University of Groningen
Autonomy and Chirality in Molecular Motors
Kistemaker, Jozef Cornelis Maria
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Kistemaker, J. C. M. (2017). Autonomy and Chirality in Molecular Motors. Rijksuniversiteit Groningen.
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93 This chapter has been published as:
J. C. M. Kistemaker, A. S. Lubbe, E. A. Bloemsma, B. L. Feringa, ChemPhysChem 2016, doi:10.1002/cphc.201501177.
Chapter 4: Molecular Motors in Viscous Media
Herein is reported: Transition state theory allows for the characterization of kinetic processes in terms of enthalpy and entropy of activation by using the Eyring equation. However, for reactions in solution it fails to take the change of viscosity of solvents with temperature into account. A second generation unidirectional rotary molecular motor was used as a probe to study the effects of temperature dependent viscosity changes upon unimolecular thermal isomerization processes. By combining the free-volume model with transition state theory, a modified version of the Eyring equation was derived, in which the rate is expressed in terms of both temperature and viscosity.
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Introduction
Chemical kinetics is not only a highly respected field in its own right, but is also used as an important tool for elucidating the characteristics of chemical reactions.[1] Although kinetic analysis does not provide information regarding the actual bonds being broken and formed in a reaction, it can be used to design a framework in which a proposed mechanism can be tested.[2] Very simple processes follow the law of mass action,[3] though for more complex processes this approach becomes far too complicated.[4]
Transition state theory is widely acknowledged to provide the best description for reaction rates.[2],[5] As such, performing an Eyring analysis is the preferred method to quantify thermal effects on chemical processes. The activation parameters thereby obtained allow comparisons of processes that take place at completely different time scales. This could never be accomplished in real time, because the reaction rates will span multiple orders of magnitude.[6],[7] Therefore often a common temperature at which all processes under investigation take place at a measurable rate is absent. To compare such processes, rates are usually extrapolated to standard conditions such as room temperature and atmospheric pressure.[8]
In gas-phase reactions this approach is very accurate. However, in the liquid phase it can fail to correct for solvent-solute effects.[9] Viscosity is a strongly temperature dependent property for most solvents.[10] Upon heating, viscosity-dependent chemical reactions are accelerated both by a higher thermal energy input and by a diminished frictional effect with the solvent.[11] These effects are linearly related,[12] especially when varying solvents, causing transition state theory to break down.[13] Therefore, comparing extrapolated rates may introduce misconceptions. Medium effects are often investigated for unimolecular processes, making this a highly relevant issue.[14,15]
Solvent viscosity is determined by the interaction of the solvent molecules constituting the system and can therefore be used to gain valuable insight into solvent-solute interactions. As such, several physical models that explain the influence of solvent viscosity on molecular transformations have been developed.[16,17] Doolittle’s free-volume model,[18] derived from Kramers’ theory,[19] indicates that translational movement of a molecule in a liquid is only possible if the amount of free volume (Vf) available is larger than its ‘critical
volume’ (volume occupied by the solvent at zero Kelvin, V0), where the total
volume (V) of the system equals the sum of V0 and Vf. The probability factor for
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MOLECULAR MOTORS IN VISCOUS MEDIA
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the fluidity (η-1). Hence, the viscosity is free-volume dependent and can be expressed by Equation 1, in which A is a proportionality factor.
/ 1
The free-volume model was applied by Gegiou et al.[20] to study the influence of viscosity on photochemical cis-trans isomerizations in stilbene. They note that in contrast to translational movement, molecular rearrangements only require a fraction of the critical volume. This fraction is denoted α, and is by definition smaller than one, since no more than the entire molecule can be subjected to frictional effects during the transition. The rate constant k of the isomerization is given by Equation 2, in which Equation 1 can be substituted to create Equation 3.
2
3
Equation 3 can be rewritten to give Equation 4 which predicts a linear relationship between ln k and ln η.
ln ln 4
Simple linear regression on the experimental data can afford the α value from the slope and the β value from the intercept. In the study of photochemical and thermal isomerizations, α can be viewed as a measure of the magnitude of the impact that increasing viscosity has on the process. Alternatively, the α value has been used to distinguish between two competing pathways, for instance in the formation of housane by photochemical denitrogenation.[21]
A classic method[20] for obtaining the α value for a given process is to vary the viscosity by variation of temperature in one solvent. However, since the reaction rate is primarily temperature dependent, increasing the viscosity in this manner shows an incomplete picture. The reaction rate is simultaneously increased by the lower viscosity and the higher temperature which leads to an overestimation of the viscosity effect. Indeed, Adam et al.[22] have shown for a viscosity dependent ratio of reaction rates an α value of 0.14 in n-butanol at various temperatures, and a mere 0.05 for a range of simple alcohols at room temperature.
Although Eyring and Kauzman already related viscosity to the thermodynamic properties of solvents using the Eyring equation,[23,24] Kierstead and Turkevich[25] argue that their findings should be simplified to the form originally proposed by Arrhenius.[26] This equation has often been used in the literature to correct for
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temperature effects on viscosity (see Appendix 1, Equation 36 and 37).[22,27,28] However, for reaction rates, the simplification relies on the assumption that the pre-exponential factor in the Arrhenius equation is temperature-independent, whereas transition state theory dictates that this is not the case. As a result, positive entropy will lead to overestimation of α, whereas a negative entropy of activation will lead to underestimation. Therefore, when comparing a process in two solvents with a different temperature dependence of viscosity, an error is introduced. Here, we propose a solution to this problem by using a modified version of the Eyring equation which takes into account the viscosity effect.
