How nanoporous silicon-polypyrrole hybrids flex their muscles in aqueous electrolytes: In operando high-resolution x-ray diffraction and electron tomography-based micromechanical computer simulations

Macroscopic strain experiments have revealed that silicon crystals traversed by parallel, channel-like nanopores functionalized with the artificial muscle polymer polypyrrole (PPy) exhibit large and reversible electrochemomechanical actuation in aqueous electrolytes. On a macroscopic scale these actuation properties are well understood. However, on the microscopical level this system still bears open questions, as to how the electrochemical expansion and contraction of PPy acts on to np-Si pore walls and how the collective motorics of the pore array emerges from the single-nanopore behavior. Here we present synchrotron-based, in operando x-ray diffraction on the evolving electrostrains in epilayers of this material grown on bulk silicon. An analysis of these experiments with micromechanical finite-element simulations, that are based on a full three-dimensional reconstruction of the nanoporous medium by transmission electron microscopy (TEM) tomography, shows that the in-plane mechanical response is dominantly isotropic despite the anisotropic elasticity of the single-crystalline host matrix. However, the structural anisotropy originating from the parallel alignment of the nanopores led to significant differences between the in- and out-of-plane electromechanical response. This response is not describable by a simple two-dimensional arrangement of parallel cylindrical channels. Rather, the simulations highlight that the dendritic shape of the silicon pore walls, including pore connections between the main channels, causes complex, highly inhomogeneous stress-strain fields in the crystalline host. Time-dependent x-ray scattering experiments on the dynamics of the actuator properties hint towards the importance of diffusion limitations, plastic deformation, and creep in the nanoconfined polymer upon (counter)ion adsorption and desorption, the very pore-scale processes causing the macroscopic electroactuation. From a more general perspective, our study demonstrates that the combination of TEM tomography-based micromechanical modeling with high-resolution x-ray scattering experiments provides a powerful approach for in operando analysis of nanoporous composites from the single nanopore up to the porous-medium scale.

Figure 1

In situ electrochemical measurement cell for x-ray diffraction. In situ XRD measurement cell with the sample, acting as the working electrode, in the center, the reference electrode, a counterelectrode, and the electrolyte solution. Depicted are as well the measurement sites for potential $E$ and current $J$ and the probing x-ray beam. In the area where the x-ray beam penetrates the in situ measuring cell the strength of the cell wall is significantly reduced to $2\mathrm{mm}$, so that the diffracted beam has still a high enough intensity when leaving the cell.

Figure 2

Electrochemical characterization of sample $S_{\text{refl}}$. (a) The graph depicts exemplary cyclic voltammetry measurements of the np-Si/PPy hybrid $S_{\mathrm{refl}}$ in $1\mathrm{mol}{\mathrm{l}}^{-1}{\mathrm{HClO}}_4$ electrolyte solution in the in situ electrochemical measurement cell. The current $J$ is plotted against the applied potential $E$ in the range of $0.4–0.8\mathrm{V}$, measured versus the standard hydrogen potential (SHE). The potential scan rate is increased from 0.5 to $10\mathrm{mV}{\mathrm{s}}^{-1}$. (b) The graph depicts values for the np-Si volume specific current $j$, averaged in the potential range of $0.55–0.65\mathrm{V}$, plotted against increasing potential scan rates $dE/dt$ from 0.5 to $10\mathrm{mV}{\mathrm{s}}^{-1}$. The red line indicates a linear regression of the first three data points which yields the capacitance $c_{\mathrm{norm},\mathrm{refl}}=(0.0293\pm 0.0004){\mathrm{Fmm}}^{-3}$ as the slope. (c) The upper graph depicts the course of the potential during the successive full $\theta \text{−}2\theta$ XRD measurements of the electrochemical actuation. The potential $E$ is stepped from $0.4\mathrm{V}$ over 0.6 to $0.8\mathrm{V}$ and back and remains at each step for as long as XRD measurement takes. The smaller, lower figures depict the course of the np-Si volume-specific current $j$ during one potential step up (left) and down.

