Although gravimetric energy density of hydrogen gas (142 MJ kg⁻¹) is at least three times larger than that of liquid hydrocarbons like conventional fuel, it suffers from low volumetric storage capacity (Schlapbach and Züttel, 2001). Compressed hydrogen in form of onboard tanks and portable devices would offer a cost-effective and sustainable near-term solution of hydrogen storage due to its low infrastructure impact and small carbon footprint involved with the effective production of hydrogen in its gaseous state by water electrolysis or water splitting. Despite the overall attractiveness of pressurized hydrogen gas storage, there remain striking issues in selection of safe and lightweight encapsulation materials. As metals suffer from material embrittlement and cracking well-below its initial yield stress and polymers cannot offer low enough permeation rates, oxidic glasses are found to be promising candidates for cost-effective, safe, and long-term storage of pressurized hydrogen in micro containers such as hollow microspheres and capillaries (Zhevago, 2016). Hence, the usage of glass capillary arrays has received progressive attention in recent years, not least because of the well-established manufacturing process (precise redrawing tubes) but due to closed-packed (honeycomb) polymer coated structuring options in combination with a rapid refueling capability (Zhevago and Glebov, 2007; Holtappels et al., 2011; Prewitz et al., 2018).

Compressed hydrogen storage in glass micro-containers demands for low permeation through the container wall and for successful development of glass compositions for which the product of hydrogen solubility and diffusion coefficient is minimal. Besides low permeability, a strong performance of the glass during hot shaping, which is expressed mainly in the form of a sufficient workability and a small crystallization tendency, as well as during service, where chemical process robustness is important, have to be taken into account before implementing new compositions into storage applications (Prewitz et al., 2018). With respect to permeation, accessibility of free volume of the network structure has been shown to be closely linked to the fundamental migration and solubility processes. For silica glass, predictions from noble gas solubility experiments under ambient conditions (Shackelford and Masaryk, 1978; Nakayama and Shackelford, 1990), high-pressure regimes (Shelby, 1976) and from molecular dynamics simulations (Chan and Elliott, 1991) result in a log-normal distribution of interstitial sites varying in size from 0.1 to 0.4 nm. Following the free volume approach, gas solubility and diffusion is then proportional to the fraction of the total interstitial volume that is connected to the main network and large enough for occupation (Shackelford, 2014).

Experimental studies, which are limited to fused silica and commercial borosilicate glasses (Johnson and Burt, 1922; Barrer, 1934; Altemose, 1961; Lee et al., 1962; Laska and Doremus, 1969; Laska et al., 1969; Morimoto et al., 1992; Shelby, 1996; Kurita et al., 2002), alkali-alkaline earth silicate glasses (Barton and Morain, 1970) and aluminoborosilicate glasses (Ried et al., 2014) show that isothermal permeability can vary up to three orders of magnitude. The underlying principles in the correlations between glass composition, accessible free volume and hydrogen permeation are still unclear. Only recently, a first attempt limited to hydrogen diffusivity was made by drawing a distinction between free volume reductions in modified and in fully polymerized networks (Welter et al., 2019).

The present paper picks up the threads that minimizing the accessible volume is a sound strategy to hinder migration and solubility of hydrogen molecules. Therefore, a broader data base is analyzed and a special focus is placed on the contributions in decreasing the total free volume that results from network modifying by creation of non-bridging oxygen (NBO = oxygen that is part of a tetrahedron but not shared with a second one. It forms the ionic bonds with the modifiers) and filling (“stuffing”) polymerized (NBO-free) silicate networks by introducing charge balanced network formers like aluminum and boron tetrahedra.

Volumetric properties of glasses can be accessed from density and chemical composition. Firstly, one can calculate the molar volume V_M (based on 1 mol oxygen atoms) as

where x_i, M_i and n_i are being, respectively, the mol fraction, the molar mass of the oxide i and the number of oxygen atoms in the oxide i with A_jO_k chemical formula. Secondly, V_M can be utilized to determine the total free volume V_free and ionic porosity IP (Carroll and Stolper, 1993). V_free and IP are, respectively, the part and fraction of the molar volume not occupied by individual atoms, which are given by:

and

where V_i = 4π N_a (jrA3+ krO3)/3 is the ionic volume the oxide i with A_jO_k chemical formula. N_A is the Avogadro constant and r_A, r_O are ionic radii using, 66 pm (Li^V), 102 pm (Na^VI), 151 pm (K^VIII), 166 (Rb^X), 188 pm (Cs^XII), 66 pm (Mg^V), 100 pm (Ca^VI), 118 pm (Sr^VI), 142 pm (Ba^VIII), 74 pm (Zn^VI), 140 pm (Pb^X), 11 pm (B^IV), 39 pm (Al^IV), 26 pm (Si^IV), 17 pm (P^IV), and 135 pm (O^II) (Shannon, 1976).

