INTRODUCTION

Spheroplastics or syntactic foams are composite materials in which microspheres are randomly distributed in a polymer binder. Due to low density and permittivity, spheroplastics are widely used in various engineering applications [1, 2]. In a recent study [3], the formation of whisker structures (nanowhiskers) has been found in a tungsten-modified spheroplastic exposed to a nanosecond beam of relativistic electrons with a density of 230 J/cm2. It is known that exposure to nanosecond electron beams produces strong electric fields and shock-wave loading in the target, making it difficult to elucidate the unambiguous reason for the formation of nanostructures.

A review of methods for obtaining various nanostructures can be found in [4, 5]. It is known that carbon nanoparticles can be produced by detonation of explosives [6, 7] or a gas mixture of acetylene with oxygen [8]. During electrical explosion of conductors, nanoparticles of metals or their oxides are formed [5]. Laser ablation with nanosecond pulses (pulse repetition rate of 10 Hz) allows the formation of nanowhiskers by the vapor–liquid–crystal mechanism [9]. During laser ablation (pulse repetition rate of 4 kHz), nanowires are formed in superfluid helium (He II) by the process of coagulation of impurities in quantized vortices of superfluid helium [10]. Shock-wave impact on metal carboxylates leads to the formation of diamond nanoparticles and metal nanoparticles with a typical size of 3–20 nm [11].

The deformation of spheroplastics under shock-wave, dynamic, and static compression has been studied in sufficient detail and is associated with the plastic deformation of spheroplastics upon collapse of the porosity formed by microspheres [12–19]. However, the formation of nanowhiskers in spheroplastics under shock-wave loading has not been observed previously.

Shock-wave pulses generated by detonation of an equidistant-surface charge of an elastic explosive produce shock-wave loads similar to those resulting from exposure to relativistic electron beams from a Kalmar accelerator [3]. In this case, strong electric fields are not generated.

The aim of this study was to experimentally investigate the possibility of the whisker formation in a spheroplastic and the changes in its dielectric and mechanical characteristics after shock-wave compression by detonation of an equidistant-surface charge of an elastic explosive.

EXPERIMENT

In the experiments, we used flat samples of a spheroplastic consisting of a polymer binder based on an organosilicon elastomer (polyphenylsilsesquioxane-polydimethylsiloxane block copolymer) and glass or tungsten-modified microspheres with a diameter of 30–130 \(\mu\)m. The weight percentage of MS-9A microspheres was 28%. The thickness of the glass wall of microspheres was 2–2.5 \(\mu\)m, and the thickness of the tungsten coating was 0.1–0.15 \(\mu\)m. The metal layer was applied to microspheres by gas phase chemical deposition. For convenience, the spheroplastic with a metal tungsten coating on the surface of glass microspheres will be denoted by , and the spheroplastic with the same parameters of microspheres (diameter, wall thickness, and chemical composition) without a tungsten coating will be denoted by .

Shock-wave loading was produced by detonation of an equidistant-surface charge of an elastic explosive (explosive) (density 1.6 g/cm3, detonation velocity 7600 m/s). The amplitude and duration of the shock-wave pulse were set by choosing the reduced mass of the explosive charge and the distance to the sample. To ensure simultaneous load application, the charge was made in the form of several strips, and detonation was initiated at the ends of the explosive strips using a multipoint beam initiation system [20].

In all experiments, the width of the detonation strip was 2 mm and the thickness of the explosive was 0.5 mm. The passage of the pressure wave through the thickness was recorded by piezofilm sensors mounted on the front and back sides of the loaded spheroplastic.

Spheroplastic samples with dimensions of 35 \(\times\)35 mm and a thickness of \(\approx\)8.5 mm were fixed on the ballistic pendulum load. The pressure pulse transmitted to the target by detonation of the explosive charge was determined from the angle of deflection of the pendulum load [21]. The maximum measurement error for the specific pressure pulse \(I_{sh}\) did not exceed 4%.

After loading, cylindrical samples with a diameter of 5 mm and a height of 8 mm were cut from the central part of spheroplastic plates in the direction of application of the pressure pulse. Mechanical characteristics were determined on an Instron 5565 universal testing machine with a moving traverse speed of 5 mm/min. The effective elastic modulus was determined in the initial section of the compression diagram (up to 10%). The results of measurements of the elastic modulus and compressive strength were averaged over the results of tests of at least five cylindrical samples.

The complex permittivity of spheroplastic was determined on samples with a thickness \(h\) = 2–2.5 mm cut from the central part of the original and loaded spheroplastic plates. The capacitance \(C\) and dielectric loss tangent tan \(\,\delta\) were measured.

