Concepts for improving hydrogen storage in nanoporous materials

Hydrogen storage in nanoporous materials has been attracting a great deal of attention in recent years, as high gravimetric H₂ capacities, exceeding 10 wt% in some cases, can be achieved at 77 K using materials with particularly high surface areas. However, volumetric capacities at low temperatures, and both gravimetric and volumetric capacities at ambient temperature, need to be improved before such adsorbents become practically viable. This article therefore discusses approaches to increasing the gravimetric and volumetric hydrogen storage capacities of nanoporous materials, and maximizing the usable capacity of a material between the upper storage and delivery pressures. In addition, recent advances in machine learning and data science provide an opportunity to apply this technology to the search for new materials for hydrogen storage. The large number of possible component combinations and substitutions in various porous materials, including Metal-Organic Frameworks (MOFs), is ideally suited to a machine learning approach; so this is also discussed, together with some new material types that could prove useful in the future for hydrogen storage applications.     

Co-pelletization of a zirconium-based metal-organic framework (UiO-66) with polymer nanofibers for improved useable capacity in hydrogen storage

We report on a concept of co-pelletization using mechanically robust hydroxylated UiO-66 to develop a metal-organic framework (MOF) monolith that contains 5 wt% electrospun polymer nanofibers, and consists of an architecture with alternating layers of MOF and nanofiber mats. The polymers of choice were the microporous Polymer of Intrinsic Microporosity (PIM-1) and non-porous polyacrylonitrile (PAN). Co-pelletized UiO-66/PIM-1 and UiO-66/PAN monoliths retain no less than 85% of the porosity obtained in pristine powder and pelletized UiO-66. The composition of the pore size distribution in co-pelletized UiO-66/PIM-1 and UiO-66/PAN monoliths is significantly different to that of pristine UiO-66 forms, with pristine UiO-66 forms showing 90% of the pore apertures in the micropore region and both UiO-66/nanofiber monoliths showing a composite micro-mesoporous pore size distribution. The co-pelletized UiO-66/nanofiber monoliths obtained improved useable H₂ capacities in comparison to pristine UiO-66 forms, under isothermal pressure swing conditions. The UiO-66/PIM-1 monolith constitutes the highest gravimetric (and volumetric) useable capacities at 2.3 wt% (32 g L^?1) in comparison to 1.8 wt% (12 g L^?1) and 1.9 wt% (29 g L^?1) obtainable in pristine UiO-66 powder and UiO-66 pellet, respectively. The co-pelletized UiO-66/PAN monolith, however, shows a significantly reduced surface area by up to 50% less in comparison to pristine UiO-66, but its pore volume only 13% less in comparison to pristine UiO-66. As a result, total gravimetric H₂ capacity of the co-pelletized UiO-66/PAN monolith is 50% less in comparison to that of pristine UiO-66, but crucially the useable volumetric H₂ capacity is 50% higher for the UiO-66/PAN monolith in comparison to pristine UiO-66 powder. The co-pelletization strategy provides a simple method for generating hierarchical porosity into an initially highly microporous MOF without changing the structure of the MOF through complex chemical modifications. The UiO-66/nanofiber monoliths offer improvements to the typically low H₂ useable capacities in highly microporous MOFs, and open new opportunities towards achieving system-level H₂ storage targets.     

Room-temperature hydrogen storage performance of metal-organic framework/graphene oxide composites by molecular simulations

Metal-organic framework/graphene oxide (MOF/GO) composites have been regarded as potential room-temperature hydrogen storage materials recently. In this work, the influence of MOF structural properties, GO functional group contents and different amounts of doped lithium (Li⁺) on hydrogen storage performance of different MOF/GO composites were investigated by grand canonical Monte Carlo (GCMC) simulations. It is found that MOF/GO composites based on small-pore MOFs exhibit enhanced hydrogen storage capacity, whereas MOF/GO based on large-pore MOFs show decreased hydrogen storage capacity, which can be ascribed to the novel pores at MOF/GO interface that favors the enhanced hydrogen storage performance due to the increased pore volume/surface area. By integrating the small-pore MOF-1 with GO, the hydrogen storage capacity was enhanced from 9.88 mg/go up to 11.48 mg/g. However, the interfacial pores are smaller compared with those in large-pore MOFs, resulting in significantly reduced pore volume/surface area as well as hydrogen storage capacities of large-pore MOF/GO composite. Moreover, with the increased contents of hydroxyl, epoxy groups as well as carboxyl group modification, the pore volumes and specific surface areas of MOF/GO are decreased, resulting in reduced hydrogen storage performance. Furthermore, the room-temperature hydrogen storage capacities of Li⁺ doped MOF/GO was improved with increased Li⁺ at low loading and decrease with the increased Li⁺ amounts at high loading. This is due to that the introduced Li⁺ effectively increases the accessible hydrogen adsorption sites at low Li⁺ loading, which eventually favors the hydrogen adsorption capacity. However, high Li⁺ loading causes ion aggregation that reduces the accessible hydrogen adsorption sites, leading to decreased hydrogen storage capacities. MOF-5/GO composites with moderate Li⁺ doping achieved the optimum hydrogen storage capacities of approximately 29 mg/g.     

