Intercomponent interactions and mobility in hydrogen-bonded rotaxanes
Jagesar, D.C.Publication date 2010
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Jagesar, D. C. (2010). Intercomponent interactions and mobility in hydrogen-bonded rotaxanes.
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C h a p t e r 2
Photoinduced Shuttling
Dynamics of Rotaxanes in
Viscous Polymer Solutions
*
Abstract
The effect of external friction, caused by medium viscosity, on the photoinduced translational motion in a rotaxane-based molecular shuttle 1 is investigated. The shuttle was successfully operated in solutions of poly(methacrylonitrile) (PMAN) of different molecular weight in MeCN and PrCN. The viscosity of the medium was tuned by changing the PMAN concentration. The rheological behavior of the polymer solution gave insight into the structure of the polymer solution on the microscopic scale. In PrCN the entanglement regime is reached at lower concentration than in MeCN. This is also reflected by the effect on the shuttling: in the PrCN/PMAN system a larger viscosity effect was observed compared to MeCN/PMAN. The shuttle is found to be slowed down in the polymer solutions but was still active at high viscosities. The observed retardation effect on the kinetics of shuttling in MeCN/PMAN and PrCN/PMAN could be correlated to the PMAN concentration through the hydrodynamic scaling model. The Stokes-Einstein relationship proved inadequate to correlate the shuttling rates to the macroscopic viscosity, but the dependence of the shuttling rate on the bulk viscosity fits well to a commonly observed power-law relationship. The viscosity effect on the shuttling was found to be weak in all cases.
* This chapter was published: Jagesar, D. C.; Fazio, S. M; Taybi, J.; Eiser, E; Gatti, F; Leigh, D; Brouwer, A. M. Photoinduced Shuttling Dynamics of Rotaxanes in Viscous Polymer Solutions. Adv.
2.1
Introduction
Interlocked molecular architectures (rotaxanes and catenanes) are promising candidates to function as active components in molecular devices[1-4] and new materials.[5-9] The possibility to control the direction and amplitude of motion along intercomponent degrees of freedom also allows the application as molecular machines[10-18] able to deliver useful work.[19,20]
The majority of the interlocked systems studied so far perform a function in solution. However, in order to realize their full potential, they will have to be organized into some array to behave collectively and, ideally, limiting the set of degrees of freedom to only the controlled translational or rotational motions. In order to suppress molecular diffusion processes, different approaches have been followed, among them immobilization on surfaces,[21-25] in polymer films[26,27] and in Langmuir-Blodgett films.[28,29] However, an almost inevitable consequence of incorporating rotaxanes in organized structures is that they are placed in a high viscosity environment, which may lead to a loss of mobility of the component parts. Therefore, a fundamental understanding of viscosity effects on the intercomponent mobility is required for the successful design of systems in which interlocked molecules can be organized with retention of their switching or motor functions.
Recently, a few studies have appeared in which the effect of the physical environment on molecular mechanical switching in rotaxanes and catenanes has been explored in different media, other than simple solvents. Stoddart et al. reported on shuttling in electrochemically switchable bistable rotaxanes and catenanes in a polymer matrix composed of acetonitrile (MeCN), poly(methylmethacrylate), propylene carbonate and LiClO4.
[26,30,31] In this medium, which may be viewed as liquid but with a viscosity approximately 104 times higher than that of a typical solvent such as acetonitrile, the switching mechanism remained unaffected. The kinetics of switching, however, exhibited a strong dependence on the environment: the rate in the polymer gel was found to be slowed down by approximately one order of magnitude compared to acetonitrile.
A systematic study of viscosity effects on the shuttling rates in a bistable rotaxane has been published by Katz et al.[32] The shuttling of a redox-active cyclophane along an immobilized thread was examined in aqueous solution of which the viscosity was tuned by the presence of different concentrations of glycerol. Despite the small viscosity range investigated (1.0 – 1.4 mPa s), a significant slowing down of the shuttling was observed.
In this chapter, the effect of viscosity in the wide range of ca. 10-4 – 10 Pa s on the performance of the rotaxane molecular shuttle 1 (Scheme 2-1) is described. Rotaxane 1 contains two potential binding stations for the macrocycle: a succinamide (succ) and a naphthalimide (ni) station. The succinamide group is known to be a better hydrogen bond acceptor than the naphthalimide station. Hence, in the thermodynamically favored conformer the macrocycle resides at the succinamide station (succ-co-conformer).[33-35] The
switching function in rotaxane 1 is based on the shuttling of the macrocycle between the two stations, which is triggered by one-electron reduction of the naphthalimide station, either electrochemically[34] or photochemically.[33] The thus formed naphthalimide radical anion has a higher hydrogen bonding affinity towards the macrocycle, which results in a net translational motion of the macrocycle towards the naphthalimide radical anion to form the energetically more favorable co-conformer ni-1●–.
The shuttling process was studied in a time-resolved way by using the electronic absorption spectrum of the naphthalimide radical anion as probe.[33] The radical anion of
1 was generated by photoinduced electron transfer from a suitable electron donor (1,4-diazabicyclo[2.2.2]octane, DABCO) to the naphthalimide triplet state. The shuttling was revealed by monitoring the precise position of the strong electronic absorption band of the radical anion near 420 nm, which undergoes a blue-shift when the macrocycle binds to the radical anion. This blue-shift is not observed for the corresponding thread and is a direct result of stabilization of the ground state of the radical anion by hydrogen bonds between the carbonyl groups of the imide anion and the NH groups of the macrocycle.[35]
Scheme 2-1 Shuttling cycle in rotaxane 1. In the activation step, the radical anion of 1 is generated by photoinduced electron transfer from 1,4-diazabicyclo[2.2.2]octane (DABCO) to the naphthalimide triplet excited state.