Loading parameters of spheroplastic samples by the equidistant-surface charge of the elastic explosive

Experiment number

Distance to target,  mm

Reduced charge mass, g/cm2

Pressure pulse, Pa\(\,\cdot\,\)s

Pulse duration, \(\mu\)s

S1_1

15

0.031

300

5

S1_2

30

0.031

150

10

S1_3

30

0.037

203

10

S1_4

30

0.048

251

10

S1_5

30

0.06

300

10

S2_5

30

0.06

300

10

For electric field frequencies \(f\) = 1–1000 MHz, measurements were performed by the coaxial line method using an E4991A lyzer and a BDS2200 radiofrequency cell with BDS2214 measuring electrodes (diameter of the measuring electrode \(d\) = 10 mm). The amplitude of the sinusoidal electric field applied to the sample was 0.5 V. In the range of electric field frequencies from 40 to 5\(\,\cdot\,\)106 Hz, an Agilent HP 4294A precision impedance analyzer was used. The amplitude of the applied sinusoidal voltage was 1 V. The amplitude and phase shift of the current flowing through the sample were measured using a two-electrode scheme. The diameter of the measuring electrode was \(d\) = 10 mm. The capacitance of the sample was calculated taking into account the edge capacitance and the capacitance of the measuring cell relative to the ground, according to the Russian State Standard (GOST) No. .

The permittivity in each of the frequency ranges was measured for at least 80 values of the electric field frequency \(f\) with a uniform logarithmic increment. The real part of the complex permittivity was calculated by the formula \(\varepsilon'= 4C\cdot h/(\varepsilon _{0}\pi d^{2})\)(\(\varepsilon _{0}\) is the electric constant). All experiments were performed at room temperature.

Structural changes in the spheroplastic were studied using a JSM-6490 scanning electron microscope. An antistatic coating was not applied to spheroplastic samples to exclude a possible methodological error.

EXPERIMENTAL RESULTS AND THEIR ANALYSIS

The table shows the shock-wave loading parameters of spheroplastics achieved in experiments by detonation of an equidistant-surface charge of an elastic explosive with a specific pressure pulse \(I_{sh}\) = 150–300 Pa\(\, \cdot\,\)s.

Fig. 1
figure 1

Typical scanning electron micrographs of microspheres in spheroplastic at a depth of 1–7.2 mm from the surface exposed to the detonation products of an equidistant-surface charge of the elastic explosive: (a) experiment S1_1; (b) experiment S1_2; (c) experiment S1_3; (d) experiment S1_5.

Full size image
Fig. 2
figure 2

Typical scanning electron micrographs of glass spheres in spheroplastic at a depth of 2 (a) and 7 mm (b) from the surface exposed to the detonation products of an equidistant-surface charge of the elastic explosive (experiment S2_5).

Full size image

In experiments S1_1 and S1_5 (\(I_{sh} \approx 300\) Pa\(\,\cdot \,\)s), spheroplastic samples were fractured into fragments. In experiment S1_4 (\(I_{sh} \approx 250\) Pa\(\,\cdot \,\)s), a through crack was formed from the center of the sample to its periphery. In experiment S1_3 (\(I_{sh} \approx 200\) Pa\(\,\cdot \,\)s), damage in the form of surface spalls was observed at the edges of the  sample. In experiment S1_2 (\(I_{sh} \approx 150\) Pa\(\,\cdot \,\)s), the  sample did not have visible damage. Note that the thickness of the fractured spheroplastic samples was practically the same as that of the original samples. In experiment S2_5 with a maximum value \(I_{sh} \approx 300\) Pa\(\,\cdot \,\)s, the spheroplastic sample has no visible changes.

Typical scanning electron micrographs of ruptures of  spheroplastics after shock-wave loading are shown in Fig. 1. It is seen that the collapse of microspheres is accompanied by the formation of many small fragments, which is usually explained by the action of both the axial force and shear stresses [17]. Since the wall thickness of a microsphere is much smaller than its diameter, the collapse of the microsphere is accompanied by the formation of a cavity in the spheroplastic. In all experiments, whiskers up to 10 \(\mu\)m long and 0.03–0.3 \(\mu\)m in diameter are formed on the inner side of the collapsed metallized microspheres. Whiskers with a diameter of 0.1 \(\mu\)m can be classified as nanowhiskers. The number of whiskers in experiments S1_1 and S1_5 is much larger than in experiments S1_2 and S1_3. That is, increasing the specific pressure pulse \(I_{sh}\) leads to more efficient whisker growth.

Typical scanning electron micrographs of ruptures of  spheroplastic after shock-wave loading (experiment S2_5) are shown in Fig. 2. As in experiments with , there is a collapse of glass spheres, but whiskers on the collapsed glass spheres are quite rare (Fig. 2a). In the vast majority of cases, unlike in , the structures formed on the inner surface of glass spheres are oriented along the surface of glass spheres and have a much larger diameter. Whisker structures oriented normal to the outer surface of glass spheres (Fig. 2b) are observed; in shock-loaded samples, this type of structures is not found. As can be seen from Fig. 2b, some of collapsed glass spheres contain structures resembling solidified jets of the polymer binder.