Automotive storage of hydrogen in alane

Although alane (AlH₃) has many interesting properties as a hydrogen storage material, it cannot be regenerated on-board a vehicle. One way of overcoming this limitation is to formulate an alane slurry that can be easily loaded into a fuel tank and removed for off-board regeneration. In this paper, we analyze the performance of an on-board hydrogen storage system that uses alane slurry as the hydrogen carrier. A model for the on-board storage system was developed to analyze the AlH₃ decomposition kinetics, heat transfer requirements, stability, startup energy and time, H₂ buffer requirements, storage efficiency, and hydrogen storage capacities. The results from the model indicate that reactor temperatures higher than 200 °C are needed to decompose alane at reasonable liquid hourly space velocities, i.e., > 60 h⁻¹. At the system level, a gravimetric capacity of 4.2 wt% usable hydrogen and a volumetric capacity of 50 g H₂/L may be achievable with a 70% solids slurry. Under optimum conditions, 80% of the H₂ stored in the slurry may be available for the fuel cell engine. The model indicates that H₂ loss is limited by the decomposition kinetics rather than by the rate of heat transfer from the ambient to the slurry tank.     

Performances comparison of adsorption hydrogen storage tanks at a wide temperature and pressure zone

Large-scale application of hydrogen requires safe, reliable and efficient storage technologies. Among the existing hydrogen storage technologies, cryo-compressed hydrogen (CcH₂) storage has the advantages of high hydrogen storage density, low energy consumption and no ortho-para hydrogen conversion. But it still needs higher hydrogen storage pressure when reaching higher hydrogen storage density. In order to reduce hydrogen storage pressure and improve storage density, solid adsorption technology is introduced in CcH₂. Activated carbon and metal-organic framework materials (MOFs) are employed as adsorbents in this paper. The gravimetric/volumetric hydrogen storage capacities of different adsorption tanks are studied and compared with the hydrogen storage conditions of 1–55 MPa at 77–298 K. The results show that the hydrogen storage density of CcH₂ combined with adsorption is higher than that of pure adsorption hydrogen storage, and the storage pressure is lower than that of pure CcH₂ under the same hydrogen storage capacity. And the combination of two hydrogen storage technologies can achieve a high hydrogen storage capacity equivalent to that of liquid hydrogen at a lower pressure.     

Carbon materials for H2 storage

In this work a series of carbons with different structural and textural properties were characterised and evaluated for their application in hydrogen storage. The materials used were different types of commercial carbons: carbon fibers, carbon cloths, nanotubes, superactivated carbons, and synthetic carbons (carbon nanospheres and carbon xerogels). Their textural properties (i.e., surface area, pore size distribution, etc.) were related to their hydrogen adsorption capacities. These H₂ storage capacities were evaluated by various methods (i.e., volumetric and gravimetric) at different temperatures and pressures. The differences between both methods at various operating conditions were evaluated and related to the textural properties of the carbon-based adsorbents. The results showed that temperature has a greater influence on the storage capacity of carbons than pressure. Furthermore, hydrogen storage capacity seems to be proportional to surface area, especially at 77 K. The micropore size distribution and the presence of narrow micropores also notably influence the H₂ storage capacity of carbons. In contrast, morphological or structural characteristics have no influence on gravimetric storage capacity. If synthetic materials are used, the textural properties of carbon materials can be tailored for hydrogen storage. However, a larger pore volume would be needed in order to increase storage capacity. It seems very difficult approach to attain the DOE and EU targets only by physical adsorption on carbon materials. Chemical modification of carbons would seem to be a promising alternative approach in order to increase the capacities.     