Figure 3A shows the isothermal permeability of hydrogen/deuterium molecules at 473 K as a function of the ionic porosity at that temperature. In order to allow for analysis on a broader data basis, permeation of helium atoms was included (Figure 3B). Overall, it is very clear that permeation of helium and hydrogen seems to follow the expected trend, i.e., a positive correlation with ionic porosity is evident. On the other hand, a network of high connectivity seems to be more effective in reducing permeability as the data points of fully polymerized network structures (NBO-free) are mainly located on the right hand side of the hatched areas of Figure 3.

Further, one can analyse that permeability is higher for helium atoms than for hydrogen molecules. Both data sets are shifted in by a factor of approximately 36, with regard to the mean value for silica glass (labeled by a red star in Figure 3). It is quite understandable that this difference can be traced back to the difference in the kinetic diameter of hydrogen, which is about 11% larger than that of helium d_H2 = 298 pm (Chambers et al., 1998), d_He = 260 pm (Matteucci et al., 2006).

Furthermore, the data sets of Figure 3 seem to follow self-similar pattern (hatched areas), which will be utilized to access volumetric dependencies with the following master-curve concept. For that reason, dimensionless ratios (the so-called “reduced permeability”) were calculated for isothermal conditions by dividing permeability through the respective value [2.2 × 10⁻¹⁷ mol m⁻¹ Pa⁻¹ s⁻¹ (H₂/D₂) and 8.0 × 10⁻¹⁶ mol m⁻¹ Pa⁻¹ s⁻¹ (He)] for silica glass. Figure 4 shows that reduced permeability declines in fully polymerized (NBO-free) glasses and depolymerized (NBO-bearing) glasses by up to four and a half orders of magnitude. It becomes clear that stuffing the network by charge compensating cations in fully polymerized networks is a viable option for considerably reducing hydrogen permeability. Particularly, these glasses are favorable when comparing their process properties as they offer a smaller crystallization tendency and a higher workability then NBO-bearing compositions.

Figure 5 shows the dependence of reduced permeability on ionic porosity for fully polymerized glasses and depolymerized glasses in separate figures. Grouping the NBO-free glasses by network former (Figure 5A) reveals that charge balancing of tetrahedral boron is less effective in decreasing reduced permeability. In particular, technical borosilicate glasses are only capable to decrease the permeability of silica by a factor <100. In contrast, when tetrahedral aluminum is stabilized by modifier ions, available data show that reduced permeability is strongly declined. Factors up to 10^4.5 in reduction are found for lithium and sodium aluminosilicate glasses. It is interesting to note that stabilization of mixed network formers (aluminoborosilicate glass) lead to an intermediate position between borosilicate and aluminosilicate compositions. On the other hand, if network modifiers are present in excess, they depolymerize the network and compensate charges of NBOs instead of tetrahedral coordinated aluminum and boron. In this case, reduction of free volume and with it the drop in reduced permeability depends on the nature of the modifier cation (Figure 5B). High-field strength cations such as Li⁺, which strongly attract NBOs, lead to a relative low reduction in ionic porosity but to a relative strong decrease in permeation, whereas low-field strength cations such as K⁺, Rb⁺ and Cs⁺, which are less effective to attract NBOs, result in stronger reduction of free volume but less decrease in permeation. The compositional dependence becomes clearer if one follows the iso-NBO/T lines. For NBO/T = 1 (in technology called disilicate compositions) on can find that lithium ions reduce permeation by a factor of 30,000, sodium ions by 1,800, and potassium ions only by 250 with respect to the permeation through silica glass. Figure 5B shows further that for Na⁺-modified glasses, which includes the mixed modifier float glass of high technical importance, the dependence of reduced permeability on ionic porosity is only slightly weaker than for binary lithium silicates glasses.

The analysis of available data show that assuming a simplistic effect of either ionic porosity or network modifier content fails to predict hydrogen permeability in silicate glasses. Fully polymerized (NBO-free) glasses, which are stuffed with Li⁺ and Na⁺ ions for charge balancing network forming tetrahedral aluminum as well as depolymerized (NBO-bearing) lithium and sodium silicate glasses, both ranging between 50 and 51.5% ionic porosity, seem to offer low hydrogen permeability that is up to 30,000 times lower than that of silica glass. This finding indicates that, the local network connectivity may control hydrogen permeability more strongly than ionic porosity.

The datasets generated for this study are available on request to the corresponding author.

TW, UM, and SR produced the manuscript. JD and RM contributed to the critical revision and direction of the manuscript.