Results and Discussion
Dynamic viscosity can be accurately described by Andrade’s equation (Equation 5), which indicates that ln η is inversely proportional to T through fitting parameters v and w.[29] By substituting Andrade’s equation and the Eyring equation (Equation 6) into Equation 4, a temperature dependent description of α can be obtained (Equation 7). For the complete derivation of Equation 7 see Appendix 1.
5
‡ ° ‡ °
6
7
where c1–c6 are dependent on fitting parameters v and w, the enthalpy of activation
Δ‡H° and the entropy of activation Δ‡S°, which are obtained from experimental
data.
Scheme 4.1. Structure and isomerization processes of motor 1.
To support the relationship expressed in Equation 7 with experimental data and put it to a critical test we studied the thermal helix inversion (THI) of second-generation molecular motor 1 (Scheme 4.1).[30] Due to the unimolecular nature of the process, the concentration of 1 is irrelevant which negates potential problems regarding diffusion rates. The thermally less stable isomer can be easily generated through
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irradiation with UV light, by a photochemical E–Z isomerization around the central double bond. The thermal process from metastable-1 to stable-1 is unimolecular and can be followed via UV-Vis spectroscopy. A related first generation motor system has previously been proven to obey the free-volume model (see Chapter 2).[31] Motor 1 has been functionalized with n-butyl chains to ensure adequate solubility. Additionally, the balance in mass of motor 1 is close to equal on both sides of the central double bond (the rotary axle), so that both halves of the molecule will undergo a nearly equal amount of displacement during the thermal helix inversion. Based on studies of similar molecular motors (see Chapter 3)[32] a half-life at room temperature between 10 and 1000 seconds in n-heptane was anticipated. Therefore, all studies could be performed at or slightly below room temperature, which makes motor 1 a highly suitable candidate from a practical point of view.
Scheme 4.2. Synthesis of motor 1. i) 2.4 eq BuLi, 1 mol% Pd(PtBu3)2, toluene, 49%; ii) Triton B,
air, pyridine, 12 h, 73%; iii) N2H4·H2O, MeOH, 16 h, 95%; iv) MnO2, THF, 66%; v) AlCl3, DCM,
methacrylic acid, −75 °C to reflux, 2 h, 31%; vi) P4S10, Lawesson’s reagent, toluene, 60 °C to reflux,
16 h; vii) 5, toluene, THF, 40 °C, 16 h, 60% over 2 steps, 1.47 g of 1.
The synthesis of motor 1 is shown in Scheme 4.2. A double alkylation starting from dibromofluorene was performed by the method described by Giannerini et al.[33] to afford fluorene 2 in 49% yield (Scheme 4.2). This was followed by a direct oxidation with air to 3 and subsequent hydrazone formation using hydrazine to give 4 in 69% yield over two steps. Oxidation of the hydrazone provided the desired diazo species 5 for the subsequent olefination. A Friedel-Crafts alkylation and in situ Nazarov cyclization of methacrylic acid onto dibutyl benzene using AlCl3 afforded ketone 6 as well as a considerable amount of alkyl-shifted side-product from which 6 could be separated by chromatography. Conversion of 6 into the
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corresponding thioketone was followed by a Barton-Kellogg coupling with 5. The expected episulfide intermediate directly underwent desulfurization to afford molecular motor 1 in a high yield (60% over two steps).
Figure 4.1. Structure of stable-1 where the arrow indicates the point of view for the geometries of
stable-1-1 to stable-1-8 in which the alkyls adopt all possible conformations.
Figure 4.2. Top view for the minimum energy geometry of metastable-1-2, top and side view of the
minimum energy transition state (TS-1-7).
To aid in the spectroscopic characterization of 1, as well as provide insight into the pathway for THI and its energetic barrier, a computational study was undertaken. The theoretical investigation started with the semi-empirical PM6 method to construct a potential energy coordinate from the dihedral (1-2-3-4 in Figure 4.1) in the fjord region. The geometries of the minima and transition state were optimized using DFT B3LYP/6-31G(d,p)[34,35] and an intrinsic reaction coordinate was calculated to ensure that the transition state connected the metastable to the stable
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MOLECULAR MOTORS IN VISCOUS MEDIA
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configuration. The barrier for thermal helix inversion (THI) was found to be higher than expected (Δ‡G°
calc 96.8 kJ·mol−1). A possible explanation might be additional longer range interactions, therefore the geometries of the minima and transition state were optimized using DFT ωB97X-D/6-31+G(d,p)[36] which gave a very similar result (Δ‡G°
calc 97.1 kJ·mol−1, 1-7 in Table 4.1). The addition of solvent (heptane, IEFPCM)[37,38] did not give a significantly different barrier for activation (Δ‡G°
calc 96.8 kJ·mol−1). The orientation of the alkyl chains was based on the simple semi-empirical calculations, which might be local minima instead of the global minimum. Therefore all possible orientations of the alkyl chains in the stable, metastable and the transition state were calculated on the ωB97X-D/6-31+G(d,p) level without additional solvent (see Figure 4.1 for the geometries of stable-1 and see Figure 4.2 for the most relevant metastable-1 and TS-1 geometries). The results are summarized in Table 4.1.
