,i ≥ 0.4 and the region with P2,i < 0.4 was considered as amorphous, and are colored red. Figure 1 shows a snapshot of a representative folded chain for the 100mer system. We note here that P2,i is undefined for methyl carbons (CH3 ), and hence they are not counted while calculating % crystallinity i.e. fraction of carbon atoms which are crystalline. We also compute average local order parameter P2 = hP2,i i. The local order parameter P2 is based on the arrangement of all chains around the central carbon. Here, a second order parameter (SCOP) is also used as an estimate of the ordering

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of carbon atoms with reference to only their own respective chain.    ˚  1 rij > 22A,

SCOP (i) = 

(3)

  0 otherwise

˚ was where rij is the distance between ith and the (i + 18)th carbon. The distance of 22A used by testing samples of “perfect” crystallinity i.e. samples with P2 > 0.95. Since this is a single chain order parameter, chain termini are included in the calculation of % crystallinity. One of the major difference which can be extracted from SCOP vs P2 is in the length of long crystalline regions. If there exist a large number of local crystalline regions, they would contribute to high P2 value. This, however, would not contribute to a high SCOP. On the other hand, in cases where SCOP is high, and P2 is low, it would mean that there are multiple ordered chains which are arranged at an angle to each other.

Hydrogen Bonds One of the effects of introducing strong polar groups such as the −OH is the incorporation of ˚ hydrogen bonding in the system. A hydrogen bond D−H. . .A is present if the H. . .A < 2.5A

Figure 2: A representative snapshot showing hydrogen bonds present in the crystalline region. Carbons are cyan, Oxygen red and Hydrogens are white. Hydrogen bonds are shown as red dashes. and 6 HAD ≤ 30◦ . 42 Here, “D” denotes the donor oxygen, and “A” is the acceptor oxygen. 9



Hydrogen bonds were computed using the TCL/Tk interface of VMD. 43 Figure 2 shows a representative snapshot containing a hydrogen bond tetramer.

Results Structure of pure semicrystalline polyethylene In order to quantify the extent of crystallization we track the order parameters P2 and SCOP of the samples while cooling. These “cooling curves” are used to determine the temperature at which significant order is present in the system. All samples here have a density range of 0.91 to 0.96 g cm−3 . In general, the density of the system increases as the hydroxyl content increases. The cooling curve for 50mer with Tonset = 440K is presented in Figure 3. Here 0.8 0.7 0.6 0.5 P2

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0.4

Tonset

0.3

Tonset+5

0.2 0.1 0

2

4

6

8

10

12

14

16

Time (ns)

Figure 3: Plot of variation of order parameter P2 (Eq: 2) with time during simulations at two temperatures, i.e., Tonset and Tonset + 5K. Here Tonset is the temperature at which significant crystallization occurs within 15 ns, and remains persistent for 30 ns. Tonset is the temperature at which significant crystallization occurs within 15 ns, and remains persistent for 30 ns. All cooling curves in the study show similar behaviour around their respective Tonset . Although the fast cooling curves for multiple sets are very similar, the Tonset can differ by as much as 20-25 K. Since we are interested in generating relatively stable semicrystalline configurations for comparison with substituted polyethylene systems, the value of the onset 10


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temperature itself is unimportant for this study. In general the onset temperature increases with chain length, and the same is observed in the current study. We also note that the onset temperatures are higher than expected. This could be due to the all-atom force field as well as anisotropic boundary conditions. In this study, we have chain sizes well below the entangle limit of polyethylene (25mer), on the entanglement borderline (50mer) and well above the entanglement limit (100mer and 1000mer). As expected, 25mer form crystals with very low amorphous content; each chain having at most one fold or bend. Chains with 50mer and higher have the well known lamellar structure of semicrystalline polyethylene. 11 As expected, crystallinity decreases as chain length increases, with 100mer and 1000mer showing multiple folds. Once crystalline structures form, however, chain length only effects the amorphous regions. Short chains have very small amorphous regions. As the chain size increases, we notice that there are some chains which are not contained within a single simulation cell, i.e. they interact with their own periodic image(s). Table 1: Ordering in the crystallized samples for pure polyethylene samples. Fraction of crystalline (%c), interphase (%i), and amorphous (%a) carbons are measured using order parameter P2 (Eq. 2) described in the text. Alternate measure of crystallinity (%SCOP) is measured by the fraction of number of carbons which are part of a straight chain (Eq. 3). Errors in estimates are all less than 1%. System 25mer 50mer 100mer 1000mer

%c 94.05 72.73 63.24 61.90

%i 1.63 4.30 9.03 11.21

%a %SCOP Tonset 4.32 94.82 415 22.97 87.52 440 27.72 80.94 445 26.89 77.52 495

As shown in Table 1, the percentage crystallinity decreases as chain length increases. The amorphous region, however, is similar for all chains which are above the entanglement limit for polyethylene i.e. 100mer and 1000mer chains. It is only the interphase region which increases - signifying that the overall number of folds are increasing, while keeping the total

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% of amorphous carbons fixed. The amorphous region increases drastically for 50mer as multiple bends and folds appear.

