An Electromechanical Approach to Understanding Binding

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An Electromechanical Approach to Understanding Binding Configurations in Single-Molecule Devices Roohi Ramachandran, Haipeng B Li, Wai-yip Lo, Andriy Neshchadin, Luping Yu, and Joshua Hihath Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b03415 • Publication Date (Web): 24 Sep 2018 Downloaded from http://pubs.acs.org on September 25, 2018

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An Electromechanical Approach to Understanding Binding Configurations in Single-Molecule Devices Roohi Ramachandran†, Haipeng B. Li†, Wai-Yip Lo‡, Andriy Neshchadin‡, Luping Yu‡, and Joshua Hihath†* †

Department of Electrical and Computer Engineering, University of California, 1 Shields

Avenue, Davis, California 95616, USA ‡

Department of Chemistry and the James Franck Institute, The University of Chicago, 929 E

57th Street, Chicago, Illinois 60637, USA *[email protected] ABSTRACT The configuration of the molecule-electrode contact region plays an important role in determining the conductance of a single-molecule junction, and the variety of possible contact configurations have yielded multiple conductance values for a number of molecular families. In this report we perform simultaneous conductance and electromechanical coupling parameter measurements on a series of oligophenylene-dithiol single-molecule junctions. These molecules show two distinct conductance values, and by examining the conductance changes, the electromechanical coupling, and the changes in the I-V characteristics coupled with a combination of analytical mechanical models and Density Functional Theory (DFT) structure calculations, we are able to determine the most probable binding configuration in each of the conductance states. We find that the lower conductance state is likely due to the thiols binding to each electrode at a gold top-site, and in the higher conductance state the phenylene π-orbitals interact with electrodes drastically modifying the transport behavior. This approach provides an expanded methodology for exploring the relationship between the molecule-electrode contact configuration and molecular conductance. KEYWORDS: Single-Molecule Conductance, Molecular Electronics, Break Junction, Binding Configuration, Electromechanical Properties 1 ACS Paragon Plus Environment

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Much progress has been made in the development and advancement of molecular electronic devices in recent years. This includes the development of several robust methods for measuring the conductance of a metal-molecule-metal junction, including single-molecule break junction (SMBJ) systems, electromigrated devices, conducting atomic force microscopy (C-AFM), and nanoparticle devices,1 as well as the determination of a wide range of both conventional and unique operational paradigms for devices, and novel transport phenomena.2-5 However, from a practical perspective, molecular devices are difficult to implement because there is a wide dispersion in the conductance values for most molecular devices, and many molecules display multiple conductance peaks.6-13 These issues have severely limited the prospects for technological implementations of molecular-electronic devices, and as such the underlying reasons for this conductance dispersion must be explored and understood in order to develop practical solutions. Theoretical works in this arena have suggested that this variety can be explained by differences in molecule-electrode binding configurations,11-16 but this hypothesis is difficult to test experimentally because the binding configuration is typically uncontrolled, and it is also difficult to determine the final configuration after the junction is formed.15-19 To overcome these issues, we apply a high-frequency (2 kHz) mechanical modulation to a single-molecule junction to extract the electromechanical coupling factor (known as the α-value) from the system to determine the most probable binding configurations.20 In this report we find two different sets of conductance values for the oligophenylene-dithiol molecular family, and by examining the electromechanical response of the system in each of the two cases, we are able to derive information about the atomic-level configuration of the molecule in each of the cases, and are able to demonstrate that the different conductance values do indeed correspond to different molecule-electrode contact configurations.

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To examine the binding configurations in oligophenylene-dithiol molecular junctions, we employ a modified SMBJ technique, as illustrated in Fig. 1a. In typical SMBJ experiments, one of the two electrodes is moved toward the second electrode until they make contact. The first electrode is then pulled away until the current drops below the detection limit (~1pA) of the current amplifier. The current is recorded during this process to obtain a current versus distance trace. This cycle is repeated and recorded thousands of times over the course of a single experiment.10, 21 In this case, in addition to this normal break junction cycle, a high-frequency (2 kHz), small amplitude (0.5 Å) sinusoidal mechanical modulation is applied to the tip. Because the current response to this mechanical signal depends critically on the stiffness of the various bonds in the electrode, molecule-electrode contact region and molecular backbone, it provides electromechanical coupling information about the device, which in turn allows contact and binding configurations to be deduced.20, 22 To see why this is the case, let us first begin with the current that is measured in a tunneljunction, which is given by I(z) = VGCe-βz, where V is the bias between the electrodes, GC is the contact conductance, β is the tunneling decay constant, and z is the distance between the electrodes. If this distance is then modulated by a sinusoidal signal (Aappl = A0 cos ωt), the total junction distance is given by z = z0 + A0 cos ωt. Next, by performing a Taylor expansion about z0 = L (where L = the molecular length) one obtains the following expression for the measured current: ≅ +

