MARTINI Coarse-Grained Models of Polyethylene and Polypropylene

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MARTINI Coarse-Grained Models of Polyethylene and Polypropylene Emanuele Panizon, Davide Bochicchio, Luca Monticelli, and Giulia Rossi J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b03611 • Publication Date (Web): 22 May 2015 Downloaded from http://pubs.acs.org on May 26, 2015

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The Journal of Physical Chemistry

MARTINI Coarse-Grained Models of Polyethylene and Polypropylene Emanuele Panizon1, Davide Bochicchio1, Luca Monticelli2 and Giulia Rossi*1 1

Physics Department, University of Genoa, via Dodecaneso 33, 16146 Genoa, Italy

2

IBCP, CNRS UMR 5086, 7 Passage du Vercors, 69007 Lyon, France

Abstract The understanding of the interaction of nanoplastics with living organisms is crucial both to assess the health hazards of degraded plastics and to design functional polymer nanoparticles with biomedical applications. In this paper, we develop two coarse-grained models of every-day use polymers, polyethylene (PE) and polypropylene (PP), aimed at the study of the interaction of hydrophobic plastics with lipid membranes. The models are compatible with the popular MARTINI force field for lipids, and they are developed using both structural and thermodynamic properties as targets in the parameterization. The models are then validated by showing their

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reliability at reproducing structural properties of the polymers, both linear and branched, in dilute conditions, in the melt and in a PE-PP blend. PE and PP radius of gyration is correctly reproduced in all conditions, while PE-PP interactions in the blend are slightly overestimated. Partitioning of PP and PE oligomers in phosphatidylcholine membranes as obtained at CG level reproduces well atomistic data. Keywords. Molecular Dynamics, Polymers, Lipid membranes

Introduction The understanding of the interaction of nanoplastics with living organisms is crucial to assess the health hazards of degraded plastics and to design functional polymer nanoparticles with biomedical applications1. On the one hand, plastic debris is released in the environment and degraded down to the micro and nanoscale, eventually entering the food chain. The effect of micro and nanoplastics on living organisms is nowadays the object of intense research efforts from the toxicological point of view,2,3 but it is still largely unexplored at the molecular level. On the other hand, polymer materials find many and diverse applications in the realm of nanomedicine and bioactive materials. Dendrimers and amphiphilic polymers, for example, can be effective drug delivery agents4; polymers with finely tunable degree of hydrophilicity and hydrophobicity can act as surface modifiers and dispersing agents5, to prevent the aggregation of liposomes, proteins or nanoparticles; polyelectrolytes find application as transfectants6 (vectors of genetic materials) and biocidal agents4.


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The interaction between polymers and biological materials involves processes covering a wide range of time and length scales, such as rearrangement of the polymer conformation7, polymer aggregation or dissolution8, polymer adsorption/desorption to proteins9, direct or indirect membrane translocation10, lipid phase change11, etcetera. Coarse grained (CG) Molecular Dynamics (MD) simulations, which can span a time range extending from picoseconds up to hundreds of microseconds, and length scales of several tens of nanometers, are appropriate to capture many physical aspects of the interaction of nano-sized synthetic materials with lipid membranes. The challenge is then to develop a CG model able to treat at one time the biological and the synthetic polymer parts of the system. To this end, Lee and Larson developed a CG model of polyamidoamine dendrimers12 which is compatible with the popular MARTINI13–15 force-field for lipids, and they applied the model to the study of the interaction between dendrimers and phosphatidylcholine membranes16. Lee et al. developed a MARTINI model of polyethylene glycol17 that was subsequently elaborated to model PEGylated lipids18. Nawaz and Carbone recently worked at a MARTINI CG model of Pluronics19, a biologically active polymer whose potential toxicity has been recently investigated7. Shinoda extended his original CG force field for aqueous surfactants20 to block copolymers, dendrimers21 and their interaction with lipid membranes22. Our group developed a MARTINI CG model of polystyrene23, that we used to study the effects of polystyrene nanoparticles on the physical properties of lipid membranes8. We have recently shown that the interaction of hydrophobic molecules (polymers such as polystyrene and smaller compounds such as hexadecane, octane, benzene, C60 fullerene) can severely affect the structure, dynamics and lateral organization of lipid membranes8,24. In the present paper we introduce new MARTINI models of two everyday-use hydrophobic polymers, polyethylene (PE) and polypropylene (PP). Our aim is twofold: on the one hand, our goal is to