Figure 3

Micromechanical formation of the simulation model. Result of 3D TEM tomography after segmentation. The position in $z$ direction corresponds to the position in the image stack, where $z$ moves from top to bottom. The scale bar in each picture has a length of $100\mathrm{nm}$. Exemplary interconnections between main pores indicated by red circles.

Figure 4

Fabrication of the simulation model. (a) Microstructure of the RVE at position $z=900$ with von Mises stress under external load in the $z$ direction displayed for cut through the mid-plane of the FE-voxel model. The scale bar represents $100\mathrm{nm}$. (b) Predicted mechanical properties as function of solid fraction $\varphi$.

Figure 5

In operando x-ray diffraction measurement in reflection geometry. (a) Diffraction geometry of the np-Si (dark gray) PPy (green) hybrid attached to bulk silicon (light gray), with incident beam $q_{\mathrm{i}}$, diffracted beam $q_{\mathrm{s}}$, the transferred wave vector $Q$, crystallographic directions, and the axis of the probed lattice mismatch $\delta a/a_{\perp }$. (b) Radial $\theta \text{−}2\theta$ scan of the (400) Bragg peak in the out-of-plane sample direction in the as-prepared state without an electrolyte solution. The ordinate is in linear scale, the abscissa shows angle $2\theta$ at the bottom and lattice mismatch $\delta a/a_{\perp }$ with respect to the main silicon peak at the top, respectively. The inset depicts the actual detector picture of the Si and np-Si/PPy signal. (c) Depicted is again the (400) $\theta \text{−}2\theta$ scan of the as-prepared sample (black square symbols). The ordinate is in logarithmic scale in contrast to (b). An equal radial $\theta \text{−}2\theta$ scan of the (400) Bragg peak in the out-of-plane direction is shown on the np-Si/PPy hybrid infiltrated with $1\mathrm{mol}{\mathrm{l}}^{-1}$ perchloric acid (red square symbols). The graphic yields a direct comparison between the two different sample states: as prepared versus electrolyte infiltrated. (d) Potential dependent x-ray diffraction measurements. The figure depicts $\theta \text{−}2\theta$ scans of the (400) Bragg peak in the out-of-plane direction of the infiltrated np-Si/PPy hybrid infiltrated by $1\mathrm{mol}{\mathrm{l}}^{-1}$ perchloric acid for applied potentials of $E=0.4$ and $0.8\mathrm{V}$, respectively. The inset represents a zoom in the Bragg peak that is caused by the np-Si layer. (e) The resulting lattice mismatch $\delta a/a_{\perp }$ of the (400) Bragg peak in the out-of-plane direction and the np-Si volume-specific charge $q_{\mathrm{V}}$ in dependence of the applied potential $E$ at each respective step.

Figure 6

Actuation kinetics of the lattice mismatch. (a) Lattice mismatch $\delta a/a_{\perp }$ of the (400) Bragg peak in the out-of-plane direction and the volume-specific charge $q_{\mathrm{V}}$ of np-Si in dependence of the applied, linearly changing CV potential $E$. (b) Exemplary profile of the (400) Bragg peaks in the out-of-plane direction of the np-Si and the bulk-silicon layer, respectively. The inset gives the actual detector picture from where the profile is extracted with intensity normalized to the Si main peak. (c) A step-coulombmetry measurement is performed in $1\mathrm{mol}{\mathrm{l}}^{-1}{\mathrm{HClO}}_4$ electrolyte solution for the determination of the electrochemical actuation kinetics of the np-Si/PPy hybrid. The applied potential $E$ (red) is changed in an instant fashion from 0.4 to $0.8\mathrm{V}$ and vice versa. The incorporated volume-specific charge $q_{\mathrm{V}}$ (blue) and the resulting lattice mismatch $\delta a/a_{\perp }$ (black, with the average in orange) are depicted versus time $t$ along with the potential $E$. (d) The time constants $\tau$ of the $\delta a/a_{\perp }$ and $q_{\mathrm{V}}$ reactions to the square potential depicted in (c).

