Functional inks based on layered materials and printed layered materials

1. An ink comprising a carrier liquid with a dispersion of flakes derived from a layered material, the ink having a concentration of said flakes at a level of at least 0.01 g/L, wherein the thickness of each flake depends on the number of layers of the layered material in the flake, and wherein the thickness distribution of the flakes includes:

at least 20% by number of single layer flakes;

at least 40% by number cumulatively of single, double and triple layer flakes; or

not more than 40% by number of flakes having ten or more layers.

2. The ink according to claim 1 wherein the thickness distribution of the flakes includes at least 60% by number of single layer flakes.

3. The ink according to claim 1 wherein the thickness distribution of the flakes includes at least 90% by number cumulatively of single, double and triple layer flakes.

4. The ink according to claim 1 wherein the thickness distribution of the flakes includes at least 80% by number cumulatively of single and double layer flakes.

5. The ink according to claim 1 wherein the thickness distribution of the flakes includes not more than 5% by number of flakes having ten or more layers.

6. The ink according to claim 1 wherein the layered material comprises one or more of graphene, a metal, NiTe 2 , VSe 2 , a semi-metal, WTa 2 , TcS 2 , a semiconductor, WS 2 , WSe 2 , MoS 2 , MoTe 2 , TaS 2 , RhTe 2 , PdTe 2 , an insulator, h-BN, HfS 2 , asuperconductor, NbS 2 , NbSe 2 , NbTe 2 , TaSe 2 , a topological insulator, a thermo-electric, Bi 2 Se 3 and Bi 2 Te 3 .

7. The ink according to claim 1 wherein the flakes have at least one lateral dimension, assessed as a number average, of at least 200 nm.

8. The ink according to claim 1 wherein the flakes have a footprint area, assessed as a number average, of at least 0.1 μm 2 .

9. The ink according to claim 1 wherein the carrier liquid is selected from one or more of water, alcohol, N-methylpyrrolidone, chloroform, benzene, toluene, di-chlorobenzene, iso-propyl alcohol, ethanol and other organic solvents.

10. The ink according to claim 1 further including one or more modifier to adjust the surface energy (y) of the ink and/or the viscosity (η) of the ink.

11. The ink according to claim 1 wherein the surface energy of the ink is in the range 30-55 mN·m −1 at 20° C.

12. The ink according to claim 1 wherein the viscosity of the ink is in the range 1-100 mPa·s at 20° C.

13. The ink according to claim 1 wherein the ink has a value for Z=1/Oh in the range 1-100, where Oh is the Ohnesorge number and Oh=(We) 1/2 /Re, where Re is the Reynolds number and We is the Weber number, Re=νρa/η and We=ν 2 ρa/γ, so that Oh=(we) 1/2 /Re=−η(γρa) 1/2

where ν[m/s] is the drop velocity, η [mPa s] is the viscosity of the ink, γ [mJm −2 ] is the surface energy of the ink, ρ [g cm −3 ] is the density of the ink, and a [μm] is the nozzle diameter of the inkjet printing apparatus.

14. The ink according to claim 13 wherein Z is in the range 1-14.

15. An ink consisting of at least 90 wt %, based on the weight of the ink, of:

a carrier liquid;

a dispersion of flakes derived from a layered material;

optionally, one or more surfactant;

optionally, one or more surface energy modifier; and

optionally, one or more viscosity modifier,

optionally, one or more dopants and nanomaterial additives,

the ink having a concentration of said flakes at a level of at least 0.01 g/L, wherein the thickness of each flake depends on the number of layers of the layered material in the flake, and wherein the thickness distribution of the flakes includes:

at least 20% by number of single layer flakes;

at least 40% by number cumulatively of single, double and triple layer flakes; or

not more than 40% by number of flakes having ten or more layers.

16. A printed layer obtained by printing using an ink comprising a carrier liquid with a dispersion of flakes derived from a layered material, the ink having a concentration of said flakes at a level of at least 0.01 g/L, wherein the thickness of each flake depends on the number of layers of the layered material in the flake, and wherein the thickness distribution of the flakes includes:

at least 20% by number of single layer flakes;

at least 40% by number cumulatively of single, double and triple layer flakes; or

not more than 40% by number of flakes having ten or more layers.

17. The printed layer according to claim 16 wherein the printed layer is electrically conductive and/or optically transmissive.

18. The printed layer according to claim 16 wherein the printed layer has a sheet resistance R s of not more than 10 3 kΩ/square.

19. The printed layer according to claim 16 wherein the printed layer has an optical transmittance of not less than 80%.

20. The printed layer according to claim 16 wherein the carrier mobility of the layer is at least 10 cm 2 V −1 s −1 .

21. The printed layer according to claim 16 wherein the printed layer is formed on a flexible substrate.

22. A device incorporating at least one printed layer obtained by printing using an ink comprising a carrier liquid with a dispersion of flakes derived from a layered material, the ink having a concentration of said flakes at a level of at least 0.01 g/L, wherein the thickness of each flake depends on the number of layers of the layered material in the flake, and wherein the thickness distribution of the flakes includes:

at least 20% by number of single layer flakes;

at least 40% by number cumulatively of single, double and triple layer flakes; or

not more than 40% by number of flakes having ten or more layers, the device being an electronic device, an optoelectronic device, an optical device, a thermal device, an energy device, and/or a radio frequency device.