cos (1)

where Idc = I(L) = VGCe-βL. The second term in equation 1 gives the high-frequency current response to the applied modulation, =

. Normalizing this quantity by the DC current,


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Idc, and the amplitude of the applied modulation, A0, yields the quantity = the electromechanical coupling factor.20,

22

Since

= −

!

, which we call

= − , we might

expect the value of α to be equal to that of β. While this can be true when tunneling through vacuum or solvent, it is not typically the case for a single-molecule junction because the mechanical modulation is absorbed partially within the electrodes and partially over the tunneling length, depending on the relative mechanical stiffness of these regions.20 It is the crossdomain coupling between α and β and between the applied modulation (A0) and the actual modulation of the molecular tunnel-junction (Ajxn) that allows the configurations to be examined. In the absence of a molecular junction, the current versus distance traces obtained are smooth exponential decays with a slope of β and a constant amplitude for the high-frequency component (Fig. 1b, red curve). α is the amplitude of the high-frequency component of the current (Fig. 1b, blue curve). By adding several thousand curves of α as a function of conductance, we obtain a two-dimensional (2D) histogram showing the most probable values for conductance and α (Fig. 1c). In experiments conducted in a clean solvent (with no molecules present), no molecular junctions are formed, and we can see that α has a roughly constant value across the range of measured conductance levels.


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Figure 1: a, Schematic of the experimental setup depicting a 2P-DT molecule bound between two Au electrodes with a sinusoidal mechanical modulation applied to one electrode. b, Example of a conductance versus time curve showing no steps (red curve). The extracted high-frequency (f = 2kHz) component gives the current response to the tip modulation (grey curve), and the amplitude of this curve gives α (blue curve). c, 2D histogram of α versus conductance, constructed from thousands of curves similar to those shown in (b). d, Example conductance (red), conductance modulation (grey), and α (blue) versus time curves for a 2P-DT junction. e, 2D histogram of α versus conductance for 2P-DT showing a maximum at a conductance ≈ 9×10-3 G0 and α ≈ 1.1 nm-1. Alternatively, when molecules are present, the current versus distance traces display clear steps, which indicate the formation of a molecular junction. In these cases, the high-frequency component of the current no longer has a constant amplitude (Fig. 1d), and the resulting 2D histogram clearly shows the most probable values for both conductance and α (Fig. 1e), in contrast with the results from experiments conducted in a clean solvent (Fig. 1c).


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In addition to the biphenyl dithiol (2P-DT) shown in Fig. 1, we also study terphenyl dithiol (3P-DT) and quaterphenyl dithiol (4P-DT), which contain two, three, and four phenyl ringsrespectively (see SI Fig. S1). This allows us to see how our measurements vary with molecular length, which grants further insight into the electronic and mechanical characteristics of these junctions. Figure 2 shows a 2D histogram obtained for a quaterphenyl dithiol (4P-DT) junction for a single conductance value. By projecting the total number of counts onto the axes, we obtain 1D histograms for both α and conductance, and thus can determine the most probable value for each (Fig. 2b,c). We repeated these measurements for all three molecules. By plotting the conductance values versus molecular length on a semi-logarithmic plot and finding the slope we find that β = 5.9 ± 0.3 nm-1 for this set of conductance values. We note that this β-value is higher than what is found in self-assembled monolayers of mono-thiol phenyls using C-AFM or in the diamine case (~4 nm-1),21, 23, 24 which are more similar to the β-value found for the higher conductance state discussed below (β ~4.3 nm-1). Moreover, since the α-values are on the order of ~1.0 nm-1, we can also see that α and β are not equivalent for these molecules, which is consistent with previous measurements performed on the alkanes.20


