4.2
Molecular Conductors
What are the necessary requirements for constructing a molecule-based conductor ?
1.
2.
3.
Molecular Conductors – 3 types
Radical Ion Conductor
Neutral Radical Conductor
Closed Shell Conductor
•
Composed of donor (D)
and acceptor (A)
molecules
•
Composed of a single
type of uncharged
radical molecule
•
Composed of a single
type of (uncharged)
closed shell molecule,
but part of the molecule
acts as a donor (D) and
part as an acceptor (A)
•
Intermolecular charge
transfer is required
•
Charge transfer is not
required
•
Intramolecular charge
transfer is required
•
Any level of band filling •
is possible
Only ½-filled bands are
possible (for simple 1D
stacks)
•
Any level of band filling
is possible
e.g., [TTF+][TCNQ-]
S
S
S
S
e.g., PLY
e.g., Ni(tmdt)2
S
S
S
S
S
S
S
S
S
Ni
TTF
(tetrathiafulvalene)
NC
CN
NC
CN
S
PLY
(phenylenyl)
S
S
Ni(tmdt)2
(tmdt = trimethylenetetrathiafulvalenedithiolate)
TCNQ
(tetracyanoquinodimethane)
Section 4.2 - 1
Radical Ion Conductors
•
2 molecular components:
Donor (D)
•
Electron transfer must occur:
•
This redox process relies on the compatibility of the frontier molecular orbitals.
D+
•
and
and
Acceptor (A)
A
-•
Q. What does this imply?
Charge Transfer (CT) Salt...e.g., TTF-TCNQ
Section 4.2 - 2
Bechgaard Salts
N.B. not 1:1
• A well-known example of a
RIC.
•
TMTSF is the donor
•
PF6 is the acceptor
How do you design a RIC or CT salt ?
Q.
What do Bechgaard salts have in common with TTF-TCNQ?
1. The donor molecules have similar molecular structures
S
S
TTF
S
Se
Se
S
Se
Se
TMTSF
HOMO
HOMO
3 b1u
2. The crystal structures both involve π-stacking such that a column of donors is
formed.
3. The heteroatoms (S and Se) have very diffuse p-orbitals and π-stacking overlap is
expected to be significant.
Section 4.2 - 3
Some RIC and CT design principles
•
The radical ions must have an extended π-system such that the SOMO is not strongly
localized.
i.e., prevent formation of Mott insulator
•
The radical ions must STACK in the solid state such that there is overlap between the
π-systems of neighboring molecules. → BAND FORMATION!
Q.
What happens if the stacking is –D-A-D-A- ?
Q.
How do you design a RIC or CT salt that stacks: -A-A-A-A-D-D-D-D- ?
HOMO and LUMO of TTF and TCNQ
S
S
NC
CN
S
S
NC
CN
TTF
HOMO
TCNQ
D2h
3 b1u
LUMO
3 b2g
These are orthogonal orbitals. Therefore, no bonding-type overlap is possible.
Section 4.2 - 4
Partial Charge Transfer: [TTF][TCNQ] & [TTF][Br]x
[TTF][TCNQ]
[TTF][Br]
σ = 104 Scm-1 @ 58 K
σ = 10-11 Scm-1
Q. Why is the conductivity Complete charge transfer
so high?
gives exactly one unpaired
electron and one (+)ve
charge per TTF molecule
[TTF][Br]0.7
σ = 102 Scm-1
Complete charge transfer
give exactly 0.7 unpaired
electrons and 0.7 (+)ve
charges per TTF molecule
A.
Why does partial charge transfer matter?
[TTF][TCNQ] – a semi-metal
•
Much of the older literature dealing with [TTF][TCNQ] states that organic CT salts
with very high conductivities are organic metals.
•
This is not strictly true since none of these materials possess a single partially filled
energy band. CT salts are either semiconductors (or insulators) or semi-metals.