The activation mechanism of 1 involves photoinduced charge separation (Scheme 2-1, a detailed description is given in section 2.4). Hence, in order to obtain the radical anion of 1, a highly polar medium is required. The rates of the shuttling dynamics of 1 are quite sensitive to medium polarity.[33] Hence, for studying the effect of the medium viscosity on the shuttling dynamics, a polar medium is required which allows us to tune the viscosity
while keeping the polarity constant. Medium viscosity is a difficult parameter to tune without modifying other solvent properties, in our case polarity. In the approach chosen in the present work, solutions of poly(methacrylonitrile) (PMAN, see Figure 2-2) in acetonitrile (MeCN) and butyronitrile (PrCN) have been used. The viscosity of these solutions can be tuned by changing the concentration of polymer. The structural similarity of the repeating unit of this polymer to MeCN and PrCN is expected to minimize the change of the medium polarity. The results of studies using solvatochromic absorption and emission probes support this idea.[36]
The translational mobility of molecules in polymer melts and solutions is of great interest to many fields and has been studied extensively. As can be anticipated, the mobility in polymer solutions is a decreasing function of the polymer concentration. However, the precise nature of this relationship is very much dependent on the polymer, solvent and concentration (dilute, semi-dilute and concentrated). The origin of the existence of different regimes lies at the molecular level: the concentration dependent interactions of polymer chains with the solvent and with each other. Generally, two regimes can be distinguished: the solvated and the entangled regime. In dilute solutions of a polymer in a good solvent, the viscosity is dominated by the hydrodynamic interactions between the polymer coils. Above the overlap concentration (defined by the concentration at which the polymer coils start to touch each other) the polymers start to interpenetrate and entangle with each other. Entanglements are topological restrictions on molecular motion resulting from the fact that the chains cannot pass through each other. In such a semi-dilute polymer solution the system’s viscosity is no longer dominated by the individual polymer-coil size but by a correlation length ξ, which is an average mesh-size of the entangled polymer network. If ξ is larger than the particle size R, the friction experienced by a moving particle is determined mainly by hydrodynamic forces. When the mesh size is smaller than the particle size (ξ <
R), the particle is trapped in the polymer network and is slowed down even more.
The diffusion of molecules in polymer solutions is well described by the hydrodynamic scaling model proposed by Phillies.[37-39] This model states that the dependence of the diffusion coefficient Ds of a solute on the polymer concentration is uniformly described by
a stretched-exponential relationship in the concentration c (Eq. 2-1).
ν αc
0
s D
D = e− Eq. 2-1
This relationship is valid over a wide range of concentration c and molecular weight Mw of the polymer. In this equation D0 is Ds at zero polymer concentration and the pre-factor α
and exponent ν are scaling factors. This scaling model is built on the assumption that the dominant polymer-solute forces are hydrodynamic in nature. Entanglements and topological effects, which are present at very high polymer concentrations and molecular mass and can become dominant, are not taken into account. Under those so-called melt-like
conditions, in some cases the hydrodynamic scaling model is not adequate and a transition from stretched-exponential to power-law concentration dependence (Ds ~ cγ) is observed.[40] The hydrodynamic scaling model has been applied successfully to many transport phenomena in polymer solutions, such as sedimentation of colloid particles[41,42] and diffusion of ions,[43] small molecules,[42,44] polymer molecules[45-47] and proteins.[42,48]
The scaling parameters α and ν both depend on the system of interest (e.g. polymer molecular weight MW and solvent quality) but their physical significance is still a subject of
debate. The pre-factor α is thought to be dominated by obstruction effects and ranges over more than three orders of magnitude.[49] The value of the exponent ν ranges from ~0.5 (for
MW > 500 kD) to ~1 (roughly: MW < 50 kD). In the transition region (50 kD < MW < 500
kD) intermediate values of ν are observed. The hydrodynamic scaling model will be used to interpret the observed medium effects on the shuttling dynamics of 1 in PMAN solutions. In addition, the shuttling rates will be analyzed using theoretical models for the dependence of diffusion and chemical reaction rates on macroscopic viscosity.
2.2
Results and Discussion
2.2.1 Rheological Behavior
The viscosity η (Pa s) is a measure of the resistance of a fluid to deformation under shear. Generally, the flow behavior of a complex fluid in terms of dependence of the shear stress τ (Pa) on the applied shear rate ∂u/∂y (s-1) can be expressed by the Ostwald-de Waele power-law equation (Eq. 2-2).
