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A summary of all the conductance data, along with attenuation factors and estimated break-off distances, is shown Table 2.5.

Molecule High Conductance (nS) Estimated Break-Off (nm) Low Conductance (nS) Estimated Break-Off (nm) Spartan Au-Au (nm) BDMT 4.14 ± 0.58 1.44 ± 0.33 0.3 ± 0.06 1.62 ± 0.28 1.4 3Ph3 2.01 ± 0.32 1.43 ± 0.28 0.12 ± 0.02 1.55 ± 0.21 1.6 4Ph4 1.21 ± 0.19 1.50 ± 0.31 0.08 ± 0.02 1.86 ± 0.29 1.9 6Ph6 0.82 ± 0.18 1.70 ± 0.31 0.04 ± 0.01 1.84 ± 0.22 2.2 β (Å-1, TB) 0.12 0.13

Table 2.5 Summary of the conductance data (attenuation factor quoted from through bond data).

As can be seen the break-off distances correspond well with the Spartan® estimated Au-Au separations, and generally decrease with the length of the molecule. Furthermore, the estimated break-off distance for each of the higher conductance groups is lower than that of each corresponding lower conductance group; this result fits well with the theory of Haiss et al. regarding multiple conductance groups69 (see section 2.1.1). According to this theory the higher conductance group is observed when the molecule is adsorbed to a step edge on the gold surface; in such circumstances the tip-substrate gap will be smaller than in the corresponding case when the molecule is adsorbed at a top site. It follows that the estimated break-off distance would be predicted to be shorter for the higher conductance groups, as is the case in the study presented herein. However, the low conductance values are smaller than expected. Indeed, the value determined for 6Ph6 is much lower than that reported by Leary et al.,56 although the conductance value determined at the elevated set point current is in good agreement with their study; this suggests that they actually missed the ‘A’ group and recorded the ‘B’ group.

76 15 20 25 30 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 ln

(

)

Through Bond Length (nm)

Figure 2.26 Comparison of the length dependence data in this work (black and red lines) to that of Haiss et al.76 for various alkanedithiols.

The attenuation factors of both the high and low conductance groups are also exceptionally small in comparison to previous examples76 involving a tunnelling mechanism (Figure 2.26); such small values are usually characteristic of hopping mediated charge transport.

As discussed in section 2.1, studies of the relatively straightforward alkanedithiol series of molecules have yielded several conflicting values for their attenuation. Haiss et al. have systematically studied the conductance of single molecules of alkanedithiols tethered to gold electrodes; the molecules in this study ranged from 3 to 12 methylene units.76 They found that for molecules containing 8 or more methylene units the conductance decays exponentially with length, which is in good agreement with previous studies. Contrastingly, for shorter molecules containing less than 8 methylene units the attenuation factor decreases with decreasing length, approaching length-independence for molecules containing less than 5 methylene units (Figure 2.27). Haiss and coworkers then performed a theoretical study and noted that an image charge dependent value of the effective hole mass results in quantitative agreement with the experimental results. The data in the current study appears to mirror the latter result, however since the molecules in this work are much longer the same argument cannot be applied.

77

Figure 2.27 Logarithm of conductance of the three fundamental single molecule conductance groups measured for alkanedithiols between gold contacts as a function

of the number of CH2 groups (N) at Ubias = 0.6V. Reproduced by permission of the

PCCP Owner Societies.76

The contribution of hopping mediated charge transport in this system appears to fit the experimental observations; this mechanism would see the benzene ring acting as a ‘hopping site’. Charge transport through the molecule would require tunnelling through the first alkyl chain, followed by localization on the benzene ring for a finite time, before tunnelling through the second alkyl chain (Figure 2.29). The orbital densities and energies discussed in section 2.5 fit well with this mechanistic description; the higher energy orbitals located on the alkyl chains function as tunnelling barriers, with the lower energy orbitals on the benzene ring acting as the hopping site. Leary et al. have investigated analogues of 6Ph6 in which substituents are introduced to the benzene ring (see section 1.6); they found that the closer the HOMO energy of the aromatic unit is to the Fermi level of gold, the higher the conductance. Whilst this was used as evidence for these molecules acting as double tunnelling barriers, the relationship between the energy of the aromatic HOMO and conductance also provides evidence for a hopping contribution to the mechanism of charge transport.

78

Figure 2.28 Charge transport though 6Ph6 via the hopping mechanism.

Since it has already been established that charge transport in the current system is HOMO mediated, it follows that hole, as opposed to electron, transfer is responsible. Similar charge hopping has previously been proposed for DNA.77 Ratner and co- workers have reported a detailed study of the efficiency of hole migration along sequences of stacked nucleobases with different numbers of adenine-thymine (AT) and guanine-cytosine (GC base pairs).78 They propose a hopping model, similar to the one described in this work, in which AT base pairs act as tunnelling barriers over which the transport takes place via incoherent hopping, with the charge residing on G bases (G has the lowest oxidation potential and hence provides the best hole hopping sites).