Table 4.1. Calculated energies and Bolzmann distributions for 1.[a]
ΔG° Metastabl e-1 (kJ·mol −1) [b] Boltzman n distrib ution of metastabl e-1 (%) Δ ‡G° TS-1 (kJ·mol −1) [b] Δ ‡H° TS-1 (kJ·mol −1) [b] ΔG° Stable-1 (kJ·mol −1) [c] Boltzman n distrib ution of stable-1 (%) 1-1FFF 1.65 9.8 99.2 87.7 0.31 21.2 1-2FFB 0.00 19.3 99.9 83.8 1.57 12.7 1-3FBF 2.66 6.5 97.9 86.2 0.00 24.1 1-4FBB 2.34 7.4 99.6 82.8 4.07 4.5 1-5BFF 1.65 9.8 99.3 88.5 0.49 19.8 1-6BFB 0.30 17.1 99.7 84.6 3.75 5.2 1-7BBF 0.81 13.8 97.9 87.2 2.72 7.9 1-8BBB 0.42 16.2 100.6 84.2 4.02 4.6 [a] Capital subscript letters after the conformer indicate front (F) of back (B) which indicates the orientation of the alkyl chain when viewed from the front of the structure in Figure 4.1 where the order is top-, left-, right-alkyl.
[b] Relative to the minimum energy of metastable-1. [c] Relative to the minimum energy of stable-1.
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6 7 24 19 22 28 23 26 30 1 5 2 3 8 4 12 18 21 27 17 20 25 29 H9 H14 H10 H16 H11 H13 H15 22 21 1 7 2 6 15 13 11 35 27 30 29 31 36 25 34 39 12 5 9 10 8 17 3 16 19 20 14 4 18 23 26 32 37 24 28 33 38 1H-NMR assignment 13C-NMR assignmentFigure 4.3. NMR spectra (top: 1H, bottom: 13C) of stable-1 with assignments on structures (middle).
Top spectrum: experimental, bottom spectrum: calculated Boltzmann corrected (scaling factors 1H:
slope −0.9187 intercept 29.334, 13C: slope −0.9766 intercept 179.78). Experimental assignments
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While there are three conformations significantly lower in energy in the stable state (1, 3 and 5), there are no major differences in energy for neither the metastable state nor the transition state. This allows all the conformers to readily undergo thermal helix inversion, though 1-3 and 1-7 are calculated to be slightly faster. Although conformer metastable-1-3 is present in the smallest amount, one can assume a fast equilibrium between all conformers and therefore the lowest barriers are of most importance. This shows that there is not a significantly reduced barrier for a specific conformer and the overall calculated barrier is Δ‡G°
calc 98.1 kJ·mol−1 (corrected for Boltzmann distributions and an assumed pre-equilibrium) which is still higher than the expected experimental barrier.
Of all conformations of stable-1 NMR spectra were calculated (DFT giao mPW1PW91/6-311+G(2d,p) in CHCl3) which were corrected for their calculated Boltzmann population and compared to the corresponding experimental NMR spectrum by obtaining scaling factors using a least squares analysis (Figure 4.3). The calculated NMR spectra agree with the experimental spectra and highlight the benefit of calculated spectra in structure elucidation. Allowing the Boltzmann populations (Table 4.1) to be freely optimized in a residual sum of squares (RSS) analysis of the calculated vs experimental NMR spectra changes the distribution significantly though it offers only a minor improvement in the goodness of fit (RSSH x RSSC improved from 86.8 to 83.1). This suggests that the calculated NMR spectra of most conformations already represent the experimentally observed spectrum rather well.
The molecular motor undergoes photochemical E–Z isomerization (Scheme 4.1) upon irradiation with UV light (365 nm) which brings about significant changes in the 1H-NMR absorption spectrum and a bathochromic shift in the UV-vis absorption spectrum (see NMR and UV-vis experiments in the Experimental Section). These changes are indicative of the formation of metastable-1 in which there is additional strain over the double bond due to its twisted nature required to prevent the pseudo-equatorially orientated methyl group clashing with the lower half of the molecule (Figure 4.2). Upon leaving the samples at room temperature, quick and full reversal to the initial absorption spectra was observed. This is completely in accordance with THI steps observed for analogous second generation molecular motors.[32]
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Table 4.
2.
Kinetic parameters det
ermined
by the di
rect Eyring analysis (F
igure 4.4) w
ith errors obt
ained by a Monte Ca
rlo experiment for
thermal
isomerizations of
metastable-1 in
a series of
n-alkanes and the tem
peratur e depen d ent paramet ers f or viscosit y n-Do deca ne 9.25± 0.27 80.6± 1.8 − 25.6±6.5 88.1± 0.1 − 5.302± 0.00 8 167 3±2 1.500 ±0.0 17 [a] Standard co nditi on: 20 °C and atmos ph er ic pressur e. n-Dec ane 7.79± 0.22 82.7± 1.5 − 17.0±5.3 87.6± 0.1 − 4.738± 0.00 5 136 3±1 0.915 ±0.0 06 n-No nan e 7.34± 0.20 80.3± 1.4 − 24.6±5.1 87.5± 0.1 − 4.580± 0.00 7 123 8±2 0.700 ±0.0 07 n-Octane 6.87± 0.18 75.9± 1.4 − 38.8±4.9 87.3± 0.1 − 4.378± 0.00 2 110 4±1 0.543 ±0.0 02 n-He ptane 6.29± 0.17 80.4± 1.5 − 22.9±5.2 87.1± 0.1 − 4.305± 0.00 1 100 1±1 0.411 ±0.0 01 n-Hex ane 5.81± 0.17 76.0± 1.5 − 37.4±5.3 86.9± 0.1 − 4.255± 0.00 1 905.9 ±0.4 0.312 ±0.0 01 n-Penta ne 5.54± 0.15 74.0± 1.3 − 43.6±4.6 86.8± 0.1 − 3.915± 0.00 2 713.4 ±0.6 0.227 ±0.0 01 t½ at rt (min) Δ ‡H° (kJ·mol −1) Δ ‡S° (J·K −1·mo l −1) Δ ‡G° (kJ ·mol −1) [a] v parameter for solvent w param
eter for solvent
η at rt (cP)
for
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The THI was followed in n-alkanes at several temperatures which allowed for the construction of Eyring plots for the isomerization processes in these solvents (Figure 4.4a). Alkanes were chosen to minimize change in other medium properties such as polarity and hydrogen bonding. Fitting the rates to the original Eyring equation allowed for the determination of the activation parameters (Δ‡H°, Δ‡S°,
Δ‡G°) of the thermal isomerization in the different alkane solvents (Table 4.2). The
experimentally observed barrier for thermal helix inversion in heptane was found to be significantly lower than the calculated barrier, as expected (Δ‡G°
exp 87.1 kJ·mol−1 vs Δ‡G°
calc 98.1 kJ·mol−1). However, the calculated enthalpy agrees much better with the experimental data (Δ‡H°
calc 82.8 kJ·mol−1 vs Δ‡H°exp 80.4 kJ·mol−1 in heptane). This then suggests that the calculated entropy is overestimated (Δ‡S°
calc −52.2 J·K−1·mol−1) with respect to the experimentally determined values (Δ‡S°
exp −17.0 to −43.6 J·K−1·mol−1 for the n-alkanes, Table 4.2).
