Nanomechanical properties of molecular-scale bridges as visualised by intramolecular electronic energy transfer

Article abstract of DOI:10.1039/c2sc21505e

A series of molecular dyads has been synthesized and fully characterised. These linear, donor-spacer-acceptor compounds comprise terminal dyes selected to exhibit intramolecular electronic energy transfer (EET) along the molecular axis. The spacer is built by accretion of ethynylene-carborane units that give centre-to-centre separation distances of 38, 57, 76, 96, and 115 A respectively along the series. The probability of one-way EET between terminals depends on the length of the spacer but also on temperature and applied pressure. Throughout the series, the derived EET parameters are well explained in terms of through-space interactions but the probability of EET is higher than predicted for the fully extended conformation except in a glassy matrix at low temperature. The implication is that these spacers contract under ambient conditions, with the extent of longitudinal contraction increasing under pressure but decreasing as the temperature is lowered. Longer bridges are more susceptible to such distortion, which is considered to resemble a concertina effect caused by out-of-plane bending of individual subunits. The dynamics of EET can be used to estimate the strain energy associated with molecular contraction, the amount of work done in effecting the structural change and the Young's modulus for the bridge.

Full text of DOI:10.1039/c2sc21505e

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Nanomechanical properties of molecular-scale bridges as visualised by
intramolecular electronic energy transfer
Delphine Hablot,a Raymond Ziessel,a,* Mohammed A. H. Alamiry,b Effat Bahraidahb and Anthony
Harrimanb,*
5
Received (in XXX, XXX) Xth XXXXXXXXX 200X, Accepted Xth XXXXXXXXX 200X
DOI: 10.1039/b000000x
A series of molecular dyads has been synthesized and fully characterised. These linear, donor-spacer-
acceptor compounds comprise terminal dyes selected to exhibit intramolecular electronic energy transfer
(EET) along the molecular axis. The spacer is built by accretion of ethynylene-carborane units that give
10 centre-to-centre separation distances of 38, 57, 76, 96, and 115 Å respectively along the series. The
probability of one-way EET between terminals depends on the length of the spacer but also on
temperature and applied pressure. Throughout the series, the derived EET parameters are well explained
in terms of through-space interactions but the probability of EET is higher than predicted for the fully
extended conformation except in a glassy matrix at low temperature. The implication is that these spacers
15 contract under ambient conditions, with the extent of longitudinal contraction increasing under pressure
but decreasing as the temperature is lowered. Longer bridges are more susceptible to such distortion,
which is considered to resemble a concertina effect caused by out-of-plane bending of individual
subunits. The dynamics of EET can be used to estimate the strain energy associated with molecular
contraction, the amount of work done in effecting the structural change and the Young’s modulus for the
20 bridge.
uncommonly short length.14 The mechanism, which has been
applied widely in biology to measure distances and/or
orientations,15 does not require orbital contact and can occur over
separations exceeding 100 Å. The requirements for efficient
50 Förster-type EET include good spectral overlap between
fluorescence from the donor and absorption by the acceptor and a
high radiative rate constant for the donor.16 Additional requisites
relate to an appropriate alignment of transition dipole moment
vectors17 and to the screening factor imposed by the surrounding
55 medium.18 This latter term is likely to be distance dependent for
short (<20 Å) separations,19 where higher-order multipoles have
to be considered,20 and where the spatial distribution of the
transition moment has to be taken into account. There are the
additional challenges of dealing with reactants subjected to
60 Brownian motion that perturbs the overall orientation factor21
and in handling cases where the transition dipole moment vectors
are degenerate.22
Introduction
Electronic energy transfer (EET) is of major importance in
biology, notably photosynthesis1 and photolyase enzymes,2 and
in modern opto-electronic devices such as OLEDs.3 The original
25 theoretical frameworks were developed4,5 more than 50 years ago
but have been subjected to considerable modification and
extension over the past few decades.6 With specific consideration
of intramolecular EET, there are three primary mechanisms that
combine to cover most cases. These include electron exchange
30 (or through-bond EET), coulombic interactions (or through-space
EET), and bridge-mediated EET.7 The latter8 applies to systems
where the donor and acceptor are bridged by a conjugated spacer
in such a way that the identities of the three components become
somewhat blurred in electronic terms. Electron exchange9
35 demands orbital overlap between donor and acceptor, often
