Intermolecular Interactions between Polyethylene, Water, and Potential Antistatic and Slip Additives: a Molecular Dynamics Study

TL;DR

This study uses molecular dynamics simulations to analyze how different additives interact with polyethylene and water, revealing their potential as antistatic or slip agents based on their microscopic interfacial structures.

Contribution

It provides new insights into the molecular interactions of additives with polyethylene and water, identifying promising candidates for antistatic and slip properties.

Findings

Additives interact mainly through polar heads with water via hydrogen bonding.

Water accumulates at polyethylene surfaces without entering the matrix.

Two additives can penetrate the polymer, affecting its structure and properties.

Abstract

Additives are essential to enhance or modify the properties of plastics for target applications. However, finding appropriate additives may be challenging, since we lack knowledge on their interactions with the plastics and with moisture, and the interplay between them. In this work, we study a commercial additive as well as two new potential additives for their antistatic and slip properties in polyethylene by means of atomistic molecular dynamics simulations. We reveal the most favorable interactions between polyethylene, each of these molecules and water, along with providing a microscopic picture of their interfacial structure. All additives interact with water mainly by their polar heads, with water acting as a hydrogen bond acceptor or donor depending on the additive. As expected, water does not enter the polyethylene matrix; it accumulates at its surface instead, without any preferencial orientation. The additives studied exhibit remarkably different structures when they are mixed with the polymer: two of them enter the polymer matrix to various degrees, either by intercalating their chains with the polyethylene ones or by forming miscellar-like structures, while the third one stays at the surface. When water is incorporated into the system, the structure of some of the additive/polyethylene systems changes. The magnitude and nature of these changes depend on the relative concentrations of all species. If the additives are in low concentrations, water stays at the surface of the material, in a drop-like shape. The additives penetrate and organize the polymer more or less depending on whether water is present or not. We predict that one of our two proposed molecules has promising antistatic properties while the other one could be applied as a slip agent. We hope that our predictions will spark interest in testing these molecules in the laboratory as polyethylene additives.

Tables

Table 1. Table 1: Force fields parameters for the additives extracted from GLYCAM06.

Non-bonded terms	${ϵ}_{ii}$ (kcal/mol)	${\sigma }_{ii}$ (Å)	$q_i$ (e)
$C_g$	0.1094	3.3996	-0.23006
3C	0.1094	3.3996	0.301333
$H_o$	0.03	0.3563	0.390500
$H_1$	0.0157	2.4713	0.000000
$H_2$	0.0157	2.2932	0.000000
$H_c$	0.0157	2.6495	0.118000
$O_h$	0.2104	3.0064	-0.644000
$O_s$	0.1700	3.0000	-0.606667
$N_T$	0.1700	3.2500	-0.938000
Bonds	$K_r$ (kcal/(molÅ2))	$r_{eq}$ (Å)
$3C-O_h$	320	1.43
$3C-O_s$	285	1.46
$O_h-H_o$	553	0.96
$C_g-C_g$	310	1.52
$3C-C_g$	310	1.52
$3C-H_2$	340	1.09
$3C-H_1$	340	1.09
$C_g-H_c$	340	1.09
$3C-N_T$	352	1.47
Angles	$K_{\theta }$ (kcal/(mol rad))	${\theta }_{eq}$ (°)
$3C-O_h-H_o$	55	109.5
$O_s-3C-H_1$	60	110
$O_h-3C-H_1$	60	110
$O_s-3C-H_2$	60	110
$O_h-3C-H_2$	60	110
$C_g-C_g-C_g$	45	113.5
$3C-O_s-3C$	50	111.6
$3C-3C-O_s$	70	108.5
$C_g-3C-O_s$	70	108.5
$3C-3C-O_h$	70	107.5
$H_c-C_g-H_c$	40	109.5
$H_1-3C-H_1$	45	109.5
$C_g-C_g-H_c$	45	112.6
$C_g-3C-H_1$	45	111
$3C-3C-H_1$	45	111
$3C-3C-H_2$	45	111
$O_s-3C-O_h$	100	112
$H_1-3C-N_T$	64	109.6
$3C-N_T-3C$	54	108.1
$C_g-3C-N_T$	67	111.6
$3C-3C-N_T$	67	111.6
Dihedrals	$V_n/2$ (kcal/mol)	d	n
$H_o-O_h-3C-H_1$	0.18	1	3
$H_o-O_h-3C-H_2$	0.18	1	3
$O_h-3C-3C-H_1$	0.05	1	3
$O_s-3C-3C-H_1$	0.05	1	3
$O_s-3C-C_g-H_c$	0.05	1	3
$O_h-3C-3C-H_2$	0.05	1	3
$H_c-C_g-C_g-H_c$	0.13	1	3
$H_1-3C-3C-H_1$	0.17	1	3
$H_c-C_g-3C-H_1$	0.17	1	3
$H_1-3C-3C-H_2$	0.17	1	3
$H_c-C_g-C_g-C_g$	0.1	1	3
$H_1-3C-C_g-H_c$	0.15	1	3
$H_2-3C-3C-3C$	0.15	1	3
$C_g-C_g-C_g-C_g$	0.45	1	1
$O_h-3C-3C-3C$	0.1	1	3
$O_s-3C-3C-3C$	-0.27	1	1
$O_s-3C-C_g-C_g$	-0.27	1	1
$3C-3C-O_h-H_o$	0.18	1	3
$O_h-3C-3C-O_h$	-0.1	1	1
$O_s-3C-3C-O_h$	-1.1	1	1
$O_s-3C-3C-O_s$	0.40	1	2
$3C-3C-O_s-C_g$	0.16	1	3
$3C-O_s-3C-C_g$	0.16	1	3
$3C-O_s-3C-H_1$	0.27	1	3
$3C-O_s-3C-H_2$	0.60	1	2
$O_h-3C-O_s-3C$	0.96	1	3
$H_o-O_h-3C-O_s$	0.18	1	3
$H_1-3C-N_T-3C$	0.25	1	3
$3C-N_T-3C-C_g$	0.1	-1	3
$C_g-C_g-3C-N_T$	0.3	-1	3
$O_h-3C-3C-N_T$	0.6	-1	3
$H_1-3C-3C-N_T$	0.1	1	3
$H_c-C_g-3C-N_T$	0.1	1	3

Table 2. Table 2: Force field parameters for polyethylene extracted from GAFF.