Structural analysis of metal hydride-based hybrid hydrogen storage systems

Hybrid hydrogen storage systems, which see the adoption of metal hydride materials charged at high pressure, can be a viable method to reach good gravimetric and volumetric capacities under selected conditions, since hydrogen is stored both as element bound to the hydride and as high pressure gas. A general structural model, which can simulate high pressure hybrid storage tanks, has been developed, with the aim of describing the performance of the system under various operating conditions. A baseline case has been simulated, comparing tanks composed of SS316 and IM6 graphite fiber reinforced epoxy composite that contain metal hydride materials that can store weight fractions of bound hydrogen ranging from 2% to 8%. Sensitivity analyses were performed for the baseline studies with the aim of determining the operating conditions that maximize gravimetric and volumetric capacities. Results show that high pressure systems are optimal (in terms of gravimetric and volumetric capacity) for tank materials having low density and a high allowable stress, while a low operating pressure is preferable for high density tank materials, especially when coupled with metal hydrides capable of storing a high weight fraction of bound hydrogen.     

MOF-5 and activated carbons as adsorbents for gas storage

This paper reports comparatively the capacities of two activated carbons (ACs) and MOF-5 for storing gases. It analyzes, using similar equipments and experimental procedures, the density used to convert gravimetric data to volumetric ones, measuring the density (tap and packing at different pressures). It presents data on porosity, surface area and gas storage (H₂, CH₄ and CO₂) obtained under different temperatures (77 K and RT) and pressures (0.1, 4 and 20 MPa). MOF-5 presents lower volume of narrow micropores than both ACs, making its storage at RT lower, independently of the gas used (H₂, CH₄ and CO₂) and the basis of reporting data (gravimetric or volumetric). For H₂ at 77 K the reliability of the results depends too much on the density used. It is shown that the outstanding volumetric performance of MOF-5, in relation to ACs, is due to the use of an unrealistic high density (crystal density) that, not including the adsorbent inter-particle space, gives an apparently high volumetric gas storage capacity. When a density measured similarly in both types of adsorbents is used (e.g. tap or packing densities) MOF-5 presents, for all gases and conditions studied, lower adsorption capacities on volumetric basis and storage capacities than ACs.     

Li-Crown ether complex inclusion in MOF materials for enhanced H2 volumetric storage capacity at room temperature

The organometallic Li-Crown ether species, formed by the complexation of lithium cation with the hydrophobic 18Crown6 ether, has been included in three Metal-Organic-Frameworks (MOF) structures with different pore size: Cr-MIL-101, Fe-MIL100 and Ni-MOF-74. X-ray powder diffraction, thermogravimetric analysis, proton nuclear magnetic resonance, infrared spectroscopy and inductively coupled plasma atomic emission spectroscopy measurements have proved the successful incorporation of the organometallic units to the three MOFs without altering their crystalline structure. Hydrogen adsorption properties of the post-synthesis modified materials have been evaluated in a wide temperature (77–298 K) and pressure (1–170 bar) range conditions. The post-synthetic modification method used based on the MOF impregnation with a Li-Crown ether complex solution produced a partial pore blocking effect on the microporous Ni-MOF-74, reducing its hydrogen adsorption capacity. However, the inclusion of the crown-ether and particularly the Li-Crown ether complex resulted in an increase of the volumetric hydrogen adsorption capacity at room temperature for Cr-MIL101 and Fe-MIL-100, due to the pore volume reduction, higher confinement of H₂ molecules in the cavities and the formation of new specific binding sites for H₂ molecules. The inclusion of Li-Crown ether complex also enhances the H₂ interaction with the mesoporous MOF structures, attributed to the additional electrostatic interactions produced by the presence of Li⁺ ions complexed to the crown ether molecules. Further work following this strategy to improve hydrogen adsorption capacity of mesoporous MOFs at room temperature should be extended to other MOF materials, checking its influence on their capacity for gas separation purposes.     

