(338al) Molecular Modeling of Hydrogen Sorption in Semi-Crystalline High-Density Polyethylene

The demand for hydrogen as an alternative energy source has grown and continues to increase at an accelerating pace. The interest in hydrogen as a transportation fuel stems from its ability to power fuel cells in zero-emission electric vehicles, fast filling time, and high efficiency. Nevertheless, its low volumetric energy density implies storage at high pressures (up to 800 bar) as a compressed gas. Cost-effective and high-performance barrier materials screening for tank liner usage is therefore crucial to enable hydrogen gas technologies optimization. In this framework, semi-crystalline polymers were demonstrated to be excellent candidates as barrier materials for gas containment and line distribution [1]. They exhibit very low gas permeabilities, withstand the required pressures, and, unlike metal tank liners, are lightweight, thus more suitable for on-board applications. The Permeability is a crucial property in the study of the performance of such materials, there is therefore the need of developing predictive models for its assessment to guide materials design and reduce the number of experimental tests required which, especially for the case of Hydrogen, can be associated with a relevant technological effort.

State of art

The Permeability across dense materials is, according to the Solution-Diffusion model, defined as the product of the Sorption and Diffusion coefficients which are, for the case of semi-crystalline polymers, both strongly affected by the presence of the crystalline domains. The experimental Sorption coefficient is drastically reduced, primarily because the crystal phase does not adsorb. On top of that, the amorphous phase fraction itself shows a lower gas solubility compared to the wholly amorphous one; that is conventionally ascribed to the presence of the crystal phase that constraints the amorphous matrix. On the other hand, the Diffusion coefficient is decreased because of the reduced amorphous volume and chain mobility caused by the amorphous phase confinement and in reason of the tortuosity induced by the impermeable crystallites.

Several modelling strategies ranging from Molecular to Thermodynamics have addressed the description of the crystal perturbation on of the sorption capacity of the amorphous phase so far [2]. Nevertheless, they modelled the solely amorphous phase and implicitly accounted for the contribution of the crystal phase by introducing an adjustable parameter aimed at mimicking such an effect. Examples are models relying on an additional fictitious pressure (constraint pressure p_c) prevailing the gas pressure [3–6] or on the fraction of elastically effective chains (tie-chains) linking the crystal domains (f) [7–11]. Nevertheless, the adjustable nature of the parameters and their limited transferability ultimately led to a modest predictive power of such models.

Methods

In the work here presented, the authors modelled Hydrogen sorption in semi-crystalline High-Density Polyethylene (HDPE) using Widom test particle insertion method [12] on molecular structures having an explicit crystal phase. They propose a fully predictive approach which exploits Molecular Dynamics simulations of the crystal-amorphous interface (PCFF [13]). In particular, they evaluated the effect of crystal confinement and the role of the fraction of tie-chains on the amorphous phase volumetric properties and consequently on the gas solubility. Different semi-crystalline structures with tailored fraction of such chains’ population where therefore built and simulated. The initial configuration of each structure was built starting with the same amount of crystal and, regardless of the structure’s fraction of ties, by setting the initial amorphous density equal to the one evaluated by MD simulation of the theoretical unconfined amorphous at T = 298 K (0.842 g/cm³). After an initial simulation pathway which involved a heating and compression stage and subsequent stepwise cooling and decompression to ambient conditions, the structures were simulated in NPT ensemble at T = 298 K and p = 1 atm for 40 ns. A snapshot of the equilibrated configurations is depicted in Figure 1.

Results

The final configurations were analysed in terms of density and orientation profile along z-axis to retrieve information of the crystal and confined amorphous pressure-volume-temperature data and the mass degree of crystallinity . An example of such analysis is exemplified in Figure 2 whereas a summary of the analysis results for all the structures is reported in Table 1.
Simulation results analysis showed interesting outputs. It was noticed that all the structures reveled an increased density of the confined amorphous phase compared to the theoretical unconfined one even for the case of mere confinement (Structure A). Moreover, the entity of the constraint increases importantly with the fraction of ties present in the structure which, in turn, is coupled with a decrease of the mass degree of crystallinity.

The last part of the study was dedicated to the evaluation of Hydrogen sorption coefficients applying Widom test particle insertion method on the equilibrated structures previously analysed. Hydrogen was modelled as an uncharged diatomic molecule with two Lennard-Jones sites [15]. The estimated Sorption coefficients for all the structures are reported in Table 2 against the experimental references. The estimated Sorption coefficient were found in excellent agreement with the experimental references. Moreover, the trend of the evaluated sorption coefficients is coherent with the confined amorphous densities previously reported hence confirming the constraint effect resulting from the intercalation of the crystal and amorphous phase.

Conclusion and Future remarks

The molecular modeling of the explicit semi-crystalline structures presented in this work allowed to quantitatively evaluate the effect of the crystal confinement and fraction of tie-chains on the confined amorphous phase volumetric properties. Moreover, the application of Widom’s test particle insertions method on the latter, figured as a reliable fully predictive method for the estimation of the solubility of Hydrogen in semi-crystalline polymers. Future work will be dedicated to the method extension to different temperatures and pressures.

References

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