Figure 3 shows deformation diagrams of cylindrical samples of the original and shock-loaded spheroplastic. The shape change of cylindrical samples under compression followed the classical pattern. The sample took the shape of a barrel, and the fracture was accompanied by the formation of a crack oriented at an angle of \({\approx}45^{\circ}\) to the loading axis. It can be seen that the decrease in the elastic modulus of the spheroplastic by shock-wave loading is the stronger, the higher the pressure pulse \(I_{sh}\). However, the strength of the spheroplastics after shock-wave loading exceeds the compressive strength of the original samples. The increase in strength can be caused by the occurrence of delamination and air porosity in the volume of the spheroplastic, which prevents crack propagation along the . Note that reliable measurements of the strength of samples in experiments S1_1 and S1_4 are difficult to perform due to the strong change in the shape of cylindrical samples during compression on the Instron 5565 machine.

Fig. 3
figure 3

Compression diagrams of cylindrical samples of spheroplastic. Original spheroplastic (Or) and the sample after shock-wave loading by an equidistant-surface charge of the elastic explosive: the experiment number on the curve corresponds to the number in the table.

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Fig. 4
figure 4

Frequency dependence of the relative permittivity (a) and dielectric loss tangent (b) of  spheroplastic. Original spheroplastic (Or) and the sample after shock-wave loading by an equidistant-surface charge of the elastic explosive: the experiment number on the curve corresponds to the number in the table.

Full size image

The frequency dependences of the real part of the complex dielectric permittivity and dielectric loss tangent of the original and shock-loaded spheroplastic samples are shown in Fig. 4. It is seen that \(\varepsilon'\) decreases with increasing field frequency. In experiments S1_1 and S1_5, shock-wave loading causes a decrease in \(\varepsilon '\) over the entire frequency range, whereas in experiments S1_2 and S1_3 at a smaller pressure pulse \(I_{sh}\), the changes in \(\varepsilon'\) are insignificant. The result indicates a significant increase in the size of air pores after shock-wave loading in experiments S1_1 and S1_5.

The dependence tan \(\,\delta (f)\) for the original spheroplastic shows two regions of the frequency dispersion of the complex permittivity: a low-frequency region at 20 kHz and a high-frequency region at over 300 MHz. It can be seen from Fig. 4 that increasing the amplitude of the shock-wave pressure pulse causes a shift in the low-frequency relaxation peak to lower frequencies and the disappearance of high-frequency relaxation regions in the spheroplastic. The characteristic frequency of the low-frequency relaxation corresponds to the Maxwell–Wagner polarization on metallized glass spheres [22]. High frequency relaxation is determined by the interaction of the electromagnetic wave with metallized microspheres. A similar effect has been repeatedly observed in polymer composites filled with particles of metals, ferromagnets, and multilayer carbon nanotubes [23–25]. The fracture of metallized glass spheres is accompanied by a change in electromagnetic wave scattering, which, with an increase in the pressure pulse, involves more and more fragments of microspheres remaining in the cavities of the spheroplastic. In addition, in experiments S1_1 and S1_4, there may be a slight decrease in the proportion of metal due to its ejection from the sample during fracture.

Thus, the change in the dielectric and mechanical characteristics of  spheroplastic is determined by the degree of fracture of microspheres, which is consistent with the results of scanning electron microscopy. The experiments confirmed the possibility of the formation of nanowhiskers during fracture of microspheres in the spheroplastics under microsecond shock-wave loading.

The relative permittivity of  spheroplastic is mainly determined by the high content of hollow glass microspheres and is \(\approx\)1.7 in the frequency range studied, and the dielectric loss tangent is \(\approx\)10\(^{ - 2}\). After mechanical loading in experiment S2_5, the change in the relative permittivity did not exceed 30% and was generally insignificant.

DISCUSSION

At present, it is difficult to unambiguously determine the mechanism of whisker formation during fracture of glass spheres in spheroplastics under microsecond shock-wave loading.

The most common method for producing semiconductor nanowhiskers is gas-phase deposition on a seed layer by the vapor–liquid–crystal mechanism [26]. For this, it is necessary to achieve evaporation of spheroplastic, in our case tungsten, and the destruction products of the polymer binder or glass and to have a liquid seed layer on the surface to initiate whisker growth.