Figure 4.4. a) Eyring plots of the THI step of 1 in n-alkanes and viscosity plots of n-alkanes, b) α
value (red line) and R2 (dashed line) of fit vs temperature, c) contour plot of calculated rate from α
and β vs temperature and viscosity, d) 3D plot of experimental data with fitted viscosity dependent Eyring equation surface.
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Fitting Equation 5 to literature data[40,41] for the viscosity of the alkanes over a temperature range allowed for the determination of their viscosity parameters (v and w in Table 4.2). With the activation and viscosity parameters known, the constants (c1–c6, Appendix 1 Equation 23, Table 4.3) can be calculated. These
parameters give the α value at any desired temperature which is plotted in Figure 4.4b. The goodness of fit of α to the experimental data is expected to vary with temperature. To evaluate the reliability of Equation 7 over a temperature range, Equation 40 (see Appendix 1) has been derived, which allows for the calculation of the coefficient of determination (R2) at any temperature, plotted also in Figure 4.4b. This reveals α to be most reliable (R2 > 99%) in the range of 283–294 K, and clearly shows that α changes significantly with temperature. Over the temperature range of the experimental data (−2–20 °C) α changes from 0.35 to 0.27 which indicates that the isomerization under investigation shows a much stronger viscosity dependence at lower temperatures. While α values higher than 0.3 have been observed before,[42–45] they remain rather exceptional.
When four additional constants are derived (d1–d4, Table 4.3), the β value (Equation
4) can be obtained from the same parameters in a similar fashion (Appendix 1, Equation 36). Substitution of the functions for α and β into Equation 4 allows for the prediction of the rate (k) at any temperature and viscosity. The data are plotted in Figure 4.4c. For the solvents under investigation the viscosity changes with temperature, though using Equation 4 we can make isoviscous predictions for the rate. Applying the Eyring equation to these rates allows for the determination of activation parameters under isoviscous conditions. The isoviscous enthalpy and entropy were found to be linearly dependent on the natural log of the viscosity as follows:
‡ ln 8
‡ ln 9
where Hη1, Hη2, Sη1 and Sη2 are parameters obtained by linear regression. Hη2 and
Sη2 are parameters that correspond to Δ‡H° and Δ‡S° in absence of viscosity,
whereas Hη1 and Sη1 are correction factors. Kramers theory for high-friction media
would predict a positive sign for the correction factors. Substitution of these functions into the Eyring equation affords the following Equation 10:
10
The viscosity corrected Eyring Equation 10 can be fitted directly to the experimental data using a least squares analysis and appropriate weighing of the
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MOLECULAR MOTORS IN VISCOUS MEDIA
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rate constants (k−2), resulting in the calculated surface as displayed in Figure 4.4d together with the experimental data. This fit affords the four viscosity corrected enthalpy and entropy parameters (Table 4.3) with a small average absolute residual error (3.2% on k) and a high coefficient of determination (R2=0.995). This shows that the viscosity corrected Eyring Equation 10 is capable of describing the variance of the rate of the thermal isomerization with temperature as well as viscosity for linear alkanes. Applying the viscosity corrected parameters to Equation 8 and 9 the free energies of activation for all alkanes are obtained at standard conditions within 0.06 kJ·mol−1 of the experimentally observed activation barrier. An investigation into the applicability of this relationship to other solvents has recently been reported.[46,47]
Table 4.3. Calculated parameters for α, β and the viscosity corrected Eyring equation (Equation 7,
40, and 10, respectively).
c1 c2 c3 c4 c5 c6
−1.99 2.24·103 −5.45·105 1.16 −1.65·103 6.01·105
d1 d2 d3 d4
−13.1 7.34·103 8.44·106 −5.05·109
Hη1 (kJ·mol−1) Hη2 (kJ·mol−1) Sη1 (J·K−1·mol−1) Sη2 (J·K−1·mol−1)
2.71±1.03 77.0±8.0 6.95±3.66 −36.6±2.8
Conclusion
We have shown that the viscosity dependence of a unimolecular thermal process — characterized by the α value — can be strongly dependent on temperature. A relationship between α and the activation and viscosity parameters has been derived which allows for the visualization of the temperature correlation of the viscosity dependence. This revealed the linear relationship between the natural log of the viscosity and the activation parameters, as we experimentally demonstrate here for the THI of molecular motor 1. Introduction of the viscosity corrected parameters into the Eyring equation provided an equation which expresses the helix inversion rate as a function of both temperature and viscosity.