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Figure 2: a, 2D histogram of α versus conductance for 4P-DT. b,c, The counts from (a) can be projected onto each axis to get a histogram from which we can determine the most probable value for α (b) and conductance (c). The pink dashed lines indicate the peak values. d, Plot of conductance (log(G/G0)) versus molecular length for 2P-DT, 3P-DT, and 4P-DT. Error bars represent the standard error of conductance with n=6 experiments for each molecule. To examine the differences between the α and β values, we model the entire molecular junction as a series of springs.20 The spring constant of a Au-Au bond (~8 N/m)25 is significantly lower than those of either the phenyl rings or the carbon-carbon bonds that comprise the


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molecular backbone. The difference between α and β is caused by this difference in spring constants, as the majority of the applied modulation is absorbed by the gold contacts and so the measured junction modulation is only a small fraction of the total applied value. The value of the actual junction modulation, Ajxn, can be extracted from the relationship α/β = Ajxn/A0, and the electrode-molecule system can be modelled as three springs, kel, kME, and kPC. The first spring, kel, represents the combined spring constants of the two electrodes, "#$% =

"#$%% + "#$&% ; kel1 and kel2 are the individual electrodes and each may include a different number of

Au-Au bonds. The second spring kME represents the two molecule-electrode contact regions, with % % one or more Au-thiol bonds and one carbon-thiol bond on each side, "'( = 2"*+ + 2"+% . The

third spring kPC represents the phenylene chain, consisting of N phenyl rings and N-1 single carbon-carbon bonds between the rings, ",% = -". % + /- − 11"%, where kBz is the spring constant of a single benzene ring and kCC is that of a single carbon-carbon bond. Furthermore, as we know both the applied amplitude (A0) and the junction amplitude (Ajxn = AME + APC), we can also find Ael = A0 – Ajxn, and we can then derive the relationship: 234 56

8

8

8

8

= - 78 56 + 8 56 < + 78 56 − 8 56 < 99

:;

=>

99

(2)

Thus, by plotting the ratio of Ajxn/Ael as a function of the number of phenyl units (N) and finding the slope and intercept of the best-fit line, we can relate our experimental measurements to our theoretical spring model (Fig. 3c).


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Figure 3: a, Histograms of α for 2P-DT, 3P-DT, and 4P-DT, showing an increase in α with molecular length. Histograms scaled vertically for clarity. b, Plot of α versus N, the number of phenyl rings in the chain. c, Plot of the ratio of the junction and electrode amplitudes, Ajxn/Ael, versus N, calculated from experimental values for α and β. Red line is a linear fit, where the 9 ACS Paragon Plus Environment

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slope and intercept relate to the spring constant ratios via equation 2. Error bars in (b) and (c) represent standard error with n = 6. Table 1: Slope, Intercept, and β Values Calculated for Different Au Binding Configurations

Expected Values

Slope, m

Intercept, b

Linkers on Top Site

Calculated Beta (nm-1) 2P-DT

3P-DT

4P-DT

Au Top-Top

0.0191

0.0694

10.9815

10.9481

10.7776

Au Bridge-Bridge

0.0381

0.1388

6.0237

6.0891

6.0738

Au Hollow-Hollow

0.0572

0.2082

4.3712

4.4694

4.5059

Au Top-Bridge

0.0254

0.0925

8.5073

8.5231

8.4301

Au Top-Hollow

0.0286

0.1041

7.6763

7.7087

7.6417

Au Bridge-Hollow

0.0457

0.1665

5.1974

5.2792

5.2898

To obtain spring constants for each of the bonds in our molecular junctions, we performed DFT calculations of a benzene molecule using Gaussian 09W with the B3LYP/6-311G(d) basis to obtain the vibrational frequency of the ring breathing mode of benzene (1014 cm-1). From this frequency, we calculated kBz = 366 N/m. For the other bonds, we used the previously calculated spring constant values of kAuS = 184 N/m, kCS = 235 N/m, kCC = 492 N/m, and kAuAu = 8 N/m.20, 25 These spring constant values are used to calculate theoretical values for kME and kPC for different electrode configurations, which have different values for kel (Table 1). We can compare these to the experimentally determined values for slope and intercept from Fig. 3c, and thus determine the most likely binding configuration for the single molecule junction. Comparing these values to the possible configurations in Table 1, we find the best fit when the thiols on both sides bind to a


