Configurational
Entropy as a function
of Material Dimensions:
A theory for strong
ropes
Tao Zheng
Supervisor: Professor Harry Bhadeshia
Richard Kemp
Outline
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space elevator.
are carbon nanotube ropes ideal
materials for space elevator project?
1 Configurational entropy
2 Stored energy and energy release rate
3 size-dependence of materials strength
Conclusion
D.V.Smitherman 2005
High strength > 62.5 GPa
Lightweight
Density
Tensile
strength
Carbon
nanotubes
1300 kg m-3
Steel
Kevlar
7900 kg m-3
1440 kg m-3
130 GPa
< 5 GPa
3.6 GPa
Bradley C. Edwards 2004
Steven L.Mielke et al (2004)
Equilibrium defect density
dF
dSm
 0  Uv  T
dC
dC
Fromhold,Albert Thomas (1976)
Regular or ideal solution model
SM  R1  xln 1  x x ln x
Quasichemical solution model
S M   R1  x  ln 1  x x ln x
q 1  2x
 q  1  2 x 
1 

 Rz 1  x  ln
 x ln

1  x  q  1
2 
x q  1 


Lecture notes of Thermodynamics H
K D H Bhadeshia (2004)
Stored energy

1
1
U s   
2
2 E
2

Energy release rate
( sound velocity):
c 
E

strength 130 GPa
modulus 0.63 TPa
Stored energy
Energy
(J g-1)
release rate
(m s-1)
Dynamit
e
Nanotub
e
Bradley C. Edwards 2004
4650
6000
5420
21500
Different tensile strength value with
different ropes length.
length of ropes
tensile strength
the order of nm
about 100 GPa
6.04µm
39 GPa
6.77µm
35 GPa
10.99µm
21GPa
2000µm
1-2.4 GPa
Data from M.-F. Yu et al (2000); MinFeng et al (2000); Z. W. Pan et al (1999)
Conclusion
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1. By applying quasichemical solution model,
more accurate configurational entropy and
equilibrium defect density can be obtained.
2. Because of high strength and low density,
carbon nanotubes have quite high stored energy
and energy release rate which may make them
not very safe in engineering application.
3. Strength of nanotube ropes will decrease
sharply with increase of length of ropes.
Thank you!