Anisotropic Liesegang pattern for the nonlinear elastic biomineral-hydrogel complex

Abstract

The Liesegang pattern is a beautiful natural anisotropic patterning phenomenon observed in rocks and sandstones. This study reveals that the Liesegang pattern can induce nonlinear elasticity. Here, a Liesegang-patterned complex with biomineral-hydrogel repetitive layers is prepared. This Liesegang-patterned complex is obtained only when the biomineralization is performed under the supersaturated conditions. The Liesegang-patterned complex features a nonlinear elastic response, whereas a complex with a single biomineral shell shows a linear behavior, thus demonstrating that the Liesegang pattern is essential in achieving nonlinear elasticity. The stiff biomineral layers have buffered the concentrated energy on behalf of soft hydrogels, thereby exposing the hydrogel components to reduced stress and, in turn, enabling them to perform the elasticity continuously. Moreover, the nonlinear elastic Liesegang-patterned complex exhibits excellent stress relaxation to the external loading, which is the biomechanical characteristic of cartilage. This stress relaxation allows the bundle of fiber-type Liesegang-patterned complex to endure greater deformation.

Fig. 1.. Characterization of the LPC.

(A) Fabrication process of LPC. A cubic HD is prepared with the volume of 4.91 cm³. # is the exposure number of biomineral precursor. For example, # = 10 means that HD is immersed in PO₄³⁻ and Ca²⁺ for 10 times, respectively. LPC showed the same size as the HD. (B) Raman spectra within 900 to 990 cm⁻¹ to study the unit sections of LPC: HAP shell, inter-HD, LP-HAP, and HD core. (C) Spatial distribution of HAP in LPC monitored through mosaic Raman mapping tool. Red indicates the strongest intensity of HAP-originated Raman signal at 960 cm⁻¹. (D) XPS of LPC. XPS spectra at 127 to 144 eV and 340 to 360 eV are related to P 2p and Ca 2p, respectively. (E) Two- and one-dimensional wide-angle x-ray scattering (WAXS) patterns of HD and LPC. Here, q is the scattering vector, where q = (4π/λ) sin(θ/2). θ and λ are the scattering angle and wavelength of the incident x-ray beam, respectively.

Fig. 2.. Mechanism of biomineralization-based Lisegang patterning.

(A) Influence of the ionic strength in the biomineralization kinetics. The ionic strength determines the position of HAP (blue line), the rate of HAP growth (yellow lines), and the size of HAP (green line). (B) The supersaturated precursor media enable deep penetration and rapid biomineralization to accomplish the Liesegang pattern and LPC. (C and D) Biomineralization scenarios during preparation (C) HSC with the nonsupersaturated media and (D) LPC at the supersaturation condition.

Fig. 3.. Comprehension of parameters influential in Liesegang patterning.

(A) Illustration of Liesegang patterning protocols and decisive parameters. (B) Images of biomineralized complexes prepared under different values of I (0.033 to 33 M) and # (5, 10). The size of all samples is identical to 2.89 cm². HSC 1 to HSC 3 mean the complexes biomineralized under I = 0.033 to 3.3 M and # = 10 conditions, while LPC corresponds to the sample biomineralized under I = 33 M and # = 10 conditions. (C) Thickness of specific regions (i.e., HAP shell, LP-HAP, and inter-HD) of HSC 1 to HSC 3, LPC biomineralized under the conditions of # = 5 (open symbols) and # = 10 (closed symbols). (D to G) Diverse LPCs obtained by differing experimental conditions, as denoted above in the images. Scale bars, 0.5 cm. (H and I) Fabrication of multiple Liesegang patterns with the (H) squares and (I) words. Because of the spec of the laser cutter, the shape of “e” was partially engraved.

Fig. 4.. Rheological investigation of the LPC.

(A) Time-temperature superposition–based investigation of the frequency sweep rheological responses. G′, α_T, and w mean the storage modulus, horizontal shift factor, and angular frequency (in hertz), respectively. (B to D) Superpositioned master curves of HD, HSC 1 to HSC 3, and LPC. The increases in G′ were denoted as the symbol Δ. (E) Loss factors of HD, HSC 1 to HSC 3, and LPC. (F) Stress versus viscosity profiles of HD, HSC 1 to HSC 3, and LPC. The uniaxial shear is applied for 2 min.

Fig. 5.. FEA to study the influence of the Liesegang pattern.

(A) Protocol of FEA. Here, the initial geometry of HD, HSC, and LPC was fixed to a cylinder. (B and C) Images of HD, HSC, and LPC when the equilibrium was reached after (B) compression and (C) torsion deformation. (D) Entire stress distribution of HD, HSC, and LPC. (E) Enlarged stress distribution near centroid. (F) Development of a spring-dashpot model of LPC to address how the nonlinear elasticity has been accomplished.

Fig. 6.. Physical studies of the biomedical potentials using LPC.

(A) FEA of the LPC-based artificial cartilage deployed at the metatarsal phalangeal joints. Here, we have assumed the case with a degenerative cartilage disease. (B) Shear creep test of the LPC. The double arrows indicate the viscoelastic response. (C) Stress relaxation profiles of the HD and LPC. The shear strains of 10 and 20% were applied. (D) Strain versus stress curves of the HD and LPC during 50-cycle compressions. The HD and LPC were compressed up to the strain of 40%. (E) Relaxed energy of LPC normalized to HD (means ± SD). (F) Photographs of f-HD and f-LPC. Below microscope image is the cross section of f-LPC. Scale bar, 200 μm. (G) Raman spectra of f-LPC within 900 to 990 cm⁻¹. The signal at 960 cm⁻¹ indicates the HAP. a.u., arbitrary units. (H) Tensile stress versus strain curves of the f-HD and f-LPC. (I) FEA of the f-HD and f-LPC bundles. Each bundle comprises 19 f-HDs or f-LPCs with a length of 20 mm.