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top site and those apex Au atoms are bound in a bridge configuration on both electrodes, as shown in schematic form in Fig. 1a. It is worth noting that this configuration is different than that obtained for the alkanedithiols using the same technique, which were found to have a most probable binding configuration with the thiols on both sides bound to a top site, and the apex Au atoms bound in a top configuration on one electrode and a bridge configuration on the other.20 While unexpected, it is reasonable to find that most-probable binding configuration is different for these two thiolated molecular families because their nearest neighbor interactions are different. The thiol is an electron withdrawing group for the phenyl ring, and as such the Mulliken charge on the sulfur atom will be different when attached to a phenyl or an alkane. Because of this difference, the binding energy of the thiol to an Au apex atom (as well as the H-atom) will also be different in each case, which could account for the differences found in binding configurations. Moreover, the difference in the binding configurations also suggests that the breakdown may occur at different positions in the two cases. While some models and experiments show that the junction breakdown force corresponds to a Au-Au bond,26 others find that the breakdown force is less than this, instead suggesting that breakdown happens in the Au-S bond.27-30 It has been suggested by theoretical models that the behavior of the H atom in the thiol (-SH) group determines whether the junction breakdown happens due to the breaking of a Au-Au or a Au-S bond.29, 30 These findings suggest that not all thiol bonds are created equal, and variation in the Mulliken charge and the behavior of the H atom in the alkane or oligophenylene could cause changes in the most probable binding configuration, which would also change the breakdown force for the junction.


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To help verify that the binding configuration deduced is the most-probable one, we can also perform a self-consistent check of our values by calculating an expected β-value for each molecule from its experimental α-value and theoretical values for Ajxn and Ael calculated using the spring constants obtained from DFT. To calculate β from these parameters: =

? 234 ⁄

=

234

=

234 A56 234

= B1 + 56 C (3) 234

From this expression, we calculate an expected β ≈ 6 nm-1 for each of the oligophenylenes when in a bridge-bridge configuration (Table 1), in excellent agreement with the value calculated from the conductance-length tunneling relationship (Fig. 2d). While the comparison provides a direct check of the mechanical model, it also assumes that the β-value is constant across the molecular family. Although this is a good assumption for alkanes,31-33 it is not true for many other molecular families.31, 34 Therefore, it is also necessary to check the assumption of a constant β-value for the oligophenylenes. Both simulations and experiments have shown a difference in the energy barrier height (which relates to the value of β) for these molecules.31,

34-39

Additionally, as noted above, the oligophenylenes have multiple

conductance peaks (Fig. 4a,b)13, each of which may have a different barrier height value, and of course different binding configurations. To examine the possibility of having a constant β-value for these molecules, we turn to current-voltage (I-V) characteristics to examine the alignment between the nearest frontier orbital and the Fermi energy of the electrodes. In this case, during the SMBJ cycle, when a step was detected in the current-distance trace, the tip retraction was halted and held still while the bias voltage was swept for one cycle to produce an I-V curve before tip withdraw recommenced. This process was repeated to collect several thousand I-V curves per molecular species. These I-Vs


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were then added to create a 2D I-V histogram, showing a typical I-V characteristic for the two different conductance states observed for each molecule (Fig. 4c). Each I-V curve was fitted with the Breit-Wigner single-level model, given by /1 =

D EF EH

# EF AEH

Itan

%

M

/(N O/P11A SF TSH R

5Q R

U − tan

%

M

/(N O/P11 SF TSH R

5Q R

U V (4)

where W/1 = W + X/Γ − ΓZ 1⁄/Γ + ΓZ 1[ ⁄2, G0 is the quantum conductance, e is the elementary charge, V is the applied bias; the fitting parameters are E0 = EF - ε, the alignment between Fermi energy (EF) and either the HOMO or LUMO level (ε), and ΓL/ΓR, the coupling constants to the left/right electrodes, respectively.40, 41 The dashed lines on Figure 4c show the average single-level fittings for the two different conductance states for 3P-DT. Figure 4d shows the most probable values for E0 and Γ = \Γ ΓZ (we combined the values of the two coupling constants as they are nearly equal) for each conductance state measured.