"HOMO"
band of
TTF
"LUMO"
band of
TCNQ
"HOMO"
band of
TTF
before CT
"LUMO"
band of
TCNQ
after CT
Source: J. B. Torrance,
Ann.N.Y.Acad.Sci., 1978, 210.
Section 4.2 - 5
Some well-known donors and acceptors that generate radical cations and radical anions
for RICs and CT salts:
DONORS
R
X
X
R
X
X
Y
X
X
Y
S
S
Se
R
X
X
R
X
X
Y
X
X
Y
S
S
Se
1.
2.
3.
4.
5.
X
R
S
H TTF
Se H TSF
S Me TMTTF
Se Me TMTSF
Te H TTeF
6. X = S HMTTF
7. X = Se HMTSF
X
8. S
9. S
10. Se
11. S
Y
S
O
Se
Se
12. DMET
BEDT-TTF
BEDO-TTF
BEDS-TSF
BEDS-TTF
S
S
S
S
13. MDT-TTF
ACCEPTORS
R
R
NC
CN
S
S
S
NC
CN
S
S
S
S
Ni
S
S
S
N
NC
R
R
14. R = H TCNQ
15. R = Me 2,5-DMTCNQ
CN
N
16. Ni(dmit)2
17. R = H DCNQI
18. R = Me 2,5-DMDCNQI
Historical Perspective
Year
1954
1962
1973
1974
1975
1978
1979
1980
1982
1983
1984
1986
1987
1988
…
Discovery
Perylene-bromide salt; first conducting molecular compound; σRT = 1 Scm-1
Semiconducting salts of TCNQ reported
TTF-TCNQ prepared; first organic metal; σRT = 500 Scm-1; TM-I = 53 K
TSF-TCNQ prepared; σRT = 700-800 Scm-1; TM-I = 40 K
HMTSF-TCNQ; TM-I < 1 K ... increased dimensionality (Se...N contacts)
HMTSF-2,5-DMTCNQ; TM-I suppressed under pressure; σ1K,10kbar = 105 Scm-1
TMTTF-tetrahalo-p-benzoquinones; no TCNQ!
(TMTSF)2 X salts; organic superconductivity @ 0.9 K; 12 kbar for X = PF6@ 1.4 K; ambient P for X = ClO4(BEDT-TTF)2 ClO4 (1,1,2-trichloroethane)0.5; metallic @ T = 298 – 1.4 K
(BEDT-TTF)2 ReO4; superconductor Tc = 1.4 K @ 4 kbar
β-(BEDT-TTF)2 I3; superconductor
Tc = 1.4 K @ ambient pressure
[TTF][Ni(dmit)2]2; superconductor
Tc = 1.6 K @ 7 kbar
Cu(2,5-DMDCNQI)2; metallic σ3.5K = 5 x 105 Scm-1
κ-(BEDT-TTF)2Cu(SCN)2; ambient pressure superconductor @ 10.4 K
... you get the picture!
Section 4.2 - 6
The Big Picture
Neutral Radical Conductors – NRCs
•
By their nature, RICs and CT salts are either semi-metals or semi-conductors
•
NRCs, in principle, are capable of exhibiting truly metallic conductivity
•
To date, there are no molecular NRCs that display metallic conducting properties.
This is mainly due to the problems associated with ½-filled bands.
hex
N
N
N
N
S
S
S
S
NMBDTA
PLY
O
N
σRT = 0.2 Scm-1 @ 5 GPa
B
O
N
hex
spiro-PLY
σRT = 5 x 10-2 Scm-1 @ ambient pressure
RECALL: WHAT ARE THE PROBLEMS WITH ½-FILLED BANDS?
Section 4.2 - 7
Closed Shell Single Molecule Conductors
•
do not rely on intermolecular charge transfer (i.e., only one type of molecule required
in the solid).
