Inorganic Nanotube Mesophases Enable Strong Self-Healing Fibers

The assembly of one-dimensional nanomaterials into macroscopic fibers can improve mechanical as well as multifunctional performance. Double-walled aluminogermanate imogolite nanotubes are geo-inspired analogues of carbon nanotubes, synthesized at low temperature, with complementary properties. Here, continuous imogolite-based fibers are wet-spun within a poly(vinyl alcohol) matrix. The lyotropic liquid crystallinity of the system produces highly aligned fibers with tensile stiffness and strength up to 24.1 GPa (14.1 N tex–1) and 0.8 GPa (0.46 N tex–1), respectively. Significant enhancements over the pure polymer control are quantitatively attributed to both matrix refinement and direct nanoscale reinforcement, by fitting an analytical model. Most intriguingly, imogolite-based fibers show a high degree of healability via evaporation-induced self-assembly, recovering up to 44% and 19% of the original fiber tensile stiffness and strength, respectively. This recovery at high absolute strength highlights a general strategy for the development of high-performance healable fibers relevant to composite structures and other applications.

.    The degree of crystallinity of polyvinyl alcohol (PVOH) content in composite fiber was calculated using the following equation; where χc, ∆Hm and ∆H0 are the degree of crystallinity in weight percentage of the whole fiber, the measured melting endothermic enthalpy, and the theoretical melting enthalpy 1 of 100% crystalline PVOH (156 J g -1 ), respectively. As the addition of double-walled aluminogermanate imogolite nanotubes did not alter the melting temperature, it was considered not to provide a contribution to the measured melting endothermic enthalpy of the crystalline PVOH.

Table S1
Composition and thermal data for double-walled aluminogermanate imogolite nanotube (DW Ge-INT)/polyvinyl alcohol (PVOH) composite fibers and pure PVOH fiber (control). Degree of crystallinity (χc), in weight fraction, determined through differential scanning calorimetry as described above. Linear density of the fibers, by direct measurement, as described elsewhere in the methods.   Table S1, and the material densities: 1.269 g cm -3 and 1.345 g cm -3 for amorphous PVOH and crystalline PVOH, 2 respectively; the DW Ge-INTs density, 3.6 g cm -3 was calculated as the ratio between the mass of a nanotube over its period divided by the corresponding volume of the two walls of the nanotubes. Atomic positions were determined via wide angle X-ray scattering analysis, 3 and adjusted to account for H atoms 4 to which X-rays are rather insensitive. The composite fiber bulk density was calculated from the rule-of-mixtures (RoM) addition of the constituent densities. The linear fiber density (in tex, Table S1), was used to calculate the mechanical properties in N/tex directly (Table S5), which were then converted to mechanical properties in GPa, using the estimated composite fiber bulk density. For reference, the measured linear density in tex, and estimated bulk density, can be converted to an implied calculated mean fiber radius, shown in the Table below. Independent measurements of the nominal (circular) composite fiber radii determined by scanning electron microscopy are also tabulated and show reasonable agreement with the density derived values; however, the linear density approach is considered to be more accurate at it averages over the whole fiber sample, and underestimates rather than overestimates the mechanical properties when diameter varies.

DW
where wt.% is weight percentage,  is density, and B is bulk density.

Orientational order parameter determination for double-walled aluminogermanate imogolite nanotube and polyvinyl alcohol fibers
As detailed in the manuscript, for the wide-angle X-ray scattering experiments, the angular scattered intensity Q values at 0.6 and 1.4 Å -1 correspond to scattering features located in the equatorial plane perpendicular to the double-walled aluminogermanate imogolite nanotubes (DW Ge-INTs) and polyvinyl alcohol (PVOH) long axes, respectively. Azimuthal scans, IQ(), in Figure S8 of the composite fibers, are fitted by Lorentzian functions, characterized by their half-width-at-half-maximum (HWHM, wd), plus two Gaussian functions at +/-28° from the Lorentzian for DW Ge-INT/PVOH ϕDW Ge-INT = 13.2% composite fiber. Note that due to the overlap of the diffuse peak of amorphous PVOH and 101 ̅ and 101 peaks of crystalline PVOH, amorphous and crystalline contributions cannot be clearly assigned. Angular intensity distribution measured in reciprocal space can be directly calculated from the orientation distribution function ( ) in direct space, with θ being the angle between the wet-spun fiber axis and the nanotube (or PVOH) long axis 5 ; where τ, θB and are the azimuthal angle, Bragg angle and a variable, respectively. Lorentzian curves in Figure S8 are well reproduced for Lorentzian functions to the power 1.5 in direct space ( 3 2 ⁄ ), so that; with, with the corresponding orientational distribution function described as The crystallite size in the DW Ge-INTs/PVOH composite fiber (ϕDW Ge-INT = 3.8%) reported in Figure 1 was compared that obtained from a diffraction experiment on a conventional, commercial PVOH fiber reference ( Figure S9).

Figure S9
Two dimensional wide angle X-ray scattering pattern of a commercial PVOH fiber Kuralon 1239, manufactured by Kuraray Co. Ltd.

Mechanical modelling equations, tabulated data and healed composite fiber stress-strain curves
The tensile stiffness of double-walled aluminogermanate imogolite nanotube (DW Ge-INT)/polyvinyl alcohol (PVOH) composite fibers can be predicted using the well-known rule-of-mixtures (RoM). However, when the reinforcing components are anisotropic, additional efficiency factors are required to take into account orientation and stress transfer variations. Krenchel's modified RoM equation is given below: , ( S12) where θ is taken from the azimuthal curves at Q = 0.6, and lDW Ge-INT and D are DW Ge-INT length (c.a. 85 nm) and diameter (c.a. 4.3 nm). 8 Gm is the shear modulus of the matrix in GPa (ca. 1.7 GPa for PVOH), 9 and KR is a constant equal to 1 for cylinders in shear lag models. 10 However, when Equation S9 was used, fitting a single semi-crystalline PVOH modulus (10-30 GPa) 11 , there was a poor fit to the data. Additional consideration of the varying crystalline/amorphous proportions was required to gain a good fit. The crystalline to amorphous content in composite fibers was determined via differential scanning calorimetry, Figure S7. Krenchel's model was then adapted as follows: where ϕm.a, ϕm.c are volume fractions of amorphous and crystalline PVOH matrix, and Em.a, Em.c are the moduli of amorphous and crystalline PVOH, respectively. Assuming, where Vf, Vm.a and Vm.c are volume fractions of imogolite reinforcement, amorphous matrix and crystalline matrix, respectively.