Non-bonded terms	${ϵ}_{ii}$ (kcal/mol)	${\sigma }_{ii}$ (Å)	$q_i$ (e)
C	0.1094	3.39967	-0.2043716
$C_T$	0.1094	3.39967	-0.2043716
H	0.0157	2.64963	0.1000000
$H_T$	0.0157	2.64963	0.1000000
Bonds	$K_r$ (kcal/(molÅ2))	$r_{eq}$ (Å)
C - C	303.1	1.535
$C-C_T$	303.1	1.535
H - C	337.3	1.092
$H_T-C_T$	337.3	1.092
Angles	$K_{\theta }$ (kcal/(mol rad))	${\theta }_{eq}$ (°)
C-C-C	63.21	110.63
$C_T-C-C$	63.21	110.63
H-C-C	46.37	110.05
$H-C-C_T$	46.37	110.05
$H_T-C_T-C$	46.37	110.05
H-C-H	39.43	108.35
$H_T-C_T-H_T$	39.43	108.35
Dihedrals	$V_n/2$ (kcal/mol)	d	n
C-C-C-C	0.18	1	3
$C-C-C-C_T$	0.18	1	3
$C-C-C_T-H_T$	0.16	1	3
C-C-C-H	0.16	1	3
$C_T-C-C-H$	0.16	1	3
$H_T-C_T-C-H$	0.15	1	3
H-C-C-H	0.15	1	3

Table 3. Table 3: Force field parameters for water.

Non-bonded terms	${ϵ}_{ii}$ (kcal/mol)	${\sigma }_{ii}$ (Å)	$q_i$ (e)
$O_w$	0.152	3.15075	-0.834
$H_w$	0.000	1.79605	0.417
Bond	$K_r$ (kcal/(molÅ2))	$r_{eq}$ (Å)
$O_w-H_w$	553	0.9572
Angle	$K_{\theta }$ (kcal/(mol rad))	${\theta }_{eq}$ (°)
$H_w-O_w-H_w$	100	104.52

Table 4. Table 4: Description of the chains in the modelled polyethylene by the number of monomers, total carbon atoms, and molecular weight.

Number of	Total carbon	$M_w$ per	Number of
monomers	atoms	chain (g/mol)	chains
15	30	422	2
16	32	450	2
17	34	478	2
18	36	506	1
19	38	534	2
20	40	562	3
21	42	590	1
22	44	618	2
23	46	646	3
24	48	674	1
27	54	758	1
32	64	898	1
34	68	954	1
38	76	1066	1
48	96	1346	1

Full text

I Introduction

The masterbatch industry provides polymer formulations in pellet form for the fabrication of final plastic products with a wide variety of properties and target uses [1, 2, 3, 4, 5, 6, 7, 8, 9]. The use of additives in these polymer formulations is essential to tailor the properties of the original resin, both within the bulk material and on its surface [10]. One of the most widely used polymers in this industry is polyethylene (PE). The existence of different types of PE depending on their density and synthesis method grants this polymer a large number of everyday life applications [11]. Furthermore, its nonpolar character and its low reactivity drive the research and development of compatible additives, considering productive, economic, and environmental aspects [12].

A wide variety of additives is available depending on the polymer of the formulation, such as antioxidants, UV protectors, plasticizers, flame retardants, thermal stabilizers [10], anti-blocking agents, glidants [13], and antistatic agents [14], among many others [15]. In particular, a central issue for several industries, such as packaging, is that of static electricity on the surfaces of various products. To reduce static in polymers, antistatic additives are used. In polyolefines, compounds from the ethoxylated amine family [4, 3] are excellent antistatic agents, as they reduce the surface resistivity of the polymer, favoring the dissipation of electrical charges [16, 1, 3, 7].

Other fundamental properties are those related to sliding, since the material must exhibit proper sliding during processing, such as in extruders. Slip additives are frequently incorporated into the polymer formulation to reduce the friction coefficient and thus improve the sliding ability. For polymers like PE, erucamide is one of the most effective slip agents known up to date [7, 6, 9, 17].

Depending on how the additives are incorporated into the polymers, they can be external or internal. The latter ones can be classified as non-migratory or migratory. Migratory additives are commonly amphiphilic molecules, with a polar head that interacts with the external environment (for example, ambient moisture) on the surface of the material. Typically, they must have the ability to migrate from the bulk of the material to its surface, and this migration is induced by the incompatibility between their polar region and the hydrophobic nature of the polymer matrix [4]. In the case of antistatic additives, it is generally hypothesized that once the polar head is exposed to the external surface, attractive or repulsive interactions are established with ambient water molecules, which are adsorbed on the surface. With respect to ethoxylated amines, it is assumed that attractive interactions with surface water can promote the formation of conduction channels that decrease surface resistivity, $R_{s}$ [14, 4].