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develop reliable models for the description of PE and PP in the melt and in different solvent environments. On the other hand, we devote special care at verifying the compatibility of our PE and PP models with the rest of the MARTINI force field13,14,25, and particularly the lipid membrane environment. Our goal is to provide CG models that can be used to study the interaction of hydrophobic plastics with biological materials, and particularly lipid membranes. We developed models for PE and PP using both structural and thermodynamic properties as targets in the parameterization. As for structural properties, we used densities and the radii of gyration of the polymers in the melt. As for thermodynamic properties, partitioning of the individual building blocks was used as a target, according to the standard MARTINI protocols. Non-bonded interactions were only slightly refined with respect to the available MARTINI parameterization, so as not to compromise the compatibility of the models with the rest of the force field. We validated our models by showing their reliability at reproducing structural properties of the polymers, both linear and branched, in dilute conditions and in a PE-PP blend. Finally, we show that the partitioning of PP and PE oligomers in phosphatidylcholine membranes, as obtained at CG level, reproduces well atomistic data.

Methods Atomistic simulations. Atomistic simulations were used during PE and PP model development, to parameterize bonded interactions and calculate target properties such as the melt density and the radius of gyration of short polymer chains in the melt and in good solvent conditions. We used the OPLS-UA26 united atom force-field. Molecular Dynamics simulations were performed with a timestep of 2 fs in the NPT ensemble, using the Parrinello-Rahman barostat27 (P = 1 bar) and the velocity-rescaling thermostat (T = 450 and 500 K) developed by Bussi et al.28. PEUA52


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and PPUA28 melt simulations were run for 200 ns. The convergence of the radius of gyration of both polymers was achieved in about 20 ns, while the rest of the run was used for sampling. Coarse grained simulations. Coarse grained MD simulations were run with a time step between 10 and 20 fs, in the NPT27,28 (P = 1 bar, T = 450 and 500 K) ensemble. The Gromacs 4.5 and 4.6 packages were used. We remark that Gromacs 4.6 implements an efficient Verlet scheme for the update of neighbor lists. Such a Verlet scheme is used in combination with a straight cut-off, with a shift of the potential to zero at the cut-off distance. The MARTINI force field has been developed using a different neighbor list update scheme, the so-called group scheme29, combined to a shift function that makes the potential continuous and differentiable at the cut-off distance. We tested the use of the Verlet scheme with the MARTINI CG force field, using a reduced cutoff of 1.1 nm (instead of the usual 1.2 nm). We simulated a box of 8000 hydrophobic MARTINI beads (type C1) in standard NPT conditions, with a 20 fs timestep, with both the standard group scheme and the new Verlet scheme. We then calculated a static property, the density, and a dynamic property, the diffusion coefficient of the beads. The density calculated using the Verlet scheme is 1% higher than with the group scheme. Such a discrepancy is comparable to the statistical uncertainty, and it is small when compared to the poor agreement between the density of CG models and the experimental target density (673 kg/m3 for MARTINI liquid butane, against the experimental 601 kg/m3). The effect of the Verlet scheme on diffusion is larger, though: the diffusion coefficient of C1 beads is 4.13 ± 0.07 10-5 cm2/s using the standard group scheme, and 3.96 ± 0.0003 10-5 cm2/s using the Verlet scheme. The two values differ by about 4%. Such a discrepancy may be regarded as irrelevant when dealing with CG models, we anyway suggest some caution when looking at dynamics within the Verlet scheme.