Acknowledgements
This work was executed in collaboration with Anouk Lubbe who performed the majority of the spectroscopy experiments. Mathematical derivations were performed by dr. Erik Bloemsma.
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Experimental Section
General Methods
Chemical were purchased from Sigma Aldrich, Acros or TCI Europe N.V.; solvents were reagent grade and distilled and dried before use according to standard procedures, if required. Column chromatography was performed on silica gel (Silica Flash P60, 230–
400 mesh). 1H and 13C-NMR were recorded on a Varian Gemini-200 (50 MHz), or a Varian
AMX400 (101 MHz). Chemical shifts are denoted in δ values (ppm) relative to CDCl3 (1H:
δ = 7.26 and 13C: δ = 77.16). For 1H-NMR, the splitting parameters are designated as
follows: s (singlet), d (doublet), t (triplet), q (quartet), p (pentet), h (heptet), m (multiplet) and app (apparent). HRMS spectra were recorded on a Thermo Fischer Scientific Orbitrap XL with ESI and/or APCI ionization sources. Melting point are taken on a Büchi B-545 melting point apparatus. UV-vis absorption spectra were measured on a Jasco V-630 spectrometer. Irradiation was performed using a Spectroline ENB-280C/FE lamp (365 nm).
Synthesis
2,7-dibutyl-9H-fluorene (2). In a dry Schlenk flask
Pd[P(t-Bu)3]2 (1.1 mol%, 0.26 g, 0.51 mmol) and
2,7-dibromo-9H-fluorene (15 g, 46 mmol) were dissolved in 200 mL of dry toluene. n-Butyllithium (2.4 equiv, 45 mL,
2.5 M, 0.11 mol) was diluted with toluene (300 mL) to reach a concentration of ~0.33 M; this solution was slowly added over 2 h by the use of a cannula. After the addition was
completed a saturated aqueous solution of NH4Cl was added and the mixture was extracted
three times with ether. The organic phases were collected, dried over Mg2SO4 and filtered.
The solvent was evaporated under reduced pressure to afford the crude product (9.6 g, 75% yield by GCMS) that was then purified by column chromatography (silica, gradient of
pentane/CH2Cl2 0–15%; C18 reversed phase gradient of acetonitrile/chloroform 0–25%)
from side-products to afford the product 2 as a slightly yellow liquid (6.3 g, 49%). 1H NMR
(201 MHz, Chloroform-d) δ 7.68 (d, J = 7.7 Hz, 2H), 7.38 (s, 2H), 7.21 (d, J = 7.7 Hz, 2H), 3.86 (s, 2H), 2.72 (t, J = 7.5 Hz, 4H), 1.70 (app. p, J = 7.2 Hz, 4H), 1.44 (app. h, J = 7.0 Hz,
4H), 1.00 (t, J = 7.2 Hz, 6H). 13C NMR (50 MHz, Chloroform-d) δ 143.46 (C), 141.30 (C),
139.58 (C), 127.05 (CH), 125.14 (CH), 119.37 (CH), 36.84 (C), 35.98 (CH2), 34.14 (CH2),
22.58 (CH2), 14.16 (CH3). HRMS (APCI-Neg): calcd for ([C21H26 - H]-) 277.1951, found
277.1952.
2,7-dibutyl-9H-fluoren-9-one (3). Through a solution of 2 (680 mg, 2.44 mmol) and Triton-B (44 mL, 0.24 mmol)
in pyridine (50 mL) in an open flask, air was bubbled using a diffuser during a 12 h period. The remaining pyridine was removed under reduced pressure and the
crude product was submitted to column chromatography affording the product 3 as a slightly
yellow liquid (520 mg, 73%). 1H NMR (201 MHz, Chloroform-d) δ 7.44 (d, J = 0.8 Hz,
1H), 7.33 (d, J = 7.5 Hz, 2H), 7.23 (dd, J = 7.6, 1.5 Hz, 2H), 2.60 (t, J = 7.2 Hz, 5H), 1.60
(app. p, J = 7.1 Hz, 5H), 1.35 (app. h, J = 7.1 Hz, 4H), 0.92 (t, J = 7.2 Hz, 5H). 13C NMR
(50 MHz, Chloroform-d) δ 194.70 (C), 143.94 (C), 142.37 (C), 134.72 (C), 134.68 (CH),
124.37 (CH), 119.94 (CH), 35.54 (CH2), 33.44 (CH2), 22.34 (CH2), 14.03 (CH3). HRMS
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MOLECULAR MOTORS IN VISCOUS MEDIA
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(2,7-dibutyl-9H-fluoren-9-ylidene)hydrazine (4). A
suspension of 3 (1.8 g, 6.2 mmol) and hydrazine monohydrate (18 mL) in MeOH (100 mL) was stirred and heated to reflux for 16 h. The reaction mixture was cooled to −20 °C and the product crystallized out of the solution. The mixture was filtered over a glass filter and
the residue was taken up in CH2Cl2. The solvent was removed under reduced pressure in the
presence of Celite and the product was subjected to column chromatography (silica, gradient
of pentane/CH2Cl2) to yield 4 (1.8 g, 5.9 mmol, 95%) as a wax. 1H NMR (201 MHz,
Chloroform-d) δ 7.71 (s, 1H), 7.61 (d, J = 7.7 Hz, 1H), 7.53 (s, 1H), 7.50 (d, J = 7.7 Hz, 1H), 7.23 (d, J = 7.2 Hz, 1H), 7.13 (dd, J = 7.7, 1.5 Hz, 1H), 6.34 (s, 2H), 2.67 (m, 4H), 1.63 (m, 4H), 1.38 (m, 4H), 0.94 (m, 6H); 13C-APT- NMR (50 MHz, Chloroform-d) δ 146.39 (C), 142.68 (C), 142.40 (C), 139.38 (C), 137.97 (C), 136.64 (C), 130.81 (C), 129.95 (CH), 128.97 (CH), 126.00 (CH), 120.72 (CH), 120.03 (CH), 119.13 (CH), 36.11 (CH2), 35.94 (CH2), 34.07 (CH2), 33.84 (CH2), 22.51 (CH2), 22.47 (CH2), 14.10 (CH3), 14.09
(CH3). HRMS (ESI-pos): calcd for ([C21H26N2 + H]+) 307.2169, found 307.2164.