Enhanced hydrogen sorption in single walled carbon nanotube incorporated MIL-101 composite metal-organic framework

Metal-Organic Frameworks (MOFs) have emerged as potential hydrogen storage media due to their high surface area, pore volume and adjustable pore sizes. The large void space generated by cages in MOFs is not completely utilized for hydrogen storage application owing to weak interactions between the walls of MOFs and H₂ molecules. These unutilized volumes in MOFs can be effectively utilized by incorporation of other microporous materials such as single walled carbon nanotubes into the pores of MOFs which could effectively tune the pore size and pore volume of the material towards hydrogen sorption. Single walled carbon nanotubes (SWNT) incorporated MIL-101 composite MOF material (SWNT@MIL-101) was synthesized by adding purified single walled carbon nanotube (SWNT) in situ during the synthesis of MIL-101. The powder X-ray diffraction patterns of SWNT@MIL-101 showed the structure of MOF was not disturbed by SWNT incorporation. Hydrogen sorption capacities of MIL-101 was observed to increase from 6.37 to 9.18 wt% at 77 K up to 60 bar and from 0.23 to 0.64 wt% at 298 K up to 60 bar. The increment in the hydrogen uptake capacities of composite MOF materials was attributed to the decrease in the pore size and enhancement of micropore volume of MIL-101 by single walled carbon nanotube incorporation.     

DFT simulation of hydrogen storage on manganese phosphorous trisulphide (MnPS3)

Manganese phosphorous trisulphide, MnPS₃, is a solid layered material. The hydrogen gravimetric storage capacities of MnPS₃ powder at 80.15, 173.15 and 298.15 K and at moderate pressures has been recently measured in experiments. The origin of the storage capacities of this material is not well understood. The main hypothesis is that hydrogen is stored in the pores of MnPS₃ powder. The pores are modelled as two parallel MnPS₃ layers separated a certain distance. Density Functional Theory simulations of the interaction of H₂ with the surface of a MnPS₃ layer have been carried out, in order to test that hypothesis. The simulations indicate that the adsorption of hydrogen on the surface of a MnPS₃ layer is energetically favourable, but only through the physisorption mechanism. Calculations of the gravimetric capacities of the pores of MnPS₃ powder have also been carried out, obtaining a reasonable agreement with the experimental results. The comparison of the calculated and experimental gravimetric capacities show that the hydrogen storage on MnPS₃ powder is mainly due to compression in the pores and that the contribution of the physisorption process to the storage is very small.     

Hydrogen storage potential in MIL-101 at 200 K

Hydrogen adsorption isotherms for MIL-101 metal-organic framework are reported within a wide pressure range for temperatures between 77 and 295 K. Data modeling with the modified Dubinin-Astakhov equation shows a good fitting with the experimental results. The calculated absolute adsorption allowed the evaluation of the total hydrogen storage capacity for high pressure storage tank filled with MIL-101 as sorbent. The results show that the gravimetric and volumetric storage capacities at 198 K and 70 MPa are within the present-day accepted DOE targets, even if the storage capacity is slightly decreased by 3–6% as compared to the tank without sorbent. Moreover, the calculations reveal that the dormancy time is much increased, as compared to a tank without sorbent, exceeding the ultimate DOE target of 14 days. The MIL-101 assisted cold high-pressure hydrogen storage at ∼200 K and 70 MPa, brings about an additional advantage and seems promising for both mobile and stationary applications.     

Multiscale study of the structure and hydrogen storage capacity of an aluminum metal-organic framework

First-principles calculations based on density functional theory and Grand Canonical Monte Carlo (GCMC) simulations are carried out to study the structure of a new Aluminum Metal-Organic Framework, MOF-519, and the possibility of storing molecular hydrogen therein. The optimized structure of the inorganic secondary building unit (SBU) of MOF-519 formed by eight octahedrally coordinated aluminum atoms is presented. The different storage sites of H₂ inside the SBU and the BTB ligand are explored. Our results reveal that the SBU exhibits two different favorable physisorption sites with adsorption energies of ?12.2 kJ/mol and ?1.2 kJ/mol per hydrogen molecule. We have also shown that each phenyl group of BTB has three stable H₂ adsorption sites with adsorption energies between ?6.7 kJ/mol and ?11.37 kJ/mol. Using GCMC simulations; we calculated the molecular hydrogen (H₂) gravimetric and volumetric uptake for the SBU and MOF-519. At 77 K and 100 bar pressure, the hydrogen uptake capacity of SBU is considerably enhanced, reaching 16 wt.%. MOF-519 has a high gravimetric uptake, 10 wt.% at 77 K and 4.9 wt.% at 233 K. It has also a high volumetric capacity of 65 g/L at 77 K and 20.3 g/L at 233 K, indicating the potential of this MOF for hydrogen storage applications.     