New more environmentally friendly, lower-cost, and more effective migratory additives are needed [18, 19, 1]. In a previous study, Cammarata et al. [20] experimentally studied the changes in $R_{s}$ in linear low-density polyethylene (LLDPE) films as a function of the concentration of a series of amphiphilic additives. These compounds contain a sugar-based polar head and an ethoxylated amine, referred to here as EA, whose structure is shown below in Figure 1. In general, it was observed that the compounds with the greatest reduction in $R_{s}$ also exhibit a drastic reduction in the water-surface contact angle. In addition, when water droplets slid on a polyethylene surface containing these compounds, a proton transfer from the surface to the water droplets was observed. These studies indicate an important interaction between the three components present at the surface: polymer, additive and water.

Tailoring these interactions by modifying the chemical groups and concentration of the additives can help tune the surface properties of the polymeric material. Computer simulations have been applied to studying these kinds of systems with promising results. Li and coworkers and Wang and colleagues have studied the microstructure and diffusion coefficients of a series of migratory additives in polyethylene by atomistic molecular dynamics simulations, providing insight into the migratory process [21, 22]. Cammarata and coworkers performed coarse-graining molecular simulation studies to study the kinetics of the migration process in PE [23]. The interactions of water with a bulk PE matrix [24, 25, 26] and with its surface, [27, 28, 29, 30] have also been explored by simulation techniques. However, to the best of our knowledge, there has never been a study in which the interplay between polymer/additive, polymer/water and water/additive interactions together with their impact on the molecular arrangements at the surface of the material is analyzed. Studying this is crucial to establishing rational design principles for improving plastic formulations.

In this work, the interactions between PE, a series of additives and water at the surface of the material are studied by molecular dynamics simulation techniques. These interactions are linked to the molecular-level arrangements, which are evaluated as a function of the relative concentration of the components. The orientations of the additives at the surface are particularly investigated, as this is crucial for their effective activity. We describe the interplay of polymer/additive, polymer/water and water/additive interactions as a function of the composition, and rationalize the molecular arrangements that result from them. Two organic amphiphilic molecules, referred to as compounds A and B (see Figure 1), were explored as prospective additives for PE. Their chemical structures are analogous to two of the compounds evaluated in a previous work [31], but with a smaller polar head, which might improve their migratory behavior. They were selected to assess their potential antistatic or slip agent behavior. To compare the behavior of these additives with a reference example and validate the model, an ethoxylated amine, referred to as EA, was also investigated. Our work offers unprecedented insight into the structural complexity of water/polyethylene/additives ternary systems, and the impact of the composition on it. Moreover, we predict that the two molecules investigated are promising candidates, one for its antistatic properties (A) and the other as a slip agent (B).

II Methods

All molecular dynamics simulations (MD) were performed with the LAMMPS package [32]. Binary and ternary mixtures containing polymer (with water, additives, or both) consisted of a polymer slab of 28.5 Å depth, to model PE industrial thin films containing additives and environmental moisture. For each system, energy data (total energy, potential, and kinetic) were collected and plotted to decide whether equilibrium was reached. Intermolecular interactions were studied by analyzing the radial pair distribution functions (RDFs) between relevant atom types. The VMD software [33] was used to compute the RDFs within the production runs. 3D periodic boundary conditions were considered in all calculations.

II.1 Systems and simulation conditions

Pure polyethylene, water, and additives were first simulated at the NPT ensemble (T = 300 K and P = 1 bar) to assess the quality of the individual force fields in terms of the equilibrium density.

Binary systems were divided into three groups: i) water-additives, ii) PE-water, and iii) PE-additives to study the intermolecular interactions between the components independently. In the first group, two cases were considered: systems with excess water (additives in water), which consisted of 4 additive molecules in a 72 Å side box with 12700 water molecules, and systems with excess additive (water in additives), formed by 7 water molecules and 35 additive molecules in a 30 Å side box. These amounts were calculated to keep the volume ratios occupied by the solvent and solute constant in both systems. For the PE-water system (group ii), 700 water molecules were added to the polyethylene slab to obtain the same volume of PE and water in the box. With the same premise, PE-additive systems (group iii) were built by adding 9 additive molecules to the polymer slab.

Two kinds of ternary systems were simulated: PE with additives in water, called herein PE-additive-excess water, and PE with water in additives, referred to as PE-water-excess additive. For the systems with excess water, 4 or 5 additive and 220 water molecules were added. In the systems with excess additive, 5 water and 8 additive molecules were added.

The initial state of all the binary and ternary systems was built by inserting a layer of the extra components (water, additives, and their combinations) over the PE slab, by random addition of the corresponding molecules. The systems were then left to evolve during the equilibration run. The length of the equilibration runs was tailored to guarantee that each system had achieved equilibrium. All the production MDs were performed at 300 K with a 0.5 femtosecond timestep. Systems without polymer were run in the NPT ensemble at 1 bar, whereas all the systems that had a polymer slab and thus needed one part of the box to be void were simulated in the NVT ensemble. Temperature and pressure were regulated using the Nosé Hoover thermostat and barostat, with relaxation timesteps of 0.3 ps and 0.5 ps, respectively. MD production runs were 7 ns long on average.

II.2 Polymer generation

PE was modelled with the General Amber Force Field (GAFF) [34], which consists of harmonic potentials to model bonds and angles, cosine-based potentials for dihedrals and a summation of 12-6 Lennard Jones (LJ) and Coulomb potentials for non-bonded interactions. The LJ and Coulomb short-range cutoff was set to 12 Å. The long-range part of electrostatics was treated with the particle-particle particle-mesh solver, with a relative error in the forces of 10*-5*. Partial atomic charges were assigned following a model previously published,[35], but to keep charge neutrality, a slight redistribution of an excess positive charge given by the terminal methyl groups had to be made due to the polydispersity of our model.