4,7-dibutyl-2-methyl-2,3-dihydro-1H-inden-1-one (6).
Dichloromethane (900 mL) was cooled down to −75 °C and aluminium chloride (12.2 g, 91 mmol) was added, followed by 1,4-dibutylbenzene (20.2 mL, 91 mmol) and finally methacryloyl chloride (8.91 mL, 91 mmol). The reaction mixture was warmed up to room temperature over 1 h after which it was slowly heated at reflux over 1 h. The reaction
mixture was poured on ice (1 L) and extracted with CH2Cl2 (3 x
200 mL). After evaporating the solvent under reduced pressure, ethyl acetate (200 mL) was added and the solution was washed with 1 M aq. HCl (2 x 100 mL), 1 M aq. NaOH (2 x
100 mL), H2O (2 x 100 mL) and brine (100 mL). The organic solvents were removed under
reduced pressure and the residue was distilled (105 °C, 3.3·10−3 bar) after which it was
subjected to reversed phase column chromatography (C18, gradient H2O/CH3CN/CH2Cl2).
The collected fraction was evaporated in vacuo and extracted with dichloromethane which after removing the solvent under reduced pressure afforded pure product 6 as a clear liquid
(7.28 g, 31%). 1H NMR (400 MHz, Chloroform-d) δ 7.26 (d, J = 7.5 Hz, 1H), 7.06 (d, J =
7.5 Hz, 1H), 3.29 (dd, J = 16.7, 7.7 Hz, 1H), 3.02 (m, 1H), 2.66 (m, 1H), 2.61 (t, J = 7.8 Hz, 2H), 2.56 (app. Dd, J = 16.7, 4.2 Hz, 1H), 1.57 (app. Dp, J = 15.7, 7.3 Hz, 4H), 1.39 (app. H, J = 7.3 Hz, 4H), 1.30 (d, J = 7.3 Hz, 3H), 0.95 (t, J = 7.3 Hz, 3H), 0.92 (t, J = 7.3 Hz,
2H). 13C NMR (101 MHz, Chloroform-d) δ 210.48 (C), 152.68 (C), 141.59 (C), 137.49 (C),
133.64 (CH), 133.16 (C), 128.58 (CH), 42.27 (CH), 33.36 (CH2), 33.26 (CH2), 32.27 (CH2),
31.48 (CH2), 31.23 (CH2), 22.84 (CH2), 22.75 (CH2), 16.52 (CH3), 14.11 (CH3), 14.10
(CH3); HRMS (ESI-pos): calcd for ([C18H26O + H]+) 259.20564, found 259.20579.
2,7-dibutyl-9-(4,7-dibutyl-2-methyl-2,3-dihydro-1H-inden-1-ylidene)-9H-fluorene (1).
To a stirred solution of 4 (1.1 g, 3.6 mmol) in THF (35 mL) was added MnO2 (1.6 g,
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The solvent was removed under reduced pressure yielding 2,7-dibutyl-9-diazo-9H-fluorene (5) (0.72 g, 2.4 mmol, 66%) as a solid which was used directly
without further purification. 1H NMR (201 MHz,
Chloroform-d) δ 7.84 (d, J = 7.9 Hz, 2H), 7.35 (s, 2H), 7.19 (d, J = 7.9 Hz, 2H), 2.81 (t, J = 7.6 Hz, 4H), 1.77 (app. p, J = 7.7, 7.3 Hz, 4H), 1.50 (app. h, J = 7.1, 7.1 Hz, 4H), 1.07 (t, J = 7.2 Hz, 6H); 13C NMR (50 MHz, Chloroform-d) δ 141.07 (C), 133.28 (C), 129.67 (C), 125.32 (CH), 120.48 (CH), 119.19 (CH), 63.10 (C), 36.10 (CH2), 34.10 (CH2), 22.57 (CH2), 14.14 (CH3).