Technical assessment of cryo-compressed hydrogen storage tank systems for automotive applications

On-board and off-board performance and cost of cryo-compressed hydrogen storage are assessed and compared to the targets for automotive applications. The on-board performance of the system and high-volume manufacturing cost were determined for liquid hydrogen refueling with a single-flow nozzle and a pump that delivers liquid H₂ to the insulated cryogenic tank capable of being pressurized to 272 atm. The off-board performance and cost of delivering liquid hydrogen were determined for two scenarios in which hydrogen is produced by central steam methane reforming (SMR) or by central electrolysis. The main conclusions are that the cryo-compressed storage system has the potential of meeting the ultimate target for system gravimetric capacity, mid-term target for system volumetric capacity, and the target for hydrogen loss during dormancy under certain conditions of minimum daily driving. However, the high-volume manufacturing cost and the fuel cost for the SMR hydrogen production scenario are, respectively, 2–4 and 1.6–2.4 times the current targets, and the well-to-tank efficiency is well short of the 60% target specified for off-board regenerable materials.     

Increased volumetric hydrogen uptake of MOF-5 by powder densification

The metal-organic framework MOF-5 has attracted significant attention due to its ability to store large quantities of H₂ by mass, up to 10 wt.% absolute at 70 bar and 77 K. On the other hand, since MOF-5 is typically obtained as a bulk powder, it exhibits a low volumetric density and poor thermal conductivity—both of which are undesirable characteristics for a hydrogen storage material. Here we explore the extent to which powder densification can overcome these deficiencies, as well as characterize the impact of densification on crystallinity, pore volume, surface area, and crush strength. MOF-5 powder was processed into cylindrical tablets with densities up to 1.6 g/cm³ by mechanical compaction. We find that optimal hydrogen storage properties are achieved for ρ ∼ 0.5 g/cm³, yielding a 350% increase in volumetric H₂ density with only a modest 15% reduction in gravimetric H₂ excess in comparison to the powder. Higher densities result in larger reductions in gravimetric excess. Total pore volume and surface area decrease commensurately with the gravimetric capacity, and are linked to an incipient amorphization transformation. Nevertheless, a large fraction of MOF-5 crystallinity remains intact in densities up to 0.75 g/cm³, as confirmed from powder XRD. Predictably, the radial crush strength of the pellets is enhanced by densification, increasing by a factor of 4.3 between a density of 0.4 g/cm³ and 0.6 g/cm³. Thermal conductivity increases slightly with tablet density, but remains below the single crystal value.     

Supercritical cryo-compressed hydrogen storage for fuel cell electric buses

Liquid hydrogen (LH₂) truck delivery and storage at dispensing sites is likely to play an important role in an emerging H₂ infrastructure. We analyzed the performance of single phase, supercritical, on-board cryo-compressed hydrogen storage (CcH₂) with commercially-available LH₂ pump enabled single-flow refueling for application to fuel cell electric buses (FCEB). We conducted finite-element stress analyses of Type 3 CcH₂ tanks using ABAQUS for carbon fiber requirement and Fe-Safe for fatigue life. The results from these analyses indicate that, from the standpoint of weight, volume and cost, 2-mm 316 stainless steel liner is preferred to aluminium 6061 alloy in meeting the required 15,000 charge-discharge cycles for 350–700 bar storage pressures. Compared to the Type 3, 350 bar, ambient-temperature H₂ storage systems in current demonstration FCEBs, 500-bar CcH₂ storage system is projected to achieve 91% improvement in gravimetric capacity, 175% improvement in volumetric capacity, 46% reduction in carbon fiber composite mass, and 21% lower system cost, while exceeding >7 day loss-free dormancy with initially 85%-full H₂ tank.     

Hydrogen storage in Ca-decorated,B-substituted metal organic framework

The feasibility to store hydrogen in calcium-decorated metal organic frameworks (MOFs) is explored by using first-principles electronic structure calculations. We show that substitution of boron atoms into the benzene ring of the MOF linker substantially enhances the Ca binding energy to the linker as well as the H₂ binding energy to Ca. The Kubas interaction between H₂ molecules and Ca added in the MOF gives rise to a large number of bound H₂'s (8H₂'s per linker) with the binding energy of 20 kJ/mol, which makes the system suitable for reversible hydrogen storage under ambient conditions.     