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Free energy calculations. We calculated the free energy profiles of PE or PP dimers across a 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) membrane, at physiological conditions (T = 310 K, P = 1 bar), by means of the Umbrella Sampling30 technique. We performed the Umbrella Sampling simulations restraining the distance between our dimers and the center of mass of the membrane, in the direction of the bilayer normal. In each simulation two molecules of the same kind (PP or PE dimers) were restrained far apart from each other, at the desired distance from the center of the bilayer, so as to minimize the effects of their interaction. This setup allows double sampling at substantially no additional cost. The potential of mean force (PMF) was recovered from Umbrella Sampling simulations using the WHAM method31,32. The error on the PMF was derived from the bootstrapping of trajectories, performed with the Gromacs tool g_wham33, after the calculation of the autocorrelation times for each window. In the atomistic simulations, we used a force constant of 3000 kJ/mol nm2. We restrained the z component of the distance between the center of mass of the dimer and the center of mass of the membrane at 35 different values between 0 and 3.5 nm, with a regular spacing of 0.1 nm. Each simulation was 100 ns long, for a total simulation time of 3.5 µs for each PMF. In the CG simulations, the force constant of the biasing potential was set to 1000 kJ/mol nm2. We used 40 windows with a spacing of 0.1 nm, sampling polymer-membrane distances between 0 and 4.0 nm. The increased range of distances in CG simulations compared to the atomistic case was necessary because of the larger thickness of the CG membrane. Each simulation was 600 ns long, for a total simulation time of 24 µs for each PMF. Results Model development


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Mapping and derivation of bonded interactions. The atomistic-to-CG mapping of PE and PP is shown in Figure 1. In the MARTINI force field, groups of four or three heavy (C, O, N, P…) atoms are represented by a single coarse-grained bead. For PE, we used the standard 4-to-1 mapping. For PP instead, our mapping corresponds to a 3-to-1 mapping as CH2 groups are shared between adjacent CG beads. Both models include bond, angle and dihedral interactions. Bonds and angles are described by harmonic and harmonic cosine functions, respectively. PE dihedrals are described by a Ryckaert-Bellemans function, while PP dihedrals are described by a sum of two proper dihedral functions with the form = (1 + cos( − )) . We parameterized the bonded interactions by trial-and-error, by comparing bond and angle distributions obtained in CG and atomistic simulations. For PE, we simulated a melt of 70 chains of PE52 (represented by 13 CG beads), for PP we simulated a melt of 70 chains of PP28 (9 CG beads). Atomistic distributions are well reproduced at CG level by the parameterization of bonded interactions reported in Table 1.

SCB

PE C1 SC1

PP

Figure 1. The atomistic (black lines) and CG (grey and blue circles) representation of polyethylene and polypropylene. C1 and SC1 are standard MARTINI types13, while the SCB type is defined in this work and used to represent short branches of PE chains.


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Table 1. Parameters of bonded interactions in the PE and PP CG models beq [nm]

kb [kJ/ mol nm2]

θeq [deg]

kθ [kJ/mol rad2]

For PE: C1, C2,… C5 [kJ/mol] For PP: kϕ [kJ/mol], ϕs [deg]

PE

0.46

2000

180

25

-19.66, 1.51, 0.17, -0.0441, -0.00202

PP

0.298

constrained

117

92

3.10, 100 and -5.9, 190

The inclusion of a torsional potential along the backbone, at CG level, is fundamental to accurately reproduce the radius of gyration of the chains in the melt and in dilute conditions. Nevertheless, in CG MD simulations, the use of torsional potentials can lead to singularities. In particular, the occurrence of two consecutive angles at 180° along the backbone can generate numerical instabilities, as described by Bulacu34 et al. Instabilities can be avoided using shorter time steps in MD simulations, and indeed most of the results reported in this work were obtained using a time step of 10-15 fs. Bulacu et al. have proposed alternative treatments of bending and torsional angles that increase numerical stability, thus allowing the use of larger MD time steps. The new angle and dihedral potentials were recently implemented in Gromacs 5.0. We thus derived alternative parameterizations of bonded interactions for both PE and PP to be used with Gromacs 5.0, using either the restricted bending (ReB) function (for PP) or the combined bending-torsion potential (for PE) as described by Bulacu et al.