PE was constructed in silico via the methodology developed by Abbot et. al. [36] as implemented in the Polymatic code [37]. This building strategy was selected because it is appropriate for modelling amorphous, linear, and polydisperse polymers, a fitting description of high-density polyethylene. In addition, it is known that migration of amphiphilic additives takes place mainly in the amorphous regions of the polymers [38] rather than the crystalline ones, so modelling an amorphous polymer is advantageous for studying potential migratory additives. The polymer construction procedure comprised 5 stages:

1) Monomer description: the monomer consisted of an ethane-like molecule with two fewer hydrogen atoms, so that the two carbon atoms are undercoordinated. Five atom types were initially defined: three carbon and two hydrogen types. One of the carbon types was described as “reactive”, which means that they can form C–C bonds. Reactive carbons become regular carbon atoms after polymerization. The “reactive” carbon type is thus absent in the final polymer model.

2) Simulation box building: A cubic 50 Å side box was filled with 1290 monomers, which corresponds to an initial density of 0.48 g/ml. Commercial high-density polyethylenes have a density in the range of 0.94-0.97 g/ml [11, 39], but a lower initial density is recommended to facilitate the polymerization [36].

3) Polymerization: three parameters must be set according to Polymatic to start polymerization: temperature (T), minimum distance at which two monomers must be from each other to form a bond, $(x_{min})$, and number of bonds to be formed per cycle (B). Several polymerization runs were performed until the optimal values for these parameters to obtain the longest possible chains were identified: $x_{min}$ = 10 Å  T = 500 K, and B = 14. The longest chain had 48 monomers (which means 96 carbon atoms), with the remaining chains containing from 2 to 38 monomers, and a fraction of isolated monomers.

4) Adding chain-ends and chains selection: the elongated chains have no terminal hydrogens, as the monomer contains only four hydrogen atoms. The terminal hydrogen atoms were added via an in-house code. After that, the chains selection was made. For this purpose, a final cubic box size of 30 Å was estimated. With a desired density of 0.95 g/ml (considering the density range mentioned before), 557 monomers are needed in the box. Therefore, the longest chains were selected so that the total sum of monomers contained was close to this value. The minimum chain length selected was 15 monomers. Shorter chains and no-bonded monomers were removed from the simulation box using another in-house code. This way, a non-branched polydisperse polyethylene model was constructed.

5) Equilibration and slab building: A box with a slab unwrapped in one direction (z direction herein) needed to be built, including void space to ensure the periodic images do not interact with each other. To have a dense slab, a spring force was applied to the center of mass of each of the chains to tether them to a fixed position, using the spring force command available in LAMMPS [40]. The polymer was equilibrated with an MD run in the NVT ensemble, followed by the ”21 steps” sequence developed by Abbot [36], keeping the spring force on all the time. The last MD of this sequence was considered enough to equilibrate the system at ambient temperature and pressure, as volume and total energy oscillated around a constant value. A 10 nanosecond-long production MD in NVT ensemble (300 K) with a 0.5 femtosecond timestep was subsequently performed to obtain characteristic information of the polymer.

II.3 Additives and water models

Simulated additive molecules are shown in Figure 1. Each additive has a distinctive colour, which will be maintained throughout the text: green for additive A, violet for B, and orange for EA, as seen in Figure 1.

The GAFF-derived force field GLYCAM06 [41], suitable for carbohydrates, was employed for the additives parametrization. All potential functional forms and cutoffs are those described before for PE. The corresponding parameters for the potentials were taken from GLYCAM06. According to this force field, sugars like galactose have carbon atoms with a partial positive atomic charge due to the electrowithdrawing effect of oxygen atoms. In contrast, carbon atoms in a non-polar hydrocarbon chain have a negative charge, as seen in polyethylene. Hence, two different carbon types must be defined to parameterize all additives. Partial atomic charges defined in GLYCAM06 were used for the sugar-moiety carbon atoms in additives A and B, and the same atom types defined for the polymer were used to model the carbon atoms in the hydrocarbon chains. Slight adjustments were made when necessary to ensure electroneutrality. Figure 10 shows the structures of the simulated molecules labelled according to their atom types. Partial atomic charges of EA were based on the monoethanolamine force field developed by Alejandre and coworkers.[42]

Water was modeled with a simple and flexible force field. Its parameters can be found in the Supporting Information (SI). [43]

III Results and Discussion

III.1 Pure systems

The polymer built contained 24 chains with different lengths and molecular weights (see SI, Table IV). The density of the polyethylene slab was 1.02 g/ml, $5.1\%$ over the maximum typical reported density of 0.97 g/ml for industrial high-density polyethylene [39, 11]. This density was obtained by averaging several manual measurements of the slab size in the equilibrated pure PE system (performed with the VMD software [33]).

The initial polymer slab was amorphous, but the chains acquired a partially ordered structure after the production dynamics, while maintaining an amorphous region, as shown in Figure S2 a,b. This is compatible with the higher density obtained and suggests the presence of crystalline domains in the simulated polymer. The ordering might be related to the fact that the simulated temperature (300 K) is above the vitrimer transition temperature of the polymer, which is experimentally found in the range 190-200 K in amorphous polyethylene [44]. The C–C RDF (Figure 11 c) clearly shows a partially crystalline structure, judging by the multiple peaks at distances above 3 Å. The result agrees with those obtained by Narten et. al. for a PE powder of $M_{w}$ = 90.000 g/mol and a density of 0.92 g/ml at 300 K [45], which indicates that the chosen force field and the methodology employed properly captures the PE structure.

