Liquid marble: A novel liquid nanofoam structure for energy absorption Open Access

The increasing interest in the protection of personnel and civil infrastructures from impact has led to extensive researches on the design of advanced energy absorbing materials and structures. In the past, various types of materials have been developed for impact protection, such as cellular materials,^1,2 granular materials,^3,4 micro-trusses,^5,6 fiber reinforced composite materials,^7,8 and many others. However, several issues have limited the energy absorption performance of these conventional materials. Firstly, upon impact, localized damage can be introduced into the foam-based system and thus, the energy absorption capacity of the system cannot be fully utilized.^9–11 Secondly, as the loading speed increases, the foam-based system may not respond fast enough to the external loading due to the length scale of the unit cell, which is typically on the micrometer level. Consequently, the incident energy can go through the protection layer with negligible mitigation and cause severe damage. In addition, for most of these materials, the reusability is nearly zero as permanent deformation is the main energy dissipation mechanism.

Recently, a liquid nanofoam (LN) system with high energy absorption efficiency was developed for high-performance protection devices.^12–17 The LN system is composed of liquid and hydrophobic nanoporous materials, the latter containing large volume fraction of nanometer pores whose surface is specially treated and non-wettable to the liquid phase.¹⁷ When an external impact is sufficiently high, the surface energy barrier is overcome and the liquid molecules are forced into the nanopores. During this liquid infiltration process, large amount of external energy is converted into solid-liquid interfacial tension and then dissipated as heat.¹⁸ For a single nanopore, it has been demonstrated that the LN system possesses both high energy absorption efficiency and ultra-fast energy dissipation rate.^15,19 In addition, the LN system can be fully reusable for up to thousands of cyclic loadings.²⁰ Therefore, the LN system is potentially an advanced energy absorber.

One remaining problem of the LN system is its heterogeneity. Naturally, the hydrophobic nanoporous particles cannot be uniformly dispersed into the liquid phase due to their surface property. As a result, in LN samples, the nanoporous particles often aggregate and form separate layers of particles and liquid. In this configuration, the nanoporous particles are not immediately accessible by the liquid phase. As a result, the liquid infiltration process is much compromised and the energy absorption performance of LN at elevated strain rates is reduced.

To solve this heterogeneity problem of LN, we have converted its structure to the liquid marble form, which is formed when a liquid droplet is brought into contact with and entirely encapsulated by hydrophobic particles spontaneously.^21–24 By examining the mechanical behavior of the LN in the liquid marble form as well as the LN in the layered structure at quasi-static and intermediate strain rates, we demonstrate that the liquid marble form possesses a superior energy absorption performance. Therefore, reconfiguration of LN into the liquid marble form offers a promising approach for the protection from blunt impact and the design of next-generation energy absorbers.

Nanoporous silica (SP-1000-20, Daiso Inc.) and saturated lithium chloride (LiCl) solution (46 wt %) were used as the nanoporous material and the liquid phase. The average particle size of the nanoporous silica was about 20 μm. The specific nanopore volume and average pore size were measured to be 0.76 cm³/g and 120 nm respectively by Mercury Porosimeter (AutoPore IV 9500, Micromeritics, Inc.). The nanopore surface of as-received silica gel was hydrophilic; therefore, the aqueous solution could enter the nanopores spontaneously in the ambient environment. Consequently, the deformability of such LN was nearly zero. In order to increase the hydrophobicity of the silica gel, a monolayer of silyl groups was grafted onto the nanopore surfaces.²⁵ First, 1 g of silica gel was dried at 100 °C and then mixed with 40 mL of anhydrous toluene. The mixture was stirred for 3 h at 90 °C, after which 10 mL of chloro(dimethyl)octylsilane and 1 mL of pyridine were injected into the mixture at room temperature. The surface treatment took place at 95 °C with gentle stirring for 5 h. The treated silica gel was filtered, washed thoroughly with ethanol, and dried at 70 °C in air for at least 24 h before use.

LN samples in two different configurations were prepared for both quasi-static and dynamic tests. The layered LN sample, denoted as LN-L, was prepared by adding 0.2 g of the treated silica gel and 0.6 g of saturated LiCl solution successively. Since the surface of the treated silica gel was hydrophobic, the silica gel was not wettable to the saturated LiCl solution, and thus the LN sample exhibited a two-layer structure. The LN sample in the liquid marble form, denoted as LN-M, contained same amount of the surface treated silica gel and saturated LiCl solution. After mixing, the liquid droplets were encapsulated by the hydrophobic particles by vigorous agitation. Since no chemical reaction occurs, the chemical composition of LN sample is not affected.^22,26 Therefore, the stability of the LN sample totally depends on the degradation of the silyl layer on the silica surfaces, which was not observed during the period of this study. For quasi-static compressive tests and dynamic impact tests, both LN samples were sandwiched by two stainless steel pistons equipped with O-rings and sealed in a stainless steel testing cell. The cross-sectional area of the pistons, A, was 286 mm². The initial length of both LN samples, l, was 5 mm.