This alternative set of

parameters is reported in Table 2 and allows the use of a 20 fs time step, commonly used in MARTINI simulations. This alternative parameterization provides good matching between the atomistic and CG distributions of bonds and angles, and we verified that it does not affect the


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structural properties of the polymer melts. Nevertheless, we remark that all the results presented in the following were obtained with Gromacs 4 and the parameterization reported in Table 1.

Table 2. Parameters of bonded interactions in the PE and PP CG models, to be used with the Restricted bending or Combined bending-torsion potentials newly implemented in Gromacs 5. beq [nm]

kb [kJ/ mol nm2]

θeq [deg]

kθ [kJ/mol rad2]

For PE: a0, a1… a4 [kJ/mol] For PP: kθ [kJ/mol]

PE

0.46

2000

180

82

-19.666, 0.509, 1.120, -4.408E-02, -2.016E-02

PP

0.298

48000

119

78

3.10, 100 and -5.9, 190

Non-bonded interactions. The MARTINI force field has been parameterized in a systematic way, based on the reproduction of partitioning free energies between polar and apolar phases of a large number of chemical compounds. MARTINI bead types range from the most hydrophobic (named “C” beads) to the most polar (named “P”) and charged (named “Q”) groups. The hydrophobic nature of both PE and PP would suggest using the most hydrophobic MARTINI beads, namely the C1 beads, to describe both PE and PP. As a first target for parameterization, we looked at the melt density. For PE, the density of the melt of PEUA52 is 750 kg/m3. In good agreement with these data, a melt of MARTINI PECG12, in which each CG bead is a MARTINI C1 type bead, has a density of 752 kg/m3 at 450 K. Experimentally, the density of PEexp71 (corresponding to PECG20) is 763 kg/m3 at 450 K35, while for PECG20 we obtain 760 kg/m3. Assuming that the specific volume, , depends on the polymer mass as = + ⁄ 35, the specific volume at infinite chain length for our CG PE model would be 1.293 10-3 m3/kg, in good agreement with the experimental 1.302 10-3 m3/kg36.


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For PP, we chose the smaller SC1 beads to represent each monomer. On the one hand, this choice leads to rather poor performance in terms of density of the PP melt (1035 kg/m3 for PPCG100, 710764 kg/m3 according to experimental data37–39). On the other hand, beads along the PP chain are connected by very short bonds (only 0.29 nm), and this is not compatible with the use of the larger and more cohesive C1 MARTINI beads. Indeed, the shorter the bond length along the backbone, the more the intra-chain Lennard-Jones interactions can overcome the chain-solvent interactions, leading to the unphysical collapse of the chain, even in good solvent conditions. Since our PP model made of SC1 beads uses standard MARTINI types, the partitioning behavior of the polymer is very good and describes well the polymer conformation in a range of different solvents (see next sections). Radius of gyration of PE and PP in the melt. In Figure 2 we plot the root mean square radius of gyration, 〈 〉/, of PE and PP obtained with our CG models, and compared to available UA and experimental data. The agreement with UA and experimental data is satisfying for both the PE and the PP CG model.


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Figure 2. Root mean square radius of gyration of PE (top) and PP (bottom) in the melt, vs. the number of CG beads in the chains, N. The number of carbon atoms in the chains is 4N for PE, and 3N for PP. For PE, UA data are from Mavrantas40 et al., Foteinopoulou41 et al. and Carbone42 et al. (the latter using the force field developed by Smit43 et al.). Small angle neutron scattering (SANS) data are from Fetters44 et al. and Horton45 et al. For PP, UA data are from Boland46 et al. and Neelakatan47 et al. The original SANS data by Ballard48 et al. are referred to much larger


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molecular weight than those considered in our simulations; the fit of Ballard’s data to a ∝ ! function is shown by a dashed line.