Additives A and B exhibited 1.01 g/ml and 0.99 g/ml densities, respectively. No experimental data on these chemical compounds are available. Still, the density values are close to those predicted by the tools integrated in $SciFinder^{n}$ CAS [46, 47] for each molecule: $1.06\pm 0.06$ g/ml for additive A, and $1.04\pm 0.06$ g/ml for additive B. These values are obtained through QSPR/QSPAR models for physicochemical properties prediction [48, 49]. A 0.90 g/ml density was obtained for EA at 300 K, in good agreement with the value of 0.88 g/ml reported at 323 K [50].

RDFs analysis of additive A revealed peaks at 1.95 Å and 3.55 Å for the $O_{h}-H_{o}$ pair, corresponding to intramolecular distances in the galactose moiety with different conformations of the pyranose form.[51] Peaks at 1.99 Å and 3.56 Å between the same atom types were obtained for additive B, consistent with reported $O_{h}-H_{o}$ distances in alcohol clusters.[52] The $O_{h}-H_{o}$ bonding distance was between 0.94 Å and 0.97 Å both for additives A and B, in good agreement with the typically reported O–H bond distance of 0.96 Å to 0.97 Å.[52]

The successful comparison between experimental and predicted data allowed validating the force fields employed for the PE and each additive.

III.2 Binary systems

III.2.1 Additives and water mixtures

The interactions of the three additives with water were studied both at excess water and excess additive conditions. Four pairs of atoms (see Figure 10) were analyzed to characterize these interactions through RDFs: $C_{g}-O_{w}$ and $O_{w}-H_{c}$ to see interactions between water and the less polar fraction of each additive (hydrocarbon chain), and $O_{w}-H_{o}$ and $O_{h}-H_{w}$ to account for hydrogen bonds and polar interactions. Visual inspection of the trajectories with additives in water revealed that all EA molecules remained together during the simulations, whereas A and B molecules were more dispersed but still formed aggregates (see Figure 12). This suggests that the additives are not soluble in water, even when a few additive molecules are present.

Repulsive interactions were identified for $C_{g}-O_{w}$ and $O_{w}-H_{c}$ pairs for the three additives, as the frequency is always below the bulk reference, as seen in Figure 13. This is expected due to the non-polar character of hydrocarbon chains.

A more interesting result was obtained from $O_{w}-H_{o}$ and $O_{h}-H_{w}$ RDFs, shown in Figure 2. Two important features of the hydrogen bond interactions in the systems can be extracted from these two atom type pairs: 1) For $O_{h}-H_{w}$, the functions have similar shapes for the three additives, but only for EA (orange curve) the frequency is close to the bulk value at a distance of 1.85 Å. The opposite tendency is observed in the $O_{w}-H_{o}$ function, where EA presents the lower frequency at 1.92 Å. This indicates hydrogen bonds between water and EA are preferably established between the oxygen of the EA $(O_{h})$ and the hydrogen of water $(H_{w})$, while for A and B, they are established between the oxygen of the water $(O_{w})$ and the hydrogen of hydroxyl groups of the sugars, $H_{o}$, instead. In the specific case of EA, a third hydrogen bond is possible between $N_{T}$ and $H_{w}$ atoms but the comparison of RDFs in Figure 2 c indicates the $O_{h}-H_{w}$ interaction is favored, as it is observed at a higher frequency.

These results can be rationalized considering that the sugar moieties in A and B are bigger than the ethoxyamine group. There is a steric hindrance that makes oxygen atoms $O_{h}$ less accessible for $H_{w}$ atoms, and as a result, hydrogen bonds between $O_{w}$ and $H_{o}$ are more favorable for additives A and B. Figure 3 illustrates additive structures highlighting their polar regions. Water molecules find less steric hindrance when getting close to the A and B hydroxyl groups by their oxygen atoms. With EA, water molecules can get close through their hydrogen atoms to $O_{h}$ or $N_{T}$ atoms, but $O_{h}$ atoms are preferred because $N_{T}$ atoms are more hindered.

Following this analysis, a polarity trend is proposed for the hydrophilic head of the three modeled additives. EA is the most polar one, not only because it can establish three types of hydrogen bonds, but this is also supported by its well-known solubility in methanol [53] and ethanol [31], likely due to the small polar head with the hydrophilic hydroxyl groups. Nevertheless, it is not soluble in water. Additive B is placed in the middle of the three, with more hydrophilic hydroxyl groups than additive A to establish hydrogen bonds, and a hydrocarbon chain akin to the polymer. The shorter $O_{w}$–$H_{o}$ hydrogen bonds obtained for additive B as compared to those obtained for additive A (see Figure 2b) support this trend. Additive A is the least polar one, probably due to the cyclic sugar moiety that implies a steric hindrance to the water interactions, besides having fewer hydroxyl groups.

2) Hydrogen bonds with A are longer than with B, as can be seen in Figure 2 b): for A, there is only one peak at 1.92 Å, while for B the first one is at 1.83 Å. Once again, it is consistent with the steric hindrance, as it is more important for A. The cyclic structure of the sugar moiety in additive A restricts movements and provides an electronic sphere that repels water molecules slightly more than in the case of B. This leads to a longer distance between $H_{o}$ and $O_{w}$ atoms, and can be correlated to a lower polarity of the hydrophilic head, as discussed above.