n y u K = ∂ ∂ τ
n
n
< 1: pseudoplastic = 1: Newtonian n > 1: dilatant Eq. 2-2The shear rate is the velocity gradient in a fluid layer with the thickness y (m) perpendicular to the applied shear with velocity u (m s-1). In Eq. 2-2, K is the flow consistency index and n is the flow behaviour index. Three categories of flow behaviour can be recognized: dilatant (n > 1), Newtonian (n = 1) and pseudoplastic (n < 1). The simplest case is a Newtonian fluid: the flow curve (τ vs. shear rate) is a straight line i.e. the viscosity remains constant upon variation of the applied shear stress (Figure 2-1A) at a given temperature. The viscosity η (Pa s) of a Newtonian liquid is therefore defined by:
∂ ∂ = y u η τ Eq. 2-3
Most semi-dilute polymer solutions are pseudoplastic or shear-thinning in nature.[50] These liquids are characterized by an apparent viscosity that decreases with increasing shear rate (Figure 2-1B). Both at very low and very high shear rates, however, most pseudoplastic
polymer solutions exhibit nearly Newtonian behavior. The value of the apparent viscosity at very low shear rate is known as zero shear viscosity (η0). Polymer solutions derive their pseudoplastic behavior from entanglements.
(A) (B)
Figure 2-1 (A): Flow curve of a 20% PMAN-50 solution in PrCN, illustrating the Newtonian behavior. The slope of the flow curve represents the viscosity (η). (B): Viscosity curve of a 30% PMAN-50 solution in PrCN. The zero shear viscosity (η0) was determined by extrapolation of
the curve to zero shear rate.
The rheological behavior of series of solutions of PMAN with MW = 50 kD (PMAN-50)
and MW = 460 kD (PMAN-460) in MeCN and PrCN was investigated. The MeCN
solutions of PMAN-50 exhibited Newtonian behavior up to 33% PMAN-50, while the more concentrated solutions were pseudoplastic in nature. Solutions in PrCN already reached this transition point at a concentration of 25%. This means that in PrCN the critical overlap concentration c*, which is the concentration where the polymer chains start to feel each other, is lower than in MeCN. A lower c* indicates that PrCN is a better solvent for PMAN. In a good solvent the polymer chain is more expanded in order to maximize the polymer-solvent contacts. A measure for the degree of expansion of the polymer chain is the radius of gyration Rg, which is defined as the root-mean square distance of the polymer
segments to its centre of gravity. Rg scales with the degree of polymerization N as Rg ~ N v
. For a good solvent v = 3/5, while for a bad solvent v = 1/3. The critical overlap concentration c* is defined as c* ~ 1/Rg
3
. This means that the larger Rg, the lower c*, i.e. the
better the solvent, the lower c*. Due to the more expanded nature of the polymer chains in PrCN, an increased number of entanglements will be present, causing the viscosity to increase more rapidly. The fact that PrCN is a better solvent for PMAN than MeCN agrees with our expectation, because PrCN is almost isomeric to the repeating unit of PMAN.
The viscosity of the PMAN solutions in MeCN and PrCN as a function of concentration is shown in Figure 2-2. In this concentration range of 0 – 50% PMAN, ln(η) changes
linearly with weight-% PMAN i.e. the viscosity changes exponentially with the PMAN concentration. The slopes of ln(η) versus weight-% PMAN are given in Table 2-1.
PMAN
Figure 2-2 Dependence of the viscosity on the concentration of PMAN-50 and PMAN-460 in MeCN and PrCN.
Table 2-1 Slopes of ln(η) versus weight-% PMAN in MeCN and PrCN
MeCN PrCN
PMAN-50 0.207 ± 0.007 0.239 ± 0.007 PMAN-460 0.44 ± 0.01 0.53 ± 0.07
Compared to MeCN, the viscosity of PrCN is more sensitive to both the PMAN-50 and PMAN-460 content and increases more rapidly with the polymer concentration. As discussed previously, this can be related to the presence of more entanglements in PrCN due to a larger Rg.
2.2.2 Shuttling
Photoactivation of 1
Transient absorption experiments were carried out to determine the shuttling rate kshuttle
of 1 in solutions with different PMAN concentration in MeCN and PrCN. The activation of the shuttling process was achieved using the same pulse energy (2.5 mJ) for all solutions. The characteristic band of the naphthalimide triplet state (3
ni*) at 473 nm appears immediately after photoexcitation (Figure 2-3A). During the first 20 ns, the T-T absorption band is obscured by the fluorescence band from the short-lived (1.6 ns) singlet state (1
ni*). The maximum T-T absorption of the naphthalimide triplet at 473 nm was 0.19 ± 0.04 for
all PMAN-50 solutions. Quenching of the triplet state by electron transfer from DABCO results in the growing in of the absorption band (λmax = 419 nm) of the thus formed naphthalimide radical anion (ni●–).
The simultaneous decay of the 3
ni* and rise of the ni●– bands were analyzed by least-squares fitting of the observed spectra as a sum of the spectra (obtained separately) of the triplet state and of the radical anion (Figure 2-3B and C). The quenching of the naphthalimide triplet excited state by electron transfer from DABCO is a diffusion limited process and is expected to be slowed down by the high viscosity conditions in the polymer solutions. As a consequence, the triplet lifetime is expected to increase with increasing PMAN concentration. Analysis of the kinetics indeed revealed a trend of increasing triplet lifetime with increasing viscosity. The kinetics of the formation of the radical anion in PrCN/PMAN-50 exhibited a similar behavior. A gradual increase of the rise time of the radical anion band to approximately a factor 2 was observed (Figure 2-4A)
(A) (B)
(C)
Figure 2-3 (A): Transient absorption spectra of 1 in 20% PMAN-50/PrCN in the presence of 10 mM DABCO recorded at 10 – 230 ns after laser-excitation (increments 10 – 70 ns: 10 ns and 70 – 230 ns: 20 ns). The arrows indicate the decrease of the absorption at 473 nm (mostly 3
ni*) and the increase of the absorbance at 419 nm due to the radical anion (ni●–). (B): Decay of [3ni*]. (C): Rise and decay of [ni●–].