facilitated by super-exchange interactions, where the rate is
attenuated exponentially with increasing separation between the
reactants.10 This mechanism is important for triplet-excited
states11 and for EET in conducting polymers.12 A special
40 situation might arise, however, when the reactants share a
common connecting vibrational mode.13
Many experimental and theoretical studies have addressed the
basic premise of how separation distance affects the dynamics of
65 EET23 while other research has used the ideal distance
dependence to estimate molecular topology.24 Such work is most
likely to succeed over modest separations but to become
increasing less reliable as the reactants approach each other. The
opposite trend, namely increasing the molecular separation,
70 introduces severe problems in terms of establishing the actual
distance between the reactants. Early work in this subject relied
on random distributions of donors and acceptors where the mean
Through-space EET, as first formulated by Förster,5 is most
often explained within the confines of the ideal dipole
approximation but this might not hold at short (<30 Å)
45 separations unless the transition dipole moment vectors are of
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HB
BH
H
B
H
B
I
BH
C
C
HB
Si
B
H
B
H
View Online
O
HB
BH
90
100
110
120
130
O
B(I)
O
O
CAR(I)
10
20
30
40
50
O
HB
BH
N
N
H
H
N
N
B
B
F
F
I
B
H
C
HB
BH
C
Si
Br
N
B
H
O
B
H
HB
BH
DPP(Br)
CAR(H)
O
O
O
O
O
HB
BH
H
B
H
B
N
B
F
F
HB
C
BH
C
Si
N
B
H
B
H
HB
BH
n = 0-5
O
B(CAR)1-5(TES)
O
O
O
O
O
O
HB
BH
N
H
B
N
H
B
N
N
F
F
HB
C
BH
C
B
N
O
B
H
B
H
HB
BH
n = 1-5
O
B(CAR)1-5DPP
O
O
Results and Discussion
Chart 1. Chemical structures of the building blocks required to prepare
the final B(CAR)nDPP compounds.
Synthesis and characterisation
separation is determined by concentration.25 This situation was
135 The compounds of interest here comprise a linear molecular wire
of variable length formed by accretion of para-ethynylene
carboranes fitted with terminal chromophores (Chart 1). We used
an iterative synthetic protocol starting from the pivotal building
blocks B(I), CAR(I), CAR(H) and DPP(Br); see Supporting
140 Information for synthetic details. Each intermediate B(CAR)nH
was used to produce the target dyad and to extend the bridge
according to Scheme 1. The initial step requires cross-coupling
of B(I) with the carborane CAR(H) in the presence of Pd(0)
under mild conditions. Deprotection of the triethylsilane group
145 with NaOH provides the first module for DPP cross-linking,
thereby giving subsequent access to the target dyad with N=1. In
fact, the B(CAR)1(H) module is easily coupled to a second
carborane unit CAR(I) which could be deprotected or involved in
further cross-linking with DPP, thus affording the next target
150 with N=2. Each member of the family, B(CAR)NDPP, was
prepared according to the strategy sketched in Scheme 1 and was
characterised fully by NMR (1H, 13C, 11B), ESI-MS, and
elemental analysis. The derived spectroscopic data are entirely
supportive of the claimed molecular entities. X-Ray crystal
155 structures being unattainable, the critical molecular dimensions
were assessed by quantum chemical computations that confirm
the fully extended conformations to be the lowest-energy species
in each case. In particular, the distances (DCC) between the
centres of the terminal fluorophores for the energy-minimised
160 structures are listed in Table 1.
55 improved by attaching the reactants to bio-molecules, such as
helical proteins26 or DNA,27 thereby allowing the distance to be
better defined. Related studies have used polymers28 to bind the
reactants but suffer badly from structural heterogeneity.29 In
attempting to design new molecular dyads that overcome these
60 structural problems, our attention was drawn to the possible use
of carboranes as building blocks by which to assemble linear
molecules of unusual length but high structural integrity.
Carboranes are polyhedral clusters built with skeletal boron
and carbon atoms terminated by hydrogen atoms which are used
65 extensively as templates for the preparation of soft matter,30
polymers,31 non-linear materials,32 rigid rods33 and self-
assembled molecular structures.34 Notably, closo-para-carborane
(C2B10H12) is an electronically closed structure stabilised with 26
electrons. This electronic and geometric shell closure makes
70 carboranes electronically, chemically and thermodynamically
rather robust.35 Furthermore, these caged clusters are transparent
to visible light and do not exhibit redox activity at normally
accessible potentials.36 This realisation prompted us to use closo-
para-carborane as a platform through which to link photoactive
75 modules in a rod-like manner (Chart 1).37 Note that the blue dye
has been chosen from the distyryl-boron dipyrromethene
(Bodipy) family38,39 while the dipyrrolopyrrole (DPP) donor is
known for its exceptional stability, ease of chemical modification
and well-defined structure.40 For both dyes, the presence of
80 adequate functions (BF2 in the acceptor and dimethylamino-
propyne in the donor) help to prevent aggregation.