The quasi-static compression tests were conducted by a universal tester (Floor Model 5982, Instron, Inc.). As shown in Fig. 1a, the LN sample was compressed at a constant speed of 2 mm·min^-1. As the external force gradually increased to 4.3 kN, the crosshead of the Instron machine was forced back at the same rate. The loading-unloading process was repeated for 3 cycles. The applied pressure was calculated as P=F/A, where F was the external force applied by the Instron machine. The specific system volume change was calculated as ΔV=A×Δl/m, where Δl and m were the thickness change of LN sample and the mass of the silica gel, respectively.

The dynamic behavior of both LN samples was characterized by a lab-customized drop tower, as shown in Fig. 1b. To minimize the friction between O-rings and pistons, during all dynamic tests, vacuum grease was applied on the O-rings as lubricant. The LN sample was impacted by the drop weight at various incident speeds of 0.65 m·s^-1, 0.90 m·s^-1 and 1.25 m·s^-1. The incident speed of dynamic tests was controlled by adjusting the free drop height. The deceleration history of the drop weight was measured by an accelerometer (353B03, PCB Group, Inc.) attached to the drop weight and recorded by an oscilloscope (PXIe-5105, NI Corp.) at the sampling rate of 10⁶ samples/s. No liquid leaking was observed during all tests. The external pressure applied on the LN sample was calculated as P=m_w×a/A, where a was the deceleration of drop weight and m_w was the mass of the drop weight which was 3.81 kg. The thickness change of the LN sample was calculated as $Δl=∬a(τ)d2τ$⁠, where τ was time. The strain rate was calculated as $𝜀̇=v¯∕l$ , where $v¯$ was the average speed of the drop weight associated with the liquid infiltration process.

The quasi-static behavior of LN samples with two different configurations, the liquid marble form (LN-M) and the layered form (LN-L) has been characterized by pressure-induced infiltration tests at the strain rate of 6.6×10^-3 s^-1. The liquid infiltration behaviors of both types of LN samples are exactly the same (Fig. 2). In the first loading cycle, as the applied pressure increases to 0.9 MPa, the slope of the loading curves decreases. The specific volume change of the LN (0.2 cm³/g) at 0.9 MPa is the elastic compression of the liquid phase and the nanoporous particles. The change in slope after 0.9 MPa corresponds to the event that the liquid molecules start to infiltrate into the hydrophobic nanopores. The infiltration pressure is governed by the classic Laplace-Young equation P_in=2γ/r, where γ is the effective solid-liquid interfacial tension and r is the effective nanopore radius.¹⁸ When the external pressure reaches 4.5 MPa, all the nanopores are filled with liquid molecules, and the slope of the loading curve correspondingly increases dramatically. The loading curve in between 0.9 MPa and 4.5 MPa has the minimum slope and is defined as the liquid infiltration plateau. The specific volume change associated with the liquid infiltration plateau is referred as the infiltration volume with the value of 0.7 cm³/g which is consistent with the pore volume of the silica gel measured by mercury porosimetry. The enclosed area under the hysteretic loading-unloading curve is the energy absorption capacity of the LN samples. The identical behavior of the two types of LN samples suggest that under the quasi-static loading condition, the structure of the LN has no effect on the energy absorption capacity of the material.

At the end of the first loading cycle, a second loading is applied immediately. The initial infiltration pressure increases to 1.2 MPa while the specific volume change associated with the liquid infiltration plateau decreases to 0.45 cm³/g. Despite the reduction in energy absorption capacity compared with the first loading cycle, the loading-unloading behavior is still hysteretic, suggesting that the LN system is reusable to some extent. This is consistent with our previous results that the nanoporous structure is not damaged in such tests because its strength is an order of magnitude higher than the applied peak pressure.²⁷ In other words, the nanoporous structure is not crushed, and the liquid infiltration is the main working mechanism for energy absorption.

From the second loading cycle on, the LN samples do not exhibit further reduction in energy absorption capacity, i.e. the LN samples are fully reusable, as suggested by the overlapped loading-unloading curves between the second and the third cycles (Fig. 2). This property eliminates the need of using a new sample for each dynamic test and allows us to use one pre-compressed LN sample (i.e. sample after the first loading-unloading cycle) throughout the tests.

The dynamic behavior of the LN samples with both configurations was characterized at strain rates of 120 s^-1, 180 s^-1, and 250 s^-1. During unloading, the drop weight bounced back faster than the upper piston, that is, the thickness change of the LN sample upon unloading cannot be captured. Therefore, only the loading curves of the dynamic tests are recorded (Fig. 3).

