49
Comment:

4048

Deletions are marked like this.  Additions are marked like this. 
Line 1:  Line 1: 
#format jsmath  
Line 3:  Line 4: 
[[attachment:CNTE.zip  CNTE.zip ]]  . [[attachment:CNTE.zip  CNTE.zip ]] . . . . [[attachment:FD.zip  FD.zip ]] . . . . [[attachment:NN.zip  NN.zip ]] Pure carbon nanotubes exhibit '''superlubricity'''  approximately ZERO friction between neighboring tubes in a bundle. In 2013, Zhang et. al. published a paper on [[ https://www.researchgate.net/profile/WZ_Qian/publication/258253770_Superlubricity_in_centimetreslong_doublewalled_carbon_nanotubes_under_ambient_conditions/links/0046353390b48ed61f000000.pdf  carbon nanotube superlubricity ]] that measured the intershell sliding force of a 1 centimeter doublewall carbon nanotube (DWCNT). Three diameters were measured, and the tiny pullout force matched theory, pa function of outer tube diameter. [[ http://oatao.univtoulouse.fr/4770/1/Laurent_4770.pdf  Laurent et. al. ]] estimates that the inner tube diameter is 0.34 nM ( $ d_{ss} $ ) less than the outer tube diameter, and that DWCNT density (g/cm³) is: $ d_{MW} = 6084 { \Large { ( d_{out} ~  ~ d_{ss} ) \over { d_{out}^2 } } } $ with $ d_{out} $ and $ d_{ss} $ in nanometers. I added my own estimations for perfect hexagonally close packed tube density, tubes/m² $ = \sqrt( 3 ) / 2 D^2 = 0.866 / D^2 $ The pullout pressure $ P = 866 F / D^2 $ MPa if F is nanonewtons and D is nanometers. Results: <2> Zhang et. al.  <2> Laurent et. al   Diameter  Pullout   Inner  Density  Tubes  Pullout  Strength   nm  Force nN   nm  kg/m³  / m²  Pressure  Kyuri   2.73  1.37   2.39  1951  1.16e17  159 MPa  81.5   2.93  1.47   2.59  1835  1.01e17  148 MPa  80.7   3.26  1.64   2.92  1672  8.10e16  134 MPa  80.1  These strengths '''for pure, perfect DWCNT''' are less than 0.2% of the minimum strength needed for a space elevator, and 2% of the strength of [[http://www.torayca.com/en/download/pdf/torayca_t1100g.pdf  Torayca 1100G carbon fiber]]. Furthermore, given these pullout forces, which will be unevenly distributed in real atomically imperfect materials, the '''stretch will not recover'''; these are not spring forces, but disassembly forces. After the material slides apart, it will not go back together, the hysteresis is unity and the creep is unlimited. This is weak taffy, not a strong elastic material like kevlar or carbon fiber, or even a weaker but low creep material like piano wire. {{attachment:ZhangCNT.png   width600 }} The situation is grim but not completely hopeless. In [[ https://doi.org/10.1557/opl.2015.251  CNT fibers  yarns between the extremes ]], Dr. Thurid Gspann et. al. suggest that defects create loadsharing crosslinks between tubes, though they reduce tube strength from the theoretical 100 GPa by 30% to 70%. Even with the theoretical "best defect" maximum of 70 GPa, and a density of 1700 kg/m, this '''theoretical''' atomicprecision macromaterial will have a strength of 41 Myuri, less than the 48 Myuri (derated by 40% to 34 Myuri) material assumed by the [[ https://www.worldcat.org/oclc/871183396  2013 Space Elevators assessment ]]. If 40 Myuri is potentially possible with '''perfect "precisiondefect" CNT''' (extrapolated from current knowledge), there ''may be'' an entirely different atomicallyperfect 3D material structure with zero hysteresis and '''50 Myuri''' strength. '''''May'' be'''; in 2017, we do not have a scintilla of a clue how to do that. Indeed, these may be pseudolifelike complex nanostructures that can repair and grow themselves under tension. The details are far beyond our current understanding and technological imagination; enough for a second rate science fiction thriller, but not for practical design. Space elevators have assumed diamondlike crystal tethers since the 1970s, and carbon nanotube tethers since the 1990s. The materials necessary have not yet been discovered, or even imagined in analyzable detail. 
CNTE
Pure carbon nanotubes exhibit superlubricity  approximately ZERO friction between neighboring tubes in a bundle. In 2013, Zhang et. al. published a paper on carbon nanotube superlubricity that measured the intershell sliding force of a 1 centimeter doublewall carbon nanotube (DWCNT). Three diameters were measured, and the tiny pullout force matched theory, pa function of outer tube diameter.
Laurent et. al. estimates that the inner tube diameter is 0.34 nM ( d_{ss} ) less than the outer tube diameter, and that DWCNT density (g/cm³) is:
d_{MW} = 6084 { \Large { ( d_{out} ~  ~ d_{ss} ) \over { d_{out}^2 } } } with d_{out} and d_{ss} in nanometers.
I added my own estimations for perfect hexagonally close packed tube density, tubes/m² = \sqrt( 3 ) / 2 D^2 = 0.866 / D^2 The pullout pressure P = 866 F / D^2 MPa if F is nanonewtons and D is nanometers. Results:
Zhang et. al. 

Laurent et. al 

Diameter 
Pullout 

Inner 
Density 
Tubes 
Pullout 
Strength 
nm 
Force nN 

nm 
kg/m³ 
/ m² 
Pressure 
Kyuri 
2.73 
1.37 

2.39 
1951 
1.16e17 
159 MPa 
81.5 
2.93 
1.47 

2.59 
1835 
1.01e17 
148 MPa 
80.7 
3.26 
1.64 

2.92 
1672 
8.10e16 
134 MPa 
80.1 
These strengths for pure, perfect DWCNT are less than 0.2% of the minimum strength needed for a space elevator, and 2% of the strength of Torayca 1100G carbon fiber. Furthermore, given these pullout forces, which will be unevenly distributed in real atomically imperfect materials, the stretch will not recover; these are not spring forces, but disassembly forces. After the material slides apart, it will not go back together, the hysteresis is unity and the creep is unlimited. This is weak taffy, not a strong elastic material like kevlar or carbon fiber, or even a weaker but low creep material like piano wire.
The situation is grim but not completely hopeless. In CNT fibers  yarns between the extremes, Dr. Thurid Gspann et. al. suggest that defects create loadsharing crosslinks between tubes, though they reduce tube strength from the theoretical 100 GPa by 30% to 70%. Even with the theoretical "best defect" maximum of 70 GPa, and a density of 1700 kg/m, this theoretical atomicprecision macromaterial will have a strength of 41 Myuri, less than the 48 Myuri (derated by 40% to 34 Myuri) material assumed by the 2013 Space Elevators assessment.
If 40 Myuri is potentially possible with perfect "precisiondefect" CNT (extrapolated from current knowledge), there may be an entirely different atomicallyperfect 3D material structure with zero hysteresis and 50 Myuri strength. May be; in 2017, we do not have a scintilla of a clue how to do that. Indeed, these may be pseudolifelike complex nanostructures that can repair and grow themselves under tension. The details are far beyond our current understanding and technological imagination; enough for a second rate science fiction thriller, but not for practical design.
Space elevators have assumed diamondlike crystal tethers since the 1970s, and carbon nanotube tethers since the 1990s. The materials necessary have not yet been discovered, or even imagined in analyzable detail.