Absorption spectra recorded for the compounds in
methyltetrahydrofuran (MTHF) exhibit the expected features
characteristic of each chromophore (Figure 1). In particular, the
2
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“blue” Bodipy dye (B) exhibits a strong absorption transition
centred at 645 nm (εMAX ≈ 123,000 M-1 cm-1), with a set of
vibronic bands stretching to higher energies.41 The corresponding
absorption transition for DPP is easily recognised42 as a series of
weaker bands starting at around 497 nm (εMAX ≈ 30,500 M-1
cm-1). The carborane-based bridge, CAR, absorbs only in the
near-UV region, with bands centred in the 300-350 nm region.
Band maxima, half-widths and molar absorption coefficients
(εMAX) recorded for both B and DPP are insensitive to the
10 molecular length but there is a progressive increase in εMAX for
CAR with increasing number of repeat units. Fluorescence
spectra (Figure 2) recorded in MTHF show emission bands
characteristic of B41 (λFLU = 662 nm) and DPP42 (λFLU = 570
nm). The blue dye can be excited selectively at 620 nm while the
15 optimal excitation wavelength for DPP is 490 nm, where B
absorbs ca. 5% of incident photons. No fluorescence is observed
from CAR following excitation at 300 nm. Throughout this
work, comparison is made to control compounds for both DPP
and B (see Supporting Information for structures).43
control compound. In contrast, preferential excitation into DPP
gives a mixture of fluorescence characteristic of DPP and B,
which can be deconvoluted spectrally to allow calculation of the
individual ΦF and τS values. It is seen that, in each case, emission
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5
35 from DPP is decreased relative to that recorded for the control
compound under identical conditions (taking due account of the
5% photon loss) while emission from B is increased compared to
what could be expected on account of the respective absorption
spectral profiles. This feature was confirmed by comparison to an
40 equimolar mixture of DPP and B in MTHF. The disparity in ΦF
and τS values measured for dyad and control compound in the
equimolar mixture increases markedly as the molecular length
decreases but becomes difficult to assess with real accuracy for
the longest dyad. Indeed, it is more meaningful, at least for the
45 longer analogues, to report the ratio (RDA) of deconvoluted ΦF
values measured for DPP relative to B. There is acceptable
agreement between the variation in ΦF and τS values along the
series, while the time-resolved emission decay curves are well
described in terms of mono-exponential fits in each case.
B(CAR)4DPP
5
4
3
2
1
B(CAR)2DPP
DPP(Br)
DPP(Br)
B(CAR)4H
B(CAR)2H
CAR(H)
CAR(H)
B(I)
B(CAR)2TES
B(CAR)4TES
0
CAR(H) B(CAR)TES
300
400
500
600
700
B(CAR)3TES
CAR(H)
λ / nm
B(CAR)5TES
B(CAR)H
50 Figure 1. Absorption spectra of the target dyads recorded in MTHF: the
arrow indicates increases molecular length.
CAR(H)
B(CAR)3H
Excitation spectra confirm that quenching of donor emission is
due to intramolecular EET from DPP to B under these
conditions. The photophysical properties of the acceptor moiety
55 are unaffected by the presence of the donor while the large
energy gap between donor and acceptor excited-singlet states
(∆ESS = 2,400 cm-1) points to unidirectional EET. Rate constants
(kEET) and probabilities (PEET) for this step, as derived from the
steady-state yields and time-resolved decay profiles, are collected
60 in Table 2. The two sets of data are in good agreement, as are the
PEET values determined from the ratio of quantum yields. For the
sake of consistency throughout the different sets of experimental
results to follow, we have opted to rely on these latter PEET
values, which are seen to decrease with increasing molecular
65 length (Table 2).
DPP(Br)
B(CAR)5H
B(CAR)DPP
DPP(Br)
DPP(Br)
B(CAR)3DPP
B(CAR)5DPP
20
Scheme 1. Protocol use for the implementation of carborane units and
preparation of the target compounds.