The trajectories of the systems with water in additives show a similar pattern for water molecules in B and EA, which differs from that of the A-containing system. Water molecules in an A environment move separately along the box during the whole dynamics and do not tend to aggregate (see Figure 14a; additive molecules were omitted for visual clarity). They interact indistinctly with the hydrocarbon chain of the additive or the sugar moiety, consistent with its lowest polarity among the three additives. In a B environment, two groups of water molecules were observed at the beginning of the trajectory, and they were always surrounded by the polar portions of B (sugar moiety). At the end of the trajectory, all water molecules were close to each other. In the EA environment, something similar happens, but five water molecules form a cyclic structure as shown in Figure 14c. The polar motives of surrounding additive molecules (galactitol and ethoxyamine groups, respectively) are oriented towards the water molecules, as expected. These results are, again, consistent with the previously proposed polarity trend of the additives, as the more polar heads of molecules B and EA can interact with water through their galactitol and ethoxyamine moieties, respectively.

These facts are reflected in the RDFs for $C_{g}$–$O_{w}$ and $O_{w}$–$H_{c}$ pairs, illustrated in Figure 15. Interactions between $C_{g}$ and $O_{w}$ are attractive only in the system with additive A, while for EA they are slightly attractive, and repulsive for additive B. Interactions between $H_{c}$ and $O_{w}$ were repulsive for the three additives, with a more defined peak only for additive A. Both RDFs are consistent with the dispersion of water molecules in the box with additive A, allowing water to interact with the polar and non-polar regions of additive A molecules. In contrast, in B and EA environments, water molecules interact mainly with the polar groups of the additives.

Concerning hydrogen bonds, the same preference for $O_{h}$–$H_{w}$ in EA was observed compared to A and B, as shown in Figures 15c and d.

III.2.2 PE with water

PE also acquired the partially ordered structure previously discussed in the presence of water; Figures 4b and c show this in two representative snapshots of the simulation box. The water molecules homogeneously cover the PE-water interface, as shown in Figure 4 a, but remain located over the PE interface, without penetrating the matrix. Due to this, the RDFs for internal PE atoms C and H, with water atoms $O_{w}$ and $H_{w}$ (not shown), exhibited repulsive interactions, as expected. Weak interactions were found only between terminal carbon ($C_{T}$) and water hydrogen atoms, as seen in the RDF of Figure 4 d and e, as these terminal atoms are more abundant at the surface of the polymer slab.

The peaks are close but still below the bulk value of the function, thus indicating a poor interaction at the interface. There is a subtle difference between the $C_{T}$–$O_{w}$ and $C_{T}$–$H_{w}$ RDFs, the former seems slightly stronger. This might suggest a predominant orientation of water molecules with oxygen atoms toward the polymer interface, like in hydrogen-bonding-capable polymers.[54] However, no orientational preference was detected upon further analysis of the trajectory of the PE-water system. Hence, the difference between the RDFs does not seem to be correlated with a significant difference in orientation. If there were a preferred orientation, it would be expected to be with one of the hydrogen atoms near the polymer, as Zhang et al. suggested in previous work [30] for non-hydrogen-bonding polymers like PE. Instead, the OH group orients normally to the PE surface; this matches the so-called ”dangling” OH group,[55] observed in other hydrophobic surfaces as well, such as alkanes and polydimethylsiloxane.[56] This orientation allows water molecules to optimize hydrogen bonds at the bulk and minimize the disturbance produced by the non-polar material.

III.2.3 PE with additives

PE with additives systems consisted of the polymer slab with a layer of additives above it and a space to avoid interaction of slabs through periodic boundaries. Important differences in the behaviour of the additives were observed within the dynamics. Figure 5 shows a representative snapshot for each additive-containing system. The additives are represented with the colors used in Figure 1, and only $O_{h}$ atoms are distinguished as red balls to identify the polar regions of the molecules. While additive A keeps its initial position over the PE slab surface without penetrating, additive B goes slightly deeper into the matrix with the polar regions (sugar moieties containing red $O_{h}$ atoms) clustering together, forming a polar pocket. This orientation resembles a micelle or a bilayer, which is consistent with the reported ability of 6-O-alkyl-galactitols to form liquid crystals.[57] A big contrast is observed for EA, as i) the polymer is partially ordered like in the pure and PE-water systems, and ii) EA molecules are immersed in the polymer matrix, with their non-polar chains aligned with the polymer chains and the ethoxyamine groups disposed at the PE-air interface. From these results, an attempt at establishing a polymer-affinity trend for the additives can be made, with increasing affinity from A to B and EA. RDFs in Figure 5 d, e, and f reflect this tendency regarding hydrocarbon chains: $C$–$C_{g}$ interactions are significantly attractive for EA, but repulsive for A and B. Multiple peaks slightly over the bulk value in the $H$–$H_{c}$ RDF in the PE-EA system are consistent with a weak long-range interaction between those atom types, as well as with the ordered structure of EA chains within the polymer matrix. The same RDFs for additives A and B show repulsive interactions. Lastly, for the $C_{T}$–$O_{h}$ pair, a strong attractive interaction is seen for EA, while it is weaker for A, and repulsive for B. Terminal carbon atoms of PE $(C_{T})$ are closer to galactose moieties and ethoxyamine groups because they are near the interface. In contrast, additive B adopts a different arrangement: polar groups cluster together inside the PE core instead of away from it, at the surface. The previously mentioned bilayer configuration for additive B was noted for the commercial slip agent erucamide,[9, 7] as reported by Dulal et. al.[8] This similarity makes additive B interesting to be tested experimentally as a potential slip agent for polyethylene.

