A new approach to foam-lined indirect-drive NIF ignition targets

Coating a rotating object with a uniform gel layer requires a sol–gel chemistry that can tolerate a certain amount of shear during gelation. The sol–gel chemistry should be purely hydrocarbon (CH_x) based and yield monolithic, low-shrinkage and mechanically robust aerogels with densities as low as 25 mg cm⁻³ that survive wetting with liquid hydrogen. So far, several pure CH_x foam systems have been developed for the triple-orifice droplet generator technique, including divinylbenzene (DVB) [19] and styrene [20] based foams. For the current application, however, these foams have too high densities, too large pores, or shrink too much during supercritical drying. These formulations have also not been tested for their shear resistance. We therefore have decided to further develop a DCPD-based aerogel chemistry [14] that is based on polymerization of DCPD monomers using the ROMP reaction (figure 2).

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The ability of the DCPD-based aerogel chemistry to tolerate shear during gelation was first tested by coating experiments in rotating horizontal glass vials (17.6 mm ID, 2 h @ 10 rpm, filled with 500 µl of a 50 mg cm⁻³ precursor solution). These tests quickly revealed that pure DCPD gels (figure 2(b)) do not form uniform films if gelled under the influence of shear. In an attempt to improve the quality of the gel coatings, we studied the effect of copolymerization with NB, since NB does not have the cross-linking functionality of DCPD (figure 2(a)). These experiments (figure 2(c)) revealed that adding 5–15 wt% NB vastly improves the uniformity of gel films formed in the rotating glass vials. The stabilizing effect of NB can be attributed to the drastic increase in the viscosity at the gel point as detected by dynamic rheology measurements [21]. For example, in the case of 50 mg cm⁻³ P(DCPD-r-NB) aerogels prepared with 0.2 wt% catalyst, these experiments revealed that both the gelation time and the viscosity at the gel point increase with increasing NB concentration, from ∼10 min and 0.05 Pa s for 0 wt% NB to ∼40 min and 10 Pa s for 10 wt% NB, respectively [21]. The resulting P(DCPD-r-NB) aerogels are monolithic, have densities as low as 25 mg cm⁻³, and are mechanically strong enough to survive wetting with cryogenic hydrogen as revealed by USAXS and x-ray microtomography (figures 2(d), (e)). Specifically, the absence of wetting/dewetting induced changes in USAXS and x-ray microtomography indicates that the aerogel retains its structure at length scales from ∼5 nm to ∼2 µm (USAXS) and ∼3 µm to ∼1 cm (x-ray microtomography), respectively.

Other promising aerogel chemistries under development and testing for this application include carbon nanotube (CNT) and graphene reinforced resorcinol-formaldehyde (RF) aerogels [22–27]. Reversible wetting with cryogenic hydrogen has been confirmed for all these materials by small angle x-ray scatting (SAXS) experiments.

The foam shell thickness is controlled by the volume of the precursor solution filled into the ablator. To achieve the required μm-scale thickness control, we developed a pressure-differential filling method that allows us to reproducibly inject 0.1–1 µl of the precursor solution (for 2 mm diameter shells, this translates into a layer thickness of 10–130 µm) into the ablator. The filling setup is described in detail in figure 3(a). It consists of a small vacuum chamber that contains a vial filled with the precursor solution and a linear feedthrough to which the ablator shell is attached. First, the chamber is slightly underpressurized (20–250 Torr below atmospheric pressure, depending on the desired foam layer thickness) while the capsule is not in contact with the precursor solution. This prevents the formation of air-bubbles attached to the fill hole that is critical for achieving the required reproducibility. The under-pressurized capsule is then submerged in the precursor solution, and filled by re-pressurizing the chamber to atmospheric pressure. Concentration changes by loss of toluene or DCPD/NB through evaporation are minimized by keeping the time between evacuation and re-pressurization as short as possible. The injected volume, as derived from weight gain measurements with the density of toluene under ambient conditions (0.867 g cm⁻³), increases linearly with the applied pressure differential (with ∼0.01 µl precision) and is almost independent of the hole diameter (figure 3(b)). The linear behaviour can be fit by an expression easily derived from the ideal gas law: ΔV = (V_s/p_o)Δp where ΔV is the injected volume, Δp is the applied pressure differential and V_s and p_o are the shell volume (4.2 µl) and standard pressure (760 Torr), respectively.