The dynamic infiltration behavior of the LN-L sample is strain rate sensitive as its deformability shows a remarkable decrease at elevated strain rates (Fig. 3a). When the strain rate is 120 s^-1, the specific volume change associated with the liquid infiltration plateau is 0.35 cm³/g, which is 78% of that in quasi-static tests. As the strain rate further increases to 250 s^-1, the deformability of the sample decreases to 0.28 cm³/g, which is 62% of the full energy absorption capacity of the LN. Despite the change in the system deformability, the infiltration pressure range (0.9∼4.5 MPa) is not affected by the increased strain rates. After all the dynamic tests, the LN-L sample is compressed under quasi-static compressive loading for one more cycle. The liquid infiltration performance is exactly the same as the one before dynamic impacts (Fig. 3a). In contrast to the reduction in energy absorption capacity of the LN-L sample, the dynamic behavior of LN-M is strain rate insensitive (Fig. 3b). Both the total deformability as well as the liquid infiltration pressure range remain the same as measured in the quasi-static compression test. These results suggest that the LN-M sample is more efficient than the LN-L sample at increased strain rates, and the energy absorption capacity of the LN is fully activated in its liquid marble form.

The only difference between LN-L and LN-M is the sample configuration (Fig. 4). The LN-L sample contains two layers, one liquid layer and one hydrophobic silica gel layer (Fig. 4a and 4b). The distance between the nanopores and the liquid phase, d, increases from zero to several millimeters as the depth of the silica gel layer increases. In comparison with the heterogeneous layered structure of LN-L, the LN-M sample has a macroscopically homogenous structure and the maximum value of d is only a few microns (Fig. 4c and 4d). As the LN samples are loaded quasi-statically, there is sufficient time for the liquid to reach the nanopores’ open ends; that is, all the nanopores are accessible before the liquid infiltration starts. As a result, the liquid is driven into all the nanopores and both LN samples exhibit the same quasi-static infiltration behavior and energy absorption capacity.

By contrast, under dynamic impact, the complete external loading cycle lasts only a few milliseconds and the rising time of the external loading from zero to 1.2 MPa, t_r, is less than millisecond (Fig. 5). During the loading process, the minimum activation time, t₀, needed for the liquid to reach all the open ends of nanopores in the LN-L sample is equivalent to the time need for the liquid to completely fill the air gaps between the hydrophobic particles. It is estimated as t₀= (1-f) × d_max/$v¯$⁠, where f is the volume fraction of the silica gel and d_max is the initial thickness of the silica gel layer. In the LN-L sample, d_max is 3 mm. If the particles are closely packed (the actual volume fraction of the particles is much lower due to the hydrophobic surface property and structural randomness), f is 74%. As the LN-L sample is impacted at 0.65 m·s^-1, the minimum required activation time is about 1.2 millisecond, which already exceeds the rising time of the external loading. Since both the rising time of the external loading and the minimum required activation time of LN-L are proportional to 1/$v¯$⁠, t₀ > t_r at all impact speeds. Consequently, only part of the nanoporous silica gel particles is involved in energy absorption under intermediate strain rate.

The assumption of the above calculation is that liquid infiltration is not activated before all the air gaps are filled by the liquid phase. However, at higher strain rates, the stress equilibrium condition which is always satisfied under quasi-static tests, is no longer valid and the local pressure at the impact end builds up first due to the inertia effect caused by the heterogeneous configuration.^28–30 As the nanoporous particles at the top of the silica gel layer have immediate contact with the bulk liquid phase, liquid infiltration process is activated and finished locally before the liquid fills all the air gaps. As a result, there is 78% of the nanoporous silica gel involved in the energy absorption (Fig. 3a). As the incident speed increases, the inertia effect is more significant, and less nanopores are activated during the loading process. Therefore, the energy absorption capacity of the LN-L further reduces to 62% (Fig. 3a).

In the LN-M sample, the size of the air gaps between the liquid phase and the nanoporous particles, d, is reduced from millimeters to microns by the macroscopically homogeneous configuration (Fig. 4b). As a result, the LN-M sample is fully activated after all the air gaps are filled by the liquid phase in less than 0.01 millisecond which is calculated as t₀. The activation time of the LN-M sample is two orders of magnitude lower than the rising time of the external impact, which also mitigates the inertia effect. Therefore, all the nanopores are exposed to the liquid phase immediately and involved in the liquid infiltration process under impact. The energy absorption capacity of LN is fully activated at different strain rates ranging from quasi-static to 10² s^-1 in the liquid marble configuration.

To summarize, the liquid infiltration behavior of LN samples with two different sample configurations, the layered form and the liquid marble form, has been characterized by quasi-static compression tests and drop tower tests. The infiltration behavior and energy absorption capacity under quasi-static compression are the same for both configurations. However, under dynamic tests, the layered form LN shows a reduced deformability as well as energy absorption capacity, which is attributed to a long activation time and inertia effect due to the heterogeneous structure. By contrast, in the liquid marble form of LN, the nanoporous particles and liquid droplets are uniformly distributed and all the nanopores are accessible upon impact, leading to the ultra-fast reaction of the LN. Therefore, the overall liquid infiltration behavior of the liquid marble form LN sample is not affected by the considerably increased strain rate. These findings suggest that the LN in the liquid marble form can perform as an efficient energy absorption system under blunt impact.

The authors would like to thank Daiso, Inc. for providing nanoporous silica gel samples for this study. The authors gratefully acknowledge Dr. Dennis Miller and Dr. Lars Peereboom for their help on mercury porosimetry. This work is financially supported by Michigan State University startup grant and Ford-MSU Alliance Program.