Bidirectionally promoting assembly order for ultrastiff and highly thermally conductive graphene fibres

Macroscopic fibres assembled from two-dimensional (2D) nanosheets are new and impressing type of fibre materials besides those from one-dimensional (1D) polymers, such as graphene fibres. However, the preparation and property-enhancing technologies of these fibres follow those from 1D polymers by improving the orientation along the fibre axis, leading to non-optimized microstructures and low integrated performances. Here, we show a concept of bidirectionally promoting the assembly order, making graphene fibres achieve synergistically improved mechanical and thermal properties. Concentric arrangement of graphene oxide sheets in the cross-section and alignment along fibre axis are realized by multiple shear-flow fields, which bidirectionally promotes the sheet-order of graphene sheets in solid fibres, generates densified and crystalline graphitic structures, and produces graphene fibres with ultrahigh modulus (901 GPa) and thermal conductivity (1660 W m−1 K−1). We believe that the concept would enhance both scientific and technological cognition of the assembly process of 2D nanosheets.


Measurement of thermal conductivity of graphene fibres and aerogel fibres.
The thermal conductivities of graphene fibres and macroscopic graphene structures are measured by an optimized steady-state electrical heating method in a vacuum chamber [2][3][4] .In contrast to most studies where two electrodes are used, we here suspended a single fibre between four copper blocks which simultaneously served as heating sinks and electrodes.A Keithley 2611B source meter is used to supply direct current and to measure the voltage drop across the middle two electrodes by a standard four-wire method.This modified steady-state electrical heating method eliminates contact resistance, enabling much more reliability of testing results.The sample chamber is continuously evacuated by a molecular pump to maintain a high vacuum environment (~10 4 Pa) in order to eliminate convective heat transfer.When a direct current fixed on the suspended fibre, temperature will increase due to the Joule heating effect and be controlled lower than 60 o C.An infrared camera (FLIR T630sc) with a close-up lens is used to measure the temperature profile along with the fibre through a zinc selenide viewport (Supplementary Fig. 27).Hence, the thermal conductivity of the measured fibre is calculated as: where, κ is the thermal conductivity, U and I are the voltage and current measured across the middle two copper electrodes, L is the half-length between the middle two contacts.A c is the cross-section area of the fibre.To is the temperature at the middle point of the measured fibre and Ta is that at an edge point.
The thermal conductivity of graphene fibres was further examined by a T-type method, which is suitable for thin fibres with diameter of 5-7 μm 5 .A Platinum hot wire suspended on two heat sinks was served as temperature sensor and one end of GF was attached to the centre of the hot wire, while the other end was linked to a heat sink.The sample chamber was continuously evacuated by a molecular pump to maintain a high vacuum level of 10 -4 Pa.The temperature of the sample holder was steadily controlled by temperature controller (Oxford Instrument, ITC503) with an accuracy of ±0.1 K.The measurement system consists of the sample, a standard resistance, a high accuracy constant power supply (Advantest R6243), and two high accuracy digital meters (Keithley 2002).
The constant power supply provides direct current and the digital meters were used to detect the voltages on sample and standard resistance.When the DC current is imposed on the hot wire without the fibre, a parabolic temperature distribution is built.After attaching the graphene fibre to the hot wire, heat was partly transported from the hot wire to the fibre and the temperature distribution became dual-arch.Comparing the average temperature change of hot wire before and after the attachment of graphene fibre, the thermal conductivity can be extracted, where  ℎ and   are the thermal conductivities of the hot wire and the graphene fibre, respectively. ℎ and  ℎ are the cross section and length of the hot wire, respectively. ℎ,1 and  ℎ,2 are the lengths of the left and right part of the hot wire, respectively.  and   are the cross section and length of the graphene fibre, respectively.∆  is the average temperature rise of the hot wire determined from the resistance change.  =  ( ℎ  ℎ ) ⁄ is the volumetric heat generation rate of the electric current heating. and  are the applied current and voltage, respectively.In the measurements, a platinum wire (99.99%,Alfa Aesar) with diameter of 25 μm is used as hot wire.
Before adhering the test sample, the physical properties of platinum hot wire were calibrated applying the DC heating method.The temperature coefficient of resistance and thermal conductivity of hot wire are measured in advance by   = ∆ ( 0 ∆) ⁄ and  =  ℎ 2   (12∆  ) ⁄ , respectively.
The measured average temperature coefficient of resistance of platinum hot wire is 0.0037 K -1 in the range of 273-298 K and the thermal conductivity of platinum hot wire is 77.2 W m -1 K -1 at 298 K.