Photophysical properties in fluid solution
For the isolated control compounds, the Förster critical
distance44 (DCD) is computed to be 54.4 Å for MTHF at room
temperature on the basis of the ideal dipole approximation (IDA)
being valid for these reactants. Now, the effective separation
70 distance (dEFF) between the centres of the reactants can be
estimated from Equation 1 and the derived values are given in
Table 2. It is apparent that the probability of Förster-style EET is
somewhat higher than expected at the longer separations,
Fluorescence quantum yields (ΦF) and excited-singlet state
25 lifetimes (τS) recorded for the B and DPP units present in the
assembled dyads was compared with those recorded for the
isolated control compounds in MTHF at room temperature. The
main results are listed in Table 1. In each case, direct excitation
into B gives fluorescence characteristic of that unit with ΦF and
30 τS being essentially unperturbed relative to those of the relevant
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although it has to be realised that the experimental uncertainty
increases with decreasing extent of fluorescence quenching.
Nonetheless, all three estimates of PEET indicate that the effective
separation distance is less than that predicted for the fully
extended geometries, except for N=1. These fluorescence
experiments were repeated as a function of concentration in order
to eliminate any effects due to intermolecular EET, which could
be a particular problem for the longer bridges where solubility is
limited and neighbouring molecules are necessarily in close
35 between the reactants is comparable to the sum of the lengths of
the transition dipole moment vectors. The carborane-based
system, which spans an unusually wide variation in separation
distance, appears to behave in the opposite sense! The most
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5
likely cause of this effect is that the molecular bridges are
40 susceptible to out-of-plane bending that provides access to
molecules with decreased DCC
.
DC6D
P
=
EET
DC6D + dE6FF
10 contact at modest concentration. However, a 20-fold dilution
(from an initial concentration of 2 µM) had no obvious effect on
the results.
(1)
45
Effect of lowering the temperature
6
5
4
3
2
1
0
It has been demonstrated experimentally that the bending rigidity
of molecular surfaces is temperature dependent.46 We might
50 expect similar behaviour for the carborane-bridged molecular
dyads under investigation here. As such, fluorescence spectra
were recorded in MTHF as a function of temperature. On cooling
the solution (Figure 3), the emission maxima recorded for DPP
and B undergo modest red shifts due to the temperature-induced
55 change in polarisability of MTHF.47 This effect is more
pronounced for B than for DPP because of the increased charge-
transfer character inherent to the former chromophore. As a
consequence, there is a progressive decrease in the spectral
overlap integral associated with intramolecular EET from DPP to
60 B, but this remains a small effect for fluid solution. On
approaching the freezing point of MTHF (i.e., 140K), the
emission maximum observed for B continues to be red shifted
but that for DPP undergoes a blue shift. This reversal in the
hypsochromicity has a marked effect on the spectral overlap
65 integral in the frozen state, which is reduced with decreasing
temperature. Lowering the temperature also causes a significant
increase in the solvent refractive index,48 which is also a factor
involved in controlling kEET. These various changes combine to
affect the magnitude of the Förster critical distance, which falls
70 from 54.4 Å at room temperature to 52.8 Å at 77K.
550
600
650
700
750
800
850
λ/nm
Figure 2. Fluorescence spectra recorded for the B(CAR)nDPP compounds
15 in MTHF at room temperature following selective excitation into DPP.
The spectra are normalized at the peak of the B emission. NB The
intensity of the DPP band seen around 570 nm increases progressively as
the molecular length increases from N=1 (black curve) to N=5 (plum
curve).
20 Table 1. Molecular lengths and selected photophysical properties
recorded for the compounds in MTHF solution at 20 0C.
(a)
(a)
(b)
(b)
Cmpd
DCC
/ Å
38
57
76
96
115
NA
NA
ΦF
τS
/ ns
0.096 0.49 0.55
ΦF
τS
/ ns
4.3
4.3
4.2
4.4
4.3
4.2
NA
Apart from the above-mentioned spectral shifts, lowering the
temperature also affects the relative ratio of intensities of the two
emission bands following preferential excitation into DPP.
Indeed, RDA tends to increase in favour of emission from DPP as
75 the temperature decreases. Consequently, as shown in Figure 4,
there is a progressive decrease in PEET on lowering the
temperature. The longest bridge, N=5, suffers from limited
solubility at low temperature and, in this case, the results should
be treated cautiously. The shortest analogue, N=1, is insensitive
80 to temperature; PEET falls from 91% at room temperature to 88%
at 77K (Table 3). On the basis of EET occurring via the Förster
IDA mechanism, this drop in efficacy could be explained in
terms of dEFF increasing from 37 Å at room temperature to 38 Å
at 77K. The longer bridges display more significant temperature
85 effects in respect of their PEET values, before approaching a near
constant value in the solid at around 100K (Table 3). One
possible explanation for this behaviour is that the average
separation distance increases as the temperature falls, perhaps
reaching the fully extended conformation in the glassy matrix.