In the experiments performed, the shock-wave pressure in the samples reached 15–60 MPa and the duration 5–10 \(\mu\)s. The strength of glass microspheres determined from the hydrostatic pressure in water that causes fracture of 50% (by volume) of microspheres was 12.4 MPa [27]. The elastic modulus of the organosilicon elastomer is much lower than that of the microsphere wall; therefore, the fracture of the microsphere leads to a displacement of the polymer binder into the resulting cavity. That is, under the action of a shock wave, the cavity in the polymer binder of a spheroplastic can act as a microreactor for nanowhisker growth. The elastic properties of the polymer binder ensure the absence of permanent deformation of spheroplastics after shock-wave loading.

Theoretical estimates of the increase in average temperature during fast plastic deformation of porous materials using the nonlinear Maxwell model were obtained in [28]. An increase in the temperature of a rapidly deformed porous material was shown to be mainly due to a change in density during compression. The original density of the spheroplastic in our experiments reached 700 kg/m3, and the density in the compressed state was close to the density of the spheroplastic without pores \(<\)2000 kg/m3. A conservative estimate shows that the increase in the average temperature over the sample does not exceed 100 K. This is not sufficient for thermal decomposition of the organosilicon binder. Indeed, in the experiments, carbon traces were observed only on the surface of the spheroplastic and were caused by the explosion products of the elastic explosive.

Analysis [29] has shown that the local increase in temperature in hot spots during shock-wave induced collapse of glass microspheres in a condensed medium is significantly higher than the volume-averaged temperature. There are several mechanisms for such heating: hydrodynamic flow, adiabatic gas heating, and plastic and viscoplastic deformation at high shear rates. The temperature of the resulting hot spots during collapse of glass spheres depends on shock-wave intensity and the viscosity of the material surrounding the pore. It is shown that in an epoxy resin polymer binder, the temperature reaches 1600 K at a pressure of \(\approx\)2 GPa and a hot-spot formation time of \(\approx\)300 ns [29]. At such a high temperature, the proportion of metal particles can decrease due to the partial transformation of tungsten into dielectric compounds, e.g., oxides. The decrease in the content of metal particles will cause a decrease in the maximum frequency of the low-frequency dispersion of permittivity, as was observed in the experiments performed (see Fig. 4).

Thus, the temperature in the microreactor formed by a locally compressed pore (up to 100 \(\mu\)m in diameter) far exceeds the volume-averaged temperature of the spheroplastic and requires a special theoretical analysis. The condensation products of the substances evaporated in the microreactor and glass structure defects on the inner surface of the glass sphere can act as a seed for whisker growth.

Note that whiskers are formed under shock-wave loading with an amplitude slightly exceeding the static strength of metallized glass spheres (experiment S1_2). Therefore, some contribution to the formation of whiskers in the experiments performed can be due to the wall yield and the change in the structure of metallized glass spheres under high-speed shear causing fracture of microspheres. As is known, severe torsional deformations change the microstructure of tungsten due to grinding of subgrains from 4 \(\mu\)m to 500 nm [30]. Because of the close packing of microspheres, it is also important to take into account the of microsphere collapse caused by their collision with closely spaced adjacent microspheres.

When analyzing the formation of nanostructures, it is important to take into account the relaxation of temperature and internal stresses in microspheres due to shock-wave loading. As shown in [31], during heterogeneous relaxation of thermal stresses upon exposure to powerful laser radiation under conditions excluding evaporation and melting of the solid, periodic nanostructured objects can form on the solid surface.

CONCLUSIONS

The experiments showed that shock-wave loading of spheroplastics \(\approx\)8.5 mm thick by detonation of an equidistant-surface charge of an elastic explosive with a pulse duration 5–10 \(\mu\)s and a pulse pressure of 150–300 Pa\(\,\cdot\,\)s led to fracture of metallized glass spheres with the formation of whiskers \(\approx\)10 \(\mu\)m long and 0.03 to 0.3 \(\mu\)m in diameter. The resulting nanostructures were oriented mainly along the normal to the internal surface of fractured microspheres. Increasing the shock-wave pressure pulse on the spheroplastic promoted the process of nanowhisker formation.

In the absence of metallization of the surface of glass spheres exposed to a shock-wave pressure pulse, the capacity for the formation of whiskers in the volume of fractured glass spheres is reduced. There is an increase in the diameter of the resulting elongated particles located predominantly along the surface of the glass sphere.

Changes in the dielectric and mechanical properties of spheroplastics subjected to shock-wave loading by an equidistant-surface explosive charge are due to the fracture of microspheres. Deformation diagrams show a decrease in the elastic modulus of the spheroplastic at a shock-wave pressure pulse of \(\approx\)150 Pa\(\, \cdot\,\)s, when the dielectric characteristics practically do not change.

Note that under conditions of shock-wave loading of polymer spheroplastic with an equidistant-surface explosive charge, the formation of whiskers has not previously been reported.

The practical significance of the observed effect is that it demonstrates the possibility of synthesizing nanowhiskers by collapse of microspheres in an elastic medium under microsecond shock-wave pulse loading.