4.3 Results and Discussion
4.3.3 Comparison of the thermodynamics and kinetics of WS 2 and MoS 2 methyl
Table 4.1. Zeta potentials for solutions of ceMoS2, ceWS2, with and without methyl iodide, as a function of time after preparation. Averages and standard deviations are based on 10 measurements, each of which is plotted in Figure 4.7.
Time elapsed since preparation
(minutes)
Zeta Potential (mV) (average ± standard deviation)
ceMoS2 ceWS2 ceMoS2 + ICH3 ceWS2 + ICH3
5 – – –31 ± 7 –56 ± 2
300 (5 hours) –57 ± 2 –62 ± 3 – –
420 (7 hours) –51 ± 5 –65 ± 1 – –
1440 (24 hours) – – –32 ± 3 –32 ± 6
1740 (29 hours) –52 ± 4 –47 ± 4 – –
The zoom-in graph from 5–25 minutes highlights a notable difference in kinetics between the ceMoS2 + ICH3 and ceWS2 + ICH3 reactions. Within the first 30 minutes of reacting ceMoS2 with methyl iodide, the zeta potential shifted from ~ –45 mV to ~ –30 mV. In contrast, the zeta potential values for ceWS2 + ICH3 stayed relatively consistent in the first 30 minutes of reaction at ~ –55 mV. We hypothesize that at t = 0 in the ceMoS2 + ICH3
reaction, the zeta potential was similar to that of ceMoS2 at ~ –60 mV and began to move in the positive direction as the reaction proceeded during the 5 minutes that elapsed for the particle size measurement. 24 hours later, the zeta potentials for both reactions averaged –32 mV. Using the zeta potential as an indirect measurement of the reaction progress, it appears that ceMoS2 reacts orders of magnitude faster than ceWS2 with methyl iodide. Given that the zeta potentials before and after functionalization are similar for both ceMoS2 and ceWS2, this data suggests that the lower methyl coverage on WS2 compared to MoS2 cannot be attributed to differences in surface potential.
4.3.3 Comparison of the thermodynamics and kinetics of WS2 and MoS2 methyl
comparison, we used a previously developed grand canonical potential kinetics (GCP-K) formulation to convert the free energies obtained by fixed charge calculations to grand canonical potential (GCP) free energies at fixed potential.106 The same process that was used in Chapter 3 (detailed in Appendix C.5) was used to interpolate the GCP free energy from potential for the initial, transition, and final states for the MoS2 + ClCH3 and WS2 + ClCH3
reactions. Six calculations for MoS2 spanning 0.8 to –0.8 V vs SHE and seven calculations for WS2 spanning 0.3 to –0.9 V vs SHE were used to interpolate the free energy vs potential curves of initial, transition, and final states. The interpolation process uses a quadratic fit of the free energy vs number of electrons, shown in Figure C.1 and discussed in Appendix C.
Figure 4.8 shows the dependence of the free energy (ΔG) of the reaction and the barrier height (ΔG‡) on the potential (V vs SHE) for the reactions MoS2 + ClCH3 and WS2 + ClCH3, with the methyl being added to S7 in both cases. At any given potential, ΔG is calculated as the final state GCP free energy subtracted by that of the initial state, and ΔG‡ is calculated as the transition state GCP free energy subtracted by that of the initial state. These calculations indicate that ΔG of 1Tʹ-MoS2 methylation is ~0.2–0.4 eV more negative than the ΔG of 1Tʹ- WS2 methylation at every potential within the interpolation range, and the ΔG‡ of MoS2 and
Figure 4.8. Interpolation in 0.1 V intervals of (a) the free energy and (b) the barrier height, of adding ClCH3 to S7 (Figure 3.1) on 1Tʹ-MoS2 and WS2. The free energies and barrier heights are calculated by subtracting the initial state grand canonical potential from the final state grand canonical potential (for the free energy) or the transition state grand canonical potential (for the barrier height) at fixed potential for each reaction.
WS2 methylation are similar at ~0.3 V vs SHE but diverge as the potential becomes more negative, with ΔG‡ for MoS2 methylation being ~0.05 eV lower than WS2 methylation within the interpolation range. At 0.3 V vs SHE (the no-reductant condition) with a difference of 0.02 eV in barrier height, the rate constant k for MoS2 methylation and WS2 methylation differs by a factor of 2 at 1.7 s-1 and 0.9 s-1, respectively. However, due to the exponential dependence of rate on the barrier height, at –0.1 V vs SHE (the nickelocene condition) with a 0.05 eV difference in barrier height, the rate differs by an order of magnitude with k = 310 s-1 for MoS2 and k = 41 s-1 for WS2. This difference in the rate constant is consistent with our observations that the zeta potential of the MoS2 methylation reaction reaches the value of the functionalized product within 30 minutes, whereas for WS2 it takes up to 24 hours.
Since our experiments show that the coverage does not change substantially after 1 day of reaction for WS2 methylation (Figure 4.4), and we used a minimum of 2 days reaction time for the MoS2 and WS2 coverage data shown Figure 2.8 and Figure 4.3, the experimental coverages for WS2 appear to be limited by thermodynamics rather than kinetics. We can deduce that the MoS2 reactions also reached their thermodynamic limit since we observed in the zeta potential measurements (Section 4.3.2) that MoS2 methylation occurs faster than WS2. Figure 4.8a predicts that at any potential, MoS2 methylation is more thermodynamically favorable than WS2 methylation and suggests that for WS2 methylation to have the same thermodynamic driving force as MoS2 methylation, the potential for the WS2 reaction should be performed between –0.3 V to –0.7 V relative to the MoS2 reaction depending on the potential. From the linear fit of the experimental coverage data in Figure 4.3, we can calculate the potential at which WS2 obtains the same methyl coverage that MoS2
obtains in the absence of reductant. The ferrocene condition at –0.1 V vs E0(Fc+/0) showed no substantial effect on the coverage relative to the no-reductant case for both materials. At this potential, the MoS2 methyl coverage is 0.44 per MoS2. When the WS2 methyl coverage is 0.44, the corresponding potential calculated using the linear fit is –0.9 V vs E0(Fc+/0), a difference of –0.8 V. Comparing this –0.8 V difference to the prediction based on the DFT thermodynamic calculations that WS2 requires an additional –0.3 to –0.7 V of applied potential in order to achieve the same coverage as MoS2, we can attribute a portion of our
experimental observations to differences in the thermodynamic favorability of the reaction, keeping in mind that these calculations are reflective of only the first methyl addition. This difference in thermodynamics between WS2 and MoS2 may be the result of tungsten having a higher electronegativity and larger size compared to molybdenum, allowing it to stabilize the negative charges on the sulfur which reduces the nucleophilicity of the sulfur atoms and makes WS2 less prone to engage in a nucleophilic addition reaction.