Stress-Strain Curves of Polyethylene 1000 800 σ (MPa)

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25mer 50mer 100mer 1000mer

600 400 200 0 0.00

0.05

0.10 e

0.15

0.20

Figure 4: Effect of chain length on Stress-strain curves for pure polyethelene semicrystalline morphologies. A typical stress-strain curve shows an initial monotonic increase characteristic of the elastic regime, followed by plastic deformation, and finally failure of the material. Figure 4 shows that the chain length has a dramatic effect on stress response to the strain applied. The shortest chains i.e. 25mer undergo failure very quickly at strain of ≈0.025. These highly crystalline chains have very few folds, hence strain energy cannot be dissipated. When the chain size is 50mer, the elastic region as well as the stress-strain slope increased and failure occurred at a strain of 0.06. Chains with 100mer, however, showed a reduction in stress response with the same strain - signifying that the amount of amorphous region has increased, and the chains have more folds which easily deform under strain and the chains reorient to align in the direction of the applied strain. Till about 0.07, all the strain energy is expended to reorient the amorphous region. As the strain increases, however, the interphase region also begins to provide a stress response. As in the previous case, the interphase region has a higher elasticity and the slope of the stress- strain curve increases. This is followed by 12


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failure at around strain of 0.10. The final case studied here is a single chain of 1000mer, which has a small crystalline domain and provides a very smooth stress-strain curve with almost no linear stress response. Oscillations in stress-strain curves have been attributed to high strain rates and also small system sizes in MD simulations. 12,40,44 However, on visual inspection of the trajectory, we find that oscillations occur when chains slide past each other and are pulled out of the crystal. 21,45 The plateau region in stress-strain curves corresponds to stress response of the amorphous region. 21 We also note that realignment of ordered strands in the direction of the strain does not contribute towards the stress response, i.e. all the strain energy is dissipated or consumed in reorienting the crystal, and not spent in extending or stressing the crystalline chains. The longest chain, on the other hand, has a smooth curve with a long elastic region.

Hydroxylated Polyethylene Hydroxylated polyethylene behaves like its pure counterpart. The onset temperatures (Tonset ) for PEOH samples are very similar to the respective pure samples. In the case of 25mer, hydroxylated polyethylene samples are considerably less crystalline. The SCOP, however, indicates that the number of bends and folds have reduced and the crystals are longer. Addition of 4% −OH seems to increase P2 for all systems 50mer onward. The increase in crystallinity is accompanied by an increase in the interphase region and a corresponding decrease in the amorphous region. Further addition of −OH reduces the crystallinity as well as the Tonset in all samples. This behaviour tends to suggest that for small chains, the substitution tends to disturb the crystalline structure, whereas longer chains seem to readjust and accommodate the hydroxyls within the lamellar structure. An analysis of the hydroxyl group distribution reveals that they do not have any preference for amorphous or crystalline regions i.e. distribution of hydroxyls is highly correlated to the amount of crystalline, interphase and amorphous regions. Table S4 in Supporting Information corroborates this. This observation is in contrast to Ref 34 where rapid cooling had resulted in hydroxyl groups to 13



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be higher in the interphase region and less crystalline content. Table 2: Ordering in the crystallized 100mer for pure polyethylene, and the corresponding 4% and 8% hydroxylated samples prepared by cooling. samples. % mol pure 4 8

%c %i %a %SCOP Tonset 63.24 9.03 27.72 80.94 445 65.36 8.33 26.31 78.30 445 51.05 12.31 36.64 69.29 435

Table 2 compares the crystallinity of 100mer and the corresponding 4% and 8% samples. It is clear from the data that cooling hydroxylated samples generates very different distributions of amorphous, interphase and crystalline regions. We have also tested and confirmed that fresh simulations results in a very different semicrystalline configurations each time. Full details of all simulations results are available in the supporting information Table 3. Hydrogen Bonds Table 3: Average number of Hydrogen bonds in system of different chain length at 300 K . System 4% OH 8% OH 25mer 12 40 50mer 10 38 100mer 12 38 1000mer 18 38

Table 3 compares average number of hydrogen bonds present in the various systems. The system with 4% hydroxyls mostly consists of isolated hydroxyls with few hydrogen bonded pairs. The 8% system has considerable number of hydrogen bonds with the trimers and tetramers also being present. It is remarkable that the number of hydrogen bonds do not vary much with chain size or crystalline environment. We also note that hydroxyls show no preference for amorphous, interphase and crystalline environments. The hydroxyl apparently can be incorporated into the crystalline structure.