(A) (B)
Figure 2-4 (A): Rise time (τrise) of the radical anion (ni●–) and (B): ratio of maximum absorption
of the radical anion of 1 (419 nm) and T-T absorption (473 nm) at different PMAN-50 concentrations in PrCN.
Surprisingly, the amount of radical anions produced was found to be gradually decreased with increasing polymer concentration. In order to quantify this decrease, the ratio of the radical anion absorbance (419 nm) and the T-T absorption (473 nm) was calculated (Figure 2-4B). The yield of radical anions was found to be decreased by a factor of 2 in the most concentrated solution. We have previously estimated the radical ion yield in acetonitrile as ca. 20%.[33,51] This is quite low. Given that 15% of the excited molecules return to the ground state via fluorescence, the maximum triplet yield could be 85%. The lifetime of the triplet state is so long that essentially 100% of the triplets should be quenched by DABCO. The electron transfer process leads to a radical ion pair in the triplet state, which cannot rapidly undergo charge recombination because it is spin-forbidden. Thus, a free radical ion yield is expected of up to 85%. It is possible that non-radiative decay of the S1 to the ground state occurs, reducing the yield of T1, but an alternative explanation can simultaneously reconcile the low yield and the effect of polymer concentration: if the radical ion pair can undergo spin inversion before the ions have fully escaped, singlet state spin recombination may occur. This is more likely when the viscosity of the medium is higher. Further experiments are needed to test this idea, but it seems a reasonable hypothesis.
Shuttling Rate Constants
The absorption maximum of the radical anion undergoes a blue-shift during the first microseconds after its formation by electron transfer. The rate of the shift of the absorption maximum is directly linked to the rate at which co-conformer succ-1●– is converted to the energetically more favorable ni-1●–.[33] This is a first-order process and can be described by a mono-exponential function. The plot of the radical anion absorption maximum (λmax) versus time indeed exhibits mono-exponential behavior with the time constant being the shuttling rate constant (kshuttle). The shuttling rate in each solution was thus determined by fitting an
exponential function to the plot of λmax versus time (Figure 2-5). The obtained values for
kshuttle of 1 in MeCN/PMAN-50 and PrCN/PMAN-50 are listed in Table 2-2. The viscosities
of the sample solutions were calculated from the weight-% PMAN by using the logarithmic relationship between viscosity and weight-% PMAN (Figure 2-2).
(A) (B)
Figure 2-5 (A): Transient absorption spectra of rotaxane 1 in 5% PMAN-50/MeCN in the presence of 10 mM DABCO recorded 30 ns after laser-excitation, and with subsequent 200 ns increments. (B): position of the absorption maximum (λmax) of the radical anion (ni●
– ) as a function of time. The solid line is the fit to a mono-exponential function.
Table 2-2Shuttling rates of 1 in PMAN-50 and PMAN-460 solutions in MeCN and PrCN.
η (Pa s) [a] kshuttle (106 s-1) [b]
%
PMAN MeCN PrCN MeCN PrCN
PMAN-50 PMAN-460 PMAN-50 PMAN-50 PMAN-460 PMAN-50
0 0.00064 0.00074 0.00089 1.30 1.30 0.29 1 0.0079 - 0.0011 1.11 - 0.24 2 0.00097 - 0.0014 1.16 - 0.21 5 0.0018 0.065 0.0032 0.90 0.72 0.15 9 - 0.037 - - 0.60 - 10 0.0051 - 0.0098 0.72 - 0.11 15 0.014 0.50 0.0032 0.72 0.38 0.083 20 0.040 - 0.099 0.58 - 0.059 23 - 16.2 - - 0.31 - 25 0.11 - 0.34 0.41 - 0.050 30 0.32 - 1.2 0.39 - 0.032 33 0.59 1250 2.4 0.34 <0.01 0.020 [c] 36 - - 4.9 - - 0.020 [c]
[a] Extrapolated from logarithmic relationship between weight-% PMAN and η. [b] Fitting error is 5 – 10%.
2.2.3 Hydrodynamic Scaling Model
Shuttling in rotaxane 1 can be treated as a diffusion process of the thread and macrocycle with respect to each other: a net translational motion of the macrocycle along the thread from one station to the other takes place. The equivalents of the diffusion constants in Eq. 2-1 are kshuttle and k0, the latter being the shuttling rate in pure solvent (Eq.
2-4). ν αc 0 shuttle k k = e− Eq. 2-4
The observed shuttling rate in 50/MeCN, 50/PrCN and PMAN-460/MeCN showed stretched-exponential dependence on the PMAN concentration (Figure 2-6). The smooth relationship between kshuttle and PMAN concentration clearly
demonstrates that entanglements, present in the concentrated PMAN solutions, do not affect the shuttling. This can be interpreted in two ways. If the size R of the moving component of the shuttle is smaller than the correlation length ξ, the entanglements do not play a role at all. Alternatively, even if ξ < R, the friction experienced by the molecular shuttle is mainly due to hydrodynamic forces and additional effects of entanglements are negligible.