Under an atmosphere of nitrogen, 6 (1.22 g, 4.72 mmol) was dissolved in toluene (50 mL)
to which P4S10 (1.33 g, 5.98 mmol) and Lawesson’s reagent (1.00 g, 2.47 mmol) were
added. The mixture was heated to 60 °C for 1 h, followed by 1 h at 80 °C and subsequently heated at reflux overnight. The solvent was evaporated under reduced pressure, after which
the residue was dissolved in CH2Cl2. The organic solution was filtered over a plug of silica
followed by a purification using short column chromatography (silica, pentane/CH2Cl2
10%). The resulting bluish liquid was directly added to a red solution of 5 (1.05 g, 3.45 mmol) in 40 mL of a toluene/ tetrahydrofuran mixture (2:1). The evolution of gas was immediately observed and the reaction mixture was heated at 40 °C for 16 h. The solvent was removed under reduced pressure and the material was purified by column
chromatography (silica, gradient pentane/CH2Cl2; C18 reversed phase, gradient
H2O/CH3CN/CH2Cl2) to yield 1 (1.47 g, 60%) as a light yellow liquid. 1H NMR (400 MHz,
Chloroform-d) δ 7.69 (d, J = 1.4 Hz, 1H), 7.66 (d, J = 7.7 Hz, 1H), 7.59 (d, J = 7.7 Hz, 1H), 7.36 (s, 1H), 7.18 (dd, J = 7.9, 1.0 Hz, 1H), 7.14 (s, 1H), 7.08 (dd, J = 7.7, 0.8 Hz, 1H), 4.15 (app. p, J = 6.6 Hz, 1H), 3.21 (dd, J = 14.8, 5.9 Hz, 1H), 2.83 (dt, J = 14.0, 8.0 Hz, 1H), 2.76 (t, J = 7.7 Hz, 2H), 2.66 (app. dt, J = 14.2, 7.6 Hz, 1H), 2.63 (d, J = 14.8 Hz, 1H), 2.61 (app. dt, J = 14.2, 7.8 Hz, 1H), 2.58 (app. dt, J = 14.1, 7.0 Hz, 1H), 2.51 (t, J = 7.6 Hz, 2H), 1.72 (app. p, J = 7.6 Hz, 2H), 1.63 (app. p, J = 7.6 Hz, 2H), 1.55 (app. p, J = 7.5 Hz, 2H), 1.46 (app. h, J = 7.4 Hz, 2H), 1.42 (app. h, J = 7.4 Hz, 2H), 1.39 (app. p, J = 7.6 Hz, 3H), 1.35 (d, J = 6.9 Hz, 2H), 1.32 (app. h, J = 7.4 Hz, 2H), 1.01 (app. h, J = 7.1 Hz, 2H), 1.00 (t, J = 7.4 Hz, 3H), 0.97 (t, J = 7.4 Hz, 3H), 0.91 (t, J = 7.4 Hz, 3H), 0.67 (t, J = 7.4 Hz, 3H). 13C NMR (101 MHz, Chloroform-d) δ 152.08 (C), 144.33 (C), 141.18 (C), 140.81 (C), 140.17 (C), 139.96 (C), 139.61 (C), 138.33 (C), 137.99 (C), 137.32 (C), 136.63 (C), 130.08 (C), 129.47 (CH), 127.60 (CH), 127.48 (CH), 127.16 (CH), 124.19 (CH), 123.50 (CH), 119.14 (CH), 118.59 (CH), 44.14 (CH), 39.75 (CH2), 36.38 (CH2), 35.94 (CH2), 34.32 (CH2), 34.10 (CH2), 34.05 (CH2), 33.62 (CH2), 32.73 (CH2), 32.55 (CH2), 22.81 (CH2), 22.56 (CH2), 22.43 (CH2), 22.07 (CH2), 19.19 (CH3), 14.21 (CH3), 14.18 (CH3), 14.15
(CH3), 14.03 (CH3). HRMS (ESI-pos): calcd for ([C39H50 + H]+) 519.3985, found 519.3973.
Kinetic Experiments
A 2·10−5 M solution of motor 1 was prepared in the selected solvents. All solvents were
purged with argon before use. Samples were prepared in quartz cuvettes (l = 1 cm). The samples were irradiated for 1 h with 365 nm light at −20 °C, 4 °C or 20 °C. The absorption at 410 nm was then measured over time until the relevant band had completely disappeared. A 400 nm cut-off filter was mounted before the light source to minimize photochemistry
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MOLECULAR MOTORS IN VISCOUS MEDIA
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occurring during the THI. All exponential decay lines were fitted using least squares. Figure 4.5 shows all recorded exponential decay lines in heptane, as a typical example.
Figure 4.5. Normalized exponential decay lines from metastable-1 to stable-1 in heptane.
Absorbance measured over time at 410 nm. UV-vis Experiments
The photochemical properties of motor 1 were studied using UV-vis spectroscopy. A
2·10−5 M solution of motor 1 was prepared in heptane and a UV-vis spectrum was recorded
(Figure 4.6). The sample was irradiated with 365 nm light at 0 °C. Spectra were recorded at regular intervals. The irradiation caused the band at 359 nm to disappear. Simultaneously, a new band appeared at 383 nm. This bathochromic shift is in accordance with formation of a higher energy isomer (metastable-1). The clear isosbestic point at 377 nm is indicative of the absence of undesired side reactions. After 30 min, a photostationary state was reached. Upon removal of the light source and heating to room temperature for 30 min, the initial absorption spectrum of the sample was fully recovered.
Figure 4.6. UV-vis spectra of stable-1 upon irradiation (365 nm, 0 °C).
NMR Experiments
The thermal and photochemical step in the rotation of molecular motor-1 were studied using
1H-NMR spectroscopy. Figure 4.7i shows the NMR spectrum of stable-1 in CD
2Cl2. The 0 5 10 15 20 0.0 0.2 0.4 0.6 0.8 1.0 A bso rban ce time / x103 s Temperature -2 °C 2 °C 5 °C 7.5 °C 10 °C 12.5 °C 15 °C 20 °C 300 350 400 450 500 0.0 0.1 0.2 0.3 0.4 A bso rb anc e wavelength / nm
110
4
sample was cooled to −40 °C and irradiated with 365 nm light. The PSS (Figure 4.7ii) was reached after 6 h and consists of a stable/metastable ratio of 24:76. Stable-1 was fully regenerated by leaving the sample in the dark at rt for 1 h (Figure 4.7iii).
Figure 4.7. NMR experiments in CD2Cl2 (400 MHz, −40 °C). i) Stable-1, ii) PSS, reached after 6 h
of irradiation (365 nm, −40 °C), iii) stable-1 regenerated upon heating to room temperature for 1 h.