The polymer-affinity trend proposed is opposite to that of the polarity of the hydrophilic heads discussed before and might seem to be inconsistent. However, some structure-behavior relations can be established. Additive A has a cyclic sugar moiety as its polar region, which could be too big to allow its migration inside the polymer when they are in contact. The polar group of additive B contains a polyhydroxylated chain; hence, hydrogen bonds between them might be optimized when they are close to each other, rather than oriented to the PE-air interface. The ethoxyamine groups in EA are small and polar enough to allow the molecules to migrate into the polymer and dispose as seen in Figure 5. In addition, this compound is part of commercially used antistatic formulations suitable for polyolefins,[58, 59], so its migratory nature is well known.[60] Its behavior in the polymer is as expected: the hydrocarbon chains are located inside the PE and polar groups oriented towards the PE-air interface,[4] so that they can interact with water and PE at the same time.[3] Thus, the explanation proposed in the previous paragraph agrees with the two mentioned trends, taking into account the experimental results.

III.3 Ternary systems

Figure 6 shows the final frame of each PE-additive-excess water trajectory, with the same color codes as in Figure 5, from two different points of view, as indicated in the figure caption.

When water molecules are located over the polymer, additive A chains exhibit a strong repulsion with water, which leads to their immersion into the polymer, with the hydroxyl groups of the galactose head pointing towards the water layer. The behavior is notoriously different from the analog system without water (see Figure 5), where no additive penetration was observed. Figure 7 a shows the $C$–$C_{g}$ RDFs for both the binary PE+A and ternary PE+A+water (excess water) systems. The difference between the two functions is clear: the interactions between these atom types are attractive when the system contains water and repulsive otherwise. This reflects the higher affinity of A with PE against water when the latter is in excess.

A minor difference was observed for additive B: the molecules are still lying mainly outside the polymer, but their orientation changed from the pocket-like structure of galactitol groups to one similar to that of additive A, with their hydroxyl groups interacting with the water molecules. These results meet the hydrophilic heads polarity trend for the hydrophilic heads proposed above, with additive B being more polar than A, as its hydrocarbon chains do not tend to avoid water, as was the case for additive A. The $C_{g}$–$O_{w}$ RDF is shown in Figure 7 b, which illustrates that this interaction is attractive only for additive B. This is consistent with the presence of chains of additive B chains at the surface, interacting both with water and PE. In contrast, the hydrocarbon chains of A and EA remain immersed in the polymer, far from water molecules, thus leading to repulsive interactions.

It is worth noting that water molecules shown in Figure 6 do not cover the entire PE surface as they did in the PE-water system, but are in a drop-like disposition and in contact with the sugar moieties of additives A and B. This suggests that the presence of these additives can modify the PE surface affinity with water, becoming, in appearance, more hydrophobic. A slight difference was observed for EA, whose molecules remained immersed in the polymer with the same orientation seen in Figure 5, and the ordered structure of the polymer was conserved too. This behavior is typical of migratory amphiphilic additives,[4] as they are expected to be akin to the polymer but also able to attract moisture from the environment in the polymeric surface through their polar heads.

Regarding hydrogen bonds, Figure 7 c shows again that this interaction is given preferably between $O_{w}$ and $H_{o}$ for additives A and B, while with EA hydrogen bonds are established between $O_{h}$ and $H_{w}$ atoms. Nevertheless, it can be seen that the $O_{w}$–$H_{o}$ interaction is also possible (attractive) for EA, but it is established at around 3.5 Å, a larger distance than for the A and B cases (around 1.82 Å). This was not observed in the binary additive-water systems with excess water analyzed above (Figure 2), and could be interpreted as a way of optimizing the interactions of EA molecules with water through their polar heads while their hydrocarbon tails are immersed in PE. This does not include the $N_{T}-H_{w}$ hydrogen bond, which is still less favored than that between $O_{h}-H_{w}$, as shown in Figure 7 d. In all this discussion, it can be seen that the additives adapt their arrangements to optimize the interactions with the polymer and with water simultaneously. Thus, the configurations seen in Figure 6 meet this purpose.

To continue the analysis, the excess additive ternary systems will be described next. Figure 8 is analogous to Figure 6, with the simulation boxes oriented in the same way.

Systems with additives A and B look similar to the ones without water: additive A remains over the PE without penetrating, whereas additive B goes only slightly deeper, with its galactitol groups (with $O_{h}$ atoms shown in red) disposed in a pocket-like configuration. This similarity was expected given that the systems are almost the same but with a few water molecules, highlighted by the yellow squares in Figure 8.

In contrast, the box containing EA does not look like its analog without water: PE acquired a less partially ordered structure, and EA molecules are not immersed in the polymer, but on its surface. This is similar to additive A. From this observation, some results can be highlighted: i) the polymer adopted the most ordered structure only when it was pure or with water or EA, in a similar amount; ii) interactions in ternary systems are very sensitive to which component is in excess (water or additives), and iii) in excess additive, it seems that the water-EA interactions can be better satisfied if EA molecules remain close to the PE surface, with their hydrocarbon chains interacting with the PE and their ethoxyamine groups near to the water molecules.

In addition, in Figures 8 d and e, the water molecules are close to each other in a cyclic configuration, like in the water in additives binary systems with B and EA. This was not observed in the A system analyzed above.