•
are not neutral radicals
•
essentially, designed as charge transfer species wherein the D and A components are
both on the same molecule
S
S
S
S
S
S
S
S
S
Ni
S
S
S
Ni(tmdt)2
(tmdt = trimethylenetetrathiafulvalenedithiolate)
2
LUMO
ΔE
HOMO
-1
σRT = 4 x 10 Scm
ΔE ~ 0.1 eV
•
Displays metallic conductivity down to 0.6 K as a single component crystal
•
Correct classification is a semi-metal
Source: Tanaka et al., Science, 2001, 291, 285.
(SN)x - a lesson in 3-dimensionality
•
(SN)x has metallic conductivity
σRT ≈ 103 Scm-1
•
Becomes superconductive at low temperature
•
Unfortunately, the starting material S4N4 and intermediate
S2N2 are highly explosive and polymerization takes several
weeks
Q. Why doesn’t (SN)x succumb to Peierls type distortions?
Section 4.2 - 8
π*
S N
π
S N
FMO manifold
of -S=Nradical fragment
band structure
of 1D (SN)x
… but (SN)x isn’t a 1D system!
Section 4.2 - 9
Fermi Surfaces and the concept of Nesting
•
The Fermi surface is the constant-energy plot, in k-space, of the highest occupied
energy levels at absolute zero (T = 0).
•
It represents the junction between filled and empty levels at T = 0.
•
For systems with filled bands, there is no Fermi surface at all, so the concept only
applies to metals.
•
The Fermi surface is simply a constant-energy surface at E = EF.
•
For a 2D lattice (shown above), there will be two values of β in the two directions.
•
If βb = 0, then clearly the result is a series of uncoupled one-dimensional chains with
no dispersion along the X → M direction.
•
If βa = βb, then a square lattice results.
•
The area (volume in three-dimensions) of the first Brillouin zone enclosed by the
Fermi surface is proportional to the band filling.
Section 4.2 - 10
•
In a one dimensional system, the Fermi surface is actually just a set of point. For the
half-filled band, it is given by the two point ±2kF (see 3.12 below)
•
In three dimensions, drawing the Fermi surface can be rather difficult.
Section 4.2 - 11
•
The concept of the Fermi surface is most useful as a tool for understanding distortions
in solids. To understand this, the concept of “nesting” of the Fermi surface is needed.
•
When a section of the Fermi surface can be moved by a vector q such that it is exactly
superimposed on another section of the surface, then the Fermi surface is nested by
this vector q.
•
The Fermi surface shown in Figure 13.6(a) is nested by an infinite set of vectors, two
of which are shown below.
•
A more complex example is shown in Figure 3.19. The dispersion behaviour of two
bands of a two dimensional structure are shown, along with the Fermi surface. The
inner two pieces of the Fermi surface come from the lower energy band and the outer
pieces from the higher energy band.
•
Although there are two distinct pieces of the Fermi surface that are nested, the nesting
vector is identical for each.
Section 4.2 - 12
•
The utility of these descriptions lies in the insights provided into electronically driven
geometrical instabilities.
•
The potential associated with the distortion may be written as
V = Vq exp(i q · r) + V-q exp(-i q · r)
where q is a reciprocal lattice vector
•
The nature of q defines the way the structure changes.
•
E.g., for a simple one-dimensional case, if q = π/a , then a distortion that leads to a
doubling of the unit cell in this direction is indicated (i.e., dimerization.)
MEANING
If there is a single vector q that nests the Fermi surface, then there is a single distortion
that can lower the energy of the system.
TAKE HOME MESSAGE
In a 1D system, it is easy to find single vector q that nests the Fermi surface, since the
Fermi surface is simply a set of points.
Adding multiple dimensions (2D or 3D) can reduce the possibility of finding a vector q
that nests the Fermi surface…
...see, for example, the dispersion curves for two interacting chains...
…in other words, a distortion that might be favoured (i.e., lower the energy) in one
direction might give rise to unfavourable interactions (i.e., raise the energy) in another.
Section 4.2 - 13