Figure 2-6 Plot of the reduced shuttling rate (kshuttle/k0) versus the weight-% PMAN-50 in
MeCN (—○—) and PrCN (—●—) and weight-% PMAN-460 in MeCN (- -□- -). The solid line is the least-squares fit to the stretched exponential in Eq. 2-4.
According to the literature, the parameter ν depends on the polymer molecular weight
MW. Values of ν are expected to be close to 1 for 50 and close to 0.5 for PMAN-460. In MeCN, ν = 1.0 and ν = 0.62, respectively (Table 2-3). The value of ν in the PMAN-50/PrCN system is smaller than that in PMAN-50/MeCN. This can be attributed to the
solvating efficiency of the solvent. As was concluded from the rheological behavior of PMAN-50 in PrCN and MeCN, the solvation of PMAN in PrCN is more efficient.
Table 2-3 Values of α and ν obtained from fitting kshuttle/k0 versus weight-% PMAN to the
stretched-exponential in Eq 2-4. MeCN PrCN PMAN-50 α 0.03 ± 0.01 0.18 ± 0.01 ν 1.0 ± 0.1 0.74 ± 0.02 PMAN-460 α 0.21 ± 0.03 - ν 0.62 ± 0.06 -
The value of α in MeCN is much larger for PMAN-460 than for PMAN-50. A high value of α indicates that there are obstruction effects, which are much larger in the PMAN-460 solution. Also, in PMAN-50/PrCN (α = 0.18), α is larger than in PMAN-50/MeCN (α = 0.03). The larger obstruction effect in PMAN-50/PrCN can be attributed to the better solvent quality of PrCN vs. MeCN.
2.2.4 Correlation with Macroscopic Viscosity
As was argued above, the shuttling in 1 can be treated as a diffusion process of the macrocycle relative to the thread. The diffusion coefficient D of particles with hydrodynamic radius RH as a function of solvent viscosity is often analyzed with the
Stokes-Einstein relationship (Eq. 2-5).
H B R T k D η π = 6 Eq. 2-5
In this equation, kB is the Boltzmann constant, T is the temperature, RH is the
hydrodynamic radius of the moving particle and η is the bulk viscosity of the solvent. The Stokes-Einstein relationship is obeyed perfectly in systems of diffusing particles in neat solvents. In the case of shuttling in 1, the analogue of the diffusion constant is the shuttling rate constant kshuttle. Assuming that Eq. 2-5 applies to our system the ratio k0/ kshuttle can be
expressed as: 0 shuttle 0 k k η η = Eq. 2-6
In this equation, k0 is the kshuttle in pure solvent and η0 is the viscosity η of pure solvent.
From Eq. 2-6 it follows that the ratio (kshuttleη)/(k0η0) = 1. The quantities k0/kshuttle and η/η0
are plotted against the weight-% PMAN in Figure 2-7. The graph clearly shows the dramatic deviation from the Stokes-Einstein relationship: (kshuttleη)/(k0η0) >1 over the entire
concentration range: the deviation is up to 104 in PMAN-460/MeCN. The measured k
shuttle is
much larger than might be expected from the bulk viscosity.
Figure 2-7 Plots of the ratios k0/kshuttle (dashed lines) and η /η0 (solid lines) versus PMAN-50
in MeCN and PrCN and weight-% PMAN-460 in MeCN.
2.2.5 Power-Law Relationship
The viscosity dependence of the rates of several types of reactions involving large amplitude motions has been found to be well described by the simple power-law equation Eq. 2-7.[52] Examples include photoisomerization reactions,[53,54] thermal isomerizations,[55,56] photoinduced release of CO from myoglobin[57] and protein folding.[58,59] This equation has long been used as a phenomenological description, but a theoretical foundation has been provided by Bagchi and co-workers.[60]
a A
k(η)= η− Eq. 2-7
In Eq. 2-7, A is a pre-factor and the exponent a represents the extent of the viscosity effect. Eq. 2-6 can be seen as a special case of Eq. 2-7, with a = -1. An important feature of this model is that kshuttle approaches zero as the viscosity approaches infinity. It should also
be noted that this model is not valid for very low values of the viscosity (η → 0). Under those conditions internal factors such as molecular conformation and internal friction may become dominant over medium viscosity. The effects of these factors could be studied if shuttling could be made to occur in the gas phase.[61]
The shuttling rates of 1 in MeCN/PMAN-50, MeCN/PMAN-460 and PrCN/PMAN-50 are plotted against the viscosity in Figure 2-8. The plots clearly show that the shuttle is slowed down upon increase of the medium viscosity. The a-values in the PMAN-50 and
PMAN-460 solutions in MeCN are found to be small (0.18). The viscosity effect is significantly larger in PrCN/PMAN-50, with a = 0.35. This difference can be explained by the presence of more entanglements at a given viscosity in PrCN compared to MeCN. It was already concluded from the rheological behavior that the correlation length ξ is smaller in PrCN than MeCN. The molecular shuttle is slowed down more in PrCN with increasing concentration of PMAN, but this is more due to the entanglements which hamper the motion than to the general increase of the viscosity.