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Since the OPLS-AA force field models the hydroxyl Hydrogen as a point charge with no short range potential, the hydroxyl poses a strong perturbation to the general polyethylene environment. This could point to the hydroxyl group effecting a change in entanglement lengths of polyethylene by offering steric hindrance to chain movement, as well as “tie” points via hydrogen bonding e.g. when disordered hydroxylated strands are surrounded by a crystalline environment, they tend to remain disordered for a longer time. 20,21 It must be noted that crystallization energies are far stronger than hydrogen bond energies. Hence presence of strong polar groups might influence slow and rare events during crystallization of the polymer. Further simulation studies focusing on the neighborhood of hydroxyls could reveal their role in nucleation mechanisms.

Stress-Strain Relations in PEOH

100

(b) 50mer Pure 4% OH 8% OH

800 600 400

600 σ (MPa)

200

(a) 25mer Pure 4% OH 8% OH

σ (MPa)

300

σ (MPa)

0 0.00 0.05 0.10 0.15 0.20 e

400 200

200 0 0.00 0.05 0.10 0.15 0.20 e

(c) 100mer Pure 4% OH 8% OH

0 0.00 0.05 0.10 0.15 0.20 e

800 600 σ (MPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(d) 1000mer Pure 4% OH 8% OH

400 200

0 0.00 0.05 0.10 0.15 0.20 e

Figure 5: Effect of hydroxyl substitutions on Stress-strain curves for (a) 25mer (b) 50mer (c) 100mer (d) 1000mer

In order to characterize the effect of presence of −OH on the stress-strain response of polyethylene, two methods are used to generate semicrystalline pure polyethylene samples.

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The first method employs the cooling protocol described earlier. Stress-strain curves obtained from these samples are presented in Figure 5. We notice that the stress-strain curves for the hydroxylated samples are very different from those of corresponding pure chains. Since the distribution of crystalline and amorphous regimes is very different in each case, the changes in the stress responses cannot be attributed to the presence of −OH alone. We observe that the crystallinity of pure 50mer (%SCOP=87.5) and hydroxylated 1000mer (8%) (%SCOP=86.3) is similar (Table 1 and 4 ). Furthermore, the stress strain relationship for both these samples show similar features and the elastic region is almost identical as shown in Figure 5 (b) and (d). From this we infer that polyethylene systems (with and without −OH) would show similar stress strain behaviour if their corresponding measures of crystallinity is similar. We also note that the crystallinities and stress responses of all other 50mer and 1000mer systems are disparate.

Dehydroxylated Systems In order to account for the changes in the stress-strain relationships due to presence of hydroxyls only, we use a second method to prepare pure samples by dehydroxylating the eight PEOH samples, as described in the simulation details. Table 4: Crystallinity data for samples having 8% OH group and corresponding dehydroxylated samples at 300 K. See Table 1 for details. System 25mer(OH) (dehyd) 50mer(OH) (dehyd) 100mer(OH) (dehyd) 1000mer(OH) (dehyd)

%c %i %a %SCOP 80.1 6.2 13.6 88.3 80.9 6.1 13.0 89.4 55.3 9.4 35.2 72.3 56.6 9.8 33.5 74.5 51.0 12.3 36.6 69.2 51.5 12.1 36.3 70.5 71.5 6.6 21.9 86.3 72.3 6.8 20.9 87.3

Table 4 confirms that the distribution of crystalline, amorphous and interphase regions remains unchanged after dehydroxylation. The full table describing the crystallinity and 16


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onset temperatures (Tonset ) of all 20 systems studied here are given in Supporting Information Table S3. Removal of hydroxyls freed and realigned the pinned carbon atoms and some of them were able to align to the nearest available crystalline nuclei, accounting for the small changes in crystallinity. Thus, any changes in the stress-strain behaviour can now be attributed to the presence of hydroxyls. Stress-Strain Relationships in Dehydroxylated PEOH 800

300

200

(a) 25mer 4% OH 8% OH

600 400

(b) 50mer 4% OH 8% OH

σ (MPa)

300

σ (MPa)

400 σ (MPa)

0 0.00 0.05 0.10 0.15 0.20 e

200

(c) 100mer 4% OH 8% OH

100

200

100

0 0.00 0.05 0.10 0.15 0.20 e

0 0.00 0.05 0.10 0.15 0.20 e

1600 1200 σ (MPa)