90
B(CAR)1DPP
B(CAR)2DPP
B(CAR)3DPP
B(CAR)4DPP
B(CAR)5DPP
B(CAR)1(TES)
DPP(Br)
0.44
0.73
0.81
0.84
NA
2.48 0.55
4.18 0.52
4.56 0.56
4.75
NA
0.54
0.56
NA
0.87
4.85
(a) Photophysical data refer to the DPP unit following preferential
excitation at 490 nm. (b) Photophysical data refer to the B unit following
selective excitation at 590 nm.
25
It can be seen that the IDA allows rather good estimation of
the molecular length (i.e., dEFF = 37 Å compared to DCC = 38 Å)
for the shortest bridge, thereby confirming an earlier report37
relating to EET across the same bridge but with different
terminals. As the molecular length increases, however, dEFF
30 becomes progressively shorter than DCC (Table 2). There are, in
fact, several reports45 in the scientific literature to indicate that
the reliability of the IDA depends on the distance separating the
reactants. Normally it is considered that Förster theory works
well at large separations but becomes suspect when the distance
4
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Table 2. Derived parameters relating to fluorescence quenching in the various dyads as a consequence of intramolecular ETT in MTHF solution at room
temperature
(a)
(b)
(c)
(d)
Compound
DCC / Å
38
57
76
96
PEET
PEET
PEET
PEET
kEET / 107 s-1(b)
dEFF / Å(b,e)
37
55
71
85
104
B(CAR)1DPP
B(CAR)2DPP
B(CAR)3DPP
B(CAR)4DPP
B(CAR)5DPP
0.90
0.43
0.12
0.032
0.011
0.910
0.485
0.166
0.064
0.020
0.90
0.49
0.14
0.060
0.022
0.89
0.48
0.16
0.073
0.025
205
19
4.1
1.4
0.42
115
(a) Probability of EET calculated on the basis of the IDA and Förster theory. (b) Calculated from the measured RDA values. (c) Calculated from the
measured τS values. (d) Calculated from the experimental fluorescence quantum yields. (e) Calculated on the basis that the IDA is valid for these
5 molecular dyads.
Table 3. Various parameters associated with the molecular dyads in frozen MTHF or as a consequence of melting the solvent at ca. 140 K
(a)
(c)
Compound
N
1
2
3
4
5
PEET
D77 / Å(b)
38
56.5
75
96
110
ST
(US/NK) / Å2
0.18
KMID / KEND
NA
∆L / Å
0.6
1.5
2.6
4.0
4.0
B(CAR)1DPP
B(CAR)2DPP
B(CAR)3DPP
B(CAR)4DPP
B(CAR)5DPP
0.88
0.40
0.11
0.027
0.012
0.016
0.027
0.035
0.042
0.036
0.28
0.38
0.50
0.32
3.8
5.3
6.8
3.9
(a) Probability of EET measured at 77K using the fluorescence ratio method. (b) Center-to-center separation distance at 77K as calculated from the
idealized dipole approximation. (c) Crude ratio of the spring constants estimated for the “end” and “middle” components of the bridge.
10 Table 4. Derived parameters relating to the temperature dependence for EET in the liquid phase
Compound
N
1
2
3
4
5
LLIQ / Å(b)
38.1
57.1
75.0
97.0
F / pN
33.4
18.2
8.2
3.6
3.5
W / perg
0.040
0.040
0.039
0.038
0.039
∆L / Å(b)
1.2
2.2
4.8
10.7
11.0
B(CAR)1DPP
B(CAR)2DPP
B(CAR)3DPP
B(CAR)4DPP
B(CAR)5DPP
109.6
(a) Center-to-center separation distance extrapolated for the liquid phase to 0K as calculated from the idealized dipole approximation. (b) Contraction of
the molecular length on heating from 0 to 295K in the liquid phase.
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.10
100
150
200
250
300
T / K
Figure 3. Effect of temperature on the emission spectrum recorded for
B(CAR)3DPP in MTHF following excitation into DPP. The temperature
15 ranges from 293 to 77K while the overall intensity increases steadily with
decreasing temperature. N.B. The black line corresponds to the spectrum
recorded at 293K.