Structure of short-chain-branched (SCB) PE in the melt. Common commercial polyethylene is made of branched PE chains. The extent and type of branching affect the density of the material, its mechanical properties, and the degree of crystallization. Among the most common polyethylene grades, linear low-density polyethylene (LLDPE) is characterized by a significant number of short chain branches (SCB), and by the absence of long branches. SCB units typically contain 2-10 C atoms and account for less than 10% of the overall chain molecular weight49. The extent of short chain branching affects the coil dimensions. At fixed molecular weight, the more SCB are present along the PE chain, the more the radius of gyration is reduced. This contraction can be quantified by the contraction factor gSCB, defined as the ratio between the radius of gyration of the branched chain, and the radius of gyration of the linear chain with the same total molecular weight:

#$%& =

〈 〉 〈 〉'


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Figure 3. Chain contraction factor, gSCB, vs. chain size for PE in the melt. Experimental data by Sun50 et al. were obtained by size exclusion chromatography (SEC), while Fetter’s et al. data44 are small angle neutron scattering (SANS) data. Ramos51 et al., performed MD simulations with the UA force field TraPPE.

We thus introduced branching units in our PE CG model, using as a target property the contraction factor of SCB chains as obtained via UA simulations and measured experimentally. As for bonded interactions, the bond connecting the branch to the backbone was the same as that used along the backbone, while we introduced a soft angle potential (θeq=90 deg, keq=25 kJ/mol rad) to prevent the branching units from overlapping with their backbone neighbors. As for nonbonded interactions, we first assigned the MARTINI type C1 to each branching unit. We built three different melt systems: a) a melt of 70 chains of linear PECG250 (molecular weight 14000 amu), b) a melt of 70 chains, with the same total molecular weight (14000 amu) and 38 SCB, corresponding to a 8% comonomer fraction in a ethylene-1-butene copolymer, and c) a melt of 70 chains, with the same total molecular weight and 100 SCB, corresponding to a 25% comonomer fraction in a ethylene-1-butene copolymer. In Figure 3 it is shown that,


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experimentally and according to UA calculations, the chain contraction upon branching increases linearly with the branching comonomer fraction. When using C1 type beads to represent SCB, the model chains contract much less than experimentally observed (in Figure 3, this set of data is labeled as “CG, with C1 beads”). We thus refined our CG model by substituting the branch beads with SC1 type MARTINI beads. MARTINI “S” beads are characterized by a shorter range of interaction with other “S” beads (0.42 nm instead of 0.47 nm), while they interact normally (0.47 nm) with the regular MARTINI beads. In order to reproduce the experimental data, we used the short interaction range (0.42 nm) to describe both SC1-SC1 (branch-branch) and SC1-C1 (branchbackbone) interactions. In order to avoid confusion with the original MARTINI naming, we will refer to our small branching beads as to SCB beads. With such parameterization, the contraction factor at CG level overlaps well the experimental and UA data, as reported in Figure 3.

Model validation Radius of gyration of PE and PP in bad and good solvents. 1,2,4-Trichlorobenzene (TCL) is a good solvent for both polyethylene and polypropylene. Its molecular formula is C6H3Cl3 and its octanol-water partition coefficient is log10P = 3.98, corresponding to a free energy of transfer between the water and the octanol phase of about 23 kJ/mol. We modeled TLC as a dimer of MARTINI beads, thus respecting the 4-to-1 mapping scheme that is commonly used by MARTINI. As for the bead type, we chose type C3. In fact, as free energies of transfer are roughly additive for short linear molecules, a dimer of MARTINI beads of type C3 (associated to 1-chloropropane in the original MARTINI publication13) should have an octanol-water partition coefficient of about 28 kJ/mol13, in reasonable agreement with the experimental value for TCL.


