Effects of porosity on dynamic indentation resistance of silica nanofoam

The dynamic indentation behaviors of monolithic silica nanofoams of various porosities are investigated. When the pore size is on the nm scale, as the porosity increases, despite the decrease in mass density, the resistance offered by silica nanofoam to dynamic indentation is maintained at a high level, higher than the resistance of solid silica or regular porous silica. This phenomenon is related to the fast collapse of nanocells, which produces a locally hardened region and significantly increases the volume of material involved in impact energy dissipation.


Results and Discussion
In the current study, we examined the porosity effect on impact indentation resistance of silica nanofoam samples, with the average pore size being kept at ~80 nm. Silica nanofoam monoliths were prepared by a sol-gel approach 17 , and the porous configurations were further adjusted by the subcritical calcination (SCC) technique 36 . When the calcination temperature and duration are in appropriate ranges, compared to the pore size, the porosity is much more sensitive to the temperature. Thus, regardless of the large difference in porosity, the variation in pore size of silica samples with the same initial component mass ratio is much less; for small pores, the variation in pore size can be negligible. In this investigation, the average pore size was measured to be ~80 nm through mercury porosimetry 36 , while the porosity ranged from ~50% to ~70%. Solid silica, employed as the reference material, was fabricated via a similar procedure, whereas the firing was fully conducted to achieve a porosity less than 1%. After polished with sandpapers (silicon carbide, from 320-grit to 2500-grit) to remove the surface layers 38,39 , the disk-shaped testing samples (Fig. 1a) had the thickness and the diameter of 4.5 mm and ~23 mm, respectively. Figure 1b shows a typical SEM image of silica nanofoam. The cellular channels were random and interconnected. Data of X-ray diffraction (XRD, Fig. 1c) confirmed that all the samples, both nanofoams and solid silica, were in amorphous phase.
Dynamic indentation experiments were performed on a custom-made testing system 32,40 , as illustrated in Fig. 2. A titanium tube was used as the striker, with the total mass being 63 g. It was projected to impact a stainless steel incident bar, by a gas chamber having the initial pressure of 15 psi. The impact speed of the striker was measured to be ~8.5 m/s by a set of EE-SPW421 photo-micro sensors (Omron, Kyoto, Japan). Then, the incident bar impacted a tungsten carbide (TC) indenter (Bal-tec, Los Angeles, CA) into the silica sample. The indenter was hemispherical-shaped, with the diameter of 4.75 mm. Its hardness was more than 91 HRA and its maximum surface roughness was 0.7 micro-inch Ra. For the silica sample, two rings were used to confine its lateral surface ( Fig. 1(a)): The inner ring was made of relatively flexible polyurethane (PU), with the initial inner radius of 9.5 mm and the outer radius of 11 mm; the outer ring was made of polyvinyl chloride (PVC), with the initial inner radius of 12.5 mm and the shrinkage ratio of 2:1. The silica sample was placed on a substrate and a transmission bar; both of them were made of the same stainless steel as the incident bar. The impact striker, the incident bar, and the transmission bar had the same 12.7 mm diameter. In the middle of the incident and the transmission bars,  a pair of strain gauges (WK-13-250BF-10C, Vishay Measurements Group) were attached, and a data acquisition system (2310B, Vishay Measurements Group) was employed to record the stress wave signals. In order to preserve the sample for further examination, only the first stress wave pulse was allowed to impact the silica sample, which was realized by a momentum trapper 32,41,42 . As shown by the inset in Fig. 2, the symmetrical configuration of the rear and the front parts of the dynamic indentation system could effectively reduce sample bending 32 . Figure 3 shows typical stress wave signals of the silica samples. Upon similar incident stress waves ( Fig. 3(a)), for the samples with different porosities, the transmitted stress waves ( Fig. 3(b)) vary significantly, owning to the difference in acoustic impedance and possibly also energy absorption 32,43 . The relationship between the peak transmitted wave pressure, |P t |, and the porosity, c, is displayed in Fig. 3(c). Compared with solid silica wherein c < 1%, |P t | of silica nanofoam is much lower; with the increase in porosity from ~50% to ~70%, |P t | decreases from ~8 MPa to ~4 MPa.
After the impact tests, the samples were examined by a VHX-1000 microscope. Through the 3D Image Stitching function, the indentation profiles were scanned, as displayed in Fig. 4. On the sample surface ( Fig. 4(a) and (b)), the indentation radius was measured ( Fig. 4(d)). Under the dynamic loading, with the porosity increasing from ~50% to ~70%, the maximum indentation depth (D) and radius (R) are maintained around 60 µm and 1050 μm, respectively; both are smaller than those of solid silica. The data suggest that silica nanofoam is effectively "harder" than solid silica, and the effective dynamic hardness is relatively unrelated to the porosity; that is, the empty nanocells do not weaken the dynamic indentation resistance, in the range of porosity under investigation. Compared to the maximum indentation depth, the difference in indentation radius between solid silica and silica nanofoam is smaller, implying that after indentation, along the depth direction the cellular structure has partially recovered.
Based on the classical theory [28][29][30] , the hardness, H, of a foam material should be highly dependent on its porosity, c: With the increase in porosity or decrease in mass density, the foam material should become softer and exhibit less resistance to indentation. In general, the hardness of a material can be evaluated as 44,45 where F is the indentation force, R is the indentation radius, and ζ is a geometric factor. Therefore, for a foam material, under a given loading, 2 where = R R R / solid is the normalized indentation radius, and R solid is the indentation size of solid silica under the same loading. Clearly, for a regular foam, the indentation radius should increase with the porosity. However, as shown in Fig. 4(d), this classical R-c relationship breaks down for silica nanofoams. The unique phenomenon may be employed to reduce the weight of an EAD without losing indentation resistance under dynamic loadings.
For self-comparison, we define an index to describe the nominal indentation resistance (NIR): 2 NIR index under dynamic loading will be denoted as Θ d in the following discussion. The reduction in normalized indentation size leads to the increase in the NIR index. In Fig. 5, with the increase in porosity, Θ d fluctuates around 1.13. It should be related to the fast collapse of nanocells 32,46 , as illustrated by the inset in Fig. 5. The crushing of nanocellular structure results in a locally hardened region at the front of indenter, which renders a much larger volume of material being involved in resisting the indenter motion.