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Coating the inside of a spherical capsule with a smooth and homogeneous film requires precise control over rotation speed and direction. Initial film formation experiments that used the tumbling motion of a capsule in a rotating vial were promising but not reproducible. We therefore decided to build a system that provides a deterministic, continuous change in orientation relative to the gravity vector, thus simulating a true microgravity environment. Such an environment can be realized with two perpendicular and independently driven rotating frames in combination with the computer controlled software (figures 4(a), (b)) [18]. The capsule, filled with a precise amount of the gel precursor solution, is mounted in the centre of rotation, which is where both rotation axes intersect. The capsule is then rotated until gelation is complete, typically for 4–24 h, depending on the aerogel density and the DCPD/NB/catalyst ratio. Independent gelation experiments, performed under stationary conditions in glass vials, have revealed that for a given catalyst concentration, the gel time increases with decreasing aerogel density and DCPD/NB ratio [21].

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Concentricity, sphericity and roughness of the resulting gel layer were assessed by x-ray imaging (figures 4(c) and (d)). The sphericity of the foam shells is determined by the sphericity of the diamond molds that have only nm scale deviations [16]. The foam shell thickness non-uniformity is typically dominated by the non-concentricity (mode 1 thickness non-uniformity) of the inner and outer foam shell surface. All non-uniformities with mode numbers higher than two are well below 1 µm. To improve the mode 1 uniformity, we are currently developing a computational fluid dynamics model that will allow us to identify the best combinations of rotational velocity and viscosity for uniform coatings.

To prevent densification of the foam by solvent evaporation through the fill hole during the prolonged coating process, the capsule is placed in a small container that is either filled with saturated vapour of toluene (used as the solvent in the aerogel precursor solutions) or with liquid water. The miscibility of toluene in water is very low (0.5633 ml/1000 ml H₂O [28]), and covering the fill hole with water thus effectively blocks the loss of toluene. To avoid periodic patterns of the rotation irrational ratios of the rotational frequencies of the two independently driven frames (typically different by a factor of $\sqrt 2 )$ were selected. The critical rotational frequency that is required to coat the inside of the rotating capsule with a smooth, uniform gel layer was estimated analytically and by a computational fluid dynamics model (details will be published elsewhere). In short, the analysis has revealed that the critical rotational velocity scales with the square of the film thickness, and the inverse of the aerogel precursor solution viscosity. For a 2 mm diameter shell and a film thickness of 30 µm, the critical rotational velocity decreases from several hundred to a few rotations per minute as the viscosity of the aerogel precursor solution increases by ∼10², starting at the viscosity of toluene (0.56 cP [29]), as the precursor solution approaches the gel point. Clearly, the viscosity of the aerogel precursor solution at the gel point is of crucial importance for the formation of smooth, uniform films inside the capsule.

The thin foam shell in fusion application targets will be used as a scaffold to bring high-atomic-number (high-Z) dopants in close contact with the DT fuel. Doping with high-Z elements also allows us to non-destructively characterize the low-density aerogel shell inside the thick, high-density ablator using x-ray imaging. Doping can be achieved by either adding functionalized monomers to the polymer solution or by doping of the final gel/aerogel layer. To test the first approach, we added an iodine-functionalized NB monomer, C₉H₁₂I₂ (full synthetic details for this new monomer will be published elsewhere). The second approach was realized by iodine addition to the remaining C=C double bonds of the DCPD/NB polymer. Iodination was achieved by either placing the ablator shell coated with the wet gel layer for several days in an iodine–toluene solution or by storing the dried shell in an iodine vapour environment. Both approaches were successful, with liquid phase doping resulting in somewhat higher doping levels as judged by the higher contrast in radiographs. We have also demonstrated that the dried foam shell can be uniformly doped using atomic layer deposition [30]. Finally, the wet gel layer was supercritically dried by direct solvent exchange with carbon dioxide. A representative radiograph of an iodine-doped foam shell inside a diamond ablator is shown in figure 5.

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