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We inserted individual PE and PP chains of different molecular weight in an equilibrated box of MARTINI TCL, and calculated their radius of gyration (Fig. 4). The scaling of the radius of gyration with the polymer size is in good agreement with the theory, being best fitted by a ∝ .)* function for both PE and PP. In Fig. 4 we plot also a comparison with the data by Liu52 et al., who performed static and dynamic light scattering experiments on high-density polyethylene and polypropylene in TCL at 423 K. The experimental data actually refer to larger molecular weights (5 104 amu and larger for PE, 105 amu and larger for PP), and the curves reported in Fig. 4 are the extension of the experimental trends to our range of sizes.

Figure 4. Radius of gyration of PE and PP in good solvent conditions.

Degree of mixing and coil dimensions in PE-PP blends. PE and PP are only partially miscible53. The structure of the blend is influenced by the molecular weight and the state of the components: the solid phase always exhibits some degree of phase separation, while in the liquid


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state the two polymers can mix above their critical solution temperature54 or at low molecular weights55. Our CG model is not aimed at reproducing the crystallization behavior of the two polymers, and indeed it could not: chain packing upon cooling is strongly influenced by the branching structure of the polymer, and the presence of the very small methyl branches of PP cannot be captured at CG level, where PP is linear. On the contrary, MARTINI models should be able to effectively reproduce the correct partitioning of the polymers in different environments, including the partitioning of the PP-PE blend. We thus performed the simulation of a blend of 30 chains of linear PEUA40 and 30 chains of PPUA40, and the corresponding CG simulation of a blend of 30 chains of PECG10 and 30 chains of PPCG13 and compared the outcomes, from the structural and energetic point of view. In terms of mixing, our united-atom simulation shows no phase separation during 260 ns of MD simulation (in agreement with the Monte Carlo data by Heine55 et al.), and neither does the CG model over a simulation time of 1 µs. To quantify the degree of mixing, we calculated the number of PE-PE, PE-PP and PP-PP contacts. In the CG simulations, two CG beads were considered to be in contact when their mutual distance was below a threshold distance, dt = 1 nm. In the UA simulations, we applied the same threshold to the center of mass of the groups of atoms used in the atomistic CG mapping (see the Model Development section). As the density in the CG system is larger than in the UA system (see previous section), we rescaled the number of CG contacts proportionally to the ratio of the CG to UA volumes of pure PE melts (PE-PE contacts), pure PP melts (PP-PP contacts) and for the liquid blend (PE-PP contacts). Then, we calculated the percentage number of contacts between PE-PE, PE-PP and PP-PP, which are reported in Table 3. There is good agreement between the UA and CG model on the percentage of pure PE-PE contacts, that is about 28%, while the CG


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model overestimates the number of PE-PP contacts and underestimates the number of PP-PP contacts. Table 3. Contacts between the two types of polymers in the liquid PE-PP blend, calculated in UA and CG simulations. Statistical uncertainties are below 1% and 0.1% for UA and CG simulations, respectively. PE-PE [%]

PE-PP [%]

PP-PP [%]

UA

28

26

46

CG

29

33

39

To characterize the conformational properties of the polymer chains in the blend, we calculated their radius of gyration. The agreement between UA and CG models is very good, with the radius of gyration differing by less than 2% for both polymers in the PE40-PP40 blend. We then performed CG simulations of a blend of PECG80 and PPCG100 and compared the radii of gyration of the two polymers in pure melts and in the PE-PP blend. We observed a slight contraction of the PE chains from 3.35 to 3.32 nm, and a swelling of PP chains from 2.22 to 2.34 nm. Although the changes appear small, they are larger than the statistical uncertainty obtained in our long CG runs (about 0.5%). Our findings are consistent with results by Heine et al., who also reported a similar structural change upon mixing. Concerning the energetics of mixing, we calculated the enthalpy of mixing as ΔH-./ = 0-./ (122 ) − (122 022 − (1 − 122 )023 ) where 0-./ (122 ) is the total potential energy, per CG bead (or CH unit in UA simulations), of the blend with 122 molar fraction of PP, and 022 and 023 are the energies per CG bead (CH