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Figure 4: a,b, 2D histograms of α versus conductance for 3P-DT in configuration A, the lowconductance state, (a) and configuration B, the high-conductance state, (b). Dashed lines are a guide to the eye. c, 2D I-V histogram for 3P-DT, showing both configurations A and B. These measurements were performed without the AC modulation. Dashed lines show fittings with the single-level model (equation 4). d, Plots of values of E0 versus N (top) and Γ versus N (bottom) obtained from the fits to the I-V characteristics for all conductance states measured. Error bars represent standard error with n = 6.


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The conductance values and binding configurations discussed above are referred to as configuration A (Fig. 5a). In Figure 4d, we can see that in configuration A (blue squares) E0 ≈ 0.7 eV is roughly constant for all three molecules. This consistent difference in the energy level alignment suggests that assuming a constant β for this set of conductance values is acceptable, and further supports the analysis performed above using a constant β-value when determining the most-probable configuration. Next, we turn our attention to the second set of conductance values, which we refer to as configuration B. It has been previously demonstrated that different binding or geometrical configurations of the molecule can cause important changes in the transport properties.11,

42-44

Here, we observed higher conductance values for all three molecules, though experimentally we were only able to extract α values for 3P-DT and 4P-DT. For these two molecules, we found this higher conductance state has dramatically lower α values (Fig. 5c, pink shaded region). The I-V curves reveal that these states have lower values for E0 and higher values for the coupling (Γ), both of which correspond to higher conductance values (Fig. 4d). We also note that the energy level alignment, E0, is not constant for these high conductance states, in contrast to what was found for configuration A. Interestingly, the very low α values obtained for these conductance values do not agree with any binding configuration examined using the spring model above. In addition, the spring model predicts an increase in the α-value with increasing molecular length, whereas these states exhibit a decrease in the α-value with increasing length. This considerable change in the α-values and their trend points to a clear limitation of the simple spring model for junction configurations that are not fully extended, and indicates that a different model for the binding geometry and transport is needed in order to explain the results for this higher set of conductance values.


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There are a few possible configurations that could lead to the decreased electromechanical coupling for these higher conductance states.45-47 In the first scenario the molecule is bound at some angle (θ) normal to the surface. In this case the π-orbitals have some overlap with the states in the electrodes, and the mechanical modulation modifies this coupling by changing the angle, which results in a modulation of the current. Kornilovitch and Bratkovsky derived an analytical model for this configuration previously,45 and it has since been shown to be applicable in some molecular cases.7,

48, 49

In this model, I ∝ sin4θ, and following the same Taylor expansion

approach used above for the tunneling case yields an alternative form for α which can be solved numerically. Importantly, if the current in these junctions does vary with angle, we would expect α to vary with the modulation amplitude A0. However, when modulation amplitudes of A0 = 1.0 Å or 2.0 Å (see SI, Fig. S2) were applied to the junction, no significant change in the α-values were obtained. Thus, these high-conductance, low-α states cannot be explained by a modulation of the junction angle. Alternatively, it could be that instead of an angle change, the molecule moves roughly in parallel with the electrodes during the modulation as shown in Fig. 5b (configuration b). In this case, the π-orbitals would still overlap with the electrodes, and the coupling and energy levels would both be modified by the modulation. While such a model has been proposed previously for some molecules,47 there is no analytical model available to deduce an expected value for α in this case. If we perform a Taylor expansion on the Breit-Wigner single-level transmission model, the resulting expression for α is consistent with the trends in our measured values for α and E0. This indicates that the change in α is due to a realignment of the energy levels across the molecular junction in the high-conductance (configuration B) state. We also note that hopping-based transport has been suggested for phenyl systems as short as three


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rings,50 and that overlap between the molecular orbitals and the metal electrodes, as is suggested here, may increase the likelihood that different transport regimes emerge. Thus, it appears that in configuration A, the applied mechanical signal results in a modulation of the junction distance, acting to compress or extend a set of springs. In contrast, in configuration B the phenyl orbitals may overlap directly with the gold electrodes, and as the tip moves away from the substrate, the molecule slides along the electrode, decreasing the overlap between the π-orbitals and the gold. In this configuration, the applied mechanical signal results in a modulation of the electronic structure (both energy alignment and coupling) of the junction. In summary, we have demonstrated that adding a small amplitude, high-frequency mechanical modulation to a single molecule break junction experiment and measuring the resulting changes in current can provide insights into the binding configurations of singlemolecule devices. For the oligophenylene-dithiol molecules, we observed two separate conductance peaks, and found that the electromechanical responses of the junction were distinct for each of the conductance values. For the lower conductance state, we found that a simple mechanical model was able to describe the experimental results and provide a most-probable binding configuration. However, for the higher conductance state, standard mechanical models based on molecular binding and the tilt-angle of the molecule were unable to describe the results, allowing us to rule-out a variety of potential configurations and suggesting a more complicated junction configuration is being encountered. This approach is thus able to provide direct insights into the effect of the molecule-electrode binding configuration on the conductance and transport properties of a single-molecule junction, and it has the potential to provide fundamental insights into the origins of multiple conductance values and the conductance dispersion obtained in