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800 400

(d) 1000mer 4% OH 8% OH

0 0.00 0.05 0.10 0.15 0.20 e

Figure 6: Comparison of Stress-strain curves for PEOH with corresponding dehydroxylated specimens (a) 25mer (b) 50 mer (c) 100mer (d) 1000mer. Solid symbols denote the hydroxylated chains, while the corresponding dehydroxylated samples are shown by open symbols. Note that 4% samples have been shifted for clarity. Stress-strain curves comparing the hydroxylated and dehydroxylated samples are shown in Figure 6. For 25mer, 50mer and 1000mer, addition of 4% −OH does not cause any significant change in the stress response; for 100mer, however, the elastic region has increased. In the case of 8% substituted samples, dehydroxylation causes a decrease in the plateau for 25mer. For 50mer, 8% hydroxylation dampens the oscillations due to chain slippage, further confirming that the hydroxyls act like tie points. For 100mer and 1000mer, hydroxylated 17



PE has a higher stress response for the same strain, as shown in Figure 6 (c) and (d). Using this method we have eliminated effects of distribution of crystalline, interphase and amorphous regions on the stress-strain curves. Changes in the stress response could be due to changes in chemistry i.e. −OH in this case, and slight reorientation of crystals during relaxation following dehydroxylation. It may be concluded that addition of 4% −OH does not change the stress-strain curves significantly and 8% −OH increases the elastic range of polyethylene. 0.83

0.66

0.62

0.65

(c) 100mer Hydroxylated 0.61 Dehydroxylated

0.64

0.82

0.60

0.81

P2

P2

0.63 P2

0.62 0.80 0.79

0.59

0.61

(a) 25mer Hydroxylated Dehydroxylated

(b) 50mer Hydroxylated Dehydroxylated

0.60

0.58 0.57

0.59 0

0.05

0.1 e

0.15

0.2

0

0.05

0.1 e

0.15

0.2

0

0.05

0.1 e

0.15

0.2

0.77 0.76 0.75 P2

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0.74 0.73 (d) 1000mer Hydroxylated Dehydroxylated

0.72 0.71 0

0.05

0.1 e

0.15

0.2

Figure 7: Comparison of local order parameter P2 for 8% PEOH systems with corresponding dehydroxylated specimens (a) 25mer (b) 50mer (c) 100mer (d) 1000mer under strain at 300 K. Figure 7 shows change in P2 with strain. For 25mer the P2 converges with time probably due to early failure of the material. This tends to suggest that for short chains addition of hydroxyls delays failure. In all other cases, hydroxyl group act like a crystalline defect and reduces the order parameter by ≈ 1%. As the strain is applied, the difference in the two samples remains constant, signifying that hydroxyls reduce the ordering of the crystals without changing the qualitative behaviour of polyethylene samples.

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Conclusions Thermal and mechanical properties of substitute or “doped” polyethylene systems are important to understand. The bulk properties of such systems have their origin in the change induced by the substitutions as well as the organization of amorphous, interphase and crystalline regions. In this paper, molecular dynamics simulations have been used to characterize the effect of low amount of hydroxyl substitution on the stress-strain relationship of polyethylene. Starting from highly randomized melts, various samples of substituted and unsubstituted semicrystalline polyethelene have been prepared and effect of 4-8 mol% of −OH studied. Since semicrystalline moities cannot be reproduced even by keeping all other simulation parameters constant, a simple transformation method is used to study the effect of substitutions on the stress response to strain. As a primary conclusion of the study we find that 4% hydroxyls do not effect the stressstain relationship in most systems. In general, 8% −OH increases the elastic range of polyethylene. Hence an improvement in dielectric properties of polyethylene does not deteriorate mechanical response functions. Furthermore, we see that hydroxyls are easily incorporated into the crystalline, interphase or the amorphous regions. Hydrogen bond analysis reveals that the net number of hydrogen bonds are invariant across chain sizes as well as distribution of crystalline regions. In this study we have taken hydroxyl concentrations similar to those in Ref. 34. However it would be interesting to see the effect of higher concentrations and perhaps tuning of mechanical properties of polyethylene. Large scale simulations with multiple samples would be useful in estimating the effect of such chemical defects on the structural and thermomechanical properties such as lamellar length, thermal conductivity and thermal expansion.

Acknowledgement We would like to acknowledge numerous discussions with the late Prof. Charusita Chakravarty, 19



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and are grateful for the guidance she provided at the initial stages of this project. GS thanks CSIR for the award of JRF. MA thanks IITD for RA fellowship. We thank the IIT Delhi HPC facility for computational resources.

Supporting Information Available All parameters of the OPLS-AA force field used in this study are available in Table S1 and S2 of the Supporting Information. Table S3 lists the distribution of crystallinity, density and onset temperatures for all the systems studied. Table S4 has the distribution of OH in the various phases.

This material is available free of charge via the Internet at http:

//pubs.acs.org/.

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