Figure 7

In operando x-ray diffraction measurements in transmission geometry. (a) Diffraction geometry of the np-Si (dark gray)/PPy (green) material attached to bulk silicon (light gray), with incident beam $q_{\mathrm{i}}$, diffracted beam $q_{\mathrm{s}}$, the wave-vector transfer $Q$, crystallographic directions, and the axis of probed lattice mismatch $\delta a/a_{\parallel }$. For the in-plane mismatch in the transmission geometry, the incident beam hits the backside of the sample, is transmitted through the sample, and leaves the sample under an angle $\theta$. (b) $\theta \text{−}2\theta$ XRD measurements of the (440) Bragg peak in the in-plane direction of the np-Si/PPy hybrid sample infiltrated by $1\mathrm{mol}{\mathrm{l}}^{-1}$ perchloric acid in comparison with a plain, unfilled np-Si sample. The abscissa shows angle $2\theta$ at the bottom and lattice mismatch $\delta a/a_{\parallel }$ with respect to the main silicon peak at the top, respectively. The inset depicts the actual detector picture of merged Si and np-Si/PPy signal. (c) $\theta \text{−}2\theta$ XRD measurements of the (440) Bragg peak in the in-plane direction of the electrolyte-infiltrated np-Si/PPy hybrid sample in dependence of the applied potentials $E=0.4$ and $0.8\mathrm{V}$. (d) The resulting lattice mismatch $\delta a/a_{\parallel }$ of the (440) Bragg peak in the in-plane direction and the np-Si volume-specific charge $q_{\mathrm{V}}$ in dependence of the applied potential $E$ at each respective step.

Figure 8

Overview of overall results. Overview of the results of the measurements conducted in reflection and transmission geometry with the different states of the np-Si/PPy hybrid, from as prepared over liquid infiltrated to two different applied potentials $E=0.4$ and $0.8\mathrm{V}$.

Figure 9

Micromechanical model of the as-prepared np-Si/PPy hybrid. (a) Distribution of microstrain ${\varepsilon }_z$ in nanoporous silicon strained by expansion of interface elements in the out-of-plane direction, i.e., $z$ direction in the model. The scale bar represents $100\mathrm{nm}$. (b) Histogram of strain ${\varepsilon }_z$ for all elements with peak position calibrated to the as-prepared state, where “average” denotes the measured out-of-plane lattice mismatch of $\delta a/a_{\perp }=+(2.40\pm 0.01)\times {10}^{-3}$. “Macroscopic” refers to the strain of the whole micromechanical model in comparison to the microstrains of single voxels. (c) Computed peak position by a transfer of microstrains in diffraction angle $2\theta$.

Figure 10

Micromechanical simulation results. Distribution of out-of-plane and in-plane strains in the RVE for different states: histograms showing the increase of out-of-plane strain along np-Si with a PPy filling, liquid infiltrated, and with applied potentials of 0.4 and $0.8\mathrm{V}$, the assignment of symbols is given in the legend on the left, the different colors denote the different states.

Figure 11

Micromechanical simulation results with images of the representative volume element. Pressure and strain distributions for the np-Si/PPy RVE for different states of liquid infiltrated and with applied potentials of 0.4 and $0.8\mathrm{V}$. The upper row depicts the pressure inside the PPy phase. The middle and lower rows show the silicon phase with strains in the out-of-plane, $z$ direction (middle row), and in the in-plane $y$ direction (lower row). White circles mark the notch regions with high out-of-plane strains. The notch region is also shown in a closeup in the middle row with arrows marking the dendritic side pores. The scale bar represents $100\mathrm{nm}$.