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unit) in the PP and PE pure melts, respectively. While ΔH-./ from UA and CG cannot be directly compared, their sign determines whether mixing is enthalpically favored (ΔH-./ < 0) or disfavored (ΔH-./ > 0). According to our CG model, mixing is favored by enthalpy. On the contrary, according to our and the previous55 UA simulations, mixing is enthalpically unfavorable and it is thus an entropy-driven effect. Partitioning of PE and PP in phospholipid membrane. In view of the application of our PE and PP models to the study of polymer-membrane interactions, we calculated the free energy profiles of dimers of PE and PP penetrating a POPC membrane from the water phase. We performed the calculations at the UA and CG level, dimers being represented by 8 carbons and 2 beads, respectively. The results are shown in Fig. 5. For the PE dimer, the CG and UA profiles have a very similar shape and are consistent with previous calculations on single C1 beads14. The most favorable position for the PE dimer is right at the center of the membrane. An inflection point is observed in both the CG and the atomistic profiles at about one third of the membrane thickness, followed by the rapid increase of the free energy as approaching the polar lipid heads. A small barrier is found in the headgroup region. The free energy difference between the water phase and the center of the membrane is 29 kJ/mol according to the CG model, and about 34 kJ/mol according to the UA model. For PP, both atomistic and CG calculations show that the dimer has to overcome a small free energy barrier (about 1.5 kBT) in the headgroup region, after which the free energy smoothly decreases until reaching a minimum at the center of the membrane. Overall, the free energy difference between the water phase and the center of the membrane is 32.5 kJ/mol for the CG model, and 29.5 for the UA one. The profile undulations in the lipid tail regions are smaller for PP than for PE (about 1. kBT) according to both the UA and CG model.


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Figure 5. Free energy profiles for PP (left) and PE (right) dimers as a function of the distance from the center of mass of a POPC membrane. Black lines refer to UA calculations, red lines refer to CG calculations. The grey region represents the density of phosphate groups in the CG simulations, where the membrane is thicker.

Discussion In the present paper we propose novel coarse-grained models for polyethylene and polypropylene. The models are compatible with the MARTINI coarse-grained force field. We used the density and radius of gyration of the polymers in the melt as targets for the development of the models, together with partitioning data. We then based our model validation on three key issues. First, we validated the models against the structural properties of the polymers in dilute conditions. Second, we assessed the accuracy of the model in capturing the mutual PE-PP affinity, by comparing a PE-PP liquid mixture simulated at the CG and atomistic level. Third, in view of the study of the interaction of hydrophobic polymers with biological membranes, we also validated the models by calculating the free energy profiles of PE and PP dimers penetrating a phospholipid membrane and comparing the results to UA calculations.


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Both PE and PP models are accurate at reproducing the structural properties of the polymers in the melt, with good agreement with the available experimental and computational data. As in its most common form PE is a highly branched polymer, we also developed and validated a PE model including branching units, reproducing the structural properties of Linear Low Density Polyethylene (LLDPE). Introducing short branches at CG level carries intrinsic limitations: in the CG model, branches can stem from the backbone at most every other CG bead, corresponding to one branch every eight carbon atoms in the atomistic representation. A higher density of CG branches would lead to an unphysical stretching of the chain due to the steric repulsion between the two adjacent CG branch beads. This limits our comparison with experimental data to low comonomer fractions (cfr. Fig. 3). Unphysical swelling of the polymer is observed also when branching beads have the same Lennard-Jones radius as the backbone beads, as shown in Fig. 3. In order to better reproduce the atomistic chain flexibility at branching sites, we reduced the Lennard-Jones radius of the first beads of PE branches. Further tests should be performed in view of future applications of the model involving PE grades with longer branches, such as High Density Polyethylene (HDPE). Indeed, we envisage that the branch bead type needs to be replaced by the standard C1 type as the branch gets longer, in order to be chemically indistinguishable from the PE backbone. A critical feature of any model developed within the framework of the MARTINI force field is its reliability at reproducing partitioning properties. For our polymer models, we addressed this issue in two ways. On the one hand, we performed free energy calculations to quantify the partitioning of PE and PP dimers into lipid membranes. This is of special importance in view of applications of the models to the study of polymer-membrane interactions, and the free energy profiles shown in Fig. 5 show a generally good agreement between the CG and the UA models.