Figure 4. Effect of temperature on the probability of EET across the
molecular dyad in MTHF. Data are shown for N=3. Corresponding plot
and tabulated data for all compounds are given in the Supporting
Information.
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Effect of applied pressure
case, the rate of change of VDA with pressure is almost linear and
does not tend towards a plateau (Figure 6). Having applied the
45 obvious correction factors, the most reasonable explanation of
these results is that high pressure causes the bridge to contract so
In this experiment, emission spectra were recorded for the
various dyads in MTHF at 20 °C as a function of increasing
pressure. It is known49 that pressure raises the density of the
solvent and has a small effect on the polarisability of MTHF.
This latter effect causes a slight red shift for the fluorescence
maxima of both emitters (Figure 5) but the spectral overlap term
does not change significantly at pressures below 550 MPa. These
spectral shifts are independent of molecular length (see
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as to bring the terminals into closer proximity (vide infra).
5
2.0
N=2
10 Supporting Information). Close scrutiny of these latter results
indicates that both DPP and B undergo red shifts of ca. 350 cm-1
over the full pressure range; the shift increasing in an almost
linear manner with applied pressure.47 In each case, the original
fluorescence profile is restored on release of the pressure.
1.5
1.0
N=3
8
7
6
5
4
3
2
1
0.5
0
100
200
300
400
500
P / MPa
Figure 6. Effect of applied pressure on the electronic coupling matrix
element for EET across the terminal as derived in MTHF at 20 0C.
50
Using the IDA model,45 the derived VDA terms can be
converted into dEFF values on the basis of Equation 4. Here, µD
(µA) is the transition dipole moment of the donor (acceptor), as
determined50 from absorption spectroscopy in MTHF at that
pressure (see Supporting Information). In fact, pressure has only
55 a minor effect on these latter values. The available data can be
interpreted in terms of the molecular length contracting steadily
with increasing pressure, with the significance of the effect
increasing with the length of the bridge. For example, the
shortest bridge is not much affected by applied pressure and
60 undergoes a minor contraction of ca. 1.6 Å. In contrast, N=4
shows the largest contraction of 6.2 Å over the same pressure
range.
0
550
600
650
λ / nm
700
15
20
Figure 5. Effect of applied pressure on the fluorescence spectrum
recorded for B(CAR)3DPP in MTHF at 20 0C after selective excitation
into DPP. The pressure range is from atmospheric to 540 MPa. NB
Pressure causes a steady increase in emission from DPP and a
corresponding decrease for B, marked by the respective arrows.
On applying pressure to a solution of the carborane-bridged
molecular dyads in MTHF at 293K there is a progressive
increase in emission from DPP and a concomitant decrease in
fluorescence from B (Figure 5). As such, we can conclude, on the
basis of the respective RDA values, that the mean PEET decreases
(2)
(3)
(4)
2π
=
2
kEET
=
VDA JDA
3
25 under pressure. The origin of this effect can be traced to several
factors; the best way to correct for these factors is to focus on the
coulombic coupling matrix element VDA rather than simply
compare PEET values. This particular term can be determined
from Equation 2 where JDA is the spectral overlap integral and s
30 is the solvent screening factor computed from Equation 3. Now,
increased pressure causes a small reduction in JDA and a minor
change in absorbance at the excitation wavelength due to
compression of the solvent.49 Such corrections are trivial,
however, and change the derived VDA values by less than 5%.
35 Elevated pressure also serves to increase the refractive index of
MTHF,49 which affects the magnitude of PEET by way of altering
s. This requires a more significant correction. Indeed, after taking
due account of the pressure-induced decrease in s, it becomes
clear that increasing pressure causes VDA to increase steadily,
40 regardless of the length of the connection. The rise in VDA is of
the order of 6, 20, 21, 13 and 8% for N=1, 2, 3, 4 and 5,
respectively, as measured over the full pressure range. In each
s =
65
2
2n +1
µDµA
4πε0dEFF
VDA
=
sκ
3
Refining the molecular length
70 With the exception of N=5, where experimental uncertainty
makes the results unreliable, the emission studies can be used to
determine the molecular length on the assumption that low
temperature favours the fully extended conformation while
applied pressure causes the terminals to approach each other. As
75 such, the effective separation distances (d77K) calculated at 77K
on the basis that the IDA45 holds for this system are listed in
Table 3. Before attempting to rationalise the variations in
molecular length associated with temperature or pressure effects
it should be noted that there is excellent agreement between D77K
2
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and DCC for N=1. It is also important to recognise the possible
limitations of the IDA approach at distances less than ca. 50 Å.