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single-molecule junction experiments, which will be vital to moving molecular-electronic devices beyond the lab setting.

Figure 5: a,b, Schematics of 3P-DT bound in configurations A (a, shaded grey) and B (b, shaded pink). c, Plot of α versus conductance for all molecules, showing two different states for 3P-DT and 4P-DT. The low-conductance, high-α states are in configuration A (grey shaded region), and the high-conductance, low-α states are in configuration B (pink shaded region). ASSOCIATED CONTENT Supporting Information.


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Experimental methods, control experiment data (PDF) AUTHOR INFORMATION Corresponding Author *Email: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT JH acknowledges financial support from the National Science Foundation (NSF) (CBET1605338) and ONR (N00014-16-1-2658). LPY was supported by NSF (DMR-1505130) and partially supported by the University of Chicago Materials Research Science and Engineering Center, NSF (DMR-1420709). REFERENCES 1.

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Figure 1: a, Schematic of the experimental setup depicting a 2P-DT molecule bound between two Au electrodes with a sinusoidal mechanical modulation applied to one electrode. b, Example of a conductance versus time curve showing no steps (red curve). The extracted high-frequency (f = 2kHz) component gives the current response to the tip modulation (grey curve), and the amplitude of this curve gives α (blue curve). c, 2D histogram of α versus conductance, constructed from thousands of curves similar to those shown in (b). d, Example conductance (red), conductance modulation (grey), and α (blue) versus time curves for a 2P-DT junction. e, 2D histogram of α versus conductance for 2P-DT showing a maximum at a conductance ≈ 9×10-3 G0 and α ≈ 1.1 nm-1. 337x166mm (300 x 300 DPI)

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Figure 2: a, 2D histogram of α versus conductance for 4P-DT. b,c, The counts from (a) can be projected onto each axis to get a histogram from which we can determine the most probable value for α (b) and conductance (c). The pink dashed lines indicate the peak values. d, Plot of conductance versus molecular length for 2P-DT, 3P-DT, and 4P-DT. Error bars represent the standard error of conductance with n=6 experiments for each molecule. 239x189mm (300 x 300 DPI)


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Figure 3: a, Histograms of α for 2P-DT, 3P-DT, and 4P-DT, showing an increase in α with molecular length. Histograms scaled vertically for clarity. b, Plot of α versus N, the number of phenyl rings in the chain. c, Plot of the ratio of the junction and electrode amplitudes, Ajxn/Ael, versus N, calculated from experimental values for α and β. Red line is a linear fit, where the slope and intercept relate to the spring constant ratios via equation 2. Error bars in (b) and (c) represent standard error with n = 6. 78x184mm (300 x 300 DPI)


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Figure 4: a,b, 2D histograms of α versus conductance for 3P-DT in configuration A, the low-conductance state, (a) and configuration B, the high-conductance state, (b). Dashed lines are a guide to the eye. c, 2D IV histogram for 3P-DT, showing both configurations A and B. These measurements were performed without the AC modulation. Dashed lines show fittings with the single-level model (equation 4). d, Plots of values of E0 versus N (top) and Γ versus N (bottom) obtained from the fits to the I-V characteristics for all conductance states measured. Error bars represent standard error with n = 6. 255x183mm (300 x 300 DPI)


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Figure 5: a,b, Schematics of 3P-DT bound in configurations A (a, shaded grey) and B (b, shaded pink). c, Plot of α versus conductance for all molecules, showing two different states for 3P-DT and 4P-DT. The lowconductance, high-α states are in configuration A (grey shaded region), and the high-conductance, low-α states are in configuration B (pink shaded region). 117x181mm (300 x 300 DPI)


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An Electromechanical Approach to Understanding Binding

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