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On the other hand, we performed the simulation of a liquid blend of PE and PP, with the aim to quantify their mutual affinity. There is qualitative agreement between the CG and UA description of the blend: the two CG polymers do mix at small sizes. Nevertheless, different energy contributions lead to mixing in the CG and atomistic models. The enthalpy of mixing is negative – thus favoring aggregation – in the CG model, while it is positive – thus contrasting aggregation – in the UA model, where the observed mixed configuration has to be driven by an entropic gain only. Some loss of entropy is intrinsic in any CG procedure. In the MARTINI model, the constrain to reproduce quantitatively partitioning free energies of the CG particles is satisfied by compensation, as the entropy loss is compensated by the overestimation of enthalpic contributions. A similar limitation of the MARTINI CG model has been observed when different types of lipids are mixed, namely saturated and unsaturated phospholipids; in that case, mixing/demixing of lipids is also determined mainly by enthalpy instead of entropy56. There is yet another reason why mixing is favored at CG level. We have observed that while the percentage of contacts between PE and PE is the same in the UA and CG simulations, in CG simulations PE-PP contacts are favored, at the expenses of PP-PP contacts. This behavior can be ascribed to the nature of SC1 bead, chosen to represent PP monomers in the CG model. SC1 beads are “small” beads compared to the usual C1 beads, as they interact with themselves via a Lennard-Jones with a reduced radius and energy of interaction (σ and ε). According to the original MARTINI parameterization, the σ and ε of the SC1-C1 interaction (PP-PE interaction) are rescaled to be the same as for C1-C1 interactions. The PP chains are thus seen by PE as extremely dense sequences of C1 beads, thus favoring PE-PP contacts in the liquid blend. A similar effect has been reported in the literature concerning fullerene interactions with the hydrophobic lipid membrane core. Indeed, fullerene has a high surface density; when coarse-


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grained using standard MARTINI C1 beads, its partitioning into the membrane core (where lipid tails are represented by chains of C1 beads) is largely overestimated57,58. Conclusions We have presented two coarse grained models of polyethylene and polypropylene, compatible with the MARTINI CG model. The models were validated by comparison with experimental data and finer level calculations, in terms of structural properties in the melt. The PE model is in excellent agreement with the available data both in terms of density and radius of gyration in the melt. The PP model overestimates the melt density, while reproducing correctly the chain dimensions in the melt. Both models performs well also in dilute conditions and in the PE/PP blend. As in its most common form PE is a highly branched polymer, we also developed and validated a PE model including branching units, reproducing the structural properties of Linear Low Density Polyethylene (LLDPE). The models reproduce the atomistic free energy profiles for the penetration of PE and PP dimers into model lipid membranes. Overall, our CG PE and PP models perform well both in terms of polymer properties in the melt and in dilute conditions, and in terms of consistency with the MARTINI force field for lipids, paving the way to applications in the realm of both material sciences and biomedicine. Supporting Information The CG distributions of bond, angles and dihedrals for PE and PP, together with the corresponding atomistic distributions used at the model development stage, are available as the Supplementary Information. This material is available free of charge via the Internet at http://pubs.acs.org/.


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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. ACKNOWLEDGMENTS Giulia Rossi acknowledges funding from the FP7 Marie Curie Career Integration Grant PCIG13GA-2013-618560. Part of the calculations was performed at CINECA under the NANOPLAS (HP10CM4EYY) grant. REFERENCES

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Table of Contents Graphic


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MARTINI Coarse-Grained Models of Polyethylene and Polypropylene

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