Hence, the spatial distribution of the components in the system, as well as the order the polymer adopts, depends on the concentration of both additives and water. This is especially relevant for EA, as it is a commercial additive. When it is in excess in the ternary system, it seems to emerge instead of staying immersed in the polymer. When water is in excess, it remains immersed, the polymer acquires a partially ordered structure, and the ethoxyamine groups interact well with water molecules at the surface. As an antistatic additive, it needs a minimum of environmental moisture to dissipate charges at the surface [4], and the results are evidence of this. Thus, it can be inferred that when water is lacking, the additive will be expelled from the polymer matrix, as it emerges at the surface and is exposed to be removed from there. Regarding the polymer ordering, the presence of an amphiphilic molecule inside the polymer or a water layer above it might be the driving force to achieve the observed partially ordered structure. And when the polymer is alone, this partially ordered configuration must be thermodynamically favored.

These results point out that the molecular arrangements strongly depend on the composition of the system, which dictates the interplay between all the possible intermolecular interactions in such a way that the energy is minimized.

To summarize these findings, Figure 9 shows the $C$–$C_{g}$ RDFs for each additive in all PE-containing systems. Comparing the PE + additive curves (continuous lines), it can be seen that interactions between additive and polymer are stronger with EA than with A and B, following the PE-additive affinity trend previously proposed. When water is introduced in excess (dashed lines), additive A becomes more akin to the polymer as a consequence of having a less polar hydrophilic head, while additive B and EA arrange to interact both with PE and water. Lastly, when additives are in excess with only a few water molecules (dotted lines), all additives seem to have a similar affinity with the polymer, although the interactions are stronger for EA. The presence of water modulates the affinity of the additives for PE and enables the systems to acquire different arrangements to optimize polar and non-polar interactions.

The results in this work can be correlated with the performance of the additives. On the one hand, results agree with the proposed working mechanism of EA as an antistatic agent [3, 4]. In addition, they suggest that additive A might perform as an antistatic agent for polyethylene when the environmental moisture is enough, and that additive B might be suitable as a slip agent for this polymer, as it seems to dispose in a similar way to erucamide [8, 9] like in the binary system PE-additive B. Also, its behavior is less dependent on the water content in the system.

IV Conclusions

In this contribution, two organic molecules (labeled as molecules A and B, more details in Figure 1) were explored as prospective additives for polyethylene industrial formulations via classical atomistic molecular dynamics simulations. To compare the behavior of these additives with a reference example and validate the model, a commercial additive (EA) was also investigated.

Simulations of the pure components confirmed that the employed force fields were appropriate for capturing structural properties with reasonable accuracy. Binary additive-water simulations show that all the additives tested are mostly hydrophobic molecules. This is in agreement with their amphiphilic chemical structure, which allows for the establishment of hydrogen bonds at the hydrophilic moieties, but with a prevalent repulsion to water. The only favorable interactions between water and the additives are hydrogen bonds that are established with the polar regions of the additives, with water acting as a hydrogen bond acceptor when combined with EA and as a donor when combined with A or B preferentially. Water molecules tend to phase separate even when they are present in low concentrations in B and EA additives.

Binary simulations containing polyethylene and water confirm its hydrophobic character, with water molecules covering the surface of the polymer but never entering its matrix. No preferential orientation was found for the water molecules. Concerning the additives, a trend of increasing polymer affinity was found when going from A to B and EA. Indeed, A stays at the surface as water does, while B partially enters the polymer matrix, forming a micellar-like structure, and EA enters deeply and intercalates with PE chains. This latter observation is in agreement with the migratory behavior previously identified for this commercial additive.

The structure of ternary systems containing PE, water, and additives strongly depends on the relative concentrations of the components. For systems containing low additive concentrations, water always stays at the polymer surface, forming a drop. The addition of water changes the relative affinity of A molecules for PE, enabling their partial penetration of the polymer matrix. This is a consequence of the strong hydrophobic character of this additive. The other two additives, which already interacted with PE in the binary simulations, only show changes in the distribution of their polar groups, which are now located close to the water molecule aggregates. In contrast, systems that contain higher additive concentrations show less penetration of EA molecules into the PE matrix and less ordering of the bulk polymer. These observations can be globally interpreted as changes in the additives structure to better interact with both water and PE at the same time.

We conclude that A molecule may be interesting as an antistatic agent when moisture is present at appreciable concentrations, while B could be tested as a possible slip agent, which would offer the additional advantage of being less water dependent than erucamide in its interactions with PE. We hope that these studies will motivate further experimental efforts in these directions.

Acknowledgements.

MMC thanks for a CONICET-Ampacet South America S.R.L PhD fellowship. RMN is a member of the Carrera de Investigador Científico of CONICET (Argentina). RS thanks the European Research Council for an ERC StG (MAGNIFY project, number 101042514). RMN and RS are grateful to the Comité ECOS Sud (France), for the ECOS Sud 2020 A20N04 project, which has enabled this collaboration.

Data availability

The data supporting this article have been included as part of the Supporting Information (SI). SI includes force field parameters and additional results that support those presented in the article.

Conflicts of Interests

The authors have no conflicts of interest to declare.

V Supporting Information

V.1 Force Field

Tables LABEL:ffaditivos, 2 and 3 show the force field parameters for all species. In all cases, dihedrals were described in the harmonic style. Cross interactions between and within phases were computed by applying the Lorentz-Berthelot mixing rules.

V.2 Pure polyethylene

V.2.1 Polymer generation

The partial atomic charges in the final polymer were of +0.1 for hydrogen atoms and -0.2044 for carbon atoms (elementary charge units). Initial coordinates of the monomer were obtained from the editor and viewer Avogadro.[61]

The polydisperse polyethylene obtained contained a total of 24 chains with different lengths, detailed by the number of monomers and total carbon atoms in each of them in Table 4.

V.3 Binary systems

V.3.1 Additives in water

V.3.2 Water in additives