Conclusions
To conclude, for silica nanofoam with the average pore size around 80 nm, under dynamic loading, when its porosity increases from ~50% to ~70% and its mass density reduces by ~40%, the indentation resistance is maintained at a similar level, higher than that of its solid counterpart and much higher than that of regular porous silica. The maximum transmitted wave pressure decreases rapidly as the porosity increases. The underlying physical mechanism is credited to the fast collapse of nanocells at the front of indenter, which forms a locally hardened layer and therefore, a large volume of material contributes to indentation resistance.

Materials.
Silica nanofoam samples were obtained through sol-gel processing 17 , and the subcritical calcination (SCC) technique was adopted to adjust their porous configurations 37 . First, with the mass ratio of 72:28 and the total weight of 800 g, Kasil-1 potassium silicate (PQ Corporation, Valley Forge, PA) and Ludox HS-40 silica sol (Sigma-Aldrich) were mixed for 30 min. Then, under vigorously stirring, 200 g formamide solution (40 wt%) was added. After stirring for another 30 min, it was poured into polypropylene (PP) plastic vials. The diameter and the height of the vials were 36 mm and 16 mm, respectively. At room temperature (RM), the mixture was aged for 24 hours. After phase separation, the gels were washed by a series of solutions at 90 °C: 1M ammonium nitrate, 1M nitric acid, and deionized water; they were then rinsed by methanol at RM for more than five times. Next, the gels were dried in a vacuum chamber for 72 hours at 80 °C. Finally, the samples were calcinated in a tube furnace (GSL-1700X, MTI Corporation, USA) for one hour at different temperatures slightly above the glass transition temperature of amorphous silica, ~1200 °C. As the reference material, solid silica samples were prepared through a similar procedure, except that in the last calcination step they were fired at 1250 °C for 12 hours, to achieve a porosity less than 1%.
Pore size. The pore size of nanofoam was assessed through mercury porosimetry 47 : d = 4σ·cosθ/P Hg , where σ is the surface tension of mercury (0.484 N/m at RM), θ is the contact angle (140°), and P Hg is the infiltration pressure of mercury.
Porosity. The porosity of nanofoam sample was estimated from the measured mass density (ρ): where ρ solid is the mass density of amorphous silica (2.2 g/cm 3 ).

SEM analysis.
Before and after the tests, scanning electron microscope (SEM) analysis was performed with a FEI-XL30 SEM at 20 kV. Prior to the examination, the samples had been coated with iridium under argon atmosphere for 6 seconds at 85 mA using a K575X sputter coater (Emitech, Houston, TX).
X-ray diffraction. The foam and solid silica samples were inspected on a Bruker D8 Advance X-ray Diffractometer with Cu Kα radiation (wavelength 1.5418 Å). The 2θ range was set to be 10-80°; the speed was 0.1 sec step; −1 the step size was 0.02°.
Impact system. Both the incident and the transmission bars were made of 17-4 PH H900 stainless steel 32 , which has the mass density of 7.75 g·cm −3 and the elastic modulus of 196.5 GPa. The diameters of the two bars were 12.7 mm, and the lengths were 1.8 m and 1.5 m, respectively. The impact striker was a Grade 9 Titanium (Ti) tube, having the inner diameter, the outer diameter, and the length of 11.4 mm, 12.7 mm, and 462 mm, respectively. Its two ends were sealed using two 17-4 PH H900 stainless steel end-caps (thickness = 5 mm), respectively, under the assistance of two stainless steel pins with the diameter and the length of 3.2 mm and 12.7 mm, respectively. The total weight of the striker, end-caps, and pins is 63 g.
Indentation profile scanning. A Keyence VHX-1000 digital microscope (Osaka, Japan) was used to characterize the indented samples. Through the function of 3D Image Stitching, the indentation profiles were scanned, with the scanning range spanning across the lowest and the highest focusing points. The scan step size was set to be less than 2 μm.