Many of these problems can be overcome by replacing the IDA
with the extended dipole method introduced by Kuhn51 and
applied by other groups.52 This was not the case here, however,
since the same values were derived by both methods.
The variation of dEFF with temperature has the appearance of
two separate effects (Figure 7). The molecular length is
reasonably constant over the temperature range where the solvent
modes that have vibrational transition energies comparable to
kBT.54 Since the carborane unit is unlikely to distort, compression
of the molecular length must be confined to the tolane-like
linkages, which are known55 to distort under ambient conditions.
View Online
5
45 The extent of molecular contraction in the liquid phase as a
function of temperature can be considered in terms of Equation
7, which is a modified form of expressions employed to account
for the bending rigidity of graphene56 and related materials.57
Here, LLIQ refers to the projected molecular length in the liquid
50 phase at 0K and F is a parameter that depends on bridge
composition and length; F has units equivalent to force such that
the product (W = F×∆LLIQ: ∆LLIQ = LLIQ - L) corresponds to the
total amount of work done in bringing about the structural
change and this remains surprisingly constant across the series.
55 Expansion of Equation 7 into a Taylor series allows further
refinement of F and shows that this term decreases markedly
with increasing N (Table 4). As such, we can conclude that the
inherent stiffness, and in particular its sensitivity towards
changes in temperature, decreases as the bridge gets longer.
60 Similar behaviour46 has been noted for certain surfactant
molecules packed into a lipid membrane.
10 is frozen but decreases by a significant amount near the melting
point. This “spring-like” effect is suggestive of the molecular
geometry being somewhat strained in the solid state but
becoming more relaxed in the fluid. In each case, the effect
occurs at ca. 140K; this is not the glass transition temperature,
15 believed to be around 90-95K, but is in agreement with estimates
(e.g., 137K)53 of the melting point of MTHF. The magnitude of
this strain, ST, can be computed from Equation 5 and, apart from
N=5, is seen to increase with increasing molecular length (Table
3). In principle, the strain energy per carborane, US/N, can be
20 calculated from Equation 6 on the basis of elastic behaviour but
this requires knowledge of the spring constant, K, associated
with geometry relaxation at each carborane unit. We have no
information on this latter term but, from comparison of the total
strain energy (i.e., the product of US and N), it appears that it is
25 not constant across the series. Rather, ∆L increases as the bridge
becomes longer. By partitioning the total strain energy into




kBT
FLLIQ
(7)
(8)
L = LLIQ exp −




∆L
P
E
=
65
spring constants related to the carborane-to-terminal units (KEND
)
LP
and to the inter-carborane units (KMID), it becomes clear that the
latter are more flexible. Furthermore, these units act
30 cooperatively to increase the total stretching length (Table 3). In
order words, these internal linkages are primarily responsible for
the geometry relaxation accompanying melting of the solvent.
The same approach can be applied to the pressure effect at
ambient temperature (Table 5). From the experimental results
highlighted above, it appears that pressure distorts the bridge so
70 as to bring the terminals into closer proximity. It is considered
that, under high pressure, the terminals are locked into the
∆L
L0
(5)
ST =
contracted geometry
– as opposed to sampling a wide
2

distribution of molecular lengths as might be expected at
atmospheric pressure.58 Separate studies have shown that the
75 photophysical properties of the DPP donor are insensitive to
applied pressure, at least in MTHF. Using the IDA approach,45
the pressure-induced changes in dEFF from atmospheric pressure
to 550 MPa are on the order of 1-7 Å and tend to increase
progressively with increasing molecular length (Table 5). The
80 driving force for this effect arises from the need to minimise the
molecular volume and this is best achieved by compressing the
bridge in a zigzag fashion (i.e., an accordion- or concertina-type
compression).



K
∆L
L0
US
=
35
(6)
2

75.0
74.0
73.0
72.0
71.0
Applied pressure causes stress on the molecule; stress is
85 normally considered as being force per unit area and has the
same units as pressure. It can also be described in terms of the
Young’s modulus, E, of the compressible material,59 although the
relationship is often nonlinear.60 For the various dyads studied
here, the isothermal compressibility data are well accounted for
90 in terms of Equation 8 where LP is the molecular length at
atmospheric pressure; again the significance of N=5 is marginal
because of experimental limitations. Now, we see that the
Young’s modulus for a carborane bridge is estimated as being on
the order of ca. 10 GPa but that the actual value decreases
95 somewhat with increasing length of the bridge (Table 5). This is
clear indication that longer bridges are more amenable to
100
150
200
250
300
T / K
Figure 7. Derived effect of temperature on the effective molecular length
for N=3 in MTHF.