Figure 2-8 Shuttling rate of 1 as a function of viscosity in MeCN/PMAN-50 (—○—), MeCN/PMAN-460 (--□--) and PrCN/PMAN-50 (—●—). The viscosities of the PMAN-50 solutions were extrapolated form the derived relationship between weight-% PMAN-50 and the viscosity (see Figure 2-2).
Table 2-4 Factors a describing the fractional dependence of kshuttle on the viscosity of PMAN
solutions in MeCN and PrCN (Eq. 2-7).
MeCN PrCN
PMAN-460 0.18 ± 0.03 -
PMAN-50 0.18 ± 0.01 0.35 ± 0.03
The dependence of the shuttling rate on the viscosity is found to be weak. For example, an increase of the viscosity in PrCN/PMAN-50 by a factor 104 slows down the shuttling only by one order of magnitude. Extrapolating the fitted relationship in Figure 2-8 suggests that the shuttle will be slowed down, but will remain active at very high viscosities. At a viscosity of 103 Pa s (33% PMAN-460 in MeCN), however, shuttling could no longer be detected on the timescale of ca. 100 microseconds accessible in our experimental setup, even though the formation and decay of the radical anions could still be observed.[36] It is
likely that at these high polymer concentrations the entanglements frustrate the large-amplitude motions needed for the shuttling process, while the diffusion of the small near-spherical DABCO molecule is not severely hampered, in agreement with the observations above that the quenching of the naphthalimide triplet state is slowed down only by a factor of ca. 2 at a viscosity of ca. 0.1 Pa s.
In the literature, widely varying values of the parameter a can be found.[52-59,62-65] Murarka et al.[60] argued that the values of the exponent a should approach 0.8 for reactions with a very small barrier crossing frequency, while a becomes small for reactions with a very strong curvature of the energy surface near the transition state. Intuitively, one associates high barrier frequency with a high barrier energy. In the case of the shuttling process in 1, the activation energy was found to be ca. 8 kcal mol-1.[36] According to our original mechanistic hypothesis, the barrier is associated with the breaking of the hydrogen bonds between the macrocyclic ring and the succinamide station. Subsequently, the ring moves along the thread in a diffusive (random) motion until it is captured by the naphthalimide anion, or unsuccessfully returns to the succinamide. According to molecular dynamics simulations, the diffusive motion in acetonitrile or chloroform along the C12 spacer is complete within 1 ns.[66] This timescale is much smaller than the reaction frequency, so it does not directly enter into the observable rate. Viscosity could affect the two steps in this process in different ways. Obstructions related to entanglements could render diffusive trajectories unsuccessful, effectively reducing the observed reaction rate. On the basis of recent experimental data, an alternative model needs to be considered, in which the detachment of the macrocyclic ring from the succinamide station is assisted by the accepting naphthalimide anion station, which forms one or more hydrogen bonds with the macrocyclic ring before this leaves the succinamide station (see also Chapter 6).[67] In this case, a different large-amplitude motion is involved, namely the approach of the imide station to the ring.
The observed viscosity effect on the kinetics of shuttling in 1 in our work is comparable with the results reported by Stoddart et al.[26,30,31] The rate of switching in electrochemically switchable bistable rotaxanes and catenanes in a polymer matrix was found to be slowed down by approximately one order of magnitude compared to acetonitrile.
We also analyzed the data reported by Katz et al.[32] using the power-law relationship (Eq. 2-7) and, remarkably, found a much larger viscosity effect: values of a ranging from 6 – 7. The small viscosity effect on our molecular shuttle 1 seems to conflict with these results. However, Stokes-Einstein analysis showed that the ratio (kshuttleη)/(k0η0) for the system
studied by Katz et al. is smaller than unity and decreases rapidly with increasing viscosity. Generally, in cases where Dη/(D0η0) < 1, the deviation is attributed to specific
interactions.[68,69] These specific interactions lead to adsorption of the particles to each other or to the polymer molecules in solution. This means that the slowing down of the shuttle cannot be solely ascribed to friction due to hydrodynamic forces, but also to specific interactions such as hydrogen bonding.
2.3
Conclusion
We have investigated the effect of external friction, caused by medium viscosity, on the photoinduced translational motion in a rotaxane-based molecular shuttle. The shuttle was successfully operated in solutions of poly(methacrylonitrile) (PMAN) of different molecular weight in MeCN and PrCN. The viscosity of the medium was tuned by changing the PMAN concentration.
The rheological behavior of the polymer solution gave some insight into the structure of the polymer solution on the microscopic scale. In PrCN the entanglement regime is reached at lower concentration than in MeCN. This is also reflected by the effect on the shuttling: in the PrCN/PMAN system a larger viscosity effect was observed in comparison to that in MeCN/PMAN.
The shuttle is found to be slowed down in the polymer solutions but was still active at high viscosities. The observed retardation effect on the kinetics of shuttling in MeCN/PMAN and PrCN/PMAN could be correlated to the polymer concentration through the hydrodynamic scaling model. The shuttling rate showed a stretched exponential dependence on the polymer concentration as predicted by the hydrodynamic scaling model for transport phenomena in polymer solutions. The parameters indicate that obstruction effects reduce the shuttling rate in PMAN solutions in PrCN more than in MeCN, which can be related with the presence of more entanglements of the polymer chains in PrCN.