Calculation of microvoids in graphene fibres.
The parameters of microvoids were calculated by Ruland's streak method with Gaussian distribution function 6,7 .
where, Bπ/2(s) is the integration breadth along azimuthal scan, s is the scattering vector  = 2 sin   ⁄ , Beq is the misorientation angle representing the preferred orientation of the microvoids and L is the microvoid length.
The value of L and Beq can be obtained from the intercept and slope of the  2 ~2   2 ⁄ 2 () plot defined in the above equation.With the approximation, we finally obtain where, Inserting the calculated values of L and Beq, the number of microvoids, n, and the average chord length in the cross-section of microvoids or diameter for short, lp, can be calculated.Then the total volume of microvoids V can be approximately be evaluated by  ∝   2 .

Simulation of sheet arrangement in the multiple shear field.
We performed a computational fluid dynamics (CFD) simulation to analyse the effect of rotating angular velocity on graphene sheet arrangement in the multiple shear-flow field 8 .The geometry parameters and the density/dynamic viscosity of graphene oxide solution were considered according to experimental condition.Shear stress transport (SST) k-omega turbulence model belonging to the family of Reynolds-averaged Navier-Stokes (RANS) two-equation model is adopted to depict the effect of turbulent flow conditions 9 .The coupled scheme is utilized to address the pressure-velocity coupling for the discretized form of the Navier-Stokes system, and the Green-Gauss cell based method is used for gradients estimation 10 .

Simulation of fibres formation.
We conducted a two-dimensional (2D) coarse-grained molecular dynamics (CGMD) simulation, using the stacking patterns of graphene chains to represent the cross-sectional shrinkage.
Subdomains containing axial and radial atoms in graphene are gathered into beads with the equal mass.Adjacent beads are connected by bonds, and the balanced distance  b is set to 2 Å .The balanced angle α between adjacent bonds is set to 180°.Utilizing the bond energy in the model to be equal to its corresponding continuous medium stretch energy, we obtained the tensile stiffness where the parameters σ and ε are determined by fitting the balanced inter-layer spacing and cohesive energy, respectively.The simulated parameters are shown in Supplementary Table 1.The simulation is performed utilizing the large-scale atomic/molecular massively parallel simulator (LAMMPS) 12 .
To simulate the formation process of fibres, we compress the graphene chains with circular constraint at 300 K until the layer spacing reaches equilibrium (circular section).The Langevin thermostat was used to control the temperature.

Crystalline model of graphene fibres.
TEM images of the axial direction reveal bundles of crystalline domain in the fibre and single crystallites in a graphitic bundle (Supplementary Fig. 14b-d).We then proposed a crystalline model and key structural factors of graphene fibre as schemed in Supplementary Fig. 14a.Generally, graphene fibre consists of giant graphene sheets with a macro-structural factor of density (ρ); these giant graphene sheets pile into continuous graphitic bundles with misoriented angle (α) and calculated orientation degree (f); perfectly stacked sheets in a bundle form single graphitic crystallites with three-dimensional crystalline size, including thickness (Lc), axial length (La∥), and transverse length (La⊥).Based on the proposed crystalline model and crystalline structural factors, we analysed the crystallinity of the fabricated graphene fibres systematically.Optimized concentric texture at ω=100 (×2π/60) rad/s is in favour to form ordered sheet-arrangement in both axial and transverse direction in final shrinked graphene fibre, which results in an improved order parameter (0.93) and enlarged crystallite sizes (Lc=68.5 nm, La ∥ =236.6 nm, La ⊥ =114.1 nm).The MSW strategy improves the sheet-arrangement order in the fibre cross-section compared to previously reported graphene fibres, thus distinctly facilitates the growth of graphitic crystallites along the thickness (Lc) and transverse length (La⊥).Concentric graphene fibre prepared at ω=100 (×2π/60) rad/s has increase rate of Lc, La⊥, and La∥ reaching 235%, 74%, and 31% compared to these without MSW spinning, respectively (Supplementary Fig. 16d).
according to the angle energy in the model to be equal to its corresponding continuum bending energy, we determined the bending stiffness  b Among them, Y and D are the Young's modulus and bending stiffness of graphene oxide, respectively; t is the thickness of graphene, and l is the length related to the graphene size L. We set  = 0.05, and assume that the strain and curvature do not vary with the change of the axial position as the axial size in the range of l.Y is set to 200 GPa and D is set to 2  B  since graphene oxide are quite flexible because of functional groups11 .t is set to 4 Å and L is set to around 10 nm.For the interaction between nonbonded beads, we used the Lennard-Jones 12-6 potential function,  = 4[(/) 12 − (/) 6 ] ,