Hydrogen adsorption and kinetics in MIL-101(Cr) and hybrid activated carbon-MIL-101(Cr) materials

Since the last 15 years, porous solids such as Metal–Organic Frameworks (MOFs) have opened new perspectives for the development of adsorbents for hydrogen storage. Among all MOF materials, the chromium (III) terephthalate-based MIL-101(Cr) is a very stable one which exhibits a good uptake capacity of hydrogen (H₂). In this study, syntheses were carried out in soft conditions without hydrofluoric acid as usually reported in literature. Moreover, activated carbon (AC) was introduced in the preparation of the MOF-based adsorbents to create hybrid materials with large specific surface areas (AC-MOF). Hydrogen storage capacities were assessed at 77 K up to 100 bar, and the measurements of adsorption isotherms were performed using both volumetric and gravimetric methods. The experimental data were shown to be in good agreement. A maximal excess hydrogen uptake of 67.4 mol kg^?1 (13.5 wt.%) has been reached by the hybrid AC-MOF adsorbent at 77 K under 100 bar. The hydrogen storage capacity was so shown to be greatly enhanced by AC addition, as a maximal value of only 41.1 mol kg^?1(8.2 wt.%) was reported for the pristine MIL-101(Cr), under the same conditions. Finally, hydrogen adsorption kinetics were examined at 77 K using experimental transient adsorption curves obtained using volumetric method, and the Linear Driving Force (LDF) model was tested for their interpretation. According to this model, diffusion coefficients could be correctly estimated only in a very low pressure range. However, for high pressures, the quasi-equilibrium assumption is not valid at the initial adsorption times, making the LDF model no more applicable for accurate determination of the average effective diffusivities. To our knowledge we present the first measurement of the adsorption kinetics of hydrogen in a hybrid carbon MOF composite material. Moreover, the adsorption performances reported in this work are the best ones achieved until now by MIL-101(Cr) doping using carbonaceous materials.     

Optimization of hydrogen storage tubular tanks based on light weight hydrides

Design of hydrogen storage systems aims at minimal weight and volume while fulfilling performance criteria. In this paper, the tubular tank configuration for hydrogen storage based on light weight hydrides is optimized towards its total weight using the predictions of a newly developed simulation model. Sodium alanate is taken as model material. A clear definition of the optimization is presented, stating a new optimization criterion: a defined total mass of hydrogen has to be charged in a given time, instead of prescribing percentages of the total hydrogen storage capacity. This yields a wider space of possible solutions. The effects of material compaction, addition of expanded graphite and different tubular tank diameters were evaluated. It was found that compaction of the material is the most influential factor to optimize the storage system. In order to obtain lighter storage systems one should concentrate on improving the ratio mass of hydride bed to mass of tank wall by screening lighter materials for the tank wall and developing hydrogen storage materials exhibiting both higher gravimetric and volumetric storage capacities.     

Performance assessment of 700-bar compressed hydrogen storage for light duty fuel cell vehicles

Type 4 700-bar compressed hydrogen storage tanks were modeled using ABAQUS. The finite element model was first calibrated against data for 35-L subscale test tanks to obtain the composite translation efficiency, and then applied to full sized tanks. Two variations of the baseline T700/epoxy composite were considered in which the epoxy was replaced with a low cost vinyl ester resin and low cost resin with an alternate sizing. The results showed that the reduction in composite weight was attributed primarily to the lower density of the resin and higher fiber volume fraction in the composite due to increased squeeze-out with the lower viscosity vinyl ester resin. The system gravimetric and volumetric capacities for the onboard storage system that holds 5.6 kg H₂ are 4.2 wt% (1.40 kWh/kg) and 24.4 g-H₂/L (0.81 kWh/L), respectively. The system capacities increase and carbon fiber requirement decreases if the in-tank amount of unrecoverable hydrogen is reduced by lowering the tank “empty” pressure. Models of an alternate tank design showed potential 4–7% saving in composite usage for tanks with a length-to-diameter (L/D) ratio of 2.8–3.0 but no saving for L/D of 1.7. A boss with smaller opening and longer flange does not appear to reduce the amount of helical windings.