The Stokes-Einstein relationship proved inadequate to correlate the shuttling rates to macroscopic viscosity, but the dependence of the shuttling rate on the bulk viscosity fits well to a commonly observed power-law relationship. The viscosity effect on the shuttling was found to be rather weak in all cases.
An alternative experimental approach to study viscosity effects, which is more appealing from a theoretical point of view, is to increase the viscosity by applying hydrostatic pressure to the solutions. Preliminary experiments on this approach were already performed; the results are discussed in Chapter 8.
2.4
Photophysics of the Naphthalimide Rotaxane
[a]Macrocycle shuttling in rotaxane 1 (Scheme 2-1) takes place after formation of the naphthalimide radical anion, the mechanism of which is displayed in Figure 2-9B. The singlet excited state of the naphthalimide chromophore (1
ni*) undergoes rapid intersystem crossing to the triplet state (3
ni*). After electron transfer from the electron donor DABCO (D) to 3
ni*, the radical anion (ni●–
) is formed. The fluorescence quantum yield of thread 2 in MeCN in the absence of an electron donor is 0.15; this means that the quantum yield of
[a] Appendix to the published paper.
intersystem crossing (Φisc) is limited to a maximum of 0.85.
[51] Electron transfer from DABCO to the triplet state is fast compared to the long triplet lifetime (τT = 43 µs), justifying the assumption that complete reduction of triplet states will take place. Consequently, we could assume that the quantum yield of radical anions will be similar to that of intersystem crossing: Φni•−≈ Φisc. The lifetime of the naphthalimide radical anion is
sufficiently long (τni•−~10
2 µs) to allow quantitative conversion of the
succ-1●– to the ni-1●– co-conformer, which occurs on the microsecond timescale. Therefore, the quantum yield of shuttling Φshuttle will be the same as that of radical anion formation: Φshuttle ≈ Φni•−.
(A) (B)
Figure 2-9 (A): Absorption (solid line) and fluorescence (dotted line, λexc = 340 nm) spectra of
thread 2 in MeCN. (B): Energy level diagram displaying the processes occurring after photon absorption by the naphthalimide chromophore (ni) of 1 and 2 in the presence of electron donor DABCO (D) The quantum yields Φf and Φisc are in the absence of the electron donor.
The non-negligible viscosity effect on the yield of radical anions (Figure 2-4B) however suggests that the assumption Φni•−≈ Φisc might not be justified. Possibly, spin inversion can
occur (in pure MeCN) before the radical ion pair can dissociate and therefore Φni•−< Φisc This effect will be stronger if the viscosity of the medium is higher. The quantum yield of radical anions was indeed found to be lower than the anticipated maximum of 0.85: Φni•−= 0.20 in the presence of 10 mM DABCO.[51] This however does not proof the above mentioned hypothesis, because in the presence of an electron donor, Φisc is already expected to be lower than 0.85 due to competition with the singlet state quenching via electron transfer. Depending on the magnitude of the singlet state quenching rate (kq[Q]), a fraction of the singlet excited states will already be deactivated by electron transfer, before intersystem crossing (with rate kisc) can occur. In order to get more insight into this issue, the fluorescence quenching of 2 by DABCO was investigated.
The time constant of fluorescence quenching (kq) of thread 2 by DABCO via electron transfer was determined with steady state fluorescence measurements. The Stern-Volmer
plot obtained with the steady state method is depicted in Figure 2-10. The plot is linear at low quencher concentration (< 40 mM), but shows an upward curvature indicating that the quenching process is not purely dynamic, but a combination of dynamic and static quenching. The curve was fitted to the Stern-Volmer equation for combined static and dynamic quenching (Eq. 2-8).[70] The ratio of the fluorescence intensity in the absence (F
0)
and presence (F) of quencher is second-order in the quencher concentration [Q]. 2 [Q] [Q] ) ( 1 D S D S 0 K K K K F F = + + + Eq. 2-8
Figure 2-10 Stern-Volmer plot of fluorescence quenching of thread 2 in MeCN by DABCO, determined with steady-state fluorescence.
From this analysis a static quenching constant KS = (6.1 ± 0.3) M
-1 is obtained, the dynamic quenching constant is KD = (30.9 ± 0.9) M
-1. The bimolecular fluorescence quenching constant kq = (1.9 ± 0.1) × 10
10 M-1 s-1 was calculated from the dynamic quenching constant KD and the fluorescence lifetime of
1
ni* (τ0 = 1.6 ns)
[51] using the relationship KD = τ0 kq.
[70] The fact that the obtained value for k
q is in the order of 10
10 M-1 s-1 reveals that the dynamic fluorescence quenching of 2 by DABCO is a diffusion-limited process. The fluorescence quantum yield in the presence of 10 mM DABCO decreases with a factor 1.4 and is estimated to be Φf = 0.11.
Discussion
In the introduction it was suggested that singlet state quenching by DABCO might compete successfully with intersystem crossing, leading to a lower Φisc. The large kq which is
at the diffusion limit indicates that this might indeed be the case. The kisc of threads 2 was
not determined, but values from the literature for similar systems can be used to evaluate this issue.