Appendix 1. Derivation of the modified Eyring equation
As a starting point consider the linear relation between the logarithms of the rate constant k and the viscosity η as expressed by Equation 4 of the main text,
ln ∙ ln , 11
where ln k and ln η are, respectively, given by the Eyring equation and Andrade’s equation (Equations 5 and 6)
ln , 12
ln ln . 13
Here T denotes the temperature, kB is the Boltzmann constant, h is the Planck constant, R represents the universal gas constant, and finally v, w are viscosity parameters and S and H are kinetic parameters of which the values are obtainable from experiment. Based on simple linear regression analysis we have the following expression for the slope α in Equation 11,
α ∑ ∑ ̅ ̅ , 14
and for the offset β we find,
̅. 15
For notational simplicity we have introduced here parameters x and y which are, respectively, defined by
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MOLECULAR MOTORS IN VISCOUS MEDIA
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ln , 16
ln ln . 17
In the above equations, the index i labels the experimental data points. Moreover, the bars
represent average values, that is, ̅ ∑ and ∑ (n denotes the total
number of data points). It can readily be seen that substitution of Equations 16 and 17 into Equations 14 and 15 allows us to determine the explicit temperature dependence of α and β. This will be demonstrated further below.
Temperature profile α (T)
It follows from Equation 14 that α is expressed in terms of xi−x and yi−y. Using Equations
16 and 17, these factors can be rewritten as,
̅ ∑ ∑
∑ ∑ Ψ , 18
and,
ln ∑ ln
∑ ∑ Ψ . 19
In order to simplify the notation in the above expressions we have introduced parameters
, , and , given by
Ψ ̅, Ψ , Ψ ̅ , Ψ . 20
Substituting Equations 18 and 19 into Equation 14 yields the following:
α ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ . 21
We can now define coefficients c1–c6 in the following way,
∑ Ψ Ψ , ∑ Ψ Ψ Ψ Ψ , ∑ Ψ Ψ , ∑ Ψ ,
∑ 2Ψ Ψ , ∑ Ψ , 22
such that Equation 21 simplifies to
α . 23
Finally, multiplication by reduces the above equation to the form shown in Equation 7,
α . 24
We stress that the six variables (c1–c6) which determine the specific temperature dependence
of α can readily be obtained from the available data. Namely, by combining Equations 20 and 22 these values are given by
∑ ̅ ̅ , ∑ ̅ ̅ ,
∑ , ∑ ̅ , ∑ 2 ̅ ,
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4
To end this section, note that it is possible to further reduce the total number of variables to
five. For example, c6 can be eliminated from Equation 24 as follows
α , 26
where the new variables ci’ relate to the original coefficients as; ⁄ .
Temperature profile β (T)
To determine the temperature dependence of β it is convenient to first introduce new parameters for the nominator and denominator of α,
α ≡ . 27
According to Equation 15, β is expressed as a linear combination of the average values of x and y. Using the definitions in Equations 16 and 17 these are given by
̅ ̅ , 28
ln ̅ . 29
Substitution of the above three equations into Equation 15 leads to the following expression for β
ln ̅ ∙ ̅ . 30
In the right-hand side (RHS) of Equation 30 we have multiplied two of the terms by
q(T2)/q(T2) which allows to rewrite the expression for β in the following form,
ln . 31
Next, multiplication of the second term of the RHS in Equation 31 by T/T leads to a combination of the second and third factors. That is, we have
ln
ln . 32
We can now make the following substitutions,
, ̅ ̅ ,
̅ ̅ , ,
. 33
which gives rise to the following formula for β
ln
ln . 34
Finally, in order to simplify the result in Equation 34 we introduce four new coefficients d1–
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MOLECULAR MOTORS IN VISCOUS MEDIA
4
̅
̅ , ̅ ̅ , ̅ ̅ ,
. 35
Substituting these variables into Equation 34 leads to the final result for the temperature dependence of .
ln . 36
Thus, the specific temperature profile of β depends on seven variables (d1–d4 and c4–c6), of
which the value for all of them can be extracted from the available experimental data.
Temperature profile R2 (T)
The coefficient of determination , where
∑ ̅
∑ ̅ ∙∑ , 37
which can be expanded to
∑ ∑ ∑
∑ ∑ ∙ ∑ ∑ . 38
Inserting Equations 16 and 17 into Equation 38 gives
∑ ∑ ∑
∑ ∑ ∙ ∑ ∑
, 39
which is simplified to the following expression
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
∑ ∑ ∑ ∑ ∑ ∙ ∑ ∑ ∑ ∑ ∑ . 40
Introducing viscosity into the Eyring equation
Equation 13 can be rewritten as follows:
ln ln ∙ ln . 41
The viscosity of solvents changes with temperature. The obtained function allows for the creation of a full three dimensional graph of viscosity, temperature and rate (Figure 4.4). Fitting the linear Eyring equation over isoviscous ranges affords isoviscous kinetic
parameters (Hη and Sη) which were found to be linearly dependent on the viscosity.
Δ‡ ln , 42
Δ‡ ln , 43
Δ‡ ln ln . 44
This leads to the viscosity-corrected Eyring equation:
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4
Using the natural logarithmic of either function for the rate k (Equations 41 and 45), very
accurate results are obtained. Both exhibit an R2 of 0.9971 and differ only slightly in residual
sum of squares (1.89·10−8 vs 2.09·10−8) which is a very small difference for functions with
a significant difference in amount of variables (ten vs four).
Additional equations
∆ ∆
, 46
where λ1 = the distance between moving layers of molecules, λ2 = the dimension of the unit
of flow, i.e., the molecule, in the direction of flow, λ3 = is the dimension of the unit of flow
perpendicular to λ1 and λ2, and λ = the distance moved by the unit of flow in passing over a
potential energy barrier.
. 47
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