A more gradual contraction is seen as the temperature
40 continues to rise and this is consistent with out-of-plane bending
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longitudinal distortion under pressure. There is also a significant
increase in bulk viscosity of MTHF over this pressure range49
well-defined area, appear curved or distorted under closer
scrutiny. Such behaviour has been recognised for graphene,62
35 where curvature is a prerequisite for formation of carbon
nanotubes, and for lipid bilayers.63 In the latter case, X-ray
and this is likely to minimize large fluctuations in dEFF
.
Information on how applied pressure affects the length of semi-
rigid molecules, in contrast to flexible polymers,61 is scarce but
recent work serves to illustrate that large-scale torsional motions
are dampened at high pressure.49 We are unaware of any prior
attempts to record E for organic-based molecular bridges,
although an E value of ca. 130 GPa has been reported57a for β-
10 SiC nanowires. This same work reports that E increases with
decreasing temperature, which is the same general trend as
observed in our work.
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5
scattering64 shows severe bumps and crevices in the surface. It
follows that long, linear molecules will also distort in solution at
ambient temperature and pressure. This is certainly the case for
40 duplex DNA65 and for conjugated polymers,66 where the
importance of cooperative domains has been stressed. Other
supposedly rigid, rod-like molecules can distort to such a degree
that their orientation in solution might differ dramatically from
that of the fully extended species. Molecular dynamic
45 simulations67 offer a means by which to inspect possible
torsional motions but do not provide experimental support for a
dynamic molecular topology. High-field NMR spectroscopy can
give meaningful structural information about molecular rigidity
in solution55 but is time consuming and requires careful
50 calibration. Here, we apply fluorescence spectroscopy to probe
the effective length of “stiff” molecular dyads equipped with
terminal fluorophores. It has been shown that, in the extreme
case, a molecular dyad with an extended molecular length of ca.
85 Å contracts by as much as 6 Å under applied pressure at
55 ambient temperature. There is a corresponding extension of ca.
10 Å on cooling to 0K. A direct consequence of this situation is
that the probability of EET between terminal groups depends
markedly on the local environment even for seemingly rigid
bridges.
Table 5. Summary of the parameters derived from the pressure
dependence recorded for the compounds in MTHF solution at 20 0C.
∆L(a)
/ Å
1.6
3.5
4.7
6.2
4.7
(b)
Compound
N
Lp
/ Å
37.0
55.4
72.8
E
/ GPa
12.48
8.52
8.34
7.42
RC
/ Å
B(CAR)1DPP
B(CAR)2DPP
B(CAR)3DPP
B(CAR)4DPP
B(CAR)5DPP
1
2
3
4
5
1.4
1.0
0.7
0.5
0.5
84.8
105.0
12.05
15 (a) Length contraction measured over the full pressure range from
atmospheric pressure to an applied pressure of 540 MPa. (b) Radius
derived from the cross-sectional area assuming the latter is circular.
stress
strain A(∆L)
FLP
E =
=
60
The molecular dyads examined herein have the crude
appearance of plate-like terminals separated by a semi-rigid
cylindrical rod and such topologies might be particularly
sensitive to pressure effects. Indeed, we consider the overall
pressure and temperature effects in terms of force applied to the
20 (9)
These results can be tested for self consistency by reference to
the fact that Young’s modulus can be expressed in terms of stress
divided by strain. This leads to Equation 9 where the force, F, is
25 taken from the temperature-dependent studies described earlier
and A is the cross-sectional area of the contractor. Taking the
latter as a circle, the radius of the contractor, RC, can be
estimated from the experimental data (Table 5). It appears that
this term has the appropriate dimensions (i.e., RC = 0.86 Å) for a
30 nanowire as might be formed from the carborane bridge.
65 flat terminals causing structural distortion (i.e., compression) at
the centre of the connector. An interesting feature to emerge
from our analysis is that the carborane-based linkages comprising
the connector act in a cooperative manner. Thus, the carborane-
terminal linkages are robust and possess relatively small spring
70 constants. The carborane-carborane connections, however, take
up more strain and the corresponding spring constant increases
with increasing number of accreted units. As such, the amount of
work needed to compress the molecule decreases substantially
with increasing number of carboranes.
Conclusion
Molecular surfaces, often represented as flat and smooth plates of
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