438
H. Kobayashi
organic radical chains constructed in 1D nanochannels. This discussion is helpful
with regard to clarifying the inter-spin interactions within 1D 4-X-TEMPO chains
in 1D nanochannels.
The line profiles of isotropic ESR spectra reflect the type and magnitude of interspin dipolar and/or exchange interactions in the specimen, as well as the inter-spin
distances between electron spins and other factors. In the absence of exchange
interactions (i.e., considering only dipolar interactions in the spin system), the
average second moment, M 2 , of the rigid spin lattice can be estimated using Van
Vleck’s formula [39, 44, 59]
M 2 = ω
2
=
3
5
γ
4
4 S (S + 1)
k
1
r k
(12.8)
where γ , S, and r k are the electron gyromagnetic ratio, the electron spin quantum
number, and the distance between two spins. In this case, the ESR profile becomes
a Gaussian function. Generally, the peak-to-peak line width ΔB pp is equal to 2
√
M 2
and the FWHM, ΔB 1/2 is equal to 2.36
√
M 2 [59]. Under the condition of the
existence of only dipolar interaction in the spin system, the peak-to-peak line width
is described by B pp
D in this chapter. It should be noted that the experimental value
for ΔB pp may be much narrower than the value estimated using Eq. (12.8), as a
result of exchange or motional averaging. Therefore, it is necessary to estimate the
inter-spin distance in the system as accurately as possible.
In our previous work regarding [(TPP) 2 -(TEMPO) 1.0 ] (1a/2a) and [CLPOT(4-X-TEMPO)] (1b/2a–d), the electron spins on the NO groups of 4-X-TEMPO
molecules in TPP or CLPOT nanochannels were found to interact with those of other
4-X-TEMPO molecules in the same or adjacent channels [39]. These interactions
are, respectively, defined as “intrachain” or “interchain” inter-spin interaction. In
1a/2a and 1b/2a–d, a single 4-X-TEMPO molecule (i.e., one unpaired electron)
was determined to be accommodated in a TPP or CLPOT unit cell formed by
two molecules. The electron spins of 4-X-TEMPO molecules in the nanochannels
were assumed to be located at the center of gravity of the molecules, so as to
simplify computation by averaging the uniaxial rotational diffusion of 4-X-TEMPO
molecules around the rotational axis (commonly considered to be parallel to the
nanochannel axis). In this case, the nearest neighbor intra-channel or interchain
inter-spin distance, respectively, corresponds to the cell parameters, such as c = 1.2
nm or a = 0.98 nm in the case of the TPP frameworks of 1a/2a [39] and c = 0.688
nm or a = 1.51 nm in the CLPOT frameworks of 1b/2a [44]. Therefore, it is
convenient to consider 1a/2a as a spin system having a sixfold symmetric spin
lattice with 1.2 nm intra-channel and 0.98 nm inter-channel inter-spin distances.
The structures of 1b/2a–d were interpreted in a similar manner.
However, subsequent studies showed that these assumptions are valid only near
room temperature. In this temperature range, 4-X-TEMPO molecules in the TPP or
CLPOT nanochannels undergo rotational diffusion in the fast-motion region on the
ESR time scale (τ R < 10 −9 s, where τ R is the correlation time for the rotational
H. Kobayashi
organic radical chains constructed in 1D nanochannels. This discussion is helpful
with regard to clarifying the inter-spin interactions within 1D 4-X-TEMPO chains
in 1D nanochannels.
The line profiles of isotropic ESR spectra reflect the type and magnitude of interspin dipolar and/or exchange interactions in the specimen, as well as the inter-spin
distances between electron spins and other factors. In the absence of exchange
interactions (i.e., considering only dipolar interactions in the spin system), the
average second moment, M 2 , of the rigid spin lattice can be estimated using Van
Vleck’s formula [39, 44, 59]
M 2 = ω
2
=
3
5
γ
4
4 S (S + 1)
k
1
r k
(12.8)
where γ , S, and r k are the electron gyromagnetic ratio, the electron spin quantum
number, and the distance between two spins. In this case, the ESR profile becomes
a Gaussian function. Generally, the peak-to-peak line width ΔB pp is equal to 2
√
M 2
and the FWHM, ΔB 1/2 is equal to 2.36
√
M 2 [59]. Under the condition of the
existence of only dipolar interaction in the spin system, the peak-to-peak line width
is described by B pp
D in this chapter. It should be noted that the experimental value
for ΔB pp may be much narrower than the value estimated using Eq. (12.8), as a
result of exchange or motional averaging. Therefore, it is necessary to estimate the
inter-spin distance in the system as accurately as possible.
In our previous work regarding [(TPP) 2 -(TEMPO) 1.0 ] (1a/2a) and [CLPOT(4-X-TEMPO)] (1b/2a–d), the electron spins on the NO groups of 4-X-TEMPO
molecules in TPP or CLPOT nanochannels were found to interact with those of other
4-X-TEMPO molecules in the same or adjacent channels [39]. These interactions
are, respectively, defined as “intrachain” or “interchain” inter-spin interaction. In
1a/2a and 1b/2a–d, a single 4-X-TEMPO molecule (i.e., one unpaired electron)
was determined to be accommodated in a TPP or CLPOT unit cell formed by
two molecules. The electron spins of 4-X-TEMPO molecules in the nanochannels
were assumed to be located at the center of gravity of the molecules, so as to
simplify computation by averaging the uniaxial rotational diffusion of 4-X-TEMPO
molecules around the rotational axis (commonly considered to be parallel to the
nanochannel axis). In this case, the nearest neighbor intra-channel or interchain
inter-spin distance, respectively, corresponds to the cell parameters, such as c = 1.2
nm or a = 0.98 nm in the case of the TPP frameworks of 1a/2a [39] and c = 0.688
nm or a = 1.51 nm in the CLPOT frameworks of 1b/2a [44]. Therefore, it is
convenient to consider 1a/2a as a spin system having a sixfold symmetric spin
lattice with 1.2 nm intra-channel and 0.98 nm inter-channel inter-spin distances.
The structures of 1b/2a–d were interpreted in a similar manner.
However, subsequent studies showed that these assumptions are valid only near
room temperature. In this temperature range, 4-X-TEMPO molecules in the TPP or
CLPOT nanochannels undergo rotational diffusion in the fast-motion region on the
ESR time scale (τ R < 10 −9 s, where τ R is the correlation time for the rotational