In the literature, an intersystem crossing rate for N-methyl-1,8-naphthalimide in MeCN has been reported: kisc = 6.5 × 109 s-1.[71] The authors also observed a low fluorescence quantum yield of Φf = 0.027 and a short lifetime of τf = 0.145 ns (the radiative decay rate kf
= Φf / τf ≈ 2 × 108 s-1). This was attributed to the small energy gap between the excited singlet and triplet state energy levels, which leads to a very efficient intersystem crossing (Φisc = 0.94). In comparison, the photophysics of the 3,6-substituted naphthalimide in 2 is slightly different due to the electron-donating tert-butyl groups: the excited singlet state energy level is lowered relative to the triplet energy level.[51] This modification is responsible for the higher fluorescence quantum yield (Φf = 0.15) and longer fluorescence lifetime (τf =
1.6 ns) of 1 and 2. Consequently, also a lower intersystem crossing rate (kisc < 6.5 × 109 s-1) can be anticipated, with a ratio (kq/kisc) > 3.
This analysis demonstrates that Φisc for 1 and 2 will indeed be significantly smaller in the presence of electron donor DABCO, because quenching of the singlet state via electron transfer occurs with a higher rate (kq ~ 1010 M-1 s-1). Despite the fact that this analysis predicts the anticipated lowering of Φisc in the presence of DABCO, it does not quantify this
decrease. Therefore, it does explain the low radical anion quantum yield, but only qualitatively and additional other causes cannot be excluded. Thus, the hypothesis that the radical anion pair can undergo spin inversion before it dissociates (resulting in Φni•−< Φisc) can not be rejected. Additional experiments are necessary to test this hypothesis. The measurement of the intersystem crossing rate (kisc) or quantum yield (Φisc) in the presence of DABCO would be very helpful.
2.5
Experimental Details
Materials
Rotaxane 1 was available from previous work.[33] Two batches of poly(methacrylonitrile) were purchased from Scientific Polymer Products Inc. and used as received. One batch had an average molecular weight (according to the manufacturer) of ca. 50 kD. This will be denoted PMAN-50. The other batch had an average molecular weight of 460 kD (PMAN-460). Acetonitrile (spectroscopic grade) and butyronitrile were freshly distilled from calcium hydride. Experimental data obtained with PMAN-460 are from the PhD thesis of S.M. Fazio.[36]
Viscosity Measurements
Solutions of PMAN were prepared by dissolving weighted amounts of the polymer in MeCN or PrCN and allowed to homogenize. The semi-dilute solutions (< 15% by weight) were already homogeneous after one night. Solutions with 20 – 36% PMAN took several days to homogenize. Rheological measurements were performed on a stress controlled
Haake RS150 rheometer with a TC501 temperature controller. The prepared polymer solutions were allowed to homogenize for at least two days prior to rheological measurements. All viscosity measurements described in this chapter were performed at 293 K using a cylinder Z41 sensor system.
Transient Absorption
Samples for transient absorption experiments were prepared as follows. Stock solutions of DABCO (0.500 ml, 0.1 M) and rotaxane 1 (0.500 ml, 0.5 mM) in either MeCN or PrCN were added to weighted amounts of PMAN. Solvent was added up to a total weight of 5 grams. Because the densities of the solutions are not known, the concentrations of DABCO and 1 could not be expressed in mol L-1. They are quite close to 10-2 M and 10-4 M, respectively. The solutions were allowed to become homogeneous. The homogeneous solutions were transferred to T-shaped cells having a bulb in which the solutions can be degassed and a 1 cm quartz cell for the spectroscopic measurements. Three freeze-pump-thaw cycles were applied, and the degassed solutions were allowed to homogenize again in the spectroscopic cell compartment. All measurements were carried out at room temperature (293 K).
Nanosecond-to-microsecond transient absorption spectra were obtained after excitation of the sample with 7 ns pulses (FWHM) of a Spectra Physics GCR-3 Nd:YAG laser at 355 nm operated at a repetition rate of 5 Hz. The excitation energy was 2.5 mJ pulse-1. A low pressure xenon flash lamp (EG&G FX505) working at 10 Hz was used as white probe light source. The probe light was split with a 50/50 quartz beam splitter in a reference beam (Iref)
and a signal beam (It); the latter irradiated the laser-excited volume through a through a slit
(10 x 2 mm) directly behind the front face of the sample cell. Both beams were sent via optical fibres to a spectrograph (Acton SpectraPro-150) coupled to a time-gated intensified CCD camera (Princeton Instruments ICCD-576-G/RB-EM). The timing of the laser, flash lamp and CCD-camera was done with two computer controlled pulse generators (a Princeton Instruments PG-200 and a BNC 555) and a delay generator (EG&G Princeton Applied Research 9650A). The signal and reference beams were recorded on separate stripes of the CCD camera by opening the gate of the detector (for 5 – 500 ns depending on the shuttling rate) at different times after the laser pulse. For each delay time, 50 spectra were averaged. The ground state absorption spectrum (A0) was calculated by taking the
logarithm of the ratio I/Iref without laser pulse. The absorption spectrum of the excited
sample (At) was determined in the same way but after the excitation pulse. The transient
absorption spectrum (∆A) was calculated as the difference At - A0. Operation of the
excitation at 5 Hz and the probing at 10 Hz, enabled the recording of the ground state spectrum before each laser pulse. This allowed us to check that photodegradation of the samples was negligible.
Acknowledgements
Jimmi Taybi is gratefully acknowledged for performing the viscosity measurements and a part of the transient absorption experiments. We also thank Dr. Erika Eiser for her assistance with the